COOLING DEVICES FOR DENSELY PACKED,

Transcription

1 COOLING DEVICES FOR DENSELY PACKED, HIGH CONCENTRATION PV ARRAYS by ANJA RØYNE A thesis submitted to the University of Sydney for the degree of MASTER OF SCIENCE March 2005

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3 ABSTRACT Photovoltaic (PV) cells under concentrated illumination experience a high heat load which must be dissipated efficiently in order to maintain a low cell temperature. Tower and dish solar concentrators typically use arrays of densely packed cells where all of the heat must be removed in the direction normal to the surface. This thesis identifies jet impingement cooling as a promising technology for this type of configuration. A prototype side drainage device is made and laboratory testing facilities are constructed in order to measure the heat transfer and flow characteristics of this device. The local heat transfer distribution under single and multiple jets is studied in detail. Correlations for average heat transfer coefficient and pressure drop are established and combined to form a model for required pumping power at a given average heat transfer coefficient. This model is used to make general predictions for the optimal cooling device configuration and to propose an optimising design procedure. Combining this model with a model for PV output as a function of temperature gives the optimal system operating range. The effect of a nonuniform heat transfer coefficient distribution on single and interconnected PV cells is investigated and found to be minor. i

4 ACKNOWLEDGEMENTS I would like to extend my warmest thanks to my supervisors, Christopher Dey and David Mills. Chris has given me invaluable effort and time and in sharing his wealth of experience in everything from home renewal to sailing has managed to make somewhat of an experimental physicist of me. David has been a great inspiration in showing me what is possible in the world of solar energy. The solar energy group consists of a bunch of always friendly and extremely knowledgeable people. Thanks to Anne Gerd, Damien, Steven, Scott, Matt, Yongbai and Ned for doing your best to answering even the stupidest questions. There are also a number of other individuals within the School of Physics who carry years of invaluable experience and knowledge. I would particularly like to thank Terry Pfeiffer for teaching me how to draw legible construction drawings and for manufacturing what I needed of experimental equipment; John Piggott for sharing his wealth of experience in designing experiments; Phil Denniss for helping me with all things electrical and Michael Proschek for teaching me to use Labview and for his patience in sorting out seemingly unexplainable problems. Brian Haynes in Chemical Engineering also took the time to put me on the right track when I was trying to understand the world of heat transfer and cooling. Outside the University, I would like to extend my warmest gratitude to my family away from home: Rolf, Cathy, Anita and Heidi Jacobsen, thank you for providing endless support, a place to feel at home, wonderful family dinners and of course Rolf s very thorough proofreading. Thanks to my sister Frida Røyne for providing inspiration from all corners of the world, to my mother Marit Larssen for keeping me up to date and thus making me feel like I m not so far away from home, and of course to my father Odd Røyne for raising me to be a scientist. Finally to Asbjørn Gjerding-Smith, my partner and the love of my life, without whom I would certainly never have done this. Thank you for being my greatest inspiration, for convincing me to work even when I have a thousand excuses made up, your thorough proofreading and for your amazing ability to cheer me up no matter how frustrated I am. ii

5 DECLARATION This thesis contains no material that has been accepted for the award of any other degree or diploma in any university. To the best of the author s knowledge and belief, no material previously written or published by another person has been included in this thesis, except where due reference is made in the text. Anja Røyne March 2005 iii

6 PAPERS PUBLISHED JOURNAL ARTICLES Royne, A., Dey, C.J. and Mills, D.R. (2005) Cooling of photovoltaic cells under concentrated illumination: a critical review. Solar Energy Materials and Solar Cells 86 (4), Royne, A. and Dey, C. (Submitted December 2004) Experimental study of nozzle geometry effects in submerged jet arrays. International Journal of Heat and Mass Transfer CONFERENCE PAPERS Royne, A., Dey, C. and Mills, D. (2004) Cooling of photovoltaic cells under concentrated illumination: a review. EuroSun 2004, Freiburg, Germany. Royne, A. and Dey, C. (2004) Experimental study of a jet impingement device for cooling of photovoltaic cells under high concentration. ANZSES Solar Life, the Universe and Renewables, Perth, Australia. iv

7 LIST OF SYMBOLS a A b C C c C d C v c d D e g h H I k k B l L m m& m b n N Nu p P q q& Q r r s Pr R R 2 Re s S t T v V W X z cell efficiency parameter area cell efficiency parameter heat transfer correlation coefficient contraction coefficient discharge coefficient velocity coefficient specific heat capacity nozzle diameter equivalent heat source diameter acceleration of gravity heat transfer coefficient enthalpy current thermal conductivity Boltzmann constant orifice plate thickness length Reynolds number dependence mass flow rate mass of bus bars Prandtl number dependence number of nozzles Nusselt number pressure power electronic charge heat flux per unit area volume flow rate radial distance series resistance Prandtl number thermal resistance correlation coefficient Reynolds number nozzle pitch solar irradiation thickness temperature mean fluid velocity voltage pumping power optical concentration nozzle-to-plate spacing Subscripts 0 stagnation point a ambient ad adhesive avg average b bus bar c cell cool cooling system conv convection c-sub cell junction to substrate el electrical f fluid fo foil g glass g-c cover glass to cell junction heat heater in inlet max maximum oc open-circuit opt optimal out outlet rad radiation rise temperature rise through substrate s surface sc short-circuit sol solder sub substrate t total w water Greek letters ε emissivity η PV efficiency κ thermal diffusivity ν kinematic viscosity ρ density σ uncertainty Stephan-Boltzmann constant σ B v

8 TABLE OF CONTENTS 1 Introduction Background Thesis aims Outline of thesis 3 2 Cooling of photovoltaic cells under concentrated illumination Introduction Cooling requirements for concentrator cells Concentrator geometries Heat transfer coefficients and thermal resistances One-dimensional thermal model of cell and encapsulation layers Examples of cooling of concentrating PV in literature Single cell geometry Linear geometries Densely packed cells Other cooling options Passive systems Forced air cooling Liquid single-phase forced convection cooling Two-phase forced convection cooling Comparison of cooling options Conclusion 34 3 Heat transfer under single-phase, submerged and axisymmetric jets Single jets Hydrodynamic flow structure of single impinging jets Radial variation in local heat transfer and the influence of nozzle-toplate spacing Effect of nozzle configuration Correlations for the stagnation point and average Nusselt number Arrays of jets Flow structure and heat transfer characteristics of jet arrays Effect of nozzle-to-plate spacing Effect of nozzle pitch Correlations for average Nusselt number Other parameters influencing heat transfer 51 vi

9 3.3.1 Surface modifications Effect of mesh screen or perforated plate between nozzle exit and impingement plate Experimental methods Conclusions Design of a jet impingement cooling device for concentrating PV 54 4 Experimental design and procedure Experimental setup Design of jet testing unit Measuring temperatures using thermographic liquid crystals Instrumentation and data acquisition Jet devices tested System characterisation Uncertainty analysis Improvements of the experimental setup for later experiments 67 5 Results and discussion Single jets Arrays of jets Predictive correlations Nozzle geometry effects Pressure drop through an orifice Total pumping power Central drainage device Conclusions 90 6 Optimised design of cooling devices Correlation for pumping power Pressure drop Two correlations for heat transfer coefficient Comparison with experimental data Model predictions Experimental validation Net PV output cooling system optimisation 101 vii

10 6.3 Guidelines for device optimisation Conclusion Effects of nonuniform temperature Influence on PV output Single cells Interconnected cells Using the metal substrate as a heat diffuser Conclusion Conclusions and recommendations for further work Conclusions Recommendations for further work Fundamental work on jet impingement cooling Photovoltaics Prototype design 117 References 118 viii

11 Chapter 1 INTRODUCTION 1.1 BACKGROUND The Sun is the world s primary source of energy. In fact, all of the energy being used on the Earth today, except for nuclear, geothermal and tidal energy, originates from the Sun. The Earth annually intercepts as much as 1.05 x GWh [1] from the Sun, a staggering amount when comparing with the 1.6 x 10 7 GWh [2] of installed electrical production capacity in the world: The energy received from the Sun in only 8 minutes equals the total installed yearly energy production. However, most of the energy that is used today is in the form of fossil fuels, which also originated from the Sun but has been stored in the Earth for millions of years. If the current trends of global energy use and demand continue, the supply of fossil fuels are predicted to be exhausted within years from now [3]. Burning fossil fuels releases stored carbon into the environment. This disturbs the global carbon cycle and leads to an increase in atmospheric CO 2 levels. There is now overwhelming evidence that the observed global warming is at least partially caused by human carbon emissions [4]. Global climate models are predicting significant temperature changes in the near future (Figure 1.1, [4]) which could have detrimental effects to ecosystems and humankind. Figure 1.1: Predicted temperature change under several emissions scenarios according to the IPCC report (Figure courtesy of [4]) 1

12 1 INTRODUCTION Because of the increase in world energy demand and the threat of global warming, there is a pressing need for the development of reliable, cost-effective sources of renewable energy. With renewable sources of energy, there is no risk of depletion such as we have with fossil fuels. They also do not introduce new carbon to the carbon cycle and do therefore not generally contribute to global warming. Renewable energy sources include indirect solar energy such as hydro, wind and biomass energy, and direct solar energy conversion through thermal receivers or photovoltaics. Photovoltaic (PV) cells are semiconductor devices that can convert sunlight into electricity. Photons below a threshold wavelength have enough energy to break an electron-hole bond in the semiconductor crystal, which in turn can drive a current in a circuit. The solar radiation consists of photons at a range of wavelengths and corresponding energies. Photons with wavelengths above the threshold are converted into heat in the PV cells. This waste heat must be dissipated efficiently in order to avoid excessively high cell temperatures, which have an adverse effect on the electrical performance of the cells. The cells are the most expensive part of a photovoltaic system. A simple way of reducing system costs is therefore to replace some of the photovoltaic area with less expensive optics such as mirrors or lenses. The optical devices focus the sunlight onto a small area of cells. Because fewer cells are needed, one can afford to use higher efficiency cells. Under high concentration there is also a considerably higher heat load that needs to be dissipated. Concentrating systems for solar energy production have been developing since the 1970s. An excellent overview of the history and current status of photovoltaic concentrators is given in [5]. Figure 1.2 shows a selection of currently installed photovoltaic concentrators: The Solar System dishes [6], the linear trough EUCLIDES concentrator [7] and the faceted dish concentrator at the University of Ferrara [8]. These systems are all described in more detail in Chapter THESIS AIMS When photovoltaic cells are used under concentrated illumination, they experience a high heat load because the photons not converted to electricity are dissipated in the cells as heat. Thus, a crucial requirement for a successful photovoltaic concentrator is a cooling system which can efficiently remove the dissipated heat while keeping the cells at the desired temperature. The aims of this thesis are to: investigate the effect of temperature on PV cells and assess what level of cooling is required for a given concentrator design; review possible cooling options and recommend on the most suitable one(s); design and conduct measurements of the cooling performance of candidate devices; develop a thermal model to simulate the cooling performance for a range of device configurations; and recommend a cooling device design or design procedure that can be used as a tool for future PV receiver design. 2

13 1 INTRODUCTION a) b) c) Figure 1.2: A collection of photovoltaic concentrators: a) The Solar Systems dish concentrators (artist s impression) [6]; b) the linear trough EUCLIDES system [7]; c) dish concentrator at the University of Ferrara [8]. 1.3 OUTLINE OF THESIS In Chapter 2, an extensive literature review is presented which looks into not only past and present methods for cooling of photovoltaic cells, but also cooling technologies from other areas of research which may be applicable to photovoltaics. This chapter shows that efficient cooling is of prime importance in concentrating photovoltaic systems, in particular for those using arrays of densely packed cells under high concentration. A number of possible cooling mechanisms are suggested, the most promising being microchannels and impinging jets. Microchannels have been widely researched and are also currently being implemented with concentrating photovoltaics in Italy [8]. Impinging jets, on the other hand, have not yet been trialled in this area. Jet 3

14 1 INTRODUCTION impingement is an attractive solution because a high heat transfer coefficient can be achieved using simple manufacturing methods and possibly with lower pumping power requirements than other options. It was therefore decided to proceed with investigating the suitability of jet impingement cooling devices for densely packed, high concentration PV. Chapter 3 presents a review of previous studies of jet impingement, limited to axisymmetric, submerged and single-phase jets for reasons explained in Chapter 3. The heat transfer characteristics of impinging jets have been extensively researched and are well known. However, the performance of a given jet device is difficult to predict because of the numerous parameters influencing the heat transfer, such as nozzle geometry, nozzle pitch, nozzle-to-plate distance Reynolds number, impingement surface conditions etc. Some general results are identified which can help predict suitable design properties. Based on the findings from the literature, four types of possible device for the particular requirements of PV cooling are presented. One of the possible devices, labelled the side drainage device was identified as the most promising and a prototype was made. The experimental facilities used to investigate the flow and heat transfer characteristics of variations of this device are described in Chapter 4. The results from the experiments are presented in Chapter 5. The local heat transfer distribution under single and multiple jets is studied in detail. Correlations are found for the stagnation point and average heat transfer coefficients and compared with correlations from the literature. Correlations are also developed for the pressure drop through the nozzles and different nozzle configurations are compared. For comparison, a few measurements were made for another one of the suggested geometries but the results presented in Chapter 5 suggest that this performs poorly. For cooling of photovoltaics, it is preferential to minimise the pumping power requirements in order to maximise the total electrical output of the system. In Chapter 6, the findings from the literature and from the experiments are combined to develop an analytical model that predicts the pumping power required for a given device configuration. The model is then used to make some general predictions on the optimised design of a cooling device and an optimisation process is outlined. It is also used to show that there exists a broad optimal operating range for a photovoltaic cell using the cooling device. Lastly, Chapter 7 discusses the issue of nonuniformity in heat transfer coefficient and temperature. One of the initial assumptions was that a uniform temperature across the cells was important for the total array efficiency. However, calculations given in Chapter 7 show that the difference in temperature across single or interconnected cells only have a weak effect on efficiency compared to that of the average temperature. For this reason, the thickness of the substrate between the cells and the cooling system should be kept as small as possible. Conclusions and recommendations for further work are given in Chapter 8. 4

15 Chapter 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION This chapter has been published in its entirety in Solar Energy Materials and Solar Cells [9]. The text and figures are identical to that published except for cosmetic changes. 2.1 INTRODUCTION Cooling requirements for concentrator cells Concentrating sunlight onto photovoltaic cells, thus replacing expensive photovoltaic area with less expensive concentrating mirrors or lenses, is seen as one method to lower the cost of solar electricity. Because of the smaller area, more costly, but higher efficiency PV cells may be used. However, only a small portion of the incoming sunlight onto the cell is converted into electrical energy (a typical efficiency value for concentrator cells is 25% [10]). The remainder of the incoming energy will be converted into thermal energy in the cell and cause the junction temperature to rise unless the heat is efficiently dissipated to the environment. Major design considerations for cooling of photovoltaic cells are listed below: Cell temperature. The photovoltaic cell efficiency decreases with increasing temperature [11-13]. Cells will also exhibit long-term degradation if the temperature exceeds a certain limit [14, 15]. The cell manufacturer will generally specify a given temperature degradation coefficient and a maximum operating temperature for the cell. Uniformity of temperature *. The cell efficiency is known to decrease due to nonuniform temperatures across the cell [16, 17]. In a photovoltaic module, a number of cells are electrically connected in series, and several of these series connections can be connected in parallel. Series connections increase the output voltage and decrease the current at a given power output, thereby reducing the ohmic losses. However, when cells are connected in series, the cell that gives the smallest output will limit the current. This is known as the current matching problem. Because the cell efficiency decreases with * Temperature nonuniformities were initially assumed to be important to the cell output but a later investigation (see chapter 7) showed that this is not necessarily the case. 5

16 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION increasing temperature, the cell at the highest temperature will limit the efficiency of the whole string. This problem can be avoided through the use of bypass diodes [18] (which bypass cells when they reach a certain temperature - in this arrangement you loose the output from this cell, but the output from other cells is not limited) or by keeping a uniform temperature across each series connection. Reliability and simplicity. To keep operational costs to a minimum, a simple and low maintenance solution should be sought. This also includes the avoidance of toxic materials due to health and environmental issues. Reliability is another important aspect because a failure of the cooling system could lead to the destruction of the PV cells. The cooling system should be designed to deal with "worst case scenarios" such as power outages, tracking anomalies and electrical faults within modules [15, 19]. Useability of thermal energy. Use of the extracted thermal energy from cooling can lead to a significant increase in the total conversion efficiency of the receiver [20]. For this reason, subject to the constraints above, it is desirable to have a cooling system that delivers water at as high a temperature as possible. Further, to avoid heat loss through a secondary heat exchanger, an open-loop cooling circuit is an advantage. Pumping power. Since the power required of any active component of the cooling circuit is a parasitic loss [20], it should be kept to a minimum. Material efficiency. Materials use should be kept down for the sake of cost, weight and embodied energy considerations Concentrator geometries It is sensible to distinguish between concentrators according to their method for concentrating (mirrors or lenses), concentration level or geometry. In this review, concentrators will be grouped according to geometry, because the requirements for cell cooling differ considerably between the various types of concentrator geometries. The issue of shading, however, is different for lens and mirror concentrators. If lenses are used, the cells are normally placed underneath the light source, and so shading by the cooling system does not occur. For mirror systems, the cells are generally illuminated from below, which makes shading an important issue to consider when designing the cooling system. Concentrators can be roughly grouped as in the following sub-sections Single cells In small point-focus concentrators, the sunlight is usually focused onto each cell individually. This means that each cell has an area roughly equal to that of the concentrator available for heat sinking, as shown in Figure 2.1. A cell under 50 suns concentration should have an area 50 times its area available for spreading of heat. This geometry means passive cooling can be used at quite high concentration levels (see Section 2.3.1). Single cell systems commonly use various types of lenses for concentration. Another variant is where larger concentrators transmit the concentrated light through optical fibres onto single cells. 6

17 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION Figure 2.1: Single-cell concentrator. The dashed line shows the area available for heat sinking Linear geometry Line focus systems typically use parabolic troughs or linear Fresnel lenses to focus the light onto a row of cells. In this configuration, the cells have less area available for heat sinking because two of the cell sides are in close contact with the neighbouring cells, as shown in Figure 2.2. The areas available for heat sinking extend from two of the sides and the back of the cell. Figure 2.2: Linear concentrator. The dashed lines show the area available for heat sinking Densely packed modules In larger point-focus systems, such as dishes or heliostat fields, the receiver generally consists of a multitude of cells, densely packed. The receiver is usually placed slightly away from the focal plane to increase the uniformity of illumination. Secondary concentrators (kaleidoscopes) may be used to further improve flux homogeneity [21]. Densely packed modules present greater problems for cooling than the two previous shown, because, except for the edge cells, each of the cells only has its rear side available 7

18 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION for heat sinking, as seen in Figure 2.3. This implies that, in principle, the entire heat load must be dissipated in a direction normal to the module surface. This generally implies that passive cooling cannot be used in these configurations at their typical concentration levels. Figure 2.3: Densely packed cells. The area available for cooling is only the rear side of the cell Heat transfer coefficients and thermal resistances The commonly used quantities for comparing the heat transfer characteristics of cooling systems are heat transfer coefficients h or thermal resistances R. These can be defined in several different ways depending on the application. When dealing with passive cooling systems, h is generally defined as q& h = T s T a, (2.1) where q& is the heat input per unit area, T s is the mean surface temperature, and T a is the ambient temperature. R, when used per unit area, is just the inverse of h. In the case of single-phase forced convection cooling, one will generally use a local heat transfer coefficient q& h = T s T f, (2.2) where T s and T f are the mean surface and fluid temperatures at any given point. For natural convection, boiling and radiation, q& is not proportional to T. R and h therefore vary with temperature [22]. In the case of radiation, a simplification is often used to linearize the calculation (given in Section ). The literature sometimes quotes values for h or R with natural convection or two-phase forced convection, and these are included in this article. However, these should be read with caution and not be assumed to be valid for a large range of temperatures. 2.2 ONE-DIMENSIONAL THERMAL MODEL OF CELL AND ENCAPSULATION LAYERS To examine the best cooling system for a given concentrator requires the development of a thermal model that will predict the heating and electrical output of cells. In this review, a one-dimensional model is used because this is consistent with a closely packed set of 8

19 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION cells where heat flow is primarily directed in the normal direction. Models for other layouts can be easily extended from this model, or they can be found in literature (e.g. [11]). Models for single-cell point focus are described in [17, 23, 24] and for linear geometry in [25-27]. The idealised cell and its mounting are shown schematically in Figure 2.4, where S is the incoming solar radiation, and t g, t ad, t c, t sol and t sub denote the thicknesses of the various layers. I S t g t ad t c t sol t sub cover glass adhesive cell solder substrate Figure 2.4: Cell and mounting layers with thicknesses t. Figure 2.5: Equivalent thermal circuit of cell, mounting and cooling system. This configuration can be represented by the equivalent thermal circuit shown in Figure 2.5, where R denotes a thermal resistance. Note that because this model is onedimensional, all relevant values are per unit area; the units of R are [K m 2 W -1 ] while the units of q& are [W m -2 ]. T g, T s and T a are the temperatures of the top surface of the cover glass, the bottom surface of the substrate and the ambient, respectively. R g-c, R c-sub and R cool denote the thermal resistances from cover glass to the cell junction, from cell junction to substrate bottom, and from substrate, through cooling system, to the ambient. T c denotes the temperature of the cell junction, which is assumed to be in the middle of the cell. This temperature determines the efficiency of the cell. The simple model assumes that all incoming radiation, S, is transmitted through the encapsulants and absorbed in the cell junction, where a percentage determined by the cell temperature is converted to electricity, and the remainder is converted to heat. It is also assumed that some heat is lost through radiation and convection from the cover glass surface, and that the remainder of the heat is removed by the cooling system on the substrate surface. 9

20 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION Heat loss through radiation and natural convection The radiative heat flux (per unit area) is related to the cover glass surface temperature as follows [28]: 4 4 ( T ) q &, (2.3) rad = 4εσB g Ta where T g is the glass surface temperature, T a is the ambient temperature, ε is the surface emissivity and σ B is the Stephan-Boltzmann constant. However, for simplification, it is common to linearise this equation in the following manner [11]: ( T ) q & B. (2.4) 3 rad = 4εσ Ta g Ta For an ambient temperature of 25 C, this approximation gives an error in q& rad of less than 50% for cell temperatures up to 170 C. By determining a thermal resistance R conv for convective heat transfer from a surface, depending on surface and ambient parameters, the heat flux through convection from the surface is simply given by Values for R conv are discussed later. T T g a q & conv =. (2.5) Rconv Electrical power output The cell efficiency varies with both temperature and concentration. There are various models for temperature and concentration dependency found in literature [11, 12, 27, 29, 30]. As shown in Figure 2.6, most of the models predict quite similar slopes in the lower temperature range. The different values predicted arise from the fact that different cells have different peak efficiencies. Therefore, a simple approach is used in this article by assuming a linear decrease in efficiency with temperature, and no dependency on concentration, as in [29]. This gives the following model: ( ) η = a 1 bt c, (2.6) where a and b are parameters from [29], and η is the cell efficiency at a given cell temperature T c. The electrical output per unit area is given by P ηs = el. (2.7) 10

21 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION Cell efficiency (%) f a Florschuetz Florschuetz [20] [29] b Sala Sala [11] [2] c O Leary O'Leary and Clements [18] [27] d Mbewe et al. 1 sun [3] [12] e Mbewe et al. 100 suns [3][12] f f Edenburn [21] [30] c e b d a Cell temperature ( C) Figure 2.6: Comparison of different models for cell efficiencies at various temperatures Energy balance If S denotes the incoming solar irradiation, and T T s a q & cool = (2.8) Rcool is the thermal energy removed by the cooling system, the following relation must be satisfied to achieve thermal equilibrium: S q & q & P q & 0 (2.9) rad conv el cool = Solving Equations 2.4 through 2.9 gives the value for T c at any given illumination value. It should be noted that q& cool is very large compared to q& rad and q& conv in most cases of concentration, and so the significance of the model and parameters chosen for these aspects of the actual cells becomes less important. Figure 2.7 shows the electrical power output that would result from various illumination levels using this model and the values given in Table 2.1. The different curves correspond to different values of R cool. There is clearly a definitive maximum power output for all curves. However, these curves must be seen together with Figure 2.8, which shows the cell temperature rise with increasing concentration. It shows that the maximum power points correspond with very high cell temperatures. The actual power output will be limited by the bounds on the cell operating temperature. This implies temperature is always the limiting factor for concentrator cells. A low thermal resistance in the cooling system is crucial, and becomes even more important with increasing concentration level. 11

22 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION Table 2.1: Parameters used in thermal model Layer Material Thickness t [ m ] Thermal conductivity k [ W m -1 K -1 ] Total thermal resistance ti R = [ K m k 2 W -1 ] i Cover glass Ceria-doped glass [14] 3 x [28] Adhesive Optical grade RTV (room temperature vulcanization) silicone [14] 1 x [11] Top half of cell Bottom half of cell Silicon [14] 6 x 10-5 [14] 145 [11] Silicon [14] 6 x 10-5 [14] 145 [11] R g-c = 2.14 x 10-3 Solder Sn:Pb:As: [11] 1 x 10-4 [11] 50 [11] Substrate Aluminum nitride [14] 2 x 10-3 [11] 120 [14] R c-s = 1.91 x 10-5 Other parameters Symbol Description Value Symbol Description Value T a Ambient temperature 25 C R conv Convective thermal resistance 0.2 K m 2 W -1 [11] ε Hemispherical surface emissivity [9] a Cell efficiency parameter [29] σ B Stephan- Boltzmann constant 5.67 x 10-8 W m -2 K -4 [28] b Cell efficiency parameter 1.84 x 10-4 K -1 [29] S Insolation 1 x 10 3 W m -2 12

23 R = 10-1 R = COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION 10 6 R= R=10-5 Power output (W/m 2 ) R=10-1 R=10-2 R= Illumination level (W/m 2 ) Figure 2.7: Electrical power output per area versus illumination level for various Rcool [K m 2 W -1 ] R = 10-3 R = 10-4 Cell temperature ( C) R = Illumination level (W/m 2 ) Figure 2.8: Cell temperature versus illumination level for various Rcool [K m 2 W -1 ]. 13

24 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION 2.3 EXAMPLES OF COOLING OF CONCENTRATING PV IN LITERATURE In the textbook Cells and optics for photovoltaic concentration, edited by Luque, there is an informative chapter by Sala on the cooling of solar cells [11]. It does not focus on concentrating PV in particular. The text presents models for calculating heat transfer through cells and the temperature effect on solar cell parameters. It also contains separate discussions on passive cooling through radiation, natural convection and conduction, and on forced liquid cooling. The text has been widely used as a reference for other research dealing with photovoltaic cooling systems. Florschuetz [29] presents another general, theoretical approach to the cooling of solar cells under concentration. He uses the relations between illumination, cell temperature and cell efficiency to find an equation for the illumination level that gives the maximum power output for a given cooling system. This would be the equivalent of the equation for a line passing through the peaks in Figure 2.7. However, as explained earlier, the maximum power points coincide with very high cell temperatures. The possibility of cell degradation has not been taken into account in this model. Florschuetz also explores the importance of contact resistance between the cell and the cooling system (represented by R c-s in Section 2.2.1). He shows that the relative importance of the contact resistance increases substantially as the illumination levels rise. This is because the temperature difference across a boundary is given by T = q& R and thus it increases with increasing heat flux q& and increasing thermal contact resistance R. In high-concentration systems where q& is large, a small contact resistance is needed to achieve the same temperature difference Single cell geometry As described in the following section, passive cooling is found to work well for single-cell geometries for flux levels as high as 1000 suns. This is because of the large area available for heat sinking, as introduced in Section Passive cooling Edenburn [30] performs a cost-efficiency analysis of a point-focus Fresnel lens array under passive cooling. The cooling device is made up of linear fins on all available heat sink surfaces (see Figure 2.9). The concentration values under consideration were 50, 92 and 170 suns. The analysis consists of using given values for the cost of aperture (lens and cell) area and for cooling device area and cost optimising the cooling geometry. Cell degradation at high temperatures is not considered. This implies that arrays that employ the passive cooling devices developed under this model must have a mechanism for defocusing under extreme thermal conditions (very low wind speed, high insolation and high ambient temperatures). In the search for cost-effectiveness, Edenburn also suggests housing the cell assembly in a painted aluminium box, and to use the bottom of this as a finless heat sink. He states that during calm air conditions, radiation is the most important component of heat loss. A finned surface will radiate less than a finless one because of the temperature drop from the base of the fins to the tips. Thus, with the finless box design, the cells could be kept below 150 C even on extreme days at a concentration level of about 90 suns, and a defocusing mechanism might not be necessary. This is still a very high temperature for photovoltaic cells. 14

25 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION Figure 2.9: Passive heat sink for a single cell as suggested by Edenburn [30]. Edenburn concludes that for point focus arrays, the cost of passive cooling increases with lens area, while it remains almost unchanged with concentration. The reason is that as the aperture area is increased, a thicker and more expensive heat exchanger is required. When concentration goes up, the heat sink optimal design does not change by much, but a low contact thermal resistance between the substrate and the heat sink becomes increasingly important to keep the cell temperature down. Miñano [23] presents a thermal model for the passive cooling of a single cell under high concentrations. Like Edenburn, he concludes that passive cooling is increasingly efficient for cells as their size is reduced. Comparing the given cell efficiencies of the GaAs cells used in this case, it seems likely that a concentration of 1000 suns would be possible as long as the temperatures are kept low. Miñano advises that cells be kept below 5 mm diameter. Heat sinks for these cells would be similar to those used for power semiconductor devices. Araki et al. [24] presents further results that show the effectiveness of passive cooling of single cells. In this study, an array of Fresnel lenses focus the light onto single cells mounted with a thin sheet of thermally conductive epoxy onto a heat-spreading aluminum plate. The concentration level is about 500 suns. Outdoor experiments show a temperature rise of cells over ambient of only 18 C, without conventional heat sinks. It is shown that good thermal contact between the cell and the heat spreading plate is crucial to keep the cell temperature low. Techniques to enhance this could be to use a thinner epoxy layer, or to increase the heat conductance coefficient of the epoxy. Graven et al. [31] have patented a single cell lens array which employs a heat sink with longitudinal fins. The thermal contact between the cells and the heat sink is provided by a set of rod springs that force the surfaces together. A thin polyester film between the cells and the heat sink ensures thermal conductance and electrical insulation Active cooling Edenburn [30] also considered using active cooling on his point focus arrays described above. He placed cells in rows, and had one rectangular coolant channel run along the back of each row. To enable a cost comparison between the different cooling regimes, he did not take into consideration the possible advantage of using the extracted heat for thermal energy supply purposes. However, he states that if this were done, active cooling would almost certainly be the most cost-efficient solution. Without this extra advantage, however, the parasitic power losses involved in pumping and in dissipating the waste heat make active cooling more expensive than passive cooling for single cells. The only exemption would be for very large lenses (more than 300 mm in diameter). At this size, the costs of active and passive cooling become almost the same. 15

26 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION Linear geometries Passive cooling Florschuetz [29] uses his model to assess both active and passive cooling options for a linear geometry. For the passive solution, the cells are mounted along either a planar or a finned metal strip. The illumination levels at the maximum power input are compared for the different cooling systems. Pin fins are found to perform better than plane ones, but because pin fins are more costly to manufacture, they may still not be the best option. The model suggests that the plane strip would be sufficient for very low concentration levels (less than 5 suns) and the finned strip only for slightly higher levels (10 suns). With 2.2 m s -1 wind speed, the plane strip should work up to about 10 suns and the finned one up to 14 suns. Note that this analysis does not take cell efficiency degradation into account. The EUCLIDES is a trough-type photovoltaic concentrator located in Spain [32]. In this system, thermal energy is passively transferred to the ambient through a lightweight aluminium-finned heat sink. The fins have been optimised for the relatively low concentration (about 30 suns) used on the EUCLIDES. The optimisation gave fin dimensions to be 1 mm thick, 140 mm long and spaced about 10 mm apart. This could not be manufactured by ordinary means, but was accomplished by stacking fin- and separator-plates, and tightening them with screws. This method is quite costly. The heat sink is projected to contribute to 15.7% of the total cost of a EUCLIDES-type plant, while the photovoltaic modules and the mirrors contribute 11.9% and 10.8%, respectively. Cells have been measured to run at about 58 C. Edenburn [30] considers the cooling of a linear trough design. In his system, the cells are mounted in two lines in a V-type geometry (Figure 2.10). The passive heat exchanger consists of a finned mast that avoids shading the concentrator. The concentration levels under consideration are 20, 30 and 40 suns. Edenburn finds that because of higher cell temperatures, resulting from the longer path length for the heat to the fins of the heat sink, passive cooling of a linear design is much more expensive than for a single cell design. Passive cooling seems not to be cost-efficient for this setup. To increase the performance, he suggests filling the cavity of the "mast" with an evaporative fluid that would work as a thermosyphon to transport heat away from the cells at a very low temperature differential. 16

27 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION Figure 2.10: Passive cooling of a linear design as suggested by Edenburn [30]. The heat pipe approach is further explored by Feldman et al. [33] on a concentration ratio of about 24 suns. The "mast" is made out of extruded surface aluminium, and the evaporative working fluid is benzene. This gives a maximum evaporator surface temperature of about 140 C. The cell temperature would be even higher than this given the thermal resistance between the cell and the evaporator surface. The model shows that the heat transfer in this system is highly dependent on the condenser surface area. The prototype has an evaporator area of 0.61 m 2 and a condenser area of 2.14 m 2. Outdoor testing also shows that the operating temperature is a strong function of wind speed, and less of ambient temperature, wind direction and mast tilt angle. Under the worst case scenario, which is an ambient temperature of 40 C and 19.2 kw m -2 illumination, a minimum wind speed of 1 m s -1 is required to keep the evaporator temperature below 140 C. The surface area would have to be increased by a factor of 2.1 to achieve the same in no-wind conditions. Thermal resistance from base surface to the ambient is K m 2 W -1 in the 1 m s -1 case. Akbarzadeh and Wadowski [34] report on a linear, trough-like system which also uses heat pipes for cooling (Figure 2.11). In this case, the reflector is not a parabola, but an "ideal reflector" which is said to give a uniform illumination across the cells. Each cell is mounted vertically on the end of a thermosyphon, which is made of a flattened copper pipe with a finned condenser area. The system is designed for 20 suns concentration, and the cell temperature is reported not to rise above 46 C on a sunny day, as opposed to 84 C in the same conditions but without fluid in the cooling system. 17

28 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION Figure 2.11: Schematic of heat pipe based cooling system as suggested by Akbarzadeh and Wadowski [34] Active cooling Florschuetz [29] considers cooling his strip of cells actively by either forced air through multiple passages or water flow through a single passage. He notes that with forced air cooling, there is a substantial temperature rise along the cells due to the low heat capacity of air. The required pumping power is also quite large compared to the effective cooling. For these reasons, forced air cooling does not seem to be a viable alternative. Water cooling, on the other hand, permits operation at much higher concentration levels. Edenburn [30] suggests a cooling system for his linear design that consists of a channel of quadratic cross-section, tilted 45, with the V-shaped PV receiver placed on two of the channel sides. Active cooling was found to be more cost-efficient than passive cooling in linear designs. O'Leary and Clements [27] give a theoretical analysis of the thermal and electrical performance for an actively cooled system. The cooling methods considered consist of various geometries of coolant flow through extruded channels, the coolant liquid being a water-ethylene glycol mixture. An optimal geometry is suggested based on maximum net collector output versus coolant flow. The required pumping power rises proportionally with increased coolant mass flow rate, which is characteristic for laminar flow in channels. Although it would seem favourable to operate at the highest possible mass flow rate in order to obtain the lowest cell temperatures and highest cell performances, there is actually shown to be a definite optimum operation region, because the rate of increase in R drops as the mass flow increases. A system of linear Fresnel lenses, cooled by water flow through a galvanised steel pipe, is described by Chenlo and Cid [25]. The system has a concentration level of about 24 suns. The cells are soft soldered to a copper-aluminum-copper sandwich, which is in turn soldered to the rectangular pipe. This mounting gives a satisfyingly low cell to steel tube thermal resistance (R = 8 x 10-5 K m 2 W -1 ). The soft soldering allows for some difference in the thermal expansions between the cells and the steel tube to be accommodated. The convective thermal resistance of the coolant tube is found to be R = 8.7 x 10-4 K m 2 W -1 18

29 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION for Reynolds number Re = This paper also presents good electrical and thermal models for uniform and non-uniform cell illuminations. Russell [35] has patented a heat pipe cooling system (Figure 2.12). His design uses linear Fresnel lenses, each focusing the light onto a string of cells mounted along the length of a heat pipe of circular cross-section. Several pipes are mounted next to each other to form a panel. The heat pipe has an internal wick that pulls the liquid up to the heated surface. Thermal energy is extracted from the heat pipe by an internal coolant circuit, where inlet and outlet is on the same pipe end, ensuring a uniform temperature along the pipe. The coolant water is fed and extracted by common distribution pipes. An alternative system where the coolant enters at one end of the pipe and leaves at the other is also considered, but found to be less preferable because this would cause a temperature gradient along the pipe length. Figure 2.12: Heat pipe based cooling system as suggested by Russell [35]. The CHAPS system at the Australian National University [36] is a linear trough system where the line of cells is cooled by liquid flow through an internally finned aluminum pipe. The coolant liquid is water with anti-freeze and anti-corrosive additives and the optical concentration is 37x. Under typical operating conditions (fluid temperature 65 C, ambient 25 C, direct radiation 1 kw m -2 ), the thermal efficiency is 57% and the electrical efficiency is 11% for the prototype collector. The cells, which are manufactured at the ANU, are run at a fairly high temperature (about 65 C). Nothing is reported about the temperature gradient along the line of cells, which would result from the single coolant pipe, and whether this has a significant result on cell performance. This may be because the preliminary results are from a shorter prototype collector where the temperature difference is insignificant Densely packed cells No reports of passive cooling of densely packed cells under concentration have been found. 19

30 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION Active cooling Verlinden et al. [37] describes a monolithic silicon concentrator module with a fully integrated water cooled cold plate. The module consists of 10 cells and is supposed to act as a "tile" in a larger array. With an optimised coolant flow rate of kg s -1 on an area of 3600 mm 2, the total thermal resistance from cell to water (including all layers in between) is measured to be 2.3 x 10-4 K m 2 W -1. The design is further described by Tilford et al. [38], with module pictures and some further specifications. However, details are not given on the way in which the water flows through the cold plate. John Lasich [39] recently patented a water cooling circuit for densely packed solar cells under high concentration. The circuit is said to be able to extract up to 500 kw m -2 from the photovoltaic cells, and to keep the cell temperature at around 40 C for normal operating conditions. This concept is based on water flow through small, parallel channels in thermal contact with the cells. The cooling circuit also forms part of the supporting structure of the photovoltaic receiver. It is built up in a modular manner for ease of maintenance, and provides good solutions for the problem of different thermal expansion coefficients of the various materials involved. Solar Systems Pty. Ltd. has reported some significant results from their parabolic dish photovoltaic systems located in White Cliffs, Australia [20, 40]. They work with a concentration of about 340 suns, and use the above mentioned patent [39] for cooling the cells. With a water flow rate of 0.56 kg s -1 over an area of mm 2 and an electrical pumping power of 86 W, they maintain an average cell temperature of C and achieve a cell efficiency of 24.0% using the HEDA312 Point-Contact solar cells from SunPower [40]. If all of the thermal energy extracted were being used, the overall useful energy efficiency in this system would be more than 70%. This demonstrates clearly the benefits of active cooling if one can find uses for the waste heat. Vincenzi et al. [8, 41] at the University of Ferrara have suggested using micromachined silicon heat sinks for their concentrator system. The photovoltaic receiver at Ferrara is 300 mm x 300 mm and operates under a concentration level of 120 suns. By using a silicon wafer with microchannels circulating water directly underneath the cells, the cooling function is integrated in the cell manufacturing process. Microchannel heat sinks will be presented in more detail in Section The reported thermal resistance is 4 x 10-5 K m 2 W -1, which is comparable to other microchannel systems (see later in Table 2.2), although perhaps slightly higher. A system is patented by William Horne [15] in which a paraboloidal dish focuses the light onto cells mounted in quite an innovative way (see Figure 2.13). Instead of being mounted on a horizontal surface, they are situated vertically on a set of rings, designed to cover all of the solar receiving area without shading. Water is transported up to the receiver by a central pipe and then flows behind the cells, cooling them, before running back down through a glass "shell" between the concentrator and the cells. In this way, the water not only cools the cells, it also acts as a filter by absorbing a significant amount of UV radiation that would otherwise have reached the cells. Normally, cells need to be protected from UV radiation by a cover glass or lenses. In Horne's case, the water also absorbs some of the low energy radiation, resulting in higher cell efficiency and a lower amount of power converted to heat in the cells. The patent incorporates a phase-change material in thermal contact with the cells, which works to prevent cell damage at "worstcase scenario" high temperatures. 20

31 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION Figure 2.13: Cooling of dense module as suggested by Horne [15]. An idea somewhat similar to that of Horne is patented by Koehler [42]. His idea is to submerge the cells in the circulating coolant liquid, whereby heat is transferred from two cell surfaces instead of just one. In this way the coolant acts like a filter by absorbing much of the incoming low-energy radiation before it reaches the cells. By choosing the right coolant and regulating the pressure, one can achieve local boiling on the PV cells, which give a uniform temperature across the surface and a much higher heat transfer coefficient. 2.4 OTHER COOLING OPTIONS Cooling problems are not exclusive to photovoltaics. Recently, extensive research has been performed on the issue of cooling of electronic devices. The rapid progress towards denser and more powerful semiconductor components require the removal of a large amount of heat from a confined space [43-48]. Other areas where much research is being conducted on the subject of cooling include the nuclear energy and gas turbine industries. Both of these have a large cooling load and strict temperature limitations due to material properties. These applications generally deal with larger areas and different geometries from the electronics industry. Research from these three fields should provide a broad base for finding better options for cooling of photovoltaics. The following section presents some studies that might be relevant for PV cooling, especially for the more demanding cases like densely packed cells under high concentration Passive systems There is a wide variety of passive cooling options available. The simplest ones involve solids of high thermal conductivity, like aluminium or copper, and an array of fins or other extruded surface to suit the application. More complex systems involve phase changes and various methods for natural circulation. It should be noted that passive cooling is just a means of transporting heat from where it is generated (in the PV cells) to where it can be dissipated (the ambient). Complex passive systems reduce the temperature difference between the cells and the ambient, or they can allow a greater distance between the cells and the dissipation area. However, if the area available for heat spreading is small and shading is an issue, no complex 21

32 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION solutions will help avoid the use of active cooling. Heat dissipation is still limited by the contact point between the terminal heat sink and the ambient, where the convective heat transfer coefficient, and less the radiative heat transfer (except at very high temperatures) are the limiting factors. Kraus and Bar-Cohen [49] give an extensive and very useful introduction to the design of heat sinks. Their book contains an overview of typical convective thermal resistances for different configurations, as a useful guide when choosing the cooling system. It also presents a step-by-step procedure for heat sink design and optimization procedures both for single fins and fin arrays. Optimum dimensions for fins of common heat sink materials are given, as well as the heat transfer properties for optimised arrays. One way of passively enhancing heat conduction is the use of heat pipes. The theory on and use of these devices is thoroughly described by Dunn and Reay [50]. It seems that the use of heat pipes is probably not feasible for high concentrations because heat pipe performance is limited by the working fluid saturation temperature and the point at which all liquid evaporates (burnout). For water, a heat flux of kw m -2 can be accommodated but only at temperatures above 140 C. Launay et al. [51] study the effect of micro-heat pipe arrays etched into the silicon wafer. They show an improvement of conductivity through the silicon, depending on the geometry of the heat pipes and the fluid charge. In the search for better cooling options for computer components, heat pipes provide an alternative for transporting the heat away from the component and to a place better suited for a fan or other heat sink (remote heat exchangers). Pastukhov et al. [52] and Kim et al. [47] show promising results for these systems. Xuan et al. [53] describe the flat plate heat pipe (FPHP), which is a flat copper shell filled with a working fluid. A layer of sintered copper powder is applied to the heated surface of the FPHP in order to enhance heat transfer. The FPHP is studied under various orientations. When installed horizontally, the extra working fluid forms a liquid layer on the heated surface and reduces heat transfer. The best result is achieved when the FPHP is installed in the vertical direction, when the working fluid is distributed across the heated surface by the capillary action of the sintered layer, ensuring there is not too much fluid at the surface at any time. It is shown that the FPHP is a good alternative to a solid heat sink due to its low thermal resistance, isothermality and lightweight features. Chen and Lin [54] study the capillary pumped loop used as a heat transfer device. Their system is capable of dissipating a heat load of 25 kw m -2 from an area of 42 mm x 38 mm while keeping the heated surface below 100 C. The device works better if the vertical distance between the evaporator and the condenser is increased above 10 mm. The effect of orientation is not included in the study Forced air cooling The thermal properties of air make it far less efficient as a coolant medium than water [49]. This implies that more parasitic power (to power fans) will be needed to achieve the same cooling performance. Air cooling also reduces the possibility of thermal energy use. Hence, air is a less favourable option in many cases. However, in some situations where water is limited, forced air may still be the preferred option. The heat transfer of forced air cooling can be enhanced in much the same ways as with water. Detailed information on the design of forced air heat sinks can be found in [49]. Other studies on forced air cooling are not included in this review. 22

33 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION Liquid single-phase forced convection cooling Microchannel heat sinks The microchannel heat sink is a concept well suited for many electronic applications because of its ability to remove a large amount of heat from a small area. Tuckerman and Pease [55] were the pioneers who first suggested the microchannel heat sink, based on the fact that the convective heat transfer coefficient scales inversely with the channel width. The best reported thermal resistance from the experiments was 9.0 x 10-6 K m 2 W - 1 for a heated area and heat sink of 10 mm x 10 mm, flow rate of 8.6 ml s -1 and a pressure drop of kpa. This paper significantly raised the experimental limit on heat removal per area, and may have allowed for further miniaturisation of electronic components. Later studies have showed two major drawbacks to the microchannel heat sink. These are a large temperature gradient in the streamwise direction, and a significant pressure drop that leads to high pumping power requirements. Much work have been published on the modeling and optimisation of various aspects of the microchannel heat sink [46]. Ryu et al. [44] presents a numerical optimization that minimises the thermal resistance subject to a specified pumping power. For a heat sink of 10 mm x 10 mm, the lowest reported thermal resistance is 9 x 10-6 K m 2 W -1. The associated pressure drop is kpa and the optimal dimensions are 56 µm channel width, 44 µm wall width, and 320 µm channel depth. More on the pressure drop and heat transfer in a heat sink of rectangular microchannels is given by Qu and Mudawar [56]. The modelling and experiments deal with laminar flow only. Channel dimensions were 231 µm width and 713 µm depth. The study concludes that conventional Navier-Stokes and energy conservation equations can accurately predict the pressure drop and heat transfer characteristics for microchannels of this dimension. An experimental study of heat transfer in rectangular microchannels by Harms et al. [57] concludes that heat transfer performance can be increased by decreasing the channel width and increasing the channel depth. Developing laminar flow is found to perform better than turbulent flow due to the larger pressure drop associated with turbulent flow. The lowest reported thermal resistance is 1.26 x 10-4 K m 2 W -1 for a flow rate of 118 ml s -1 over an area of 3930 mm 2 and a 169 kpa pressure drop. Owhaib and Palm [58] present an experimental study which verifies the best correlations to use for modelling heat transfer in circular microchannels. Tubes of three different diameters were studied. The results show that in the laminar flow regime, the heat transfer coefficient is largely independent of channel diameter, while in the turbulent regime (Re > 6000), smaller channels are clearly better. The best reported thermal resistances are 10-4 K m 2 W -1 for 0.8 mm tubes in the turbulent flow regime, and 4 x 10-4 for laminar flow. No data on pressure drops or flow rates are given. The effect on tip clearance on the thermal performance of microchannels has also been studied. Tip clearance denotes the spacing between the channel walls and the top surface. It has generally been assumed that tip clearance would lower the efficiency of the heat sink because of the phenomenon of flow bypass: as the tip clearance is raised, for a given pumping power, the flow rate will decrease between the channels while increasing through the tip clearance. As a result, less heat is transferred near the base of the channels. However, Min et al. [59] found that in microchannel heat sink, the added heat 23

34 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION transfer through the fin tips lead to an increased heat sink performance as long as the ratio of tip clearance to channel width is kept below 0.6. Similar results are found by Moores and Joshi [60] for a shrouded pin fin heat sink. The search of a microchannel design that deals with the problem of non-uniform temperatures and pressure drops has been carried out by a number of researchers, and several innovative solutions have been found. Alternating flow directions is one way of reducing the streamwise temperature gradient in the microchannel heat sink. This was first proposed by Missagia and Walpole [61]. Their design consists of a silicon wafer with microchannels machined into them, attached to a manifold plate that directs the water to flow in alternating directions through the channels. The results indicate a thermal resistance of 1.1 x 10-5 K m 2 W -1, for a laminar flow of 28 ml s -1. The associated pressure drop for a 100 mm long heat sink would be 452 kpa. Vafai and Zhu [43] suggest using two layers of counter-flow microchannels. Numerical results show that the streamwise temperature gradient is significantly lowered compared to a one-layer structure. This in turn allows for a smaller pressure drop to fulfil the same cooling requirements. No specific data for thermal resistances or pressure drops are given. Chong et al. [46] optimised the counter flow principle for single and double layer channels as the two described above. The simulation models both designs for laminar and turbulent flows. The results show that laminar flow is to be preferred over turbulent for both cases. The single layer counter flow heat sink gives an overall thermal resistance of 4.8 x 10-6 K W -1 with a pressure drop of kpa. For the double layer design the values are 6.6 x 10-6 K W -1 and 54.6 kpa, both under laminar flow conditions. The paper does not arrive at any conclusions as to whether single or double layer counter flow is the preferable alternative. A two-layered microchannel heat sink with counter flow, called the manifold microchannel heat sink, is also designed to lower the temperature gradient and pressure drop. This design has been successfully modelled and optimised by Ryu et al. [48] (Figure 2.14). In the manifold microchannel heat sink, the coolant flows through alternating inlet and outlet manifolds in a direction normal to the heat sink. This way the fluid spends a relatively short time in contact with the base, thus resulting in a more uniform temperature distribution. With laminar flow, it is shown that the thermal resistance is lowered by more than 50% compared to the traditional microchannel heat sink, while drastically reducing the temperature variations on the base. A number of numerical calculations are performed to find the optimal channel depth, channel width, fin thickness and inlet/outlet width ratios. All optimisations are constrained by a given pumping power. Optimal dimensions are found to be divider width 500 µm and inlet width + outlet width 1000 µm, with an associated thermal resistance of 3.1 x 10-6 K m 2 W

35 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION Figure 2.14: Manifold microchannels as suggested by Ryu [48]. Inspired by the superior mass flow capacity of the mammalian circulatory and respiratory system, Chen and Cheng [62] use this idea to design a fractal net of microchannels. On a purely theoretical basis, they conclude that fractal-like microchannels can increase the heat transfer while reducing the pressure drop when compared with parallel microchannels. This is based on the assumptions of laminar, fully developed flow, and negligible pressure drop due to bifurcation Impinging jets Very low thermal resistances (generally K m 2 W -1 ) [63] can be achieved through the use of impinging liquid jets. When high velocity liquid is forced through a narrow hole (axisymmetric jet) or slot (planar jet), into the surrounding air, a free surface forms. The impinging jets are capable of extracting a large amount of heat because of the very thin thermal boundary layer that is formed in the stagnation zone directly under the impingement and extends radially outwards from the jet. However, the heat transfer coefficient decreases rapidly with distance from the jet. To cool larger surfaces, it is therefore desirable to use an array of jets. A problem arises when water from one jet meets the water from the neighbouring jet. Disturbances arise which are very hard to model but have been shown to decrease the overall heat transfer drastically [64, 65]. If measures are taken to deal with this "spent flow" (through drainage openings), impinging jets have been predicted to be a superior alternative to microchannel cooling [65] for target dimensions larger than the order of 0.07 m x 0.07 m. Webb and Ma [64] give an extensive overview of the literature available on liquid impinging jets. The review distinguishes between free and submerged jets, and axisymmetric and planar jets, and deals with single phase jets only. The article points out a number of areas where further studies are needed. These include the effect of curved surfaces and spent flow, and the local heat transfer coefficient at points other than the stagnation zone directly underneath the jet. 25

36 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION Womac et al. [66] present an experimental study of the heat transfer coefficient in free and submerged 2x2 and 3x3 arrays of liquid jets without treatment of spent flow. The effect of nozzle-to-plate spacing is studied, and found to be insignificant for free jets, but to have an effect on submerged jets. Correlations for the heat transfer in both types of jets are presented Two-phase forced convection cooling By allowing the coolant fluid to boil, the latent heat capacity of the fluid is used to allow for a significantly larger heat flux and an almost isothermal surface. However, two-phase flows are more complicated to model and to predict. Any comprehensive heat transfer textbooks such as [28] will give an introduction to forced convection boiling. When the bulk liquid is below saturation temperature, but the heat flux is high enough that liquid at the surface can reach saturation temperature, subcooled boiling occurs. Under subcooling, bubbles will collapse as they are released from the wall and travel into the surrounding liquid. Subcooled forced convection boiling in small channels is among the most efficient heat transfer methods available [67, 68]. This is often used in applications with extremely large heat fluxes such as fusion reactors first walls and plasma limiters. The most important parameter in this case is the critical heat flux (CHF). If the heat flux is raised above the CHF, a very large increase in temperature will occur and most likely result in overheated and damaged equipment. Thus, to achieve maximum cooling, one wants to run the system close to the CHF, but never above. Higher heat transfer coefficients, and thus lower wall temperatures, can be found at lower heat fluxes. Predicting the CHF is difficult because it depends on a number of parameters. High velocities, large subcoolings, small diameter channels and short heated lengths are known to increase the CHF. Two-phase flows may be a good option for the cooling of photovoltaic cells when the heat fluxes are high. The saturation temperature of water can be brought to 50 C at a pressure of 0.13 bar [28]. To avoid pressurised systems, other working fluids may be used such as Vertrel XF used in [45]. A number of studies are devoted to the detailed analysis of bubble formation, onset of different boiling regimes, and CHF for subcooled boiling. These include [67, 69, 70]. Bartel et al. [71] present a very good literature review on subcooled boiling. The review points out that there is a lack of available data on local measurements in the subcooled boiling region. There are a number of studies dealing with two-phase flow in microchannels. Ghiaasiaan and Abdel-Khalik [68] give an extensive literature review of the subject. Microchannels with hydraulic diameters of the order 0.1 to 1 mm and long length-to-hydraulic diameter ratios are considered. The review includes a thorough description of flow regimes in horizontal and vertical channels, correlations for pressure drops, forced flow subcooled boiling and CHF. Detailed studies of bubble formation and flow boiling in microchannels are found in [72-74]. Hetsroni et al. [45] describes a microchannel heat sink that keeps the electronic device of a temperature of C, a temperature highly suited for photovoltaic purposes. The working fluid is Vertrel XF, which has the desired saturation temperature and is dielectric, so that it can be brought into contact with the active electronics. The study was performed at relatively low heat fluxes (< 60 kw m -2 ). Results show a much more 26

37 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION uniform temperature across the surface compared to water cooling at comparable flow rates (5 C as opposed to 20 C). However, some nonuniformities in heat transfer occurred because of two circumstances specific to parallel microchannels: the two phases may split unevenly on entering the channels, leading to different heat transfers for different channels; secondly, the wall superheat for the onset of nucleate boiling is very low, something which leads to pressure fluctuations and uneven heat transfer. Temperature and pressure fluctuations were also found to be characteristic of boiling in minichannels by Hapke et al. [75]. The lowest thermal resistance reported by Hetsroni et al. [45] was 9.5 x 10-5 K m 2 W -1 at a mass flux of 290 kg m -2 s -1. Inoue et al. [76] study the use of boiling in confined jets to cool a very high heat flux (nearly 30 MW m -2 ) in a fusion reactor (Figure 2.15). This system proposes an innovative way of dealing with the spent flow, and at the same time preventing splash of water from the violent boiling that may occur at the surface under these conditions. The jets proposed are planar jets, but the experiments only look at the two-dimensional version. Therefore, the potential problem of outgoing water heating the incoming water and thus lowering the cooling capacity is not considered. The CHF is studied as a function of jet flow velocity, subcooling and curvature of heated surface. The results show that the CHF in confined flow is almost double that of a free flow jet. Surface curvature does not seem to give any significant effect. Figure 2.15: Confined planar jet as suggested by Inoue et al. [76]. Water is fed through the inner tube, forms a planar jet through the slit in the bottom, and then returns through the outer tube. 2.5 COMPARISON OF COOLING OPTIONS It is problematic to compare such a wide range of cooling options. Depending on the application, one may want to compare parameters such as pumping power, weight, materials use, ease of manufacturing and maintenance, maximum heat removal, temperature uniformity, shading etc. All of these criteria can obviously not be incorporated into one review. In addition, literature generally does not give information on all of these aspects. Table 2.2 gives a summary of the various cooling options described in this review. In order to enable a comparison of pumping powers, which is an important parameter when it comes to power generating systems, the pumping power has been calculated as 27

38 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION P = m& p in cases where only mass flow rate and pressure drops are given. It should be noted that pressure drops may or may not incorporate manifolds or other external factors. Articles also may use slightly different definitions for thermal resistances. Extra care should be taken when comparing different systems such as jets versus passive cooling or two-phase versus single-phase flows. Thermal resistances, flow rates and pumping powers are all given per unit area for easier comparison. All precautions taken, Figures still provide a comparison between options. The letters in the graphs mark where they are taken from in Table 2.2. There is a wide variety between the different studies, even within the same categories. This shows that experimental work is still very important for determining the best cooling methods. What seems to do best in all comparisons is the category "improved microchannels" which includes various forms of alternating flows. This method provides the clearly lowest thermal resistance along with low power requirements. In all microchannel studies, laminar flow seems to outperform turbulent. Etching microchannels into the silicon substrate as a part of the manufacturing process of photovoltaic modules may prove a very good option for photovoltaic cell cooling (eg. [8]). Impinging jets seem to be a promising alternative, provided measures are taken to deal with spent flow. No studies have yet come up with a solution to this problem when dealing with single-phase liquid flows. Thermal resistance (K m 2 /W) f l a b s B h u d e i k g c m r t n v x y passive cooling, no wind forced air water, plane surface water, channels water, microchannels water, improved microchannels water, impinging jets microchannels, two-phase flow o p w j q z 10-6 A 10-7 Figure 2.16: Comparison of different cooling options. The letters refer to the references listed in Table 2.2. Note that the position on the x-axis is of no significance. 28

39 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION 10-3 water, microchannels water, improved microchannels microchannels, two-phase flow Thermal resistance (K m 2 /W) Pumping power (W/m 2 ) Figure 2.17: Comparison of different cooling options and the pumping power they require. Thermal resistance (K m 2 /W) v x y z f l w g m h forced air water, channels water, microchannels water, improved microchannels water, impinging jets microchannels, two-phase flow n r p u q B Flow rate (kg/m 2 s) Figure 2.18: Comparison of different thermal resistance cooling options and flow rates. The letters refer to the references listed in Table

40 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION 10-3 water, microchannels water, improved microchannels microchannels, two-phase flow Thermal resistance (K m 2 /W) B v w r u q x y p Pressure drop (kpa) Figure 2.19: Thermal resistance versus pressure drop for different cooling options. The letters refer to the references listed in Table

41 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION Table 2.2: Values cited in references Work Configuration Heated area m 2 Sala [11] Air cooling, plane surface, - Water cooling, plane surface: laminar mode - turbulent mode - Florshuetz [29] No extruded surface, calm air - Finned strip, calm air - Forced air through multiple passages 1.52 x 10-1 Water cooling 1.52 x 10-1 Impinging jet, nozzle-plate distance = 0.16 cm 2.58 x 10-3 Feldman et al. [33] Finned heat pipe, calm air 6.10 x 10-1 Luque et al. [32] Finned strip, calm air - Chenlo and Cid [25] Water flow through rectangular steel pipe - * Use caution with thermal resistances for natural convection or two-phase flow (see Section 2.1.3) Pump power W m Pressure drop kpa Mass flow rate kg m -2 s x x x Thermal resistance K m 2 W x 10 0 * 2.6 x x x 10-2 * 1.1 x 10-2 * 2.6 x x x x 10-3 * 2.2 x x 10-4 a b c d e f g h i j k 31

42 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION Table 2.2: Values cited in references (continued) Work Configuration Heated area m 2 Coventry [36] Water flow through internally extruded channel 1.15 x 10-1 Verlinden [37] Water cooled cold plate 3.60 x 10-3 Vincenzi et al. [8] Microchannels 3.40 x 10-5 Kraus and Bar- Cohen [49] Parallel fin heat sink, calm air 1.68 x 10-2 Harms et al. [57] Microchannels 3.93 x 10-3 Owhaib and Palm [58] Circular microchannels, laminar flow turbulent flow - Missaggia and Walpole [61] Microchannels, single layer counter flow 2.30 x 10-4 * Use caution with thermal resistances for natural convection or two-phase flow (see Section 2.1.3) + Calculated from given data as P = m p. Pump power W m x x x Pressure drop kpa x x 10 2 Mass flow rate kg m -2 s x x x x x 10 2 Thermal resistance K m 2 W x x x x 10-3 * 1.3 x x x x 10-5 l m n o r s t u 32

43 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION Table 2.2: Values cited in references (continued) Work Configuration Chong et al. [46] Microchannels, single layer counter flow, laminar turbulent Microchannels, double layer counter flow, laminar turbulent Ryu et al. [44] Manifold microchannels Rohsenow et al. [63] Impinging jets Hetsroni et al. [45] Two-phase microchannels + Calculated from given data as P = m p Heated area m x x x 10-4 Pump power W m x x x x x x 10 2 Pressure drop kpa 1.18 x x x x x 10 0 Mass flow rate kg m -2 s x x x x x x 10 2 Thermal resistance K m 2 W x x x x x x x 10-5 B v w x y z A 33

44 2 COOLING OF PHOTOVOLTAIC CELLS UNDER CONCENTRATED ILLUMINATION 2.6 CONCLUSION With single-cell geometries, research shows that passive cooling is feasible for concentration values of at least 1000 suns, provided the cells and lenses are kept small. Linear concentrators can also be cooled passively, but the heat sinks tend to get very intricate and therefore expensive for concentration values as low as 20 suns. A heat pipe based solution is one way to increase the passive cooling performance. Different ways of active cooling by water or other coolants have also been found to work well and should be considered for concentration levels over 20 suns. For densely packed cells, it seems that active cooling is the only feasible solution. At high concentrations, the high heat flux makes a low contact resistance from cell to cooling system extremely important. There are also numerous challenges for the cooling system itself in order to achieve a low thermal resistance for a low pumping power requirement with a simple, reliable and inexpensive system. New solutions such as microchannels or impinging jets may prove to be good solutions, especially if incorporated in the cell manufacturing process. Owing to the complexity of obtaining accurate modelling results, careful experimental work is still important for determining the best method of cooling for a given application. However, the comparisons in this review provide a good background to assessing the different options. Because the use of microchannels as a cooling technique for concentrating PV is already being trialled in Italy, it was decided to proceed with investigating the possibility of jet impingement cooling. A closer literature study of this particular technique was therefore needed. The results of this study are presented in the following chapter. 34

45 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS Chapter 3 a This chapter contains a literature survey on jet impingement cooling. It is limited to jets that can be characterised as axisymmetric and submerged. The term axisymmetric refers to jets issuing from round holes, as opposed to planar jets issuing from slots. Arrays of axisymmetric jets have been found to yield a higher total heat transfer per unit flow rate than planar jets [77]. The term submerged refers to jets issuing into a pool of the same fluid, while free-surface jets impinge into a less dense medium such as water into air. Several studies [66, 78, 79] have established that submerged liquid jets yield a higher overall heat transfer than free-surface liquid jets. One of the most important parameters for jet flow behaviour is the ratio of nozzle-to-plate spacing z, to nozzle diameter, d. Only relatively small ratios (z/d < 6, sometimes referred to as confined) are considered here because the heat transfer deteriorates significantly beyond this spacing. This behaviour is further explained in Section In arrays consisting of many jets, the jets close to the drainage point are affected by the spent liquid from jets further away. This spent liquid is referred to as crossflow. Because crossflow generally has an adverse effect on heat transfer, this study is limited to single jets and relatively small arrays where the effect of crossflow is minor or negligible. When dealing with convective heat transfer, the Nusselt number, Reynolds number and Prandtl number are dimensionless groups that are frequently used. The Nusselt and Reynolds numbers are based on a characteristic length, which in the case of jets is taken to be the nozzle diameter unless otherwise explained. The Nusselt number is a dimensionless form of the heat transfer coefficient, given as hd Nu =, (3.1) k where h is the heat transfer coefficient and k is the fluid thermal conductivity. By definition, the Nusselt number is the ratio of convective heat transfer to the conductive heat transfer that would have occurred in the fluid under stagnant conditions. The Reynolds number is based on the fluid mean velocity, and is proportional to the inertial force divided by the viscous force. At low Reynolds numbers, the viscous effects dominate and the flow is laminar. Inertia effects become more important at higher 35

46 3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS Reynolds numbers, followed by a transition to turbulent flow. The Reynolds number is defined as vd Re =, (3.2) ν where v is the mean fluid velocity and ν is the kinematic viscosity of the fluid. In jet impingement heat transfer, the thermal and boundary layers are important concepts. In essence, the thermal boundary layer is the region of fluid close to the heated surface which feels the temperature of the wall. The velocity boundary layer is the region of fluid that feels the no-slip condition along the wall. The fluid outside the boundary layers is completely unaffected by the heated surface. The Prandtl number Pr denotes the ratio of the thickness of the velocity boundary layer to the thermal boundary layer. This value is constant for a given fluid at a given temperature. Water at room temperature has Pr ~ 7, while air at room temperature has Pr ~ 0.7. The Prandtl number is defined as the ratio of kinematic viscosity to thermal diffusivity (a material constant which describes the rate at which heat is conducted through the medium) κ : ν Pr =. (3.3) κ 3.1 SINGLE JETS Hydrodynamic flow structure of single impinging jets Figure 3.1 depicts the characteristic flow regions of a single impinging jet. As the jet issues from the nozzle, the outer layer of the jet, called the mixing region, interacts with the surrounding liquid. The centre of the jet, often referred to as the potential core, remains undisturbed for a region of about 3-8 nozzle diameters beneath the jet exit. The exact length of the potential core depends on the jet Reynolds number and nozzle configuration [78, 80]. Interaction with the surrounding liquid causes the jet velocity to fall off proportionally with the vertical distance below the tip of the potential core. As the jet approaches the impingement plate, it is deflected and slowed down. The deflection region is found to extend nozzle diameters from the impingement plate surface [81]. Due to jet deceleration and the resulting increase in pressure, hydrodynamic and thermal boundary layers are formed in the impingement zone directly beneath the jet, which may only be a few micrometers thick [64]. The thin thermal boundary layer is what causes the high heat transfer capabilities of impinging jets. The region of flow parallel to the impingement surface is often referred to as the wall jet. In this region, the jet velocity rises rapidly to a maximum before it falls off radially away from the impingement zone. For some configurations, there is a transition from laminar to turbulent flow close to the stagnation point. The thermal and velocity boundary layers grow thicker with radial distance from the jet axis until they encompass the full thickness of the jet flow. 36

47 3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS d 1 l z Figure 3.1: Flow regions of an impinging jet (from Jambunathan et al. [81]). 1: Potential core; 2: mixing region; 3: deflection region; 4: wall jet; 5: stagnation point. The nozzle diameter, orifice plate thickness and nozzle-to-plate distance are denoted by d, l, and z, respectively Radial variation in local heat transfer and the influence of nozzleto-plate spacing The local heat transfer under an impinging jet is strongly dependent on r/d, which is the ratio of radial distance away from the stagnation point to the nozzle diameter. Figure 3.2 shows the typical radial variation of Nusselt number under a single jet for nozzle-to-plate spacing to diameter ratios of 2 z/d 24 [81]. The distributions for all spacings are characterised by high heat transfer close to the stagnation point (r/d = 0), followed by a rapid decrease in heat transfer in the wall jet region. For z/d 6, the distributions tend to converge, apart from local variations which are explained below. This is because these spacings are within the length of the potential core, where the jet velocity remains unchanged from the nozzle exit. Although the heat transfer remains relatively unchanged for spacings within the potential core, some studies have found that the overall magnitude increases slightly with z/d due to increased turbulence [78]. For higher nozzleto-plate spacings, the overall heat transfer is drastically reduced because of interaction with the surrounding liquid. For r/d > 7, the Nusselt number distributions for all z/d start to converge. This is because flow deflection and interaction with the surrounding liquid has completely reshaped the initial flow structure. At low z/d, two peaks appear in the Nusselt number distribution. The inner peak at r/d ~ 0.5 occurs partly because of acceleration of the fluid out of the stagnation region, which decreases the thickness of the thermal boundary layer, and also because of the influence of shear layer generated turbulence. The inner secondary peak has been found to become less pronounced as the Reynolds number is decreased and the nozzle-to-plate distance is increased[82]. The outer peak at r/d ~ 2 is caused by the transition from laminar to turbulent flow. The location of this peak has been found to move away from the stagnation point as Re or z/d is increased. For z/d beyond the length of the potential core (z/d ~ 6), the maximum Nusselt number is found at the stagnation point and there are no secondary maximums. 5 37

48 3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS z/d r/d Figure 3.2: Radial variation of heat transfer coefficient under a jet impinging on a flat plate for various nozzle-to-plate spacing to diameter ratios (reproduced from [81]). The studies of Womac et al. [78] and Garimella and Rice [79] suggest that the optimal nozzle-to-plate spacing for single jets is found at z/d ~ 3-4. Womac et al. [78] studied nozzle-to-plate separations of 1 z/d 14.5 for a variety of nozzle diameters and Reynolds numbers, and found that the average heat transfer coefficient was relatively insensitive to separation distance at low Reynolds numbers (Re 4000). For higher Re, the average heat transfer remained undisturbed or increased slightly with increasing z/d for 1 z/d 4 and dropped off as the separation distance was further increased. This was used to determine that the length of the potential core was approximately four nozzle diameters. Garimella and Rice [79] studied the local heat transfer under submerged jets with square-edged orifices over a range of nozzle-to-plate spacings (1 z/d 14). The working fluid was FC-77 which is a dielectric liquid with Pr ~ 25. The stagnation point heat transfer coefficient was found to be almost constant up to z/d = 4, but to decrease from z/d = 5, which corresponded with the length of the potential core for this configuration. For z/d < 5, secondary peaks appeared at r/d ~ 2. The magnitudes of these peaks were found to increase with increasing Reynolds number. The local and average Nusselt number was highest for all nozzles at z/d ~ 3. The stagnation point heat transfer coefficient is generally highest at the very end of the potential core. This was shown by, among others, Webb and Ma [64] who found that the stagnation point heat transfer reached a maximum at z/d ~ 5. However, lower z/d tends to shift the Nusselt number peak outwards from the stagnation point, so that the region of high heat transfer occupies a relatively larger area. The highest average heat transfer is thus generally found slightly below the end of the potential core. The shape of the radial heat transfer distribution is a complex function of r/d, z/d, Re and nozzle configuration, something which makes it a challenge to find accurate correlations. Hoogendoorn [83] gave a correlation based on turbulence intensity values at 38

49 3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS radial positions in a free jet. This requires extensive measurements before the correlation can be used and is thus not very practical for design purposes. Jambunathan [81] presented a correlation for the local Nusselt number under single jets of the form a Nu = k Re, (3.4) where a = f ( r / d, z / d ) and k = f(r/d,z/d, nozzle configuration). While a is given explicitly, k remains to be found graphically from [81], which makes this a poor correlation for making predictions. In this form only qualitative assumptions can be made for the detailed heat transfer under impinging jets Effect of nozzle configuration The heat transfer coefficient is highly sensitive to the level of turbulence in the flow, which in turn is determined by the nozzle configuration. Orifice nozzles have generally been found to introduce a higher level of turbulence and thereby a higher heat transfer coefficient than pipe-like nozzles [84]. Figure 3.3 shows an overview of commonly used orifice nozzle configurations. d d d a) b) c) Figure 3.3 : Overview of orifice nozzle configurations: a) square-edged, b) sharp-edged, c) countersunk. The liquid flows though the nozzle from above. Garimella and Nenaydykh [80] found the developing length of the nozzle (l/d) to be a major influence on the heat transfer under liquid jets. The range under consideration was 0.25 l/d 12. It was found that short developing lengths (l/d < 1) yielded the highest stagnation point heat transfer coefficients. At l/d = 4, there was a minimum in the heat transfer coefficient, with a slight increase for l/d above this value. These trends were explained by the separation bubble which is formed at the inlet of a nozzle. Previous studies had shown that the reattachment length for this bubble is between 0.8 and 1.9 nozzle diameters. For short developing lengths, the separation bubble would not reattach within the nozzle, thus resulting in a reduced effective cross-section of the nozzle. The higher velocities created by this contraction were thought to cause the high heat transfer for l/d < 1. For l/d > 1, the flow reattaches within the nozzle. The increase in heat transfer above l/d = 4 was attributed to the flow velocity profile changing from uniform to fully developed. The fully developed flow has a higher velocity in the centre and lower velocity along the edges. This would result in a higher heat transfer coefficient at the stagnation point. The heat transfer characteristics of sharp-edged, square-edged and an intermediate case of nozzles were compared by Lee and Lee [84] for air jets for 5000 < Re < The sharp-edged orifice was found to yield the highest local and average Nusselt number because of its more vigorous turbulence behaviour. It also shows a stronger Reynolds number dependence than the straight and intermediate nozzles. The sensitivity to nozzle configuration was found to be stronger at low z/d, which ranged from 2 to 10 in this study. This finding was supported by Garimella and Nenaydykh [80], who explained this phenomenon by the fact that interaction with ambient fluid downstream from the jet exit tends to smooth out differences in the original flow structure. 39

50 3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS When designing an optimum jet impingement device, it is generally relevant to optimise the system for a given pump power instead of a given flow rate. The pump power is proportional to the product of flow rate and pressure drop across the device. Most studies of the effect of nozzle configuration do not take the pressure drop into account, which make them incomplete as a tool for designers. Brignoni and Garimella [85] performed a study comparing the heat transfer and pressure drop characteristics for orifice nozzles countersunk at two different angles compared with a regular square-edged orifice nozzle. Previous studies have found that countersunk orifices yield lower heat transfer coefficients when compared with square or sharp-edged orifices. However, Brignoni and Garimella showed that countersinking the nozzle significantly reduced the pressure drop while only slightly lowering the heat transfer coefficient. A countersunk angle of about 30 (angle to normal) seems to yield the best result. At higher angles, the nozzle again starts to resemble a sharp corner which increases the pressure drop through it. The difference in heat transfer between different nozzles was found to become more significant with increasing Reynolds number. Lee et al. [86] stated that the nozzle diameter, with all dimensionless parameters held constant, had an influence on the Nusselt number in the impingement zone out to r/d ~ 0.5. In this region, the local Nusselt number was found to increase by about 10% from the smallest to the largest nozzle. Long pipe nozzles were used to ensure fully developed flow at the nozzle exit. The length of the potential core (in units of nozzle diameter) was shown to increase with increasing nozzle diameter. This indicates that for the same z/d, large nozzles create a higher mean velocity. The turbulence level was also higher for the larger nozzles. The higher velocity and turbulence intensity would account for the increased heat transfer under the larger nozzles. Only relatively large nozzles of d = 13.6 to 34.0 mm and one Reynolds number of Re = were used in this study [86]. Garimella and Rice [79] also found the stagnation point Nusselt number to be dependent on the nozzle diameter but could find no systematic relationship Correlations for the stagnation point and average Nusselt number Table 3.1 presents a summary of correlations for the stagnation point (Nu 0 ) and average Nusselt number (Nu avg ) under single jets. Following from theoretical hydrodynamic studies of the jet flow structure, the correlations for stagnation point Nusselt numbers are generally of the form m n Nu 0 = C Re Pr. (3.5) The Reynolds number dependence, m, is normally determined experimentally and found to lie in the range 0.4 m 0.7, and is strongly dependent upon nozzle configuration. Because most studies looks only at one liquid at one temperature, the Prandtl number dependence n is most commonly assumed. Most correlations use n ~ 0.4. Li and Garimella [87] performed a study using different Prandtl number liquids to obtain the Prdependence as a part of the curve-fitting process. The resulting correlation for confined and submerged jets for a range of fluids is given in Table 3.1. Other correlations, valid only for specific fluids but with a smaller error, are given in Li and Garimella [87]. Garimella and Nenaydykh [80] proposed a correlation with correction factors for z/d and l/d. The data for the smallest nozzle (d = 0.79 mm) was not included in the correlation because it showed a somewhat different behaviour from the other nozzles. Very small nozzles have often yielded unexpected results (an example is Womac et al. [78]), 40

51 3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS something which suggests there is a size dependency which becomes more significant for small nozzle diameters. The same correlation was used by Garimella and Rice [79]. Lee and Lee [84] proposed specific correlations for different nozzle configurations, but because they contained no Prandtl number dependence they are not easily compared with or applied to other cases, and are therefore not included in Table 3.1. The correlations for average Nusselt number under single jets are generally based on area averaged heat transfer coefficients over either round or square heated areas with the jet centred on the heater. Round heaters are characterised by their radius in units of r/d while square heaters have side lengths L heat. The common usage of heaters to study the heat transfer characteristics of impinging jets is described in Section 3.4. The correlation of Womac et al. [78] assumes a square heater with sides of length L heat. The first part of the equation describes the impingement region while the second describes the wall jet region. Reynolds number dependences of m = 0.5 and 0.8 are assigned to each part respectively to represent laminar and turbulent flow. Garimella and Rice [79] presented a correlation for the average Nusselt number over a heater with constant dimensions of 10 mm x 25 mm. The square-edged nozzles had diameters in the range 0.79 mm d 6.35 mm. The average heat transfer for a given area will be highly dependent on nozzle diameter, but is not included in the correlation. This correlation is thus relevant only for a limited number of cases. Another correlation is given by Li and Garimella [87] which is corrected for the ratio of equivalent heat source diameter, D e, to nozzle diameter. The correlation is calculated for a heated area, A heat, of any geometry and is thus more useful for a variety of cases within the range of validity for this correlation. The correlation of Tawfek [88] is valid for a circular heater area of radius r out for 2 r/d 30, but only for large z/d (z/d > 6). By including a correction factor which is a function of both z/d and r/d, Huang and El-Genk [89] obtained a correlation which was valid for a circular heater area for r/d < 10. The derivative of this function provides the basis of a correlation for maximum average Nusselt number, which can be used to find the optimum z/d for a given r/d. The optimal z/d is given as z / dopt = b/ 2c, (3.6) where b and c are defined in Table 3.1. This correlation can be useful for single nozzles but as will be shown in Section 3.2, other factors come into play with arrays of nozzles which influence the choice of z/d. 41

52 Table 3.1: Correlations for stagnation point and average Nusselt numbers under single jets Reference Range of validity Liquid Nozzle configuration Correlation Average (maximum) deviation (%) 42 Garimella and Nenaydykh [80] Garimella and Rice [79] Huang and El- Genk [89] Re z/d l/d d Re z/d l/d d Re z/d l/d r/d d mm mm mm FC-77 FC-77 air square-edged Nu ( ) ( ) orifice 0 = Re Pr z / d l / d square-edged orifice Nu avg = Re Pr 0.4 z d 0.11 fully developed Nu ( ) ( ) flow avg Re Pr a + b z / d + c z / d a = b = c l d [ ] [ ( r / d ) 19.6( r / d ) ( r / d ) 9.04( r / ) ] =, 4 10 d [ ( r / d ) ( r / d ) 0694( r / d ) ( r / ) ] d [ ( r / )] 4 = d., 10 (N/A) 14 (N/A) 12 (15) 3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS

53 Table 3.1: Correlations for stagnation point and average Nusselt numbers under single jets (continued) Reference Range of validity Liquid Nozzle configuration Correlation Average (maximum) deviation (%) 43 Li and Garimella [87] Martin [97] Tawfek [88] Re z/d l/d d Pr D e Re z/d r/d Re z/d r/d d mm mm mm comparison of results for a range of liquids air square edged nozzles various nozzle configurations Nu Nu = Re Pr avg Re e = Re Ah π 1/ 2 Pr D =, Nu F avg ( Re) Pr D d e l d l d d A r =. De 1.1( d / r) [( z / d ) 6]( d / r) A D d r e D d e d F Pr r =, = 2Re Re air tapered nozzles 1/ ( ) ( ) Nu avg Pr Re z / d r / 0.5 = d A r, 9.08 (27.12) 8.57 (27.79) N/A 10 (N/A) 3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS

54 Table 3.1: Correlations for stagnation point and average Nusselt numbers under single jets (continued) Reference Range of validity Liquid Nozzle configuration Correlation Average (maximum) deviation (%) 44 Womac et al. [78] Re z/d l/d d Pr mm 7, 25 water and FC-77 contoured Nu Lheat,avg nozzle heat heat 0.785Re A Re * ( 1 A ) L Pr = 0.4 d L d r L L L =, (.5 2L 1.9d ) + ( 0.5L 1.9d ) 0 heat heat If A r > 1 or L heat < 0, A r should be set equal to 1. 2, A r = π r ( 1.9d ) L 2 heat (16) 3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS

55 3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS 3.2 ARRAYS OF JETS Flow structure and heat transfer characteristics of jet arrays For cooling of large surfaces, it is most often beneficial to use an array of multiple nozzles. Submerged jets in an array interact with each other in two fundamental ways. The first is interference between the mixing regions of the two jets before impingement as shown in Figure 3.4. This phenomenon is most pronounced at close jet-to-jet spacings s/d and at high z/d due to mixing region expansion beneath from the jet exit. The effect of this interference is probably a weakened jet and a subsequent lowering of the overall heat transfer [90]. On the other hand, Womac et al. [66] thought the jet interference to lead to a higher heat transfer because of the increase in turbulence level. The second effect occurs when two wall jets meet face-to-face. If the jets are otherwise equal, this interaction occurs along the centreline between two adjacent jets. At low flow rates and large s/d, it will result in increased turbulence and higher heat transfer in the region of interaction. At high jet velocities, however, the interaction can become strong enough to cause a jet fountain to form. This can cause heated fluid to re-enter the core of the jets as seen in Figure 3.5, and result in a lower overall heat transfer under the array. Several studies have shown that the stagnation point Nusselt number is not sensitive to array configuration in well-drained arrays where crossflow is negligible. Huber and Viskanta [82] showed that spent air exits located between the jets in a 3x3 jet array had negligible effect on the heat transfer except for very low nozzle-to-plate spacings (z/d = 0.25). This suggests that the spent flow tends to drain well between the jets without creating adverse effects in arrays of this size. Huber and Viskanta [91] also showed that there is little difference between the heat transfer under central and perimeter jets in 3x3 arrays, except for a slight asymmetry in the perimeter jets caused by the higher flow restriction towards the centre of the array Effect of nozzle-to-plate spacing Aldabbagh and Sezai [92, 93] modelled an array of square, laminar jets at low Reynolds numbers ( ), and found the Nusselt number to be significantly higher at very small z/d ( ) than at z/d = 2. This was attributed to the fact that no upwash fountain has room to form at these low spacings, and thus the jet fills up the whole space. Garimella and Schroeder [94] observed the same trend in an experimental study of confined multiple air jets. For 0.5 z/d 4, a reduction in nozzle-to-plate spacing leads to an increase in the average heat transfer coefficient, with the effect being stronger at higher Reynolds numbers (5000 Re ). The authors explain this effect by the turbulence intensity of the jet being increased by stronger interaction with the spent flow from neighbouring jets, at the same time as there is less effect of heated liquid reentering the jets at small z/d. However, the heat transfer distribution was found to be less uniform at low nozzle-to-plate spacings. 45

56 3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS Interference z Figure 3.4: Jet interference before impingement (reproduced from San and Lai [90]). Fluid from the mixing regions of the two jets interacts and can cause a weakening of the jet, thereby resulting in a decrease in heat transfer. Fountain z Deflection Figure 3.5: Interference along centreline of jets (reproduced from San and Lai [90]). The depicted jet fountain can form for high Reynolds numbers and close jet-to-jet spacings, and cause heated fluid to re-enter the core of the jets. When studying spacings of 2x2 and 3x3 arrays of liquid jets, Womac et al. [66] found a reduced heat transfer for sparse arrays at small z/d and, similarly, for dense arrays at large z/d. The authors gave no explanation for these phenomena. A reason for the discrepancies could be the complex interaction between Re, z/d and s/d. At low Re, the upwash fountain becomes less significant, and the heat transfer can be increased at high z/d by increased turbulence levels. Lower s/d also needs a lower z/d to avoid interaction before impingement. 46

57 3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS Effect of nozzle pitch As the jets are placed closer together, the total mass flow rate over a given area will increase for a given Reynolds number. For those studies where the average heat transfer is calculated for a given area, this will in most cases lead to an increased average heat transfer. If the average is calculated for a unit cell around one jet, the average should also increase for a decreasing nozzle pitch because relatively more of the unit area is covered by the high heat transfer impingement zone. However as jets are moved closer together, negative interference effects such as the jet fountain and shear layer interference will become more significant. Womac et al. [66] studied 2x2 and 3x3 in-line arrays of liquid jets and compared the total heat transfer over the heater surfaces. For the 2x2 array, two pitches (s/d = 6.22 and 9.96) were tested. The overall heat transfer was found to be higher for the smaller pitch. The authors attributed this to less area being covered by the weak wall jet, as well as mutual interactions before impingement, which were thought to induce turbulence and to enhance heat transfer. In the case of the large pitch, the nozzles were placed almost in the corners of the square heater, whilst for the smaller pitch they were centred on each quadrant of the heater. Yan and Saniei [95] used a pair of impinging air jets to study the detailed heat transfer between the two jets. The nozzle pitch under consideration ranged from 1.75 to 7.0. The pipe-type nozzle provided fully developed flow, and only one Reynolds number was used (Re = ). It was shown that as the jet pitch decreases, the region of influence of one jet on the flow field and the heat transfer of the other increases until it encompasses the entire jet. The heat transfer under one jet deteriorates on the side facing the other jet, probably due to the reversed pressure field where the two jets meet. An area of enhanced heat transfer was observed along the centreline between the jets. For low nozzle pitches (s/d < 3.5), the magnitude of this heat transfer coefficient maximum exceeded that at the stagnation point. Note that these observations can not directly be translated to arrays of nozzles because each jet was meeting another jet only on one side, which made the flow conditions asymmetric, compared with arrays where the jets meet other jets on all sides. San and Lai [90] searched for optimal values for the jet-to-jet spacing in staggered arrays with five air jets. The Reynolds numbers under consideration were The analysis is based on the central jet stagnation point heat transfer coefficient only, which means that only the deteriorating effects of jet interference before and after impingement are taken into account. Maxima were found for two different nozzle pitches. When s/d is increased, the stagnation point heat transfer coefficient is increased because of less interference before impingement, but also decreased because the temperature of the jet fountain is raised as the wall jet area is increased. The first maximum is found where the former effect loses dominance to the latter. At larger s/d, the heat transfer starts to increase as the jet fountain is diminished, and at the second maximum the stagnation point Nusselt number is equal to that of a single jet. Note that the jet fountain effect is highly significant at these high Reynolds numbers. The second relative maximum disappeared at low Re (~10 000) because of the weak jet fountain. Optimum nozzle pitches were found for each combination of Re and z/d. For Re = and z/d = 4 and 5, the optimum pitch was found at s/d = 6.0. Brevet et al. [96] studied the heat transfer under a row of impinging jets with nozzle pitch varying from 2 to 10. The heat transfer over a given area was compared on the basis of 47

58 3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS total mass flow rate. It was found that to optimise the total heat transfer rate, one should increase s/d, which in turn decreases the number of nozzles and increases the Reynolds number. A nozzle pitch of s/d = 4-5 was identified as an optimal value. Reducing the nozzle pitch below this would not be efficient because the small increase in heat transfer is not justified by the larger increase in mass flow. This result is supported by Huber and Viskanta [82]. They found the heat transfer under a jet in an array to be significantly lower (14 21%) than that under an equivalent single jet. This was attributed to adjacent jet interaction prior to impingement. As expected, the influence of adjacent jets was found to decrease as the nozzle pitch was increased or the nozzle-to-plate spacing was decreased. Jet interference was also observed to dampen the secondary peaks in Nusselt number and thus create a more uniform distribution. Optimizing on a mass flow basis, it was found that increasing the nozzle pitch and thereby increasing the Reynolds number would increase the average heat transfer of the total array. The Reynolds numbers were in the range When comparing only two nozzle pitches of s/d = 3 and 4, Garimella and Schroeder [94] found the heat transfer coefficients for s/d = 3 to lie above those of s/d = 4 for r/d 2, but to drop below them for r/d > 2. As a result, the average heat transfer of the two configurations was found to be the same (within 5%). There was also a slight increase in heat transfer compared with single jets in the area where the two jets meet. When comparing the effectiveness of a single jet with an array of four jets, the array clearly provided the higher heat transfer coefficient. Compared on a mass flow basis, however, the single jet yielded the higher heat transfer. This was on the other hand accompanied by a very large pressure drop and, in a comparison based on total pressure drop, the array again performed better. No comparison was made for total pumping power in their study Correlations for average Nusselt number The correlations for average Nusselt numbers presented below are all given along with their range of validity in Table 3.2. The correlation given by Womac et al. [66] is made for arrays of liquid jets on a square heater of length L heat. As in Womac et al. [78], it contains one part for the impingement region and another for the wall jet region. Nusselt numbers for the four jet array of small nozzles (d = mm) were only about half that of the rest and were not included in the correlation. Garimella and Schroeder [94] presented a correlation for a square heat source with a fixed area of 20 mm x 20 mm. Nozzle-to-plate spacing is included as a correction factor, but the effect of nozzle pitch was recognised as being not researched well enough to be taken into account in the correlation. Huber and Viskanta [82] include a correction factor for s/d in their study, which is based on the average heat transfer for a square unit cell under the central jet in the array. The correlation given by Martin [97] has been verified in several studies, including Garimella and Schroeder [94] and Huber and Viskanta [82]. This correlation is based on a unit cell in an array and includes correction factors for z/d and s/d. 48

59 Table 3.2: Correlations for average Nusselt numbers in jet arrays Reference Range of validity Fluid Nozzle configuration Correlation Average (maximum) deviation (%) Garimella and Schroeder [94] Re s/d air square-edged Nu ( ) orifices avg = Re Pr z / d 9 (28.2) z/d Huber and Viskanta [82] Martin [97] l/d d Re s/d z/d l/d d Re s/d z/d mm mm air square-edged orifices no crossflow (open spent air exits) Nu ( z / d ) ( s ) avg 0.285Re Pr / = d air N/A / 3 Nu = 0.5KG Pr Re, avg z / d f f K = 1 +, 0.6 G = 2 f, ( z / d 6) f ) 2 π d f = 4 s. 10 (20) N/A 3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS

60 Table 3.2: Correlations for average Nusselt numbers in jet arrays (continued) Reference Range of validity Fluid Nozzle configuration Correlation Average (maximum) deviation (%) 50 Womac et al. [66] Re z/d s/d l/d d mm water and FC-77 pipe-like nozzles 0.5 L heat 0.8 Lheat Nu avg, L = 0.509Re Ar 0.363Re * ( 1 Ar ) heat d + L *, d L 2 Nπd A r = (A r = 1 if it exceeds unity) 4L L = 2 heat [( 2s / 2) 1.9d ] + ( s / 2) 2 [ 1.9 ] * d 9.93 (30) 3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS

61 3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS 3.3 OTHER PARAMETERS INFLUENCING HEAT TRANSFER Surface modifications Modification of the impingement surface by adding small extended surfaces generally leads to an increased heat transfer in single-phase convective cooling systems because of the increased total surface area and the increased turbulence level of the flow. However, because of the specific characteristics of jet impingement flow, surface modifications can in some instances have an adverse effect on the heat transfer [64]. Priedeman et al. [98] studied the effect of surface enhancements on the heat transfer under single, free-surface liquid jets of both water and FC-77. Roughening of the surface was found to enhance the heat transfer by disrupting the momentum boundary layer, but this effect was most pronounced for the liquids with higher Prandtl number. In the case of water, the total heat transfer increased by as much as a factor of 3. The ability of the surface modification to increase heat transfer was observed to decrease with increasing Reynolds number, the range of which was 6000 < Re < In comparison, Webb and Ma [64] found that surface effects became more pronounced with increasing Reynolds number, due to thinning of the boundary layer leading to a larger fractional penetration of the roughness elements. Although surface modifications and surface roughening generally have a positive effect on the heat transfer from liquid jets, this effect was shown to be most significant for liquids with high Prandtl number, such as FC-77. For water (Pr ~ 7), surface modifications could sometimes lead to a decrease in heat transfer. Chakorun et al. [99] found surface roughness to increase the local and average Nusselt numbers by up to 28%, increasing with increasing Reynolds number (6500 Re 1900) Effect of mesh screen or perforated plate between nozzle exit and impingement plate Techniques for enhancing the turbulence level of the jet by disturbing the flow can be used as a way to increase the heat transfer under the jet. One such method is the installation of a perforated plate between the nozzle and the impingement plate. Lee et al. [100] found this to significantly increase the average Nusselt number, but also to increase nonuniformity under the single jet. The best results were obtained for small perforation holes. The vertical position of the perforated plate with respect to the nozzle and impingement plate was found not to have a large effect. A pipelike nozzle of large diameter (d = 34 mm) was used to provide fully developed flow and high spatial resolution in the measurement. Zhou and Lee [101] investigated the effect of a mesh screen inserted upstream of the jet nozzle exit. A small increase in heat transfer (less than 4%) at z/d = 4 was observed. Smaller enhancements were observed for smaller z/d, while for larger z/d the mesh screen had an adverse effect on the heat transfer. 3.4 EXPERIMENTAL METHODS In order to obtain correct information both on local and average heat transfer coefficients in experimental investigations of impinging jets, a high spatial resolution is necessary because of the highly nonuniform heat transfer distribution. When not enough measurement points are obtained, the calculated average heat transfer could have serious errors. The spatial resolution can be increased by either decreasing the distance between measurement points, or by increasing the size of the jet. However, because very high 51

62 3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS heat transfer coefficients are achieved, especially in liquid jet measurements, the size of the heated area is often limited by the available power supply. Depending on the heater configuration, thermocouples can be attached to the back of a heated foil or in holes in a heater block. Some studies have used a single thermocouple located on the back of a stainless steel foil heater, which was in turn moved in small increments relative to the jet. The spatial resolution is in these cases limited by the size of the thermocouples and their spacing. Several studies have used thermographic liquid crystals (TLC) as a way of obtaining a very high spatial resolution. The TLC is generally applied as a coating on a black background. The colour of the TLC coating typically passes from black to red and through the whole colour spectrum back to black at prescribed temperatures. The colour changes are fully reversible. A CCD camera is used to record the colour distribution and digital image analysing tools are used to translate these values into temperatures and then into heat transfer coefficients or Nusselt numbers. Some researchers calibrate the TLC hue versus temperature, which allows them to take only one picture at one power setting, provided the TLC gives a colour response across the entire surface. Others use optical filters to obtain pictures of isothermal contours, which are obtained at several power settings. The TLC is normally applied to the back of a thin film or foil metal heater such as stainless steel or gold. Transient measurements have also been made using TLC, but only for air jets with relatively low heat transfer levels so that the time constants obtained are long enough to make reliable measurements. Infrared thermography is another method of obtaining a high spatial resolution which has been used by some researchers, but since the equipment is expensive compared to TLC, it is less commonly used. Table 3.3 shows an overview of the experimental methods used in the studies mentioned in this chapter. 3.5 CONCLUSIONS ON JET IMPINGEMENT The local heat transfer and flow structure characteristics of single impinging jets have been studied extensively and are well known. The exact shape of the local heat transfer distribution has, however, not been successfully correlated because it is such a complex function of Reynolds number, nozzle diameter, nozzle-to-plate spacing and nozzle configuration. The nozzle configuration has a significant influence on the heat transfer because it determines the level of turbulence in the flow. More accurate correlations exist for the stagnation point and average heat transfer coefficients of single jets. In jet arrays, adjacent jets can interfere destructively prior to impingement and either constructively or destructively where the two wall jets meet, depending on Reynolds number, nozzle pitch and nozzle-to-plate spacing. A number of different correlations predict the average heat transfer coefficient under of arrays of jets with different ranges of validity. Surface modifications have been found to increase the average heat transfer coefficient by as much as a factor of three for water jets, and more for liquids with higher Prandtl number. However, some methods of surface modifications can lead to a decrease in heat transfer. Other methods of disturbing the flow such as inserting mesh screens or a perforated plate have shown the same trend of mostly increasing, but sometimes decreasing, the average heat transfer coefficient. 52

63 3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS Measuring the local heat transfer coefficient for impinging jets is a challenge because of the high spatial nonuniformity achieved. When using thermocouples, the spatial resolution is limited by their size and spacing. Infrared thermography can be used with good results but involves costly equipment. Most recent studies have used a coating of thermographic liquid crystals applied to a heater foil and recorded the temperature distribution using a CCD camera. This method can yield high spatial and temperature resolutions. Table 3.3: Overview of experimental methods used in literature. Reference Brevet et al. [96] Brigoni and Garimella [85] Chakroun et al. [99] Garimella and Nenaydykh [80] Garimella and Rice [79] Garimella and Schroeder [94] Huang and El-Genk [89] Huber and Viskanta [82] Huber and Viskanta [91] Lee and Lee [84] Lee et al. [100] Lee et al. [86] Li and Garimella [87] Priedeman et al. [98] San and Lan [90] Womac et al. [66] Yan and Sanei [95] Zhou and Lee [101] Womac et al. [78] Experimental method Infrared thermography on plate of epoxy resin with copper circuit heaters Single thermocouple on back of moving stainless steel heater 37 thermocouples on back of heated plate Single thermocouple on back of moving stainless steel heater Single thermocouple on back of moving stainless steel heater Single thermocouple on back of moving stainless steel heater 29 thermocouples on back of stainless steel foil Isothermal contours from TLC with stainless steel foil Isothermal contours from TLC with stainless steel foil Isothermal contours from TLC with gold film Isothermal contours from TLC with gold film Isothermal contours from TLC with gold film Single thermocouple on back of moving stainless steel heater 32 thermocouples in heater block 26 thermocouples on back of stainless steel foil 7 thermocouples in heater block Transient TLC with hue calibration 37 thermocouples on back of gold film 7 thermocouples in heater block 53

64 3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS 3.6 DESIGN OF A JET IMPINGEMENT COOLING DEVICE FOR CONCENTRATING PV As shown in Chapter 2, it is of utmost importance in high concentration photovoltaic systems to ensure a high average heat rate transfer across the entire surface. A jet impingement cooling device for PV should therefore incorporate drainage of the cooling fluid in a direction perpendicular to the impingement surface. One may consider a range of designs that incorporate back drainage. Two possibilities are shown in Figure 3.6. In setup a), water enters into a plenum chamber ending in an orifice plate, through which the jets impinge onto the heated surface. The water then returns through an outlet cavity which encompasses the plenum chamber. An advantage of this configuration is that the flow patterns under the jet array are thought not to be affected by the drainage flow. A disadvantage might be that the heat can be transferred from the higher temperature water in the return chamber to the plenum chamber fluid. However, because the water spends just a short time in contact with the heated surface, the temperature difference is most likely too small to cause any significant heating. The same effect would be more or less equally relevant for any back drainage configuration. Another issue with the side drainage is that the area along the edges might experience a lower heat transfer coefficient due to eddy formation along the steep corners of the outlet cavity or because the jets are not placed close enough to the edges. The second option, shown in Figure 3.6 b), is a central drainage configuration in which it is possible to place the jets very close to the edges and thus diminish any eddy formation. However, it is possible that the relatively small return flow pipe would disturb the pressure distribution and thereby the flow pattern of the jet array. a) b) Figure 3.6: Example of jet configurations with drainage direction normal to the impingement surface: a) side drainage and b) central drainage. If the number of nozzles required for the cooling module is found to be large enough that effects of crossflow become significant, it may become necessary to have distributed drainage exits throughout the cooling device. Two examples of possible distributed drainage configurations are presented in Figure 3.7. The first configuration was used with air jets by Huber and Viskanta [82]. It consists of a thick orifice plate through which long nozzles are drilled in a square configuration. Between the rows of nozzles, outlet pipes are drilled through the length of the plate, perpendicular to the nozzles. The spent liquid flows into the outlet pipes through drainage holes along the bottom of the pipes. Shown in Figure 3.7 a) is a cross-section of the orifice plate. The next configuration, Figure

65 3 HEAT TRANSFER UNDER SINGLE-PHASE, SUBMERGED AND AXISYMMETRIC JETS b), is a simplified variation of the first. The water enters through parallel inlet pipes and impinges through holes along the bottom of the pipes. The water is drained through gaps between the pipes into an outlet chamber. a) b) Figure 3.7: Two examples of distributed drainage configurations: a) drainage through channels in impingement plate; b) drainage between plenum pipes. The side drainage configuration shown in Figure 3.6 a) was chosen for the first jet impingement prototype in the present study. A detailed description of the orifice plates chosen and the experimental setup is given in Chapter 4. Because so much is known about the effect of z/d (Section and 3.2.2) and s/d (Section 3.2.3) for both single jets and arrays, it was decided to look more closely at the effects of nozzle configuration as well as general characteristics of the side drainage device such as the heat transfer along the edges. Particular attention is given to how the pressure drop and pumping power is related to average heat transfer, as this is a topic which is highly relevant in power producing systems but one that is not well covered in literature. The results of the measurements are presented in Chapter 5. 55

66 Chapter 4 EXPERIMENTAL DESIGN AND PROCEDURE In order to study the heat transfer characteristics of the side drainage jet device described in Section 3.6, a testing unit was designed and constructed. The major challenges in the design process were finding a heat source which would supply a large but uniform heat flux, and measuring local temperatures accurately with high spatial and temperature resolutions. Following on from prior research on experimental methods for jet impingement studies (see Section 3.4) it was decided to use a thin stainless steel foil as a heated surface with thermographic liquid crystals to measure local temperatures. The experimental design and procedures are described in this chapter. Results are presented in the following chapter. 4.1 EXPERIMENTAL SETUP Water outlet Water inlet Clamping rod Return flow chamber Plenum chamber O-ring seal Stainless steel heater foil Orifice plate showing three nozzles Silicone seal Aluminium L-support Aluminium bus-bar Bakelite support base Camera view Figure 4.1: Schematic diagram of jet testing unit. 56

67 4 EXPERIMENTAL DESIGN AND PROCEDURE Design of jet testing unit A schematic overview of the jet testing unit is given in Figure 4.1. Photographs of the setup in the laboratory are shown in Figure 4.2. The interchangeable jet part consists of a 90 mm x 90 mm stainless steel top plate with 8 mm tube fittings for water inlet and outlet. The water flows through the inlet into a plenum chamber manufactured from a 21 mm long x 20 mm wide square stainless steel tube, with a wall thickness of 1.2 mm and rounded corners. This tube was welded onto the top plate. A stainless steel orifice plate was welded onto the bottom of the plenum chamber. The water is forced through the orifice and impinges onto the heated surface. It then returns through a 25 x 29 mm 2 return flow chamber, the outer walls of which consist of a 21 mm thick Perspex plate. The corners of the outlet chamber were rounded for ease of manufacturing. Figure 4.2: The jet testing device as it appears in the laboratory. The camera is normally attached to the metal device seen attached to the wooden support. In the picture on the left one can see how the power supply is connected through thick cables to the bus bars. The picture above shows a head-on view without the power leads connected. The heater consists of a 31 mm x 25 mm, 0.05 mm thick stainless steel foil supplied by AllFoils Pty Ltd. The area of the heater is limited to this size because of the large currents required to achieve the desired heat fluxes. The foil is clamped and stretched tightly between two aluminium bus-bars. The power was supplied from a Variac variable AC power source, with the voltage further stepped down in a second transformer. Heat losses from the bottom of the foil can be assumed to be negligible because the expected heat transfer coefficient from foil to water is orders of magnitudes higher than that of natural convection and radiation under the foil. The foil was stretched by adjusting screws through the bus bars and two aluminium L-supports that were attached to the bakelite base. To make a water tight seal the foil was clamped between Perspex support pieces and the Perspex outlet chamber piece over a width of about 1 mm on either side so that the resulting heater area is 25 mm x 29 mm. The power dissipated in the outer 1 mm of the foil was assumed to lead to Perspex heating only, and not to have a significant effect on the temperature measurements of the adjacent foil due to lateral conduction. This assumption was confirmed through Finite Element Modelling using the software package Strand7 [102]. Silicone sealant is used to make a water tight seal between the Perspex, the bus bars and the heated foil. Threaded rods through the top plate, the 57

68 4 EXPERIMENTAL DESIGN AND PROCEDURE Perspex plate and the bakelite base are used to clamp the jet testing unit to the support frame shown in Figure Measuring temperatures using thermographic liquid crystals The stainless steel foil temperature distribution was recorded using Thermographic Liquid Crystals (TLC) and a digital camera with a CCD chip. The camera was placed below the jet testing unit and looked at the foil through a circular hole in the bakelite base. A sheet of R35C1WA TLC supplied by Liquid Crystal Resources Pty Ltd was attached to the back of the heated foil. The sheet was manufactured with the following layers: adhesive, black backing ink, TLC and a polyester sheet. The TLC nominally turns from black to red at 35 C and then through the rest of the spectrum to blue at 36 C. The colour change was in practice found to take place at lower temperatures, with red showing up at about 32 C. The colour change was calibrated by impinging the unheated foil with water of a known temperature and recording the colour distribution of the foil. The change in colour with 0.3 C increments is shown in Figure 4.3. Because of the high heat transfer coefficient associated with impingement, the foil can be assumed to have the same temperature as the impinging water. The foil was illuminated by two LED lights from the sides through the Perspex support pieces. A characteristic of the LED lights is that they produce only small amounts of heat, which meant the influence of heat radiation from the lamps can be assumed negligible C 33.3 C 33.9 C 34.2 C 34.5 C 34.8 C Figure 4.3: Development of colours for increasing temperatures with the TLC premade foil from Liquid Crystal Resources. The reasons for and consequences of the nonuniform colours are discussed in Section 4.3. For each series of measurements, a single calibration picture was taken at 33.8 C. At this temperature, the TLC across nearly the entire surface of the heated foil had a response within the most sensitive colour range, as Figure 4.3 shows. This temperature therefore 58

69 4 EXPERIMENTAL DESIGN AND PROCEDURE gave the most accurate temperature calibration. The nonuniform TLC response and its consequences are discussed in Section 4.3. After taking the calibration picture, the camera and lighting were left undisturbed for the duration of the measurements. This ensured that the lighting and placement of the camera would remain identical for the calibration and the measurement pictures. When taking the actual measurements, the water temperature was turned down to 32.4 C and pictures were taken at increasing electrical power levels. Some typical thermal images at increasing power levels together with the calibration picture are shown in Figure 4.4. q& = 20.5 kw/m 2 q& = 30.4 kw/m 2 Calibration picture at 33.8 C q& = 42.8 kw/m 2 q& = 80.4 kw/m 2 Figure 4.4: Typical thermal images recorded at increasing power levels. A calibration picture is shown on the left. The data from the thermal images were compared with the calibration picture using a procedure developed in Matlab software. A colour image of m x n pixels can be treated in Matlab as an m x n x 3 matrix, where each pixel is assigned a value of red, green and blue (RGB). Each picture was compared pixel by pixel with the calibration picture. If a pixel (i,j) had the same RGB value as the (i,j) pixel in the calibration picture, the (i,j) cell in an m x n matrix was assigned the calibration temperature. The other cells were assigned a value of zero. The temperature was translated into a heat transfer coefficient using q& h = T fo T w, (4.1) where h is the local heat transfer coefficient, T fo and T w are the temperatures of the foil and the water, respectively, and q& is the power per area dissipated in the foil. Finally, the heat transfer matrixes from all of the pictures were combined to produce an overall map of the heat transfer distribution for the given flow rate. Holes in the matrix due to the finite power intervals at which the pictures were taken were smoothed out using a linear 59

70 4 EXPERIMENTAL DESIGN AND PROCEDURE interpolating algorithm. This resulting matrix was used to find the maximum and average heat transfer coefficients. The stagnation point heat transfer coefficient was found as an average of the 5% highest values in the matrix in order to minimize the effect of errors Instrumentation and data acquisition The water was circulated and kept at a constant temperature using a Julabo F20 circulating chiller. A manual ball valve at the water outlet was used to control the flow rate. The temperature of the inlet and outlet water was measured by two PT100 platinum resistance thermometers in copper temperature pockets. The response time of the temperature sensors in the pockets is in the order of one minute because of the thermal mass of the copper, so care was taken to use measurements recorded only after the readings had stabilized. The chiller was found to keep the water at a given temperature with a precision of ± 0.03 C. The flow rate was recorded by a Dataflow Compact Inline Flow Transmitter. The transmitter consists of a sensor body with a twin-vaned turbine rotor, which rotates at a speed proportional to flow rate. As the rotor spins, the blades interrupt the continuous infra red signal from opposing photo-transistors mounted on opposite external sides of the clear sensor body. This is converted into a pulse signal which can be read by a standard counter. The pressure was recorded by a micro differential pressure transducer placed between the inlet and outlet pipes of the jet testing unit as shown in Figure 4.5. The pressure transducer is based on a piezoresistive bridge construction, and gives a millivolt output proportional to pressure difference. Figure 4.5: Placement of the pressure transducer. The voltages, temperatures and pressure difference were read by several Fluke FL4428A digital multimeters and recorded by Labview software to a laptop computer through an IEE-488 GPIB interface and a GPIB-USB converter. A Datalogger DT505 was used to count the pulses of the flow meter and this was transmitted to the computer through a serial interface and serial-usb converter. Thermocouples were used with the Datalogger and computer to monitor the ambient air temperature as well as the temperatures of the bus bars and Perspex of the jet testing unit. Figure 4.6 shows an overview of the data acquisition setup. 60

71 4 EXPERIMENTAL DESIGN AND PROCEDURE Temperature pockets Differential pressure transducer Jet testing unit Shunt resistor V Transformer Variac Valve V Flow meter Camera Circulating chiller Support frame Computer Figure 4.6: Schematic of experimental setup and data acquisition system Jet devices tested For the first set of experiments (results discussed in Sections ), nine different orifice plates were tested, shown in Table 4.1. The first two had nine nozzles of small diameter, d = 0.7 mm, the next four had four nozzles with d = 1.4 mm and the last three had a single nozzle of varying diameter. All of the arrays had the same nozzle pitch to diameter ratio s/d = The two dimensional placement of the nozzles is shown in Figure 4.7. The nozzle-to-plate spacing to diameter ratio was set to z/d = 3.57 for the four-nozzle arrays because several studies have shown that the maximum average heat transfer coefficient for submerged jets occurs at a nozzle-to-plate spacing z/d 3-4 [78, 79]. However, because the distance between the orifice plate and the impingement plate was kept constant at 5 mm, the dimensionless spacing z/d was twice as large for the ninenozzle arrays as for the other four. The single nozzle arrays had z/d = 3.33, 2.5 and 2 for increasing nozzle diameter. The thickness of the orifice plates was 1 mm for all plates except for the one called long/straight which was 2 mm thick. The contouring of the sharp-edged and countersunk nozzles was made using a conventional 30 countersinking tool. a) b) a) Figure 4.7: Two-dimensional placement of a) nine/dense nozzles, b) nine/sparse and c) fournozzle arrays. 61

72 4 EXPERIMENTAL DESIGN AND PROCEDURE Table 4.1: Overview of orifice plates used in the experiments. Device Number of nozzles N Nozzle diameter d (mm) Nozzle-toplate spacing z/d Nozzle pitch s/d Nozzle configuration nine/dense nine/sparse short/straight long/straight sharp-edged countersunk single S single S single S SYSTEM CHARACTERISATION To become more familiar with the thermal characteristics of the experimental setup, a number of tests over a range of flow rates, water temperatures and power settings were performed using the short/straight jet array. The inlet and outlet water temperatures, pressure drop across the device, bus bar temperature and power level were recorded. The pressure drop through the system as a function of flow rate was found to follow a parabolic curve as shown in Figure 4.8. No effects of temperature and the corresponding change in viscosity could be detected. This gives an indication that the level of uncertainty for the flow rate measurements is relatively large. This is further discussed in Section 4.3. For each water temperature and flow rate, the rate of change of enthalpy H & of the water was calculated from ( ) H & = cm& T out T, (4.2) in where c and m& are the specific heat capacity and mass flow rate of the water. A temperature-dependent heat capacity calculated at the water input temperature was used. The rate of enthalpy change for a range of temperatures and flow rates without power supplied to the foil is shown in Figure 4.9. Around room temperature, which was just below 20 C, the rate of change in enthalpy was found to increase linearly with flow rate. This suggests a linear relationship between flow rate and heating by friction through the 62

73 4 EXPERIMENTAL DESIGN AND PROCEDURE jet device. When the water is at a different temperature from the ambient, there is some exchange of heat between the water running through the pipes and the surrounding air. For water temperatures below room temperature, the graphs are seen to curve downwards. At low flow rates, heating by friction is low while the heat gain from the ambient, which decreases at higher flow rates, dominates. This results in the rate of change in enthalpy decreasing for increasing flow rates up to the point where heating by friction becomes dominant, whereby H & starts to increase. Above room temperature, especially at low flow rates, heat is lost to the ambient. This causes the graph to curve upwards p [ kpa ] Q [ ml s -1 ] T water 10 C 15 C 20 C 25 C 30 C 35 C 40 C 45 C 50 C Figure 4.8: Pressure drop versus flow rate for a range of water temperatures. The second degree polynomial regression lines that fit the data for the various temperatures are also shown H [ W ] T water 10 C 15 C 20 C 25 C 30 C 35 C 40 C 45 C 50 C Q [ ml s -1 ] Figure 4.9: Rate of change of enthalpy of water versus flow rate at various water temperatures together with the linear or polynomial regression lines. 63

74 4 EXPERIMENTAL DESIGN AND PROCEDURE Figure 4.10 shows the relationship between the rate of change in enthalpy for water and the power input to the foil. In all cases the valve was fully open, so that the flow rate was at maximum. The difference in H & between the different temperatures agrees well with the expected heat exchange with the ambient through the pipes. The y-intercept of the linear fit, corresponding to zero power input, agrees well with the expected power loss or gain at this temperature and maximum flow rate according to Figure 4.9. The slope of the fit is about 0.91 for all temperatures. This suggests that an extra 9% of the heat is lost, not through exchange with the ambient through the pipes but somewhere else in the system. The voltage across the foil was measured where the cables were connected to the bus bars, so that any voltage drops through the bus bars would be included. 70. H [ W ] Twater 10 C 15 C 20 C 25 C 30 C 35 C 40 C 45 C 50 C P [ W ] Figure 4.10: Rate of change of enthalpy of water versus input power at a range of water temperatures and the corresponding linear fits. The temperature rise in the bus bars was recorded in order to investigate if bus bar heating could account for the missing 9%. The bus bars are made of solid aluminium, and their thermal mass can be calculated accurately by finding their volume and multiplying by the known heat capacity of aluminium. The thermal mass of the bus bars was found to be cm b = 60 J K -1. Figure 4.11 shows the relationship between the rate of temperature change in the bus bars and the total input power. The scatter arises from the uncertainty associated with the thermocouple, which was attached with tape to the outside of the bus bar. No correlation was found between bus bar temperature rise and water temperature. Because the rate of temperature rise in the bus bars is given by which can be rewritten as q& b = cm T, (4.3) b & & b q T& =, (4.4) cm b the relationship between bus bar temperature rise and total power input can be written as 64

75 4 EXPERIMENTAL DESIGN AND PROCEDURE qb / cm T& & = b q & t, (4.5) q & where q& t is the total power input and q& b is the power dissipated in the bus bars. The gradient of temperature rise versus power input is found to be dt& dq& t q& = t / b cmb 4 1 q& i = KJ. (4.6) Thus, the relationship between total power input and power dissipation is found as q& q& dt& b = cmb = t dq& t for each bus bar, which amounts to 0.09 = 9% for the two bus bars. This is in good agreement with the extra heat loss that occurs when the foil is electrically heated. (4.7) The temperature of the bus bars was found to remain at about 19 C even when the outlet temperature of the water was at 10.3 C Because the temperature is still rising in the bus bars when the water temperature is lower than the bus bar temperature, it must be assumed that the temperature input to the bus bars comes from electrical heating of the bus bars directly and not from the foil via contact with the water. It is not clear why the power dissipation in the bus bars is so high, but it could arise from resistive heating in the aluminium, the stainless steel screws conducting current, or contact resistance between the aluminium and the stainless steel foil T [ K s -1 ] Twater 10 C 15 C 20 C 25 C 30 C 35 C 40 C 45 C 50 C P [ W ] Figure 4.11: Rate of temperature change of bus bars plotted versus input power for different water temperatures. The slope of the linear fit is 7.48 x 10-4 K J UNCERTAINTY ANALYSIS The standard deviations of the flow meter, pressure transducer, PT100s and voltage measurements were all calculated from a range of measurements and found to be stable for measurements made on different days and under different conditions. However, because of a problem with the pressure transducer in the earlier series of measurements, 65

76 4 EXPERIMENTAL DESIGN AND PROCEDURE only the pressure data for later measurements are included in the subsequent chapters. The measured foil area was estimated to have an uncertainty of ± 0.5 mm in each direction which for an area of 25 mm x 31 mm results in a total uncertainty of 3.4%. The dominant uncertainties contributing to the uncertainty in h avg are those of the foil area and the foil temperature. Because the same heater was used for all measurements, the area uncertainty yields a systematic error and would not influence trends or increase the scatter in h avg. The error in foil temperature, however, is not systematic. The TLC sheet did not yield a uniform colour when it was unheated and impinged with water of a known temperature, as seen in Figure 4.3. The reason for this is a variation in the sheet adhesive as it was supplied from the manufacturer. This was partly corrected by comparing each pixel individually against the calibration picture, as explained in Section As Figure 4.12 shows, the TLC colour sensitivity is very high and results in a maximum error of ± 0.2 C. However, the camera shutter had to be released manually, which made the camera move slightly. This meant the pixels were sometimes compared with calibration picture pixels with a slight displacement. In addition, the camera s automatic focus would sometimes focus at the bus-bars or the support instead of the TLC, so that the foil was sometimes out of focus. An analysis of the repeatability of the measurements showed that the total uncertainty in heat transfer coefficient was less than 8%. The uncertainty in the temperature distribution was inferred from this value to be about 7.2%. Fraction of pixels recognized T water [ C ] Figure 4.12: TLC colour sensitivity over a range of temperatures. Images of a range of water temperatures at 0.1 C increments are compared with a calibration picture taken at 33.8 C. With the uncertainty σ given in terms of a percentage of the mean value, the combined uncertainty in a variable y = f( x 1,,x i ) is calculated from 66

77 4 EXPERIMENTAL DESIGN AND PROCEDURE 2 σ =. (4.8) total σ i i The uncertainties in power and temperature difference, and subsequently heat transfer coefficient, are calculated in this manner. The resulting list of uncertainties is given in Table 4.2. There were also some uncertainties associated with the heat transfer near the edges of the array. There is poor thermal resolution in the edge region due to experimental difficulties such as stray silicone sealant along the edges of the foil and poor adhesion of the TLC to the foil. These contribute little to the value of h avg, but complicate the interpretation of local heat transfer maps. Figure 4.13 shows a typical map of heat transfer coefficients along with typical errors and their sources. Array edge effects are discussed in more detail in Chapter 5. Table 4.2: Uncertainties of the measurements along with the associated combined uncertainties. Measurement Uncertainty (%) Foil area 3.4 Foil temperature 7.2 Flow rate 4.2 Pressure 0.6 Water temperature 0.1 Foil voltage 0.1 Shunt voltage 0.1 Power 3.4 Temperature difference 7.2 Heat transfer coefficient IMPROVEMENTS OF THE EXPERIMENTAL SETUP FOR LATER EXPERIMENTS For some later measurements (the ones described in Section 5.7 and 6.1.5), the camera and TLC setup was slightly improved. A method was found by which the camera could be remotely controlled. This allowed the same placement and focus of the camera throughout the measurements. Also, to diminish the nonuniformity of the TLC film, a new TLC spray coating was used, which eliminated the need of adhesive. A black backing paint and the liquid TLC was applied using an airbrush. This gave a much more uniform result, as shown in Figure The temperature window response for the TLC was chosen to be closer to room temperature, in order to reduce the effect of heat loss to the surroundings. The water was kept at 25.3 C during these measurements. Due to 67

78 4 EXPERIMENTAL DESIGN AND PROCEDURE these improvements, the accuracy of the later measurements is thought to be slightly higher than in the first measurements. However, not enough data were collected to perform an accurate uncertainty analysis. stray silicone sealant dust particles on camera lens or TLC surface variations in TLV adhesive combined with camera movement Figure 4.13: Sources of errors in local heat transfer distribution maps. Figure 4.14: Airbrush applied TLC coating at 26.5 C. 68

79 Chapter 5 RESULTS AND DISCUSSION This chapter presents the results of the measurements of the side drainage device as well as some measurements of the central drainage device, using the experimental setup described in Chapter SINGLE JETS As introduced in Table 4.1, three different single jet orifice plates (labelled S1, S2 and S3) were tested. There were two motivations for studying single jets. Firstly, the shape of the distribution of local heat transfer under a single jet needed to be investigated and compared with findings from the literature, both to verify the experimental method and to gain more insight into the characteristics of jet impingement cooling. Secondly, it was necessary to investigate how the edges and corners of the return flow cavity of the side drainage device would affect the overall heat transfer of the device. Figure 5.1 shows a typical heat transfer distribution under a single jet. While being quite symmetrical around the centre, the perimeter region appears flattened. A better representation of the local heat transfer distribution is given by the cross-section through the impingement area (shown in Figure 5.2). The impingement zone (r/d < 1) is seen to be characterised by a region of high heat transfer in the centre followed by a sharp drop at about r/d ~ 0.4. For r/d > 1, the local heat transfer drops off monotonically. As shown in Figure 5.3, the shape of the heat transfer curve can be estimated reasonably well by a linear function, which reaches the value of half maximum at r/d ~ 3.5: 1 h = h max 1 r / d. (5.1) 7 This simplification helps to facilitate the estimation of temperature variations across the heated surface, a subject which will be discussed in more detail in Chapter 7. 69

80 5 RESULTS AND DISCUSSION h [ W m -2 K -1 x 10 4 ] Distance along bus-bar [ mm ] Distance between bus-bars [mm] Figure 5.1: Local heat transfer distribution for the S2 single nozzle at Re = h / [ W m -2 K -1 ] Re = Re = Figure 5.2: Two cross-sections through the stagnation point of local heat transfer coefficients for the single S2 nozzle. r /d 70

81 5 RESULTS AND DISCUSSION h [ W m -2 K -1 h / W m -2 ] K -1 Re = Re = Linear (Re = ) Linear (Re = 5 610) r / d Figure 5.3: Shapes of the local heat transfer distribution for the single S2 nozzle estimated by linear functions. The experimental curves in Figure 5.2 can be compared with the theoretical distributions in Figure 3.2. The theoretical distributions show an inner secondary peak at r/d ~ 0.5, something which is not visible in the experimental results. This is as expected because the experimental data are obtained at relatively low Reynolds numbers, and the inner secondary peak is expected to become less pronounced and to disappear as Re decreases. Figure 3.2 also predicts a change in slope or a secondary peak at r/d ~ 2 caused by the transition from laminar to turbulent flow. A slight change in slope at this position can be recognised in both of the experimental curves given. The magnitude of this change is also small because of the low Reynolds number. Another interesting aspect of Figure 5.2 is the dramatic drop in heat transfer near the edge which is visible only on the left hand side of the graph. An equivalent drop is likely to be present on the right hand side as well, but it is not visible because of the problems with the liquid crystals and stray silicone sealant described previously. According to Figure 2.2 and other studies, no such drop in heat transfer is expected for jets impinging on a smooth surface. Finite element modelling using the software Strand7 showed that the effects of lateral conduction from the edges of the foil would be insignificant 0.5 mm away from the edges, whereas the drop found in the experiments extended up to 2-3 mm. This indicates that the drop in heat transfer coefficient is most likely caused by eddy formation along the steep edges of the outlet cavity. 71

82 5 RESULTS AND DISCUSSION As a numerical verification, the experimental local heat transfer distribution is compared with the model from Tawfek [88] given in Table 3.1. This model predicts the average heat transfer coefficient in a circular area around the impingement zone for a given r/d. The average heat transfer coefficient is calculated from the measured distribution of heat transfer coefficients by numerical integration of the following: h avg r 2 = r h dr. 2 r (5.2) The values and trends are found to be in reasonable agreement with the results for the single S2 nozzle at two different Reynolds numbers as shown in Figure 5.4. Perfect agreement is not expected because the Tawfek correlation is only valid for z/d 6, which corresponds to jet impingement beyond the potential core. The measured values are for z/d = 2.5. A higher Reynolds number dependence is also expected for the higher nozzle-to-plate spacing because of turbulence created in the interaction with the surrounding liquid. This is evident from Figure 5.4 in that the correlation graph changes more with differing Reynolds number than the measured values. The shape of the correlation graph corresponds well with the measured values for mid range values of r/d, but overestimates the values for the areas close to the edges because of the heat transfer deterioration along the edges of the cavity. 0 have [ W m -2 K -1 ] Re = Re = Tawfek, Re = Tawfek, Re = r/d r/d Figure 5.4: Comparison of area averaged heat transfer for the single S2 nozzle with the correlation from Tawfek [88]. 72

83 5 RESULTS AND DISCUSSION 5.2 ARRAYS OF JETS The distribution of local heat transfer for each individual jet in an array was found to be similar to that of a single jet. The heat transfer coefficient drops off monotonically with radial distance away from the stagnation point, and reaches a value of half that of the stagnation point at about r/d ~ 3.5. However, as expected, interactions between the jets lead to some heat transfer characteristics that are different from those of single jets. Figure 5.5 presents a typical heat transfer coefficient distribution for an array of four nozzles, while Figure 5.6 shows a cross-section of the local heat transfer coefficient through two stagnation points for a range of Reynolds numbers. One of the characteristics of jets in an array is a slight asymmetry in the outer jets, which is seen in Figure 5.5. The heat transfer distribution is found to drop off more steeply towards the middle of the array than towards the outside. The same phenomenon was found by Huber and Viskanta [91]. The reason for this is that the jet experiences less restriction in the outward direction, and is thus decelerated more slowly. Jet interference region Location of the outlet pipe h [ W m -2 K -1 x 10 4 ] Distance along bus-bar [ mm ] Distance between bus-bars [ mm ] Figure 5.5: Heat transfer distribution for the countersunk orifices at Re =

84 5 RESULTS AND DISCUSSION h (W/m [ W m 2-2 K) K -1 ] Cross-section along the dotted line Centreline between nozzles r/d r/d Jet interference effects Re = Re = Re = Re = 982 Figure 5.6: Cross-section through impingement zones under the long/straight array, plotted against r/d measured from the centre of the upper jet, for various Reynolds numbers. Jet interaction can be seen from r/d = 2.4 or 1.2 diameters away from centreline between the nozzles. No systematic difference in local heat transfer distribution could be found between individual nozzles of different placements within the array. The shift in placement of the central jet in the nine/dense array (Figure 5.7) is caused by a small inaccuracy in the drilling of the holes. There was no similar asymmetry in the nine/sparse array (Figure 5.8). Because the drainage exit was situated in the corner of the return fluid chamber (indicated in Figure 5.5), it was expected that crossflow could deteriorate the heat transfer of the jet situated closest to the exit. This was not observed, something which suggests a symmetric flow pattern in the lower region of the return chamber. The central jet of the nine nozzle array had a similar or only slightly higher stagnation point heat transfer coefficient compared with the surrounding jets, something which further indicates that there are negligible crossflow effects. 74

85 5 RESULTS AND DISCUSSION h [ W m -2 K -1 x 10 4 ] 25 Distance along bus-bar [ mm ] Distance between bus-bars [ mm ] Figure 5.7: Local heat transfer distribution for the nine/dense nozzle array at Re = h [ W m -2 K -1 x 10 4 ] 25 Distance along bus-bar [ mm ] Distance between bus-bars [ mm ] Figure 5.8: Local heat transfer distribution for the nine/sparse nozzle array at Re = The poor resolution and apparent difference in the perimeter jets are due to a problem with the camera focus on the day of testing. 75

86 5 RESULTS AND DISCUSSION In Figure 5.5 a region of enhanced heat transfer in the area along the centreline between the nozzles is indicated. This region was observed for all Reynolds numbers in both the nine and four nozzle arrays. However, because of the lower resolution achieved for the smaller jets, the pattern is not seen as clearly in Figure 5.7 and Figure 5.8. The pattern is caused by increased turbulence where the neighbouring wall jets meet head-on (see Section 3.2.1). The heat transfer coefficient profiles in Figure 5.6 show that this interaction region extends about nozzle diameters away from the centreline between the jets. This value was found to be relatively constant for all of the four-nozzle arrays, while it extended about 1.5 nozzle diameters for the nine-nozzle arrays. Where the interaction region starts, the heat transfer distribution stops decreasing and instead increases slightly towards the centreline. Studies in the literature also predict a possible deterioration because of jet interference before impingement (Section 3.2.1). No indication of this was found, which is as expected because s/d is relatively large and Re is low. None of the previous studies referred to in Chapter 3 had documented any temporal instability of the flow patterns of the jet arrays. Nevertheless, in the current measurements, oscillations were clearly observed for all of the four-nozzle arrays. In the nine-nozzle arrays some flow instability was observed around the perimeter of the array, but not to the same extent as with four nozzles. This might be related to the poorer spatial resolution of the measurements with the smaller nozzles. The oscillations observed in the four-nozzle arrays were characterised by the interaction region between the jets not being constant along the centreline, but shifting slightly toward the stagnation point of one jet and then the other in an irregular manner. The positions of maximum heat transfer at the stagnation points of the jets remained constant. The oscillations were not regular enough to enable an accurate analysis of amplitude and frequency to be performed with the current experimental setup. The amplitude of the movement was found to be about 1.5 mm. The frequency of the oscillations could not be established. No significant difference in oscillation pattern could be found between the different nozzle configurations. One possible reason for the oscillations could be the remaining structure of the jet which is formed at the inlet of the plenum chamber, as shown in Figure 5.9. Other studies of jet impingement have often had diffusing structures such as honeycombs or meshes located in the upper region of the plenum chamber to ensure a very low fluid velocity at the nozzle inlet. However, because the current study is not so much concerned with the basic mechanisms of jet impingement as to provide understanding of the performance of real impingement devices, no such mechanisms were included since they were thought to add an unnecessary pressure drop. The orifice plate is located a distance of 4.9 inlet diameters beneath the water inlet. At this distance, the inlet jet is likely to have much of its original structure left. The oscillations probably arise due to temporal structures in the turbulence of the jet propagating through the orifice plate. Another phenomenon which had not been expected prior to the measurements was the problem of blocking of holes in the smaller orifices. The 0.7 mm diameter nozzles had a tendency to become blocked, resulting in a highly deteriorated local heat transfer, something which is shown in Figure The cause of the blocking could not be found, but was thought to be small particles suspended in the water. Although clean water was used, there was no filter in the circuit and thus there were always some particles present. This is an important factor in the design of practical jet devices. The presence or absence of a filter is a determining factor for the minimum safe nozzle diameter. In real systems it should be kept significantly larger than the 0.7 mm nozzles used here. 76

87 5 RESULTS AND DISCUSSION water inlet ambient fluid potential core turbulent interaction zone nozzles Figure 5.9: Flow regions in the plenum chamber. a) b) Figure 5.10: Heat transfer distributions for nine/dense array with the top-right hole a) partially and b) fully blocked. The colour scales are not the same for the two images. 77

88 5 RESULTS AND DISCUSSION 5.3 PREDICTIVE CORRELATIONS As explained in Section 3.1.4, it is common to correlate the stagnation point and average heat transfer coefficients for impinging jets using the basic form Nu m n 0, Nu avg = C Re Pr. (5.3) This form was chosen to correlate the experimental results. Because the Prandtl number dependence was not investigated, the dependence n = from the study of Li and Garimella [87] was used. The coefficients C and m for the stagnation point Nusselt number for the orifices studied are given in Table 5.1 along with the correlation coefficient R 2, which gives a measure of how the correlation fits the data. R 2 = 1 for a perfect fit. Table 5.2 gives C and m for Nu ave. In the case of the single nozzles, not enough measurements were made to justify making correlations. Table 5.1: Correlations for stagnation point Nusselt numbers for experimental data. Table 5.2: Correlations for average Nusselt numbers for experimental data. Orifice C m R 2 nine/dense nine/sparse short/straight long/straight sharp-edged countersunk Orifice C m R 2 nine/dense nine/sparse short/straight long/straight sharp-edged countersunk The results were also compared with correlations from the literature. Figure 5.11 shows the experimental stagnation point Nusselt numbers plotted with the correlations from Garimella and Nenaydykh [80] and Li and Garimella [87] given in Table 3.1. The slope of the Garimella and Nenaydykh [80] correlation agrees well with the experimental data on a log-log plot, which indicates that the Reynolds number dependence is correct. The correlation is accurate to within 2% for the four-nozzle arrays but overestimates the results for the nine-nozzle arrays and the single nozzles by about 7%. Because the nozzle diameter in the nine-nozzle arrays falls outside the range of validity for the correlation, a discrepancy for these arrays is expected. The developing length of the single nozzles is also outside the range of validity. The experimental results therefore confirm the accuracy of the Garimella and Nenaydykh [80] correlation within its range of validity. The correlation from Li and Garimella [87] fits very well to the nine-nozzle results but underpredicts the results for the other arrays. This is somewhat surprising because the nine-nozzle arrays have a smaller diameter and a higher value of z/d than what this correlation is valid for. The other nozzles all fall within the range of validity but are under predicted by about 3%. This correlation is built on a range of measurements for different liquids and is made to encompass them all with a relatively large average error of 9%. The four-nozzle results therefore fall within the range of uncertainty of the correlation. The almost perfect fit for the nine nozzle arrays is most likely coincidental. 78

89 5 RESULTS AND DISCUSSION 1000 a) Nu Pr 0.4 (z/d) (l/d) Nu Pr (l/d) (De/d) Re 1000 b) nine/dense nine/sparse short/straight long/straight sharp-edged countersunk single-s1 single-s2 single-s3 correlation Re Figure 5.11: Comparison of experimental results for the stagnation point Nusselt number with correlations from a) Garimella and Nenaydykh [80] and b) Li and Garimella [87]. In Figure 5.12, the average Nusselt numbers for the four and nine nozzle arrays are compared with the correlations from Huber and Viskanta [82], Martin [97] and Garimella and Schroeder [94] given in Table 3.2. All of the correlations agree reasonably well with the experimental data. The Huber and Viskanta [82] correlation has the poorest fit to the experimental results, underestimating the values by around 6% for the nine and 16% for the four nozzle arrays. This can be explained by the correlation being valid for only one developing length (l/d = 1.5) and one nozzle diameter (d = 6.35 mm). The latter is substantially larger than the nozzles used in the current experiments, and the nozzle diameter is known to have some influence on the Nusselt number as discussed in Section

90 5 RESULTS AND DISCUSSION Nuave Nuave Nuave 0.127Pr 0.4 (z/d) KGPr Pr 0.33 (z/d) (s/d) a) nine/dense nine/sparse short/straight long/straight 100 sharp-edged 1000 countersunk Re 1000 correlation b) Re c) Re Figure 5.12: Comparison of average Nusselt versus Reynolds number for nine and four nozzle jet arrays with the correlations from a) Huber and Viskanta [82], b) Martin [97]and c) Garimella and Schroeder [94]. The Martin [97] correlation agrees with the experimental data within about 3% and has thus the best fit of the average heat transfer correlations. However, it tends to overestimate the values for the nine-nozzle arrays and underestimate those of the fournozzle arrays. The overestimation of the nine-nozzle arrays is probably due to the fact that the correlation is based on a square area with side lengths s around the central jet, while in the present study the area around the array is also included, with a larger area of low heat transfer taken into account. The fact that the orifice plates of the four-nozzle arrays all had short developing length probably contributes to the underestimation of these values, as the Martin correlation is made on the basis of several experimental studies with a range of nozzle configurations but has no correction for developing length. The correlation by Garimella and Schroeder [94] overestimates the values for nine-nozzle arrays and underestimates them for four-nozzle arrays just like the Martin 80

91 5 RESULTS AND DISCUSSION correlation, but with a higher error of about 5.5%. The overprediction for the ninenozzle arrays is expected, both because of the geometry of the heated area, as explained above, and because of the z/d for these arrays being outside the range of validity. The correlation is only claimed to be valid to within 9%, which makes the agreement with the current results satisfactory. 5.4 NOZZLE GEOMETRY EFFECTS Figure 5.13 shows how the stagnation point Nusselt number (Nu 0 ) varies with Reynolds number for the different nozzle configurations. Examining Nu versus Re is equivalent to comparing the heat transfer under different jets at the same jet velocity. When comparing the nine-nozzle arrays to those with four nozzles, the former are found to yield a significantly lower Nu 0 than the latter. This could be related to nozzle size, as previous studies have found larger nozzles to yield slightly higher Nusselt numbers [86] because of increased turbulence levels. However, in the current measurements this effect is overshadowed by the higher nozzle-to-plate spacing. For the smaller nozzles, this was well above the length of the potential core (z/d = 7.14), while the larger nozzles can conservatively be assumed to impinge within the potential core (z/d = 3.57). This would explain the lower stagnation point heat transfer under the nine-nozzle arrays. Out of the four-nozzle arrays, the sharp-edged nozzle was found to yield the highest heat transfer coefficient. This is the result expected from previous findings in the literature, which attribute this effect to the higher turbulence levels introduced by the sharp edge of the entrance to the orifice. Differences in the heat transfer behaviour of the other configurations can not be distinguished within the range of uncertainty. Nu nine/dense nine/sparse short/straight long/straight sharp-edged countersunk Re Figure 5.13: Stagnation point Nusselt number versus Reynolds number for different nozzle configurations. Error bars are shown for the countersunk nozzles only to show the typical uncertainties. 81

92 5 RESULTS AND DISCUSSION In the design of jet impingement cooling systems, it can be more useful to compare the value of the stagnation point heat transfer coefficient h 0 for a given flow rate per nozzle QN -1. This is depicted in Figure 5.14, which shows that for a given flow rate, the smaller nozzles yield a higher heat transfer coefficient, despite their larger nozzle-to-plate spacing. This illustrates how the stagnation point heat transfer coefficient is much more dependent on jet velocity than parameters like z/d. For a given flow rate, if one wants to achieve the highest possible heat transfer coefficient over a small area, the smaller nozzles would yield the better result because of their high velocity. However, the local heat transfer coefficient distribution drops off monotonically away from the stagnation point and reaches a value of half maximum at about r/d ~ 3, which means there is a smaller area of high heat transfer under the small nozzle jets h0 [ W m -2 K -1 ] nine/dense nine/sparse short/straight long/straight sharp-edged countersunk Q N --1 [ ml s -1 ] Figure 5.14: Stagnation point heat transfer coefficients versus flow rate per nozzle for different nozzle configurations. havg [ W m -2 K -1 ] nine/dense nine/sparse short/straight long/straight sharp-edged countersunk Q [ ml s -1 ] Figure 5.15: Average heat transfer coefficient versus total flow rate for different nozzles. 82

93 5 RESULTS AND DISCUSSION Figure 5.15 shows how the average heat transfer coefficients across the entire heated surface for the different nozzle configurations vary with total flow rate through the array. In this figure, the nine-hole arrays are found to yield results comparable with the fournozzle arrays. The shift from high performance in terms of h 0 (Figure 5.14) to average performance in terms of h avg arises mainly because of the the increase in number of nozzles and thereby flow rate serves to eliminate the advantage of the smaller nozzles for a given nozzle flow rate. While the smaller nozzles yield a higher stagnation point heat transfer coefficient, the local heat transfer distribution drops off more quickly in the radial direction. To achieve the same uniformity of heat transfer, it is necessary to use the same nozzle pitch ratio s/d and therefore more nozzles for a given area. It can also be seen that the nine/dense array yield a higher heat transfer coefficient than the nine/sparse array, because there is a large perimeter area in the nine/dense array that is only cooled by the significantly weakened wall jet. The nine/sparse array performs similarly to the sharp-edged nozzles while the nine/dense array has an average heat transfer coefficient within the range of the remaining four-nozzle arrays. 5.5 PRESSURE DROP THROUGH AN ORIFICE When designing a jet impingement device, it is not only the flow rate which is important, but also the pressure drop through the device. The preferred cooling system will in many cases be the one that delivers the highest rate of cooling at a given pumping power. The total pumping power is proportional to the product of flow rate and pressure drop. The pressure drop through the various models can be easily predicted from theory. Bernoulli s equation gives the relationship between fluid velocity, gravitational head and pressure for an incompressible fluid in steady flow as [103] 2 2 p1 v1 p2 v2 gz = gz2 + +, (5.4) ρ 2 ρ 2 where subscripts 1 and 2 refer to conditions immediately before and after the orifice, respectively. This can be used to find the pressure difference across the orifice. Assuming the height difference is negligible across the orifice, the z-term can be left out. This is justifiable because, for the minimum flow rate of these measurements, g z/ v 2 3 x In this experiment, v 1 is also sufficiently small compared with v 2 to be ignored. The resulting expression for p becomes 2 =. (5.5) p 83 ρ 2 v 2 Other pressure drops through the jet device include the contraction from supply pipe to inlet pipe, expansion from inlet pipe to jet chamber, expansion after orifice plate, deflection at impingement plate and in outlet chamber, contraction to outlet pipe and expansion from outlet pipe to drainage pipe. These are all at least two orders of magnitude smaller than the pressure drop through the orifice and can thus be ignored. It is also assumed that all of the kinetic energy in the jet is dissipated and lost by frictional effects after the jet hits the wall and mixes, so that the pressure after the nozzle does not increase back to the original free stream value. The velocity after the orifice must be found using the area of the vena contracta instead of the nozzle area. The vena contracta refers to the phenomenon of a jet continuing to

94 5 RESULTS AND DISCUSSION contract for some distance after exiting the nozzle. Thus, the resulting cross-sectional jet area is smaller than the nozzle area. The vena contracta arises because of a transverse pressure gradient between the edge and centre of the nozzle. The pressure at the centre is higher than the ambient pressure at the edge, which causes the jet to continue to accelerate after leaving the nozzle until ambient pressure is achieved throughout the cross-section [104]. The area of the vena contracta is determined by the nozzle geometry, which is characterised by the contraction coefficient C c, given as A d =. (5.6) d c C c = An The value of C c is 0.6 for a perfectly sharp lip, and rises to C c 1 for a bell-mouthed opening. From theoretical limitations, the absolute limits for the contraction coefficient are 0.5 C c 1 [103]. Taking into account the losses through the orifice, the theoretical velocity is reduced by a factor C v called the velocity coefficient, defined as the ratio of actual to theoretical velocity at the orifice exit. Typical values for C v lie between 0.95 and 0.99 [103]. Because C v and C c are difficult to measure independently, they are often combined to a discharge coefficient C d = C v C c. The resulting expression for pressure drop through the device is 1 1 Q 2 c 2 n p = ρ v2 = ρ = ρq Cd A2 N π Cd d. (5.7) The discharge coefficient is known to vary slowly with Reynolds number, and can be assumed constant for the range of Re in this study. A least-square fitting to the experimental data gave the discharge coefficients given in Table 5.3. The pressure drop distributions with the correlations are shown in Figure The coefficients of determination for all correlations were R As the expected values for C d lie in the range 0.6 x x 0.99 = , the experimental values are quite low. In fact, the value obtained for the sharp-edged nozzle lies outside the expected range, although it is not below the theoretical limit of 0.5 x 0.95 = However, it is known that very small diameter orifices behave differently from larger orifices (see Section 3.1.4). Most data for contraction coefficients exist for measuring orifices that are 50 mm in diameter or larger [105]. A value of C d = 0.52 for the sharp-edged orifice is therefore not unreasonable. Comparing the different four-nozzle arrays, C d is found to be highest for the countersunk and lowest for the sharp-edged nozzle. The straight nozzles are both intermediate cases. The difference in discharge coefficient for the straight, contoured and sharp-edged nozzles can be explained by the degree of sharpness at the flow inlet. In addition, the measured C d is lower for the short/straight nozzle than for the long/straight nozzle. This difference is not easily explained in terms of sharp or gradual variations. Garimella and Nenaydykh [80] found a significant change in heat transfer coefficient for l/d <1 and l/d > 1. They explained this by the observation that at a small developing length, a separation bubble is formed at the inlet. This acts as a contraction, and results in the effective nozzle area being only 60% of the actual cross-section. At higher l/d, the separated flow at the nozzle entrance reattaches within the nozzle, and the reduction of the effective nozzle area is eliminated. This change in effective nozzle area would also 8 84

95 5 RESULTS AND DISCUSSION explain the smaller pressure drop through the longer nozzles. In this study, l/d = 0.7 for the short/straight and 1.4 for the long/straight nozzle. Table 5.3: Coefficients of discharge for different nozzle configurations. Nozzle configuration C d short/straight long/straight sharp-edged countersunk p [ p kpa ] short/straight Cd = long/straight Cd = sharp-edged Cd = countersunk Cd = Q [ ml s -1 ] Figure 5.16: Pressure drop correlations for different nozzle configurations. 5.6 TOTAL PUMPING POWER As discussed above, the optimal nozzle configuration for a given system will be determined by two factors: the required pressure drop and the flow rate required to achieve a given average heat transfer coefficient. To improve the performance of an orifice plate with simple straight nozzles, one could choose to countersink the holes to reduce the pressure drop, thereby achieving a higher heat transfer coefficient at the same pumping power. Alternatively, one could make the holes sharp-edged to achieve a higher heat transfer at a comparable flow rate. It is not immediately obvious which configuration would prove optimal. Figure 5.17 shows how the flow rate and pressure drop varies with average heat transfer coefficient for the various four-nozzle arrays. It shows that, to achieve a given heat 85

96 5 RESULTS AND DISCUSSION transfer coefficient, the short/straight nozzles involve the highest pressure drop. The long/straight nozzles perform a little better, while the results for the countersunk and sharp-edged nozzles are virtually indistinguishable. This relates to the fact that while the sharp-edged nozzles yield a higher pressure drop at a given Reynolds number, they also are better in terms of higher heat transfer coefficient at lower Reynolds numbers. At the same time, the sharp-edged orifices require a lower flow rate for a given heat transfer coefficient than the other orifices. This leads to the conclusion that for a given pumping power, the nozzle configurations yield increasing average heat transfer coefficients in the order: short/straight, long/straight, countersunk and finally sharp-edged. Q [ ml s -1 ] p [ kpa ] 40 short/straight 35 long/straight 30 sharp-edged 25 countersunk h [ W m -2 K -1 ] Figure 5.17: Flow rate and pressure versus average heat transfer coefficient for different nozzle configurations. A good indication of the pumping power required for the various orifice plates is illustrated by the maximum average heat transfer coefficients shown for each configuration (Figure 5.15). The values for the highest achieved h avg and Q are also given in Table 5.4 for easier comparison. The maximum flow rate for each device is achieved when the valve is fully open, so that the flow circuit outside the jet device itself is identical. These values therefore correspond to the same pumping power. Comparing the short and long straight nozzles, the decrease in pressure drop and the corresponding increase in flow rate for the longer nozzles result in a higher maximum heat transfer coefficient for the longer nozzle, which would imply that l/d > 1 is the preferable configuration for straight nozzles. The countersunk and sharp-edged nozzles yield maximum heat transfer coefficients which can not be distinguished within the range of uncertainty. However, as the sharp-edged nozzle yields this result at a considerably lower flow rate, this could be the preferable option in many systems. 86

97 5 RESULTS AND DISCUSSION Table 5.4: Maximum flow rates and average heat transfer coefficients for different nozzle configurations. Device Maximum Q (ml s -1 ) Maximum h avg (10 4 W m -2 K -1 ) nine-nozzle 23.2 ± ± 0.2 short/straight 29.9 ± ± 0.3 long/straight 31.7 ± ± 0.3 sharp-edged 27.7 ± ± 0.3 countersunk 33.3 ± ± CENTRAL DRAINAGE DEVICE Because of the lowered heat transfer in the perimeter region of the arrays discussed in Section 5.1, a central drainage device (see Section 3.6 and Figure 3.6b) was constructed in order to try to improve the perimeter heat transfer by placing the jets closer to the edges. In this device the nozzles had diameters of 2.5 mm, to allow for a higher flow rate, in a 1 mm thick orifice plate. A total of 12 nozzles were distributed on the array as shown in Figure The minimum nozzle pitch was s/d = 2.24 and the nozzle-to-plate distance was z/d = 4. location of water inlet water outlet Figure 5.18: Central drainage orifice plate. This device was found to function poorly for several reasons. Firstly, the nozzle pitch chosen was, as expected for reasons described in the previous section, small enough to cause a significant level of interaction between the jets prior to impingement. In addition, the inlet jet located in one corner of the array gave a very asymmetric flow field under the array. The central jets were found to perform even more poorly than the perimeter ones. This is most likely caused by crossflow and the high velocity of drainage water at the small outlet pipe. During the first measurements with this device, there were so many disturbances in the flow that none of the individual jet stagnation points could be recognised in the temperature distributions. Typically there would be a cool area close to the water inlet and a highly oscillating temperature field decreasing towards the far corner. Sometimes 87

98 5 RESULTS AND DISCUSSION cooler areas would appear and disappear at other positions on the heated foil. It was recognised that this highly asymmetric temperature distribution was due to the inlet jet, which in this configuration is located towards one corner of the array. To diminish the effect of this jet, several layers of wire mesh were inserted in the upper region of the plenum chamber. This caused the flow to become more uniform, and the stagnation points of the perimeter jets could be recognised. However, the flow was still highly unstable. Some pictures of the TLC taken at successive power settings are shown in Figure This shows how the placements of the different temperature regions vary with time. It is also very difficult to see any cooling effect of the central nozzles. Due to the highly oscillating flow, the images could not successfully be used to produce a heat transfer distribution map. An approximate distribution is shown in Figure The very low heat transfer shown in the perimeter region is probably due to poor lighting, as seen in Figure 5.19, but a closer inspection of the thermal images indicated that a low heat transfer region is present along the edges despite this design having the jets placed closer to the edges. Thus it seems that central drainage might not be useful for diminishing the eddy formation along the edges Figure 5.19: Recorded temperature distributions under the central drainage array with diffusing mesh inserted, shown at increasing power levels. The locations of the cooler areas vary significantly with time due to the highly unstable flow. As mentioned above, it was difficult to see any cooling effects of the four central nozzles. It was thought that this might relate to the jets being strongly affected by the pressure field around the outlet, in effect getting sucked into the exit before impinging onto the heated surface. To try to diminish this effect the outlet pipe was extended down from the orifice plate as shown in Figure 5.21 so that the exit was located 2 mm above the impingement plate. This was not found to yield any significant change in the 88

99 5 RESULTS AND DISCUSSION temperature distribution. It is therefore likely that the low heat transfer under the central jet is caused by a combination of crossflow from the perimeter jets and, more importantly, vortex formation around the outlet. h avg [ W m -2 K -1 x 10 4 ] Figure 5.20: Approximate heat transfer coefficient distribution under the central drainage jet array. Because of the unstable flow conditions, it was not possible to record an accurate distribution. The apparently low heat transfer along the edges is due to lighting problems. a) b) Figure 5.21: Central drainage cooling device a) without and b) with extended outlet pipe. 89

100 5 RESULTS AND DISCUSSION 5.8 CONCLUSIONS The shape of the local heat transfer distribution was found to be relatively similar for single jets and jets in arrays. It can be approximated by a linear function reaching a value of half maximum at r/d = 3.5. A significant drop in heat transfer coefficient was identified for the perimeter region up to 3 mm away from the edges of the impingement area, which is attributed to eddy formation along the sharp corners of the return flow cavity. The local heat transfer beneath the jet arrays was characterised by asymmetry away from the centre of the array, due to the difference in flow restriction, and by interference creating a region of increased heat transfer coefficient along the centreline between jets. Temporal oscillations were identified in the interaction regions of the four-nozzle arrays. The stagnation point and average heat transfer coefficient were correlated using a standard form, with good agreement. The experimental data were also shown to agree well with several correlations from the literature. The pressure drop through the nozzles could be correlated using the coefficient of discharge for each nozzle. When comparing the total pumping power required for a certain average heat transfer coefficient, the countersunk and the sharp-edged nozzles were found to outperform the straight nozzles. The central drainage device was also tested but did not eliminate the problem of low heat transfer along the edges. On the contrary, the average heat transfer achieved with this device was low compared with the side drainage device. This was due both to nonuniform flow patterns created because the inlet jet was placed off-centre, and to vortex formation around the narrow outlet pipe. The results obtained for the impinging jet device are highly promising when comparing to previously reported results for microchannel devices. The highest average heat transfer coefficient obtained in the experiments (h = 3.5 x 10 4 W m -2 K -1 which is equivalent to R = 2.9 x 10-5 K m 2 W -1 ) is higher than most of the results reported for regular microchannels and only slightly poorer than the typical values obtained with improved microchannels (see Figure 2.16). At the same, the pressure drop through the device is about an order of magnitude lower than what is typical for microchannel devices (Figure 2.19). Considering that there is much room for improvement of the proposed jet device design, there is a strong possibility that impinging jets may prove superior to microchannels in terms of heat transfer and pumping power. Possibilities for optimising the jet device design are explored in Chapter 6. 90

101 Chapter 6 OPTIMISED DESIGN OF COOLING DEVICES The aim of studying the characteristics of jet impingement devices is to gather enough knowledge to be able to design an optimised cooling device. This thesis seeks to find a device for cooling PV at a low pumping power requirement which ensures the highest possible net electrical output from the PV array. In this chapter, correlations for average heat transfer coefficient and pressure drop are used to build a model which predicts the pumping power requirements for a jet impingement device at a given h avg. This model can be used to optimise the size and number of nozzles for a give size of cooling unit. Subsequently, it can be used to find the flow rate settings which will yield the highest PV output at a given illumination value. 6.1 CORRELATION FOR PUMPING POWER Pressure drop The pumping power W required for any forced convection device is given as the product of flow rate and pressure drop W = pq. (6.1) As shown in Section 5.5, the pressure drop through an orifice device is correlated by Equation 6.2 can be substituted directly into Equation p = ρq. (6.2) N π Cd d In the subsequent sections it will be assumed that C d is independent of nozzle diameter. This is consistent with the theory from textbooks such as [103], however some studies suggest that small diameter nozzles show a slightly different behaviour (see Section 5.5) Two correlations for heat transfer coefficient The next objective is to eliminate the flow rate Q from the equation. This can be done by including the correlation for average heat transfer coefficient h avg in terms of Q, solving for Q, and substituting this into Equation 6.1. Several correlations exist that can be used for the heat transfer part of the model. It was decided to use two different models with different s/d dependence. The first is the Martin [97] correlation presented in Section 3.2. The second model, which will be referred to as the Huber model, has a better fit to the experimental results from the current study. It incorporates the constant C and Reynolds 91 8

102 6 OPTIMISED DESIGN OF COOLING DEVICES number dependence m from the experimental data (Section 5.3) with the Prandtl-number dependence from Li and Garimella [87] and the s/d dependence from Huber and Viskanta [82]. As seen in Figure 6.1, the two chosen models are qualitatively different with respect to their s/d dependence. The Martin model has a negative second derivative, while the Huber model has the opposite shape. This will be shown to result in quite different behaviours for the pumping power correlations made using these models. Nu Nu Martin Huber s/d s Figure 6.1: Predicted Nusselt number as a function of s/d using the correlations from Martin [97] and Huber and Viskanta [82] for an arbitrary jet configuration The Martin model The Martin [97] model is described in Section 3.2.4, but is repeated below: where Nu avg 2 / = 0.5KG Re Pr, (6.3) ( / ) z d f K = 1 +, (6.4) 0.6 an G f = 2 f (6.5) ( z / d 6) f 2 π d f =. (6.6) 4 s The correlation is rewritten in terms of h and Q instead of Nu and Re: and k k h = d d 2 / avg = Nu 0.5KG Re Pr, (6.7) 92

103 6 OPTIMISED DESIGN OF COOLING DEVICES so that vd 4Q Re = =, (6.8) ν Nπdν Solving for flow rate, Q, yields 2 / 3 4Q 0.42 h avg = 0.5KG Pr. (6.9) k d Nπdν Nπν Q = d 4 5 / 2 havg Pr 0.5KGk / 2. (6.10) Substituting 6.2 and 6.10 into 6.1 gives us a correlation for pumping power W: W = pq = ρq 2 = ρ N = ρ N = ρ N 8 2 π C d Nπν d = ρ 2 8C N π C d d 2 d 8 2 π C d 2 d 8 2 π C d 2 d 2 d / 2 4 Q 3 Q Nπν d 4 5 / 2 3 Nπν 4 d havg Pr 0.5KGk havg Pr 0.5KGk 15 / 2 havg Pr 0.5KGk / / / 2 (6.11) The Huber model The second model, which incorporates the experimental correlations from Chapter 5 with the Huber s/d dependence, is given by Nu ( s / ) C Re m Pr, (6.12) = d where C and m are correlation coefficients given in Section 5.2. In terms of h avg and Q this becomes Solving for Q yields h m k 4 m avg = C Q Pr / d d Nπdν ( s ). (6.13) havgd Q = Ck 1/ m Nπdν Pr 4 The resulting pumping power correlation becomes / m / m ( ) s / d. (6.14) 93

104 6 OPTIMISED DESIGN OF COOLING DEVICES 1/ m 8 havgd Nπdν / m / m W = ρ Pr ( / ) s d (6.15) N π Cd d 4 Ck For simplicity, in the following sections only square arrays of jets are considered so that the number of jets is restricted to N = n 2 where n is an integer, and the heated surface is supposed to be square with sides L heat. The jet pitch, s, is then given as a function of N and L heat by Lheat s =. (6.16) N Comparison with experimental data a) 1.00 W [ W ] b) h avg [ W m -2 K -1 ] nine/dense short/straight long/straight sharp-edged countersunk nine/dense, model short/straight, model long/straight, model sharp-edged, model countersunk, model 1.00 W [ W ] h avg [ W m -2 K -1 ] Figure 6.2: Experimental results for pumping power from the different configurations plotted together with predictions from a) the Martin model and b) the Huber model. The Huber model shows a better fit to the experiments, which is expected because it is built on these data. The Martin model overpredicts the pumping power required for the four-nozzle arrays and underpredicts that for the nine-nozzle arrays. 94

105 6 OPTIMISED DESIGN OF COOLING DEVICES Figure 6.2 shows the pumping power W = pq from the experiments together with the predictions from the Martin and Huber models. As expected, the Martin model does not quite fit the experimental values. This is because the Martin model underestimates the heat transfer coefficient for the four-nozzle arrays and overestimates it for the ninenozzle arrays, as described in Section 5.3. The Huber model on the other hand fits the data closely because it is built on these results. The slopes of the two correlations are quite different, and this becomes apparent if they are compared for a similar device over a range of heat transfer coefficients, as shown in Figure 6.3. Outside the range of the experimental data, the two lines cross over and the Huber model starts to predict higher W levels than the Martin model W [ W ] Martin Huber h avg [ W m -2 K -1 ] Figure 6.3: Variation of pumping power for a range of average heat transfer coefficients using the Martin and Huber models. These observations show how important it is to have accurate values for the characteristics of the orifice types under consideration in order to make reliable predictions. Ideally, the discharge coefficient C d as well as the Reynolds number dependence for the possible configurations should be determined experimentally. However there is available information regarding this in literature for standard type orifices which may be used Model predictions The major difference between the predictions from the Martin model and the Huber model is shown in Figure 6.4. While the former predicts a definite optimal nozzle diameter, d opt, for a set of conditions, the latter recommends always using the smallest possible nozzles. This discrepancy arises from the difference in s/d dependency for the Martin and Huber correlations shown in Figure 6.1. It is the K and G correction factors of the Martin correlations that lead to an optimum pitch value (s/d) opt, which since s/d is a function of L heat, N and d, gets translated into an optimum nozzle diameter. K and G are functions for s/d and z/d only, and will therefore predict an (s/d) opt for each value of z/d. Figure 6.5 shows how the product KG varies with s/d within the z/d range of validity. In all cases, (s/d) opt < 6, and for the lower values of z/d there is no optimum to be found. However, the values of d opt and the corresponding (s/d) opt predicted from the 95

106 6 OPTIMISED DESIGN OF COOLING DEVICES pumping power correlation did not coincide with the optimal s/d shown in Figure 6.5. This indicates that the optimum nozzle diameters predicted are determined by an interaction between the pressure drop and heat transfer correlations. 10 a) b) W / [ W ] W W [ / W ] d /[ mm ] d [/ mm ] h avg = h avg = h avg = h avg = Figure 6.4: Pumping power from varying nozzle diameter at different h levels (N = 4) using a) the Martin model and b) the Huber model. KG s /d z/d = 2 z/d = 3 z/d = 4 z/d = 5 z/d = 6 z/d = 7 z/d = 8 z/d = 9 z/d = 10 z/d = 11 z/d = 12 Figure 6.5: Variation of KG as a function of s/d for a range of z/d according to the Martin correlation. The existence of a d opt seems intuitively correct. When the nozzle diameter is decreased, the increase in jet velocity leads to a higher heat transfer coefficient. This, however, comes at the cost of a highly increased pressure drop. Moreover, the heat transfer distribution drops off more rapidly away from the impingement point. At some specific diameter, the negative effects would be expected to become dominant and to lead to an increased pumping power for a given h avg, as the Martin model predicts. Both models predict a lower pumping power for a higher number of nozzles, independent of other variables. This result is contrary to the conclusions from several studies that optimise against flow rate. Brevet et al. [96] found that a decrease in the number of nozzles, and the subsequent increase in Reynolds number, would result in a higher h avg. However, the pressure drop, which was not taken into account in this optimisation, increases drastically when the total orifice cross-section is decreased. Garimella and Schroeder [94] also found the heat transfer to be highest for a single jet 96

107 6 OPTIMISED DESIGN OF COOLING DEVICES when optimised for flow rate, but noted that the pressure drop, and thus the pumping power, would be lower for a high number of nozzles. As we have seen, increasing the number of nozzles and thereby reducing s/d is beneficial to the average heat transfer coefficient. However, when the jets are too closely spaced, the negative effects of jet interaction before impingement (see Section 3.2.1) become increasingly significant. Beyond a certain s/d, the benefit gained by adding nozzles is lost to increased jet interference. Garimella and Schroeder [94] found the average heat transfer to level off for s/d < 4. The Huber and Martin models are also only valid down to s/d = 4 and s/d = 4.43, respectively. A spacing of s/d = 4 seems therefore to be a reasonable lower limit for design purposes. The predicted pressure drop variation with nozzle diameter is shown in Figure 6.6 for a range of N. The Huber model predicts the smaller nozzles to be superior under all conditions, and shows no difference in trend for the different numbers of nozzles. The Martin model, on the other hand, predicts an optimum nozzle diameter which shifts towards smaller nozzles for increasing N. The latter makes sense because with fewer nozzles, a larger area has to be covered by each jet. Increasing the nozzle diameter makes the local heat transfer distribution fall off more slowly away from the stagnation point in terms of absolute distance, so that a larger area is covered by the central high heat transfer region. W / [ W ] NN=1 NN=4 NN=9 W [ W ] W / W 10 a) b) NN= d [/ mm ] d [/ mm ] Figure 6.6: Varying nozzle diameter for different numbers of nozzles (L heat = 80 mm, h avg = W m -2 K -1 ) using a) the Martin model and b) the Huber model. The optimal nozzle diameter, d opt, is found to be independent of h avg, C d and Pr. However it depends on N and L heat as shown in Figure 6.7. This figure also includes the required pumping power per area for h avg = 10 4 W m -2 K -1 to illustrate the large variation in pumping power for an increasing number of nozzles. Note that W/A also increases with the heater size. This reflects back on the benefit of a high number of nozzles per area. As N is kept constant but the area is increased, W/A increases as well. The optimal nozzle diameter is also dependent on the nozzle-to-plate spacing z/d as shown in Figure 6.8. It can be seen that d opt decreases linearly with increasing z/d. The slope of the graph is dependent on N but independent of L heat. In the Martin model, the nozzle-to-plate separation, z/d, has an effect in that it shifts the size of d opt (Figure 6.5). It also predicts a higher h avg at low z/d. In the majority of the measurements made for 97

108 6 OPTIMISED DESIGN OF COOLING DEVICES this thesis the parameter z/d was kept constant at z/d = 3.57 because several studies had observed the maximum h avg to occur at 3 < z/d < 4 (Section 3.1.2). These studies generally found very little change in h avg with changing z/d within the length of the potential core. However, other studies including Martin [97] have found low z/d to be favourable, especially at low s/d. d dopt / [ mm ] N = 1 N = 4 N = 9 N = 16 W /A W [ / W m -2 ] L heat /[ mm ] L heat [/ mm ] Figure 6.7: Optimal nozzle diameter as a function of heater size, with the corresponding power requirement per area for h avg = 10 4 W m -2 K -1 using the Martin model. The results for d opt are independent of h avg dopt [ mm ] d opt / mm L heat = 100 mm L heat = 80 mm L heat = 60 mm L heat = 40 mm L heat = 20 mm z /d Figure 6.8: d opt as a function of z/d for a range of L heat. The value of s/d at d opt was calculated for all of the examples mentioned. It was found to vary with z/d only, and not to drop below the critical value of s/d = Experimental validation Both the Martin and the Huber models predict that for a given pumping power, a higher h avg will be achieved with a greater number of nozzles, provided s/d > 4. It was decided to run some simple measurements to test if the predicted trends could be verified experimentally. An already existing orifice plate (the short/straight) was modified to perform measurements with one, four and nine nozzles. To get nine nozzles in this plate, additional holes were drilled between the corner nozzles. The single jet measurements were made last by blocking the outer nozzles using epoxy glue. Because the model presented in this chapter assumes the nozzles are placed evenly across the surface, with a 98

109 6 OPTIMISED DESIGN OF COOLING DEVICES distance of s between each jet and s/2 between the edge and the nearest jet, the average heat transfer coefficient was calculated for an area of sides L heat = 20 mm for the four and one nozzle arrays, and L heat = 15 mm for the nine-nozzle array, as shown in Figure 6.9. Figure 6.9: Areas from which the average heat transfer coefficients are calculated for the single, four and nine-nozzle arrays. First, a few measurements were performed with the original four nozzles to confirm that the results obtained with the new TLC coating and the water running at a different temperature were consistent with those from the previous experiments. The measurements showed excellent agreement with previous results. Figure 6.10 shows the predicted curves for the various numbers of nozzles. The N = 4 results shown in pink are calculated from the previously measured heat transfer coefficient distributions, and the corresponding curve is calculated for this water temperature. The predictions shown are thus all for different water temperatures and different L heat and can therefore not be directly compared against each other. Due to experimental limitations, only a very limited range of flow rates could be obtained for the single nozzle. However, the values of h avg and W obtained fall nicely onto the predicted curve as seen in Figure This serves as a good verification of the model. It also gives an indication that for the s/d used in the four nozzle arrays, jet interaction does not play a significant role. If it did, then the correlation constants C and m found for the four nozzle array would not have predicted the correct heat transfer coefficient for the single nozzle. 99

110 6 OPTIMISED DESIGN OF COOLING DEVICES W [ W ] N = 1 N = 4 N = 9 N = 1 results N = 4 results N = 9 results h [ W m -2 K -1 ] Figure 6.10: Predicted and measured pumping power versus average heat transfer coefficient for single, four and nine-nozzle arrays. Figure 6.10 shows that the average heat transfer coefficients under the nine-nozzle arrays were much lower than predicted. The reason for this is illustrated in Figure 6.11, which shows a highly nonuniform local heat transfer distribution under the nine-nozzle array. The heat transfer coefficient was found to be highest under the central jet, and to become lower for jets further away from the centre. The worst performance was found for the corner jets. The bottom middle jet indicated in Figure 6.11 a) yielded a low heat transfer coefficient due to imperfections in the nozzle. In order to eliminate the effect of this, only the top half of the distribution was used in the calculation of h avg. It is likely that this pattern of nonuniform heat transfer between the different placement nozzles is caused by some form of jet interaction. Because s/d is only 3.57 for the nine-nozzle array, some amount of destructive interference prior to impingement is expected. The jet fountain effect may also play a role although it should not be significant at such low Reynolds numbers. In addition, it seems from the pattern in Figure 6.11 that the flow from the central jet drains diagonally between the middle jets and interferes with the corner jets, resulting in a further deterioration in the corners. These findings serve to further emphasize the importance of keeping s/d >

111 6 OPTIMISED DESIGN OF COOLING DEVICES areas used for calculating h avg a) b) low heat transfer coefficient due to nozzle imperfections Figure 6.11: Comparison of local heat transfer distribution for a) nine nozzles and b) four nozzles at similar Reynolds numbers. The colour scales for the two plots are the same. 6.2 NET PV OUTPUT COOLING SYSTEM OPTIMISATION In Section 2.2 a one-dimensional thermal model for PV cells was presented which could be used to predict the electrical output from the cell as well as the cell temperature as a function of illumination level and cooling system thermal resistance. As explained in Section 2.1.3, the heat transfer coefficient h is just the inverse of the thermal resistance, R. This model can therefore be used together with the correlation for pumping power as a function of h avg presented in this chapter to find the optimal cooling performance for a given illumination level. Figure 6.12 shows typical plots of the net PV output for different conditions. The blue line shows the PV output as a function of h avg, while the green line shows the change in cell temperature. These two graphs are from the model presented in Section 2.2. As expected, a low average heat transfer coefficient results in a high cell temperature and a subsequent low cell output. The pink line shows the net electrical output, which is the cell output minus the power required for the cooling system as given by the Martin or Huber model. The pumping power is slightly underestimated because only the mechanical, not electrical, power requirement is calculated. The graphs in Figure 6.12 are based on an area of 50 mm x 50 mm, and the parameters N = 4, d = 1.4 mm, C d = 6.1, C = 1.96 and m = The cell properties are given in Table

112 6 OPTIMISED DESIGN OF COOLING DEVICES P [ W ] P [ W ] P / h avg [ W m -2 K -1 ] a) b) T [ C ] T [ C ] P [ W ] P / h avg [ W m -2 K -1 ] h avg [ W m -2 K -1 ] c) d) P [ / W ] h avg [ W m -2 K -1 ] T / [ o C C ] T [ / o C C ] PPcell PPtotal Tcell Figure 6.12: Cell and total power output and cell temperature plotted for cooling system average heat transfer coefficient for various models and concentration levels: a) 200 suns, Martin model; b) 200 suns, Huber model; c) 500 suns, Martin model; d) 500 suns, Huber model. From Figure 6.12 it can be seen that there is a definite optimal, although broad, h avg at which the net electrical output reaches a maximum. The predictions from both the Martin and the Huber models are shown for concentration levels of for 200 and 500 suns. In this range there is not much difference between the two models. The Huber model predicts a lower W for a given h avg below h avg = 42 x 10 3 W m -2 K -1 and a higher W above this level because the two models cross over as shown in Figure 6.3. For a concentration level of 200 suns, the Martin model gives the optimal h avg to be 27 x 10 3 W m -2 K -1 while the Huber model predicts it to be h avg = 28 x 10 3 W m -2 K -1. For 500 suns the same models predict the optimal h avg to be found at 38 and 37 x 10 3 W m -2 K -1, respectively. 6.3 GUIDELINES FOR DEVICE OPTIMISATION The correlations developed in this and in previous chapters can be employed to find an optimal device design. The design process is outlined in the following steps, which are described more closely below: 1) Determine the size of the cooling unit, L heat, 2) Determine the number of nozzles, N, 102

113 6 OPTIMISED DESIGN OF COOLING DEVICES 3) Find a suitable nozzle-to-plate to diameter ratio, z/d, 4) Find the optimal nozzle diameter, d, 5) Determine the nozzle configuration and possible surface modifications, and 6) Find the optimal operating conditions. The size of the cooling unit is an external parameter which is set by the size of the surface that needs to be cooled. For large arrays of closely packed, small PV cells, it can be preferable to build up the array of individual modules, each complete with one cooling unit. A practical size for a module could be about 100 mm x 100 mm. The number of nozzles, N, should be made as high as possible while still being low enough to avoid negative crossflow effects. 3x3 arrays have been shown not to experience negative crossflow effects. The performance of 4x4 arrays may be slightly reduced, but considering the large increase in heat transfer that can be achieved by increasing the number of nozzles, the 4x4 arrays can probably be used with benefit. However in the configuration with back drainage around all four sides, on which most of the attention has been focused in the previous chapters, 4x4 should probably be used as the maximum number of nozzles for a unit cell. If another drainage configuration is found where exits for spent liquid are distributed throughout the array (Section 3.5), it would be preferable to use the highest possible number of nozzles, only limited by s/d > 4. The nozzle-to-plate distance was kept at z/d = 3.57 in the experiments performed here, but there is likely to be a benefit from reducing this distance. This will make the unit less bulky and in some studies [94, 97] it has also been predicted to increase the array performance. The Martin model is only valid down to z/d = 2, which it predicts to be the most favourable separation. Depending on manufacturing constraints, z/d = 2 can be used as the optimal separation distance, with the possibility of being increased up to z/d = 4 without a significant penalty. In the next part of the design procedure, the nozzle diameter d opt is found as a function of L heat, N and z/d. If s/d is found to be below 4 for this configuration, the nozzle diameter or number of nozzles should be reduced. Reducing d would have a smaller impact on W, however a lower limit to d can be set from practical reasons. In addition to manufacturing constraints, perhaps the most important restriction on nozzle diameter has to do with the clogging of the nozzles due to small particles in the coolant water. In the experiments, the 0.7 mm nozzles had a tendency to be easily blocked. If no filter is used in the coolant circuit, the nozzle diameter should probably be at least 1.5 mm. The choice of the parameters described above is independent of nozzle configuration. When d opt is determined, the next step is to decide on the type of nozzle. Countersinking the orifices from above or below is found to reduce W significantly (Section 5.6), but the improvement has to be weighed up against the cost of an extra manufacturing step. Another factor to consider is surface modification. As explained in Section 3.3.1, this can lead to as much as a threefold improvement in h avg if done successfully. However, the type of modifications must be chosen with care, as some have been found to lead to a decrease in heat transfer. If a method of surface modification is known to increase the heat transfer to a level high enough to justify the extra manufacturing work, this should be included in the device design. 103

114 6 OPTIMISED DESIGN OF COOLING DEVICES When the final design is known, some simple experiments are needed for the subsequent optimisation. One approach could be to connect the cooling unit and the PV cells and run the assembly at a range of flow rates while monitoring the module short-circuit current, water temperature and pressure drop across the unit. If the properties of the PV cells are well-known, the average junction temperature can be inferred from the module short-circuit current, and this in turn can be used to find h avg. Other methods include thermographic liquid crystals or some other way of measuring the heated surface temperature. A series of measurements will give the heat transfer correlation constants C and m which are used in the Huber model (Section 5.3) and the discharge coefficient C d. Orifices are commonly used as flow rate measurement devices and an extensive collection of data for C d values for larger, standard orifice nozzles have been developed in literature which could be applicable in the design process. The final stage of the optimisation procedure is to find the optimal value of h avg at which to run the cooling system, as described in Section 6.2. The electrical and thermal properties of the PV cells to be used in the system need to be known and incorporated in the model for PV output presented in Section 2.2. To predict the required pumping power for the cooling system, it is better to use the Huber model, using the constants C and m found in the above described measurements, because it is built on experimental data and thus gives more accurate predictions within the experimental range. By performing this final optimisation, one can find the optimal operating conditions for the system at any illumination level, and predict the typical electrical output for the chosen conditions. 6.4 CONCLUSION The correlations for pressure drop and average Nusselt number presented in Chapters 3 and 5 can be combined to predict the pumping power required for a given average heat transfer coefficient and jet array configuration. When using the Martin [97] correlation for Nusselt number, the model predicts an optimum nozzle diameter for any given number of nozzles. The Huber [82] correlation, on the other hand, predicts increasing heat transfer with decreasing nozzle diameter without an optimum point. Both models predict a higher number of nozzles to yield a significantly higher heat transfer coefficient at a given pumping power. The pumping power model can in turn be used together with the correlation for PV output as a function of temperature which was presented in Section 2.2 to find the optimal operating conditions for a given illumination level. A broad optimum operating range exists. The recommended design procedure for jet impingement photovoltaic cooling devices was presented in Section 6.3. The predicted optimal nozzle diameters were not verified experimentally because of time constraints. Some studies (Section 5.5) suggest that the discharge coefficient C d might be dependent on nozzle diameter, while the model predictions rely on the assumption that C d is constant. It is not thought that the possible diameter dependence would have a large influence on the model predictions, but this should still be investigated experimentally in later studies. 104

115 Chapter 7 EFFECTS OF NONUNIFORM TEMPERATURE All categories of cooling systems inherently produce some degree of nonuniformity in temperature across a uniform heat flux surface. A uniform heat flux would, naturally, only be found in ideal cases, but this assumption is necessary to isolate the effects of a nonuniform heat transfer coefficient from the effects of other nonuniformities. With water running through channels, nonuniformities arise due to gaps between the channels and along the length of the channel because of heating of the coolant. As seen in Chapter 5, impinging jets produce a highly nonuniform local heat transfer distribution. This is something which should be taken into account when designing an optimised jet array. Nonuniformities across an array of photovoltaic cells may have both electrical and mechanical implications. The latter refers to stresses in the material resulting from different thermal expansions across the surface, which may result in adhesion problems or cracking. Despite being an important problem, the mechanical aspects of PV arrays are beyond the scope of this thesis and it will therefore not be further addressed. The question of how nonuniform temperatures influence the output from single and interconnected PV cells is investigated in Section 7.1. Section 7.2 describes how the temperature nonuniformities can be reduced by introducing a sheet of metal of appropriate thickness between the cells and the impinging jets, and discusses the tradeoff between reduced nonuniformity and increased average temperature which is caused by this extra layer. An issue which is often confused with nonuniform temperature is the occurrence of hot spots resulting from nonuniform illumination of a PV array. When one cell in a series connection is shaded, its short circuit current is severely degraded and the cell is easily driven into reverse bias, dissipating energy instead of producing it. This results in a considerable loss of power, and may lead to irreversible damage because of overheating of the cell. As shown in Section 7.1, however, the degradation resulting from temperature alone is much less severe and does not necessarily lead to the cell being driven into reverse bias. 105

116 7 EFFECTS OF NONUNIFORM TEMPERATURE 7.1 INFLUENCE ON PV OUTPUT Single cells Even in cases where the incident solar flux is perfectly uniform, temperature nonuniformities are always present in concentrator cells, as a result of imperfections (voids) in the cell-to-substrate bond [16] or as a result of the cell and heat sink geometry [17]. Despite this, only two studies could be found that investigate the effect of temperature nonuniformities under uniform illumination. Sanderson et al. [16] addressed the problem of hot areas caused by voids in the bond. A theoretical model was made in which the unit cell was divided into element areas, each operating at a unique temperature. The model was verified experimentally by impinging the back of the cell mounting plate with water of two different temperatures, separated by a divider. The electrical characteristics of the cells were then found for a number of illumination values ranging from 1 to 100 suns. The experimental results showed good agreement with the model, except at high concentrations, when voids and nonuniform illumination caused by the Fresnel lens became more pronounced. For a step function in temperature with T = 50 K, the predicted cell efficiency was found to decrease from 13.1% to 12.2% at 100 suns and from 12.6% to 11.6% at 10 suns. More specifically, the nonuniform temperature was found to result in a decreased open-circuit voltage. Mathur et al. [17] used a slightly different approach, subdividing a circular cells into concentric rings with a temperature gradient from the centre to the edge of the cell, which is realistic for a circular cell bonded onto a large, flat heat sink. It was found that with increasing thermal nonuniformities, the short-circuit current would show an increase, whereas the open-circuit voltage and conversion efficiency would both decrease. However, both of the above studies indicate that the effects of temperature nonuniformities across one cell are relatively small Interconnected cells To obtain an understanding of how a temperature difference between cells connected in a module affect the electrical output, it is sufficient to study the behaviour of two cells at different temperatures connected in series and parallel. The connections are shown in Figure 7.1, where T 1 T 2. The electrical characteristics of the cells are found using a semi-empirical model for concentrator silicon solar cells presented by Mbewe et al. [12]. The open-circuit voltage and short-circuit current for a cell of area A c (cm 2 ) at a given temperature T c (K) and concentration level X (suns) are given by and V oc log X = 1.25 Tc (7.1) [ ( 300) ] T I sc = 0.034Ac X c. (7.2) When V oc and I sc are known, the current I can be calculated at any voltage level V < V oc iteratively from the transcendent function I V Ir s Voc = I sc 1 exp (7.3) ktc / q 106

117 7 EFFECTS OF NONUNIFORM TEMPERATURE where r s denotes the series resistance, which is assumed to be a cell property independence of temperature. Equation (6.3) can be rearranged to yield an expression for V: kbt c Isc I V = ln + Voc Irs q I. (7.4) sc The values r s = 0.02 Ω cm -2, A c = 1 cm and X = 100 suns are all chosen for the subsequent calculations. Figure 7.1: Two cells at temperatures T 1 and T 2 connected in a) series and b) parallel. When the two cells are connected in series, the current I through the two must be equal. If the two cells are of different temperature, I sc will increase and V oc decrease in the hotter cell, while the opposite takes place in the colder cell. The following procedure is used to find the maximum power point for the series connection: 1) V oc and I sc are calculated for each cell. 2) A suitable range of voltages V 1 for the hotter cell is established, all below V oc1. 3) For each V 1, the current I is found by iteration. 4) V 2 is found as a function of I. 5) The maximum power point is found where P = I (V 1 + V 2 ) has its maximum value. This value of P is used to find the cell efficiency η = P el / S, where P el is the electrical output and S is the incident solar flux. By keeping the average cell temperature constant and changing the temperature difference between the two cells, one can study how the module efficiency changes as a function of temperature difference. The results are shown in Figure 7.2 together with the corresponding values of V oc1, V oc2, V 1 and V 2. In essence, the results show virtually no effect from temperature difference on the total conversion efficiency. Figure 7.3 shows the total and short-circuit currents for the two cells. As seen from Equations 7.1 and 7.2, V oc and I sc are both linear functions of cell temperature, something which is also evident from Figure 7.2 and Figure 7.3. As the short-circuit current of the colder cell degrades relatively slowly, it does not go below the original maximum power point current even for 107

118 7 EFFECTS OF NONUNIFORM TEMPERATURE very high temperature differences. On the other hand, there is an equal but opposite change in V oc for the two cells, which results in a nearly equal but opposite change in V at a constant current. As the gain in power for one cell equals the loss in power from the other cell, the total conversion efficiency stays constant. Only at very high temperature differences, where the cells are at unrealistic operating temperatures, does the shortcircuit current of the cold cell degrade below I η [ / % ] V V [ V / V ] efficiency η V1 V 1 V2 V 2 V oc1 Voc1 V oc2 Voc T /[ K ] Figure 7.2: Efficiency and voltages in two silicon cells connected in series with a constant average temperature of T avg = 320 K I Isc1 I sc1 Isc2 I sc2 3.5 I [ A ] I / A T T [/ K ] Figure 7.3: Current and short-circuit currents for two cells at different temperatures connected in series, T avg = 320 K. 108

119 7 EFFECTS OF NONUNIFORM TEMPERATURE A similar approach is used for two cells connected in parallel. The voltage across the two cells must be equal, while the currents are allowed to differ. The following procedure is used: 1) V oc and I sc are calculated for each cell. 2) A suitable range of currents for Cell 1 is established, all below I sc1. 3) The value of V is calculated for each value of I 1. 4) I 2 is found by iteration. 5) The maximum power point is found and used to calculate the cell efficiency. Contrary to the results from series connected cells, the total efficiency does decrease with temperature difference for two cells connected in parallel. This is seen in Figure 7.4, which shows that the efficiency is a relative 12% lower when T = 100 K than when the cell temperatures are equal. As the voltage across the parallel connection must be equal for the two cells, the currents I 1 and I 2 must be adjusted up and down to keep the conversion efficiency constant. However, I 2 quite quickly approaches I sc2, forcing the voltage down. The voltage degradation is shown in Figure 7.5, and is the reason for the reduction in efficiency over a parallel connection. However, as the change is very small and a temperature differential of 100K is highly unlikely, it seems that a temperature differential across a parallel connection should not be a major cause for concern in concentrating PV modules. η [ % / % ] T /[ K ] I I [ A / A ] efficiency η I1 I2 I 1 I 2 Isc1 I sc1 Isc2 I sc2 Figure 7.4: Efficiency, currents and short-circuit currents in two cells connected in parallel with a constant average temperature of T avg = 320 K. 109

120 7 EFFECTS OF NONUNIFORM TEMPERATURE V [ V ] V / V T T [ / K ] V V oc1 Voc1 V oc2 Voc2 Figure 7.5: Voltage and open-circuit voltages in two cells connected in parallel with a constant average temperature of T avg = 320 K. 7.2 USING THE METAL SUBSTRATE AS A HEAT DIFFUSER A simple solution for reducing thermal nonuniformities across the cells is to use a metal substrate between the cells and the cooling system as a thermal diffuser. A thick substrate allows for more lateral conduction to take place and hence a lower temperature difference across the cells. However, the increased uniformity comes at the cost of an additional temperature rise through the substrate, T rise, which is linearly proportional to the substrate thickness and is given by qt & T rise =. (7.5) k Here, q& is the heat flux, t is the substrate thickness and k is the thermal conductivity of the substrate. The temperature through a copper substrate (k = 400 W m -1 K -1 ) of thickness t for q& = 2.5 x 10 4 W m -2 is shown in Figure 7.6. Trise [ K ] t [ mm ] Figure 7.6: Increase in temperature, T rise, through a copper substrate of thickness t for q& = 2.5 x 10 4 W m

121 7 EFFECTS OF NONUNIFORM TEMPERATURE A two-dimensional finite element model was used to investigate how the level of nonuniformity is affected by the substrate thickness. The model is shown in Figure 7.7 together with a typical temperature result obtained using the software package Strand7 [102]. Strictly speaking, an array of axisymmetric jets impinging on a surface should be represented by a three-dimensional model. However, it is conceptually easier to work with the problem in two dimensions, and the results should be comparable. The twodimensional model represents two infinitely long planar jets separated by a distance s. The local heat transfer coefficient is estimated by a linear function (see Section 5.1 for justification). Only the region from the stagnation point of one jet to the centreline between the two jets is modelled, because of symmetry. No region of increased heat transfer between the jets due to interference has been included. There is also a constant heat flux along the bottom and a constant ambient (coolant) temperature. h 1 h 2 t T 1. T 2 q s/2 Figure 7.7: Two-dimensional thermal model of a copper substrate with h avg = 7.5 x 10 4 W m -2 K -1, q& = 2.5 x 10 4 W m -2, h 1/h 2 = 4, s = 10 mm, t = 2 mm and ambient temperature T a = 300 K. The model was solved for a substrate of copper with a range of nozzle pitches (10 mm s 40 mm) and substrate thicknesses (2 mm t 10 mm). For the same average heat transfer coefficient, four different slopes were used for the linear heat transfer coefficient distribution so that h 1 /h 2 = 2.5, 3.0, 2.5 and 4.0. These values were chosen because they represent reasonable nozzle pitches and nozzle diameters. The corresponding nozzle diameters and s/d values for the range of s and h 1 /h 2 used were calculated using the linear correlation for local heat transfer distribution given as Equation 5.1. The resulting values are given in Table 7.1. For each configuration, the temperature difference across the bottom surface, T s = T 2 T 2 where T 1 and T 2 are shown in Figure 7.7, was calculated. The results for q& = 2.5 x 10 4 W m -2 and h avg = 2.5, 5.0 and 7.5 x 10 4 W m -2 K -1 are given in Figures 7.8 through to On solving the model for a range of heat fluxes it was found that T s varies linearly with q&. A simple dependency of h 1, h 2, t or s on T s could not be found. 111