Vertical Mantle Heat Exchangers for Solar Water Heaters

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1 for Solar Water Heaters Y.C., G.L. Morrison and M. Behnia School of Mechanical and Manufacturing Engineering The University of New South Wales Sydney 2052 AUSTRALIA Abstract The characteristics of a narrow gap mantle heat exchanger on vertical tank for solar water heater was investigated. An unwrapped mantle excluding the storage tank was modelled numerically using the CFD modelling package. The predicted results show that the inlet jet impingement induced a small region of localised turbulence on the inlet adjacent walls and the heat transfer in the mantle was dominated by forced convection. The annual performance of a pumped circulation solar water heater with a mantle heat exchanger is being evaluated using TRNSYS solar modelling package to provide initial design sensitivity data for the sizing of mantle heat exchanger solar water heaters. 1. INTRODUCTION Solar domestic water heaters (SDWHs) installed in southern and central Australia require protection from freeze damage. The most common types of thermosyphon SDWHs use a heat exchanger to transfer thermal energy from the collector working fluid to the potable water in the storage tank. By separating the collector working fluid from the potable water, anti-freeze (glycol/water mixture) can be used in the collector loop for night-time freeze protection. Heat exchangers in SDWHs also help to avoid blockage of the collector riser tubes by calcium deposits and sludge, resulting in a longer collector life. Heat exchanger configurations for SDHWs include plain or finned coils or tubes that are either immersed in or wrapped around the storage tank, or as an annular space around a storage tank (known as mantle or jacket heat exchanger). The conventional fin and tube heat exchangers for SDWHs have been adopted in North America, Canada and Europe. However, such designs are very expensive. A mantle heat exchanger (MHE) has the advantage of simplicity, low cost and good thermal performance. MHEs have been developed and used in horizontal tank thermosyphon systems in Australia and other countries and vertical tanks with MHEs are used in Danish low flow SDWHs. Generally, the gap used in the MHEs varies from 5 mm in horizontal thermosiphon tanks to a width of 35 mm in Danish tanks. This paper reports on an investigation of the performance of narrow MHEs on vertical tanks. The overall project aim is to investigate the range of mantle designs from the narrow mantle of this paper to the very wide mantle adopted in Europe. 2. MANTLE HEAT EXCHANGERS FOR SOLAR WATER HEATERS In a MHE used for SDWH, the flow pattern is complicated as the heat transfer may be dominated either by forced convection (pump circulating system), by natural convection or by mixed convection. To model these heat exchangers, a range of heat transfer correlations for both horizontal and vertical MHEs for SDWHs is required. Using an empirical heat transfer correlation for laminar forced flow between two parallel flat plates, Baur et al. (1993) were the first to develop a numerical model of vertical MHEs for SDWHs implemented in the TRNSYS solar modelling package. To match the simulated and measured results, they found that a correction factor of the order of 1.8 was needed in the standard parallel plate heat

2 transfer coefficient correlation. The reason for the higher heat transfer coefficient was thought to be due to mixing induced by the higher velocities near the inlet port and mixed convection in the mantle gap. Baur suggested that more experimental data was needed to develop general heat transfer relations for MHE. Morrison et al. (1998) experimentally and numerically investigated the flow patterns and heat transfer in thermosyphon SDWHs with horizontal MHEs. The study was based on a 5 mm width mantle wrapped around a horizontal tank with the inlet and outlet both located the bottom of the mantle. Their analysis showed good overall heat transfer, but poor stratification in the tank was found due to the location of the inlet port, which resulted in recirculation flow regions. In 1999, Morrison et al. modelled a thermosyphon SDWH with a MHE in the TRNSYS solar simulation package to predict the long-term performance. They found that the predicted monthly energy savings were within two-percentage error points of outdoor measurements. Rosengarten et al. (2001) extended this work by using a rectangular cavity as a simplified geometric representation of a horizontal MHE with a narrow gap (radius ratio > 0.9). The mean Nusselt number correlation was developed as a function of Reynolds number, Prandtl number and cavity dimensions. Their correlation included a stratification correction parameter that described the effect of stratification in the storage tank. Investigations of vertical MHEs with a 33.5 mm mantle gap have been made by Shah and Furbo (1998), based on typical Danish low flow (0.4 kg/min) pumped-circulation SDWHs. Using a Computational Fluid Dynamics (CFD) model validated by experimental measurements, their analysis showed that the heat transfer in the mantle was dominated by natural convection and thus the local Nusselt number was correlated in term of Rayleigh number as follows: x 11 Nu x = Ra x for mantle gap = 33.5 mm and Ra x < 10 (1) Dhydraulic where x is the distance from the top of the mantle. Their modelling also showed that the thermal stratification in the tank was not disturbed by a cooler fluid flowing into the mantle. Shah et al. (1999) investigated experimentally the flow pattern in the mantle using a Particle Image Velocimetry (PIV) system and modelled the heat flux distribution in the mantle using CFD. Good agreement in flow pattern using both methods was obtained. For a high inlet temperature into the mantle, they found that the flow was dominated by buoyancy and complex recirculation paths were observed in the top 20 % of the mantle. When the inlet temperature was lower than the hot mantle fluid, a large re-circulation zone was induced at the top two-thirds of the mantle, resulting in lower heat transfer. The highest heat flux levels, varying from 1 to 1.5 kw/m 2, were found in the top 10 % of the mantle for both cases. Using the CFD simulation results, Shah (2001) developed a new local Nusselt number correlation (eqn. (2)), which was independent of the mantle flow rate, for wide vertical MHEs with a top inlet port w x 10 Nux = 0.28 Rax for Ra x < 10 (2) ri H where w is the mantle gap, r i is the outer radius of the inner wall of the mantle and H is the height of the mantle. This correlation was valid for a wider range of MHE designs than that derived by Shah and Furbo (1998), including the variation of mantle gaps (18 to 54 mm) and height-diameter ratios (1.11 to 6.9). However, this correlation over-predicted the heat transfer for wider mantle gaps, lower height-diameter ratio or higher mantle flow rate cases. These inaccuracies reflect that mixed convection may occur in the mantle and the Reynolds number might need to be included into the heat transfer correlation for the mixed flow operation. More recently, Knudsen and Furbo (2004) continued this research by conducting experimental and numerical investigations on the flow pattern and the heat transfer in vertical MHEs for low-flow SDWHs, with both top and lower mantle inlet positions. When the inlet temperature was lower than Solar 2004: Life, the Universe and Renewables Page 2 of 9

3 the tank temperature at the mantle level, they found that the lower mantle inlet port design helped to maintain the tank thermal stratification as the scale of the recirculation zone at the top of the mantle decreased compared to the top mantle inlet. This was different from the investigations made by Shah et al. (1999) based on an initially mixed tank. Using the CFD modelling results of vertical MHEs with lower inlet port, Knudsen (2004) derived a local Nusselt number correlation by dividing the mantle into an upper half (mixed convection) and a lower half (natural convection). In the upper half of the mantle, the Nusselt number was correlated as a function of Rayleigh number and inlet Reynolds number (due to the impinging jet at the inlet), eqns. (3) and (4). Above mantle inlet: Below mantle inlet: 0.22 z Raz H Nu z = for 2 Re inlet 0.25 z Raz H Nu z = for 2 Re inlet 2 inlet Ra z Re < 10 (3) 2 inlet Ra z Re < 10 (4) 4 4 where H 1 and H 2 are the distance from the mantle inlet to the top of the mantle and to the bottom of the mantle respectively, and z is the vertical distance from the mantle inlet. In the lower half of the mantle, Knudsen found that the local Nusselt number was independent of Rayleigh number and could be expressed in terms of mantle geometry as: A flow Nu z = for A A heat transfer < Aheat transfer flow (5) It was concluded that heat transfer calculated by these correlations showed good agreement with CFD modelling and better predictions were obtained than those reported by Shah (2001). 3. CURRENT PROJECT In this project, a pumped-circulation (1.5 L/min) solar water heater, as shown in Figure 1, with a narrow gap vertical MHE is being investigated. This MHE design differs from the typical Danish MHEs (Shah and Furbo, 1998; Knudsen and Furbo, 2004), which have gap widths approximately 10 times larger and are low flow rate systems. The flow in a narrower gap MHE is evenly spread over the mantle heat transfer surface with approximately uniform velocity (Figure 2b) compared to the recirculation flow at the top 20 % of a wider gap MHE found by Shah et al. (1999) as shown in Figure 2a. Thus, the heat transfer in the narrower gap MHE is expected to distribute evenly over the heat transfer wall and to be dominated by forced convection. This is different from the wider gap MHE investigated by Shah et al. (1999) where natural convection dominates and the heat transfer is concentrated in the top of the mantle. High flow rates used in conventional pumped-circulation SDWHs can maximize the collector efficiency by improving heat transfer in the collector risers, however high flow rate may disturb the thermal stratification in the tank. Both laminar and turbulent models will be investigated in the mantle side. Solar 2004: Life, the Universe and Renewables Page 3 of 9

4 Figure 1 Schematic diagram of SDWHs with narrower gap vertical MHEs. (a) (b) Figure 2 Flow patterns in vertical MHEs. (a) Wider mantle gap and low flow rate (summarised from Shah et al., 1999). (b) Narrower mantle gap and high flow rate. 4. EXPERIMENTAL SETUP The prototype being investigated in this research consists of 2 flat plate solar collectors coupled to a 260 L vertical storage tank with a narrower gap MHE (less than 5 mm). Thermocouples were located at different levels in the storage tank to measure the volume-weighted averaged tank temperatures. To determine the useful energy transferred from the collector fluid to the water inside the tank, mantle flow rate, inlet and outlet temperatures were recorded. A pyranometer was mounted at the angle of 34 on the collector plane to measure the irradiation, which is needed to determine the collector efficiency. Schematic diagram of the instruments locations is shown in Figure 3. Solar 2004: Life, the Universe and Renewables Page 4 of 9

5 Figure 3 Schematic diagram of an outdoor experimental setup, showing locations of instruments in the storage tank and the mantle. 5. NUMERICAL MODEL A three dimensional numerical model of a vertical MHE with narrower gap was modelled using the computational fluid dynamics (CFD) modelling package, FLUENT V6.1. In this preliminary study, a numerical model of a mantle heat exchanger (excluding the storage tank) was developed by assuming a constant heat transfer coefficient on the tank side of the mantle and a uniform temperature in the tank for steady state conditions. Figure 4a shows the boundary conditions specified in this numerical model. Due to large aspect ratio of the mantle (tank diameter divided by mantle gap width), the flow and heat transfer in the curved gap can be approximately by an unwrapped rectangular flow zone (Rosengarten et al., 1999). This simplified geometry is easier and simpler to model in CFD. A total number of 107,136 grid points were used in the computational domain with a uniform mesh except in regions around the inlet and outlet ports where high resolution and non-uniform grids were used. Figure 4b shows the mesh of the CFD model in front view. In this paper, a laminar model was used due to the low Reynolds number of 528 in the mantle. In a high flow rate narrow gap MHE, the heat transfer is dominated by forced convection. As buoyancy has only a minor significant effect on the heat transfer process the Boussinesq approximation was applied in the numerical model in order to obtain faster convergence. The Boussinesq approximation model assumes constant fluid properties in all governing equations except for the buoyancy term in the momentum equation (induces natural convection). A second order upwind discretisation scheme was used to obtain a second order accuracy. Figure 5a shows the predicted velocity vectors in the mid plan of a narrow gap mantle heat exchanger. Even though the flow inside the mantle was laminar (Reynolds number was less than 1000), the inlet jet impingement induced a small region of localised turbulence around the inlet and its adjacent walls. At the inlet corner of the mantle, a small recirculation zone is observed. Therefore, a careful investigation using the turbulence model is needed to accurately predict the flow and heat transfer of MHEs as a large part of the heat transfer occurs close to the inlet port. After the flow impinged on the wall, the hot fluid was driven down uniformly to the outlet by forced convection. The flow in the middle section of the mantle has an approximately constant velocity of 0.05 m/s as expected for high flow rate and narrower gap MHEs used in pumped-circulation SDWHs. In the corners away from the inlet and outlet ports, small dead zone regions are indicated. Solar 2004: Life, the Universe and Renewables Page 5 of 9

6 (a) (b) Figure 4 (a) Boundary conditions in the CFD model. (b) Grid for unwrapped MHE. (a) (b) Figure 5 Velocities in a narrower gap mantle heat exchanger with an inlet temperature of 40 C, a flow rate of 1.5 L/min, for 30 C tank temperature and 50 W/m 2 K heat transfer coefficient on the tank side of the wall. (a) Velocity vectors in the mid plane. (b) Velocity vectors around the inlet port showing impingement flow (side view). The distribution of simulated heat flux on the inner wall of the mantle is shown in Figure 6a for 40 C mantle inlet temperature, tank temperature of 30 C and tank side heat transfer coefficient of 50 W/m 2 K. Approximately 50 % of the heat transfer occurs in the inlet quarter of the mantle. The peak heat flux was adjacent to the inlet due to the high velocity caused by the jet impingement. For the rest of the mantle, the heat transfer was distributed and decreased gradually towards the outlet. Figure 6b shows the temperature contours in the mid plane of the mantle. At the top 80 % of the mantle, the fluid temperature decreases gradually from the incoming hot fluid towards the outlet due to heat transfer through the inner wall of the mantle. In this region, the isothermal lines are perpendicular to the flow direction which indicates that forced convection was dominating in the mantle. For the other 20 % at the bottom of the mantle, the temperature was stratified due to the buoyancy force. Solar 2004: Life, the Universe and Renewables Page 6 of 9

7 (a) (b) Figure 6 Numerical results for the narrow gap mantle heat exchanger with an inlet temperature of 40 C, a flow rate of 1.5 L/min, tank temperature of 30 C temperature and tank side heat transfer coefficient of 50 W/m 2 K. (a) Heat flux contours at the inner wall of the mantle. (b) Temperature contours in the mid plane. 6. MODELLING ANNUAL SYSTEM PERFORMANCE The annual performance of a pumped circulation solar water heater incorporating a mantle heat exchanger requires heat transfer correlations for the heat transfer in the mantle gap and on the tank side of the mantle surface. Models of heat exchangers in hot water storage tanks are available in system modeling programs such as TRNSYS (Kline 2001) and T*SOL (Valentin 2004). The TRNSYS heat exchanger model is written in general for with the tank side heat transfer coefficient specified in standard Nusselt Nu number Rayleigh number Ra correlation form eqn. (6) where the coefficients C and n can be specified to suit the equipment configuration. n Nu = C Ra (6) In the TRNSYS model the heat transfer coefficient on the pumped circulation side of the heat exchanger is modelled using standard pipe flow correlations, however, it can be modified to include new mantle gap heat transfer correlations. The only published work on modelling forced circulation dominated mantle heat exchangers in pumped circulation water heaters was by Baur et al.(1993) who used the developing flow laminar correlation for the mantle gap heat transfer coefficient given in eqn. (7). Solar 2004: Life, the Universe and Renewables Page 7 of 9

8 Nu ( x) Dh RePr 4.9 x = + Dh RePr x Pr 0.1 (7) As mentioned above this correlation was found to under estimate the mantle gap heat transfer coefficient and a correction factor of 1.8 was proposed due to increased heat transfer as a result of mixed flow conditions. For forced convection dominated flow conditions in the mantle the overall heat transfer coefficient is mainly limited by the tank side free convection. The mantle side heat transfer coefficient for forced convection conditions is significantly larger than the tank side heat transfer coefficient. For such conditions the performance of a mantle heat exchanger depends on thermal stratification in the tank over the depth of the mantle. Free convection flow on the tank side of the mantle also depends on the heat flux distribution over the mantle. For the free convection dominated conditions in wide gap mantle heat exchangers the heat flux distribution is significantly higher in the top section of the mantle as shown in Figure 2a while for forced convection in the mantle the heat flux distribution is more uniform as shown in Figure 6a. Changes in the heat flux distribution for different mantle configurations will influence the overall performance of the heat exchanger. For forced convection dominated conditions in a mantle and correspondingly uniform heat flux distribution conventional heat transfer correlations for free convection on vertical surfaces (eqn. (6)) are likely to be applicable on the tank side of the heat exchange surface. Except for the impingement region near the inlet the heat transfer coefficient on the mantle side of the heat transfer surface for approximately uniform heat flux will be larger than the uniform temperature heat transfer correlation (eqn. (7)) used by Baur et al. The correction factor proposed by Baur et al. relative to the constant wall temperature correlation could be due to a combination of the influence of impingement, uniform heat flux and tank side stratification influences. The measurement program commenced in this project will provide operational data on a number of mantle heat exchanger configurations that will be used to quantify the appropriate heat transfer correlations. A TRNSYS model based on correlations given by eqns. (6) and (7) was used to provide initial design sensitivity data for the sizing of mantle heat exchanger solar water heaters. The performance of a directly coupled collector-tank system and two systems based on a mantle heat exchanger are shown in Fig 7. The position of the electric boost element in the mantle tank system was varied to evaluate possible interaction between the mantle heat exchanger and the position of the electrically heated layer above the mantle. The initial simulations indicate that the convective heat transfer coefficient on the tank side of the mantle heat exchange surface can be significantly affected by the location of the electric boost element Energy savings No heat exchanger Mantle heat exchanger with high level boost element Mantle heat exchanger with boost element at top of mantle JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Figure 7 Energy savings for direct-coupled system and mantle heat exchanger systems. Solar 2004: Life, the Universe and Renewables Page 8 of 9

9 7. CONCLUSION A project to investigate the characteristics of narrow gap mantle heat exchangers for vertical tank solar water heaters has been commenced. For narrow gap mantles CFD model results show that the flow distributed approximately uniformly over the heat transfer surface. Although the flow in the mantle was laminar with Reynolds number less than 1000, the inlet jet impingement induced localized turbulence around the inlet and its adjacent walls. More detailed turbulence modelling may be needed to accurately predict the flow pattern and heat transfer in the mantle. In a narrow gap mantle heat exchanger, the heat flux was distributed uniformly over the mantle and was dominated by forced convection. This is different from the mantle heat exchangers for vertical tanks with larger gaps investigated by Shah et al. (1999) where natural convection was dominating flow in the mantle and the heat flux distribution was significantly higher in the top section of the mantle. Changes in heat flux distribution will affect the overall performance of the different configurations mantle heat exchangers. A TRNSYS model of a mantle heat exchanger has been developed based on a conventional vertical wall Nusselt-Rayleigh correlation on the tank side and laminar heat transfer in the mantle gap. Currently, the TRNSYS model based on the Baur et al. correlation for conditions in the mantle is being used to provide initial design sensitivity data for the sizing of mantle heat exchanger solar water heaters. The preliminary investigations indicate that the electric boost element in single tank systems must be positioned well above the top of the mantle heat exchanger in order to avoid interaction between the collector loop and the electric boosting. 8. REFERENCES Baur J. M., Klein S and Beckman W. A. (1993), Simulation of Water Tanks with Mantle Heat Exchangers, Proceedings, ASES Solar93, pp Klein S.A et al. (2001), TRNSYS Version 15 User Manual, University of Wisconsin Solar Energy Laboratory. Knudsen, S. and Furbo, S. (2004), Thermal stratification in vertical mantle heat exchangers with application to solar domestic hot-water systems, Applied Energy, 78, Knudsen, S. (2004), Investigation and optimisation of heat storage tanks for low flow SDHW systems, PhD thesis, Technical University of Denmark, Department of Buildings and Energy, Report 075, ISBN Morrison, G.L., Nasr, A., Behnia, M. and Rosengarten, G. (1998), Analysis of horizontal mantle heat exchangers in solar water heating systems, Solar Energy, 64 (1-3), Morrison, G.L., Rosengarten, G. and Behnia, M. (1999), Mantle heat exchangers for horizontal tank thermosyphon solar water heaters, Solar Energy, 67 (1-3), Rosengarten, G., Morrison, G.L. and Behnia, M. (2001), Mixed convection in a narrow rectangular cavity with bottom inlet and outlet, International Journal of Heat and Fluid Flow, 22, Shah, L.J. and Furbo, S. (1998), Correlation of experimental and theoretical heat transfer in mantle tanks used in low flow SDHW systems, Solar Energy, 64 (4-6), Shah, L.J., Morrison, G.L. and Behnia, M. (1999), Characteristics of vertical mantle heat exchangers for solar water heaters, Solar Energy, 67 (1-3), Shah L.J. (2000), Heat transfer correlation for vertical mantle heat exchangers, Solar Energy, 69 (1-6), Valentin (2004), T*SOL Energies software. Solar 2004: Life, the Universe and Renewables Page 9 of 9