Correlation to predict heat transfer of an oscillating loop heat pipe consisting of three interconnected columns

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1 Available online at Energy Conversion and Management xxx (2008) xxx xxx Correlation to predict heat transfer of an oscillating loop heat pipe consisting of three interconnected columns Gökhan Arslan, Mustafa Özdemir * Istanbul Technical University, Mechanical Engineering Faculty, Istanbul, Turkey Received 3 June 2007; accepted 14 January 2008 Abstract In this paper, heat transfer in an oscillating loop heat pipe is investigated experimentally. The oscillation of the liquid columns at the evaporator and condenser sections of the heat pipe are driven by gravitational force and the phase lag between evaporation and condensation because the dimensions of the heat pipe are large enough to neglect the effect of capillary forces. The overall heat transfer coefficient based on the temperature difference between the evaporator and condenser surfaces is introduced by a correlation function of dimensionless numbers such as kinetic Reynolds number, c p DT/h fg and the geometric parameters. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Oscillating loop heat pipe; Overall heat transfer coefficient; Kinetic Reynolds number 1. Introduction Heat pipes are widely used in many industrial applications today. Their investigation, beginning with the twophase closed thermosyphons (TPCTs), has continued to the loop heat pipes and miniature heat pipes. Several types of heat pipes having different working conditions and geometries are manufactured. In recent years, researches have been conducted on oscillating heat pipes. A general review on heat pipes including their developments is made by Vasiliev [1]. Vasilev summarizes the developments on conventional heat pipes, miniature and micro heat pipes, loop heat pipes, spaghetti heat pipes, pulsating heat pipes and some heat pipe applications. Maydanik [2] also discusses recent developments in loop heat pipes and their applications. Investigations on the heat transfer characteristics of TPCTs have still continued by several investigators. Noie [3] studied, experimentally, the effects of working fluid * Corresponding author. Tel.: x2544; fax: address: ozdemirmu4@itu.edu.tr (M. Özdemir). filling ratios, input heat transfer rates and evaporator lengths on the effectiveness of thermosyphon type heat pipes. Said and Akash [4] also studied experimentally the effects of the tilt angles of TPCTs on the heat transfer performance of heat pipes having a wick and no wick. They showed that the overall heat transfer coefficient varied with tilt angles. Farsi et al. [5] conducted an experimental and theoretical investigation of the transient behavior of TPCTs. Kiatsiriroat et al. [6] studied, experimentally, the performance of a thermosyphon using binary working fluids, ethanol water and TEG water. The boiling behavior of the binary working fluid changes the performance of the heat pipes. Ethanol water mixtures give a higher heat transfer rate than water with a low temperature heat source. Many recent researches on different types of heat pipes and their applications are available in the literature. The open and closed-end looped pulsating heat pipes are the most popular research areas. The working fluid in heat pipes consisting of capillary meandering channels oscillates between the evaporator and condenser regions. Phase change and capillary induced oscillation in these types of heat pipes increase the heat transfer between the evaporator /$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi: /j.enconman

2 2 G. Arslan, M. Özdemir / Energy Conversion and Management xxx (2008) xxx xxx Nomenclature c p d 1 d 2 d 3 h fg specific heat diameter of brass connection pipes inner diameter of glass columns outer diameter of heater and cooler tubes latent heat k heat conductivity l characteristic length l c heat pipe height (Fig. 1) l d distance between centerlines of evaporator and condenser (Fig. 1) l o distance between centerlines of evaporator and free column (Fig. 1) l 1 temperature probe location (Fig. 1) l 2 temperature probe separation (Fig. 1) P _Q; Q t instantaneous vapor pressure heat input, heat load time T h time averaged heater temperature T c time averaged cooler temperature T h time and space averaged heater temperature T c time and space averaged cooler temperature T w cooling water set temperature DT ð¼ T h T c Þ temperature difference U overall heat transfer coefficient V vapor volume z vertical coordinate, instantaneous liquid column heights z 01, z 02 oscillation axis of liquid columns Greek symbols q, q l, q g density, liquid density, vapor density x radial frequency l dynamic viscosity dimensionless parameters p i and condenser effectively (Sakulchangsatjatai et al. [7], Rittidech et al. [8]). The heat transfer rate between the surfaces of the evaporator and condenser and the fluid is increased by the phase change and the fluid motion if an oscillating motion of the fluid occurs at the evaporator and condenser of the heat pipe. Özdemir [9] has studied, experimentally, a different type of oscillating loop heat pipe consisting of three interconnected columns. Different from loop heat pipes, the existence of the third column causes large amplitude oscillations in the evaporator and condenser regions. He restricted his research by the heat load so that the phase change process remained stable. In this paper, the experimental study on the same experimental setup introduced by Özdemir [9] is conducted in a wide range of heat load. The heat transfer behavior of such oscillating loop heat pipe is investigated and introduced by using dimensionless numbers such as kinetic Reynolds number, c p DT/h fg and the geometric parameters. 2. Experimental setup In this study, the experimental set up used by Özdemir [9] is modified in order to measure the heated wall temperature and, simultaneously, to measure the vapor pressure and vapor volume. The experimental set up is constructed by connecting three vertical glass pipes with each other using brass pipes and fittings. The vertical glass pipes are named evaporation column (1) condensation column (2) and free column (3) as shown in Fig. 1. The geometric sizes are given in Table 1. The evaporation, condensation and free columns are made of glass tubes of 35.2 mm inner diameter. The glass columns are then interconnected by brass tubes of 35.8 mm inner diameter. The other geometric sizes are listed in Table 1. The vapor pressure is measured by a Validyne differential pressure transducer at the mid-point of the top brass tube between the evaporation and condensation columns. The temperatures of the vapor and liquid phases are measured using four NiCr type temperature probes at the cross sections as shown in Fig. 1. The whole system shown in the figure is thermally insulated except for a narrow vertical stripe on the glass tubes. Thus, the oscillating motion of the liquid columns can be recorded by the camera by means of the vertical stripes on the glass tubes. The mean temperature of the whole system is approximately just over 85 C, so the water mass diffusion to air becomes significant at the liquid-air interface in the third column. Thus, a purposely made vapor trap was fitted at the outlet of the third column in order to minimize the mass loss. z 3 8 d 2 l l o l z 1 l d d Fig. 1. Experimental setup, (1) evaporator column, (2) condenser column, (3) free column, (4) heater tube, (5) cooler tube, (6) pressure transducer, (7) temperature probes, (8) vapor trap. 6 z 2 l c

3 G. Arslan, M. Özdemir / Energy Conversion and Management xxx (2008) xxx xxx 3 Table 1 Geometrical sizes of the experimental setup mm Distance between the centerlines of evaporator and condenser, l d 345 Distance between the centerlines of evaporator and free column, l o 445 Heat pipe height, l c 610 Temperature probe location, l Temperature probes separation, l Inner diameter of the glass columns, d Diameter of the brass connection pipes, d Outer diameter of the heater and cooler tubes, d 3 18 The heater and cooler tubes are placed concentrically in the evaporator and condenser columns. The heater and cooler tubes are made of copper tubes 730 mm long and 18 mm in outer diameter. As shown in Fig. 2, there is an electric heater inside the heater tube, and the surface temperature is measured at ten locations by NiCr type thermocouples. Four thermocouples are located on the heater section of the heater tube in order to measure the temperature of the heated surface. All the cables of the electrical heater and the thermocouples are taken out by passing them inside the tube. The cooler tube is made of two concentric copper tubes. Cooling water enters the inner tube, which is 8 mm in diameter, and leaves from the outer tube, which is 18 mm in diameter. Nine thermocouples are welded on the cooler surface, and the leads are taken out by passing them through the cooling water. The thermocouple locations on the heater and cooler tubes are listed in Table 2. A computer controlled data acquisition system (Keithley 2700 and 7700 multiplexers) is used to collect the temperature and pressure data l c =610 1 z Fig. 2. The heater and cooler tubes Table 2 Thermocouple locations on the heater and cooler tubes Heater thermocouples Cooler thermocouples No z 1 [mm] z 1 [mm] No z 2 [mm] z 2 [mm] T T T 1 36 T T T T T T T T T T T T T T T T The vapor volume is determined by the data extracted from the video records of the liquid columns. An optical sensor (CNY 70) is placed on the free column in order to measure the pressure and the liquid column height, simultaneously. The signals of the optical sensor and the pressure transducer are recorded with same multiplexer. Then, the measured liquid column height is matched with the data collected by the video records. The air is discharged by filling the experimental set up with hot water completely. After marking the water level of the free column, the electrical heater is switched on. The cooling water is supplied by an adjustable thermostatic bath, Neslab, RTE-300. The water inside the evaporator begins to boil, and the vapor accumulates in the upper side of the set up. At this time, 0.5 l of water is taken out of the system to prevent overflow. After the vapor region extends to the glass columns, the whole system starts to oscillate with a certain frequency. At the end of an experiment, 0.5 l of water is added back to the system, and the level of the third liquid column is checked Uncertainty analysis Uncertainty in the experimental data is considered by identifying the main sources of errors in the primary measurements such as current, voltage, height, pressure and temperature. The power supplied to the heater in the evaporator column is determined by monitoring the applied voltage and current with accuracy of 1%. Thus, the uncertainty in the heat input rate is calculated as 1.4%. The heights of the liquid columns are manually read on the video recordings. Hence, the picture quality and the thickness of distance markers cause an uncertainty of ±4 mm in the column height readings. The effective vapor pressure is measured by a Validyne differential pressure transducer with an accuracy of 0.25%. The temperatures are measured by a computer controlled data acquisition system with an accuracy of ±1 C. The number of collected temperature and pressure data is 512 readings at any location for every experimental case. 3. Experimental results and discussion The water mass is kept constant at 1.76 ± 0.14 kg in the thirty three experiments reported in this study. The input power and cooling water temperature are varied in the

4 4 G. Arslan, M. Özdemir / Energy Conversion and Management xxx (2008) xxx xxx range of W and C, respectively. The cooling water temperature can be changed at an interval of 8 C for a certain DC power input. Otherwise, the vapor volume increases or decreases to some extent when the oscillation collapses. Nucleate boiling occurred or is not observed in the experiments, according to the heater power and cooling water temperature after oscillation begins. In the cases that nucleate boiling can not be observed, evaporation mainly takes place on the wetted heater surface as remarked by Özdemir [9]. In these cases, the heater surface is dried out by the downward motion of the liquid column. On the other hand, nucleate boiling and a bubbly flow regime are observed in most of the experiments reported in this study The motion of the liquid columns and pressure volume variation of the vapor phase The time variations of the liquid column heights are seen in Fig. 3 for the case of heater power ± 7 W and cooling water temperature 87 C. The oscillation axis of the third column is higher than that of the other columns, different from the study of Özdemir [9]. The total water amount is more than in the experiments of Özdemir [9], so that, the oscillation axis of the third column is raised. The fitted curves to the experimental data of the column heights are harmonic functions as follows; z [cm] sensor t [s] Fig. 3. The position-time curves of oscillating liquid columns, _Q ¼ 227:05 W, Cooling water set temperature = 87 C. z 1 z 3 z 2 z 1 ðtþ ¼31:2 þ 9:7 cosð4:87t 2:6Þ z 2 ðtþ ¼29:8 þ 9:7 cosð4:87t þ 1:7Þ z 3 ðtþ ¼51:2 þ 7:2 cosð4:87t 0:5Þ Three data points taken from the optical sensor located at z 3 = 45 cm of the third column are also seen in Fig. 3. Thus, the third column data and the pressure data taken from the pressure transducer connected to the same multiplexer with the optical sensor are approximately recorded in a simultaneous manner. For this case, the time variation of the vapor pressure is seen in Fig. 4 with the fitted curve defined by two harmonic functions as follows; PðtÞ ¼102694:8 þ 895:3 sinð4:87t 4Þþ407 sinð9:74t 1:3Þ Pa ð2þ As seen in the above equation, the second radial frequency is two times that of the first one. The vapor volume can be calculated easily by the formula below. Here, the first and second column heights are known from their fitted curves (Eq. (1)), V ¼ pd2 1 4 ðl d þ d 2 Þþ p 4 ðd2 2 d2 3 Þ½ðl c z 1 Þþðl c z 2 ÞŠ ð3þ Therefore, according to the fitted curve of the pressure data and the calculated vapor volume from the fitted curves of the column heights, the variation of the vapor pressure with vapor volume is seen in Fig. 5. There is a time delay between the multiplexer channels connected to the optical sensor and the pressure transducer. This time delay between the measurements of the optical and pressure signals is s. On the other hand, there is 0.11 s between two signals of the optical sensor. Because of these reasons, a time delay of approximately ±0.2 s may be occurring between the vapor and pressure data. If we consider a time delay of 0.1 s or +0.1 s, the variation of the pressure and volume is different from that of Fig. 5 as shown in Fig. 6a and b. As seen from the above figures, the possible error of ±0.1 s causes a big difference in the P V relation, so the vapor pressure and vapor volume should be measured by a more accurate way. ð1þ P [Pa] Fig. 4. The time variation of vapor pressure and the fitted curve, _Q ¼ 227:05 W, Cooling water set temperature = 87 C. t [s]

5 G. Arslan, M. Özdemir / Energy Conversion and Management xxx (2008) xxx xxx 5 P [Pa] V [lt] Fig. 5. Vapor pressure versus vapor volume Time averaged surface temperatures of the heater and cooler Time averaged surface temperatures of the heater tube are shown in Fig. 7. The section from 236 mm to 408 mm corresponds to the electric heater part of the heater tube and the rest to the unheated part of the heater tube. On the electric heater section, the surface temperatures for all the cases peak approximately at the mid-point of the heater. The surface temperatures in the vapor section and the temperatures on the electric heater increase with increasing heat input as expected. The time and space averaged surface temperature of the electric heater part of the heater tube is calculated by using the measured values of the temperatures, T 3, T 4, T 5 and T 6 on the heater tube. Time averaged surface temperatures of the cooler tube are shown in Fig. 8. It can be clearly seen that the temperature varies slightly, averaging almost to the values of the cooling bath water temperature Heat transfer coefficient in evaporator and condenser The surface temperatures of the heated and cooled sections of the heater and cooler tubes can be measured depending on the position and time. Some thermocouples remain in the vapor or liquid phase, because of the t= t=+0.1 s P [Pa] P [Pa] V [lt] V [lt] Fig. 6. Pressure versus volume (a) time delay Dt = 0.1 s, (b) time delay Dt = 0.1 s T w =80 o C 200 Th [ o C] Exp. No:6,Q=230.1 W Exp. No:30,Q= W Exp. No:29,Q=212.5 W Exp. No:31,Q=151.2 W z [mm] Fig. 7. Time averaged surface temperatures on heater tube. Cooling water set temperature = 80 C.

6 6 G. Arslan, M. Özdemir / Energy Conversion and Management xxx (2008) xxx xxx Q= W 84 Tc [ o C] Exp. No:9,Tw=78 C Exp. No:11,Tw=86 C Exp. No:10,Tw=82 C Exp. No:30,Tw=80 C z [mm] Fig. 8. The time averaged surface temperatures on the cooler tube. _Q ¼ 164:05 W. oscillation of the liquid columns. Temperatures and the liquid column heights can not be measured simultaneously so it is not possible to be certain that a temperature location is in the vapor or liquid regions. Considering the time and area averaged surface temperatures of the heated or cooled surfaces and defining an overall heat convection coefficient for the evaporator and condenser are seen as a good way to characterize the heat transfer. On the other hand, liquid water enters the evaporator and exits the condenser as a compressed liquid. Therefore, in the evaporator, water is heated first up to the saturated temperature, and then, it boils. It is impossible to differentiate experimentally between the heat input as heat spent for sensible heat transfer and the heat input as spent for boiling heat transfer. There is the same trouble in the condenser section to determine the heat convection coefficient Overall heat transfer coefficient The heat convection coefficients in the evaporator and condenser can not be determined experimentally because of the problems mentioned in the previous section. If we consider the time and space averaged temperatures of the heated and cooled surfaces and the heat input, an overall heat transfer coefficient for the whole heat pipe can be defined as follows; _Q U ¼ ð4þ A h ðt h T c Þ The heat transfer between the evaporator and condenser is calculated by subtracting the total heat loss from the measured heat input, since it is impossible to measure the heat carried away by the cooling water accurately. The heat losses caused by evaporation from the air-liquid interface on the third column and by the loss from exposed surfaces are estimated to be 15% of the heat input. Heat transfer between the evaporator and condenser can be determined by using dimensional analysis. First, z 01 we consider the adiabatic section between the evaporator and condenser as shown in Fig. 9. The tube diameter, d 1, nominal length l between the evaporating and condensing interfaces and the oscillation amplitude of l as z o1 + z o2 are taken as the characteristic dimensions during the heat transfer. The characteristic length l, is the distance between the oscillation axis of the liquid columns. It is calculated as follows. l ¼ l d þðl c z 01 Þþðl c z 02 Þ The other physical quantities that have a role in the heat transfer are chosen as q l q g ffi q l ; c p ; DT ¼ T h T c ; U; x; l; k and h fg. After applying the Buckhingam p theorem to find the dimensionless numbers, we easily get the following numbers, p 1 ¼ Ul k ; p 4 ¼ d 1 l ; p 2 ¼ Re w ¼ d2 1 x m ; p 3 ¼ c pdt h fg ; p 5 ¼ z o1 þ z o2 ; p 6 ¼ Pr ¼ c pl l k The dimensionless number based on the overall heat transfer coefficient can be written as a function of the other dimensionless numbers. The fourth, fifth and sixth dimensionless numbers are taken as constants for all the experiments, so the first dimensionless number can be defined as a function of the others as follows; p 1 ¼ Ul k ¼ f ðre w; p 3 Þ l Fig. 9. The characteristic dimensions in the vapor region. d 1 z 02 ð5þ ð6þ

7 G. Arslan, M. Özdemir / Energy Conversion and Management xxx (2008) xxx xxx = = = Rew Fig. 10. The variation of the dimensionless overall heat transfer coefficient with kinetic Reynolds number and the third number. Table 3 All physical quantities considered in the correlation equation Exp.No _Q ½WŠ T w [ C] T h ½ CŠ T c ½ CŠ U[W/ m 2 K] w [rad/s] z o1 [m] z o2 [m] In Fig. 10, the variation of the dimensionless overall heat transfer coefficient with kinetic Reynolds number and the number based on temperature difference and latent heat is shown. In the experiments, the third dimensionless number can not be held as constant directly, but some experiments can be classified with this dimensionless number as seen in Fig. 10. By considering the classified data, a correlation equation for the dimensionless overall heat transfer coefficient can be suggested as follows; p 1 ¼ ARe b w pc The correlation equation can be found by using the multi-parameterized regression analysis as seen in the following, p 1 ¼ 4: Re 1:98596 w p 0: ð8þ All the experimental data that are used in obtaining the correlation equation are given in Table 3. The experimental and correlating dimensionless parameters representing the overall heat transfer coefficient are seen in Fig. 11. Bycomparing the experimental values and the correlation (Eq. (8)), the correlation equation can represent 17 experimental Experimental values - π R 2 = Correlated values - π 1 ð7þ Fig. 11. Dimensionless overall heat transfer coefficient and the correlation equation.

8 8 G. Arslan, M. Özdemir / Energy Conversion and Management xxx (2008) xxx xxx data with an error of 10% and 25 experimental data with an error of 15%. 4. Conclusion In this paper, heat transfer in an oscillating loop heat pipe is investigated experimentally. The overall heat transfer coefficient of the oscillating loop heat pipe is investigated and introduced by using dimensionless numbers such as the kinetic Reynolds number, c p D T/h fg and the geometric parameters. We try to determine the relation between the vapor pressure and volume, experimentally. The time delay in the measurement of the third column height and vapor pressure is approximately ±0.2 s, and the variation behaviour of the vapor pressure and volume is strongly affected by a possible error of ±0.1 s. Thus, we have observed that the vapor pressure and vapor volume should be measured by a more accurate way. We can control only the heat input and the cooling water temperature. The oscillation frequency, surface temperatures, oscillation amplitudes etc. change automatically. The parameters that affect the self induced oscillation frequency can be determined by theoretical studies. The theoretical studies on the parameters affecting the bahaviour and performance of the present heat pipe configuration are continuing. References [1] Vasiliev Leonard L. Heat pipe in modern heat exchangers. Appl Therm Eng 2005;25:1 19. [2] Maydanik Yu F. Loop heat pipes. Appl Therm Eng 2005;25: [3] Noie SH. Heat transfer characteristics of a two-phase closed thermosyphon. Appl Therm Eng 2005;25: [4] Said SA, Akash BA. Experimental performance of a heat pipe. Int Commun of Heat and Mass Trans 1999;26: [5] Farsi H, Joly JL, Miscevic M, Platel V, Mazet N. An experimental and theoretical investigation of the transient behavior of a two-phase closed thermosyphon. Appl Therm Eng 2003;23: [6] Kiatsiriroat T, Nuntaphan A, Tiansuwan J. Thermal performance enhancement of thermosyphon heat pipe with binary working fluids. Exp Heat Transf 2000;13: [7] Sakulchangsatjatai P, Terdtoon P, Wongratanaphisan T, Kamonpet T, Murakami M. Operation modeling of closed-end and closed-loop oscillating heat pipes at normal operating condition. Appl Therm Eng 2004;24: [8] Rittidech S, Dangeton W, Soponronnarit S. Closed-ended oscillating heat-pipe (CEOHP) air-preheater for energy thrift in a dryer. Appl Energy 2005; doi: /j.apenergy [9] Özdemir M. An experimental study on an oscillating loop heat pipe consisting of three interconnected columns. Heat and Mass Transf 2007;43: