HEAT AND MASS TRANSFER INVESTIGATION IN THE EVAPORATION ZONE OF A LOOP HEAT PIPE

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1 HEAT AND MASS TANSFE INVESTIGATION IN THE EVAPOATION ZONE OF A LOOP HEAT PIPE Mariya A. Chernysheva, Yury F. Maydanik Institute of Thermal Physics, Ural Branch of the ussian Academy of Sciences, Amundsen St., 106, Ekaterinburg, 60016, ussia Tel: (7-343) , Fax: (7-343) , maidanik@etel.ru Abstract Heat and mass transfer investigation in the evaporator of a loop heat pipe (LHP) is a topical task for the development of evaporators with a low thermal resistance. In the paper a two-dimensional model of the flat evaporator active zone is presented. The calculation model assumes the existence of three modes: evaporation into the vapor grooves, volume evaporation in the two-phase region and volume evaporation in the presence of dried regions close to the heating surface. The conditions of mode changing have been formulated. The structural characteristics of the s, such as pore-size distribution, porosity, breakdown radius - were taken into account. The task was solved by the numerical-analytical method. The heat load dependence of the temperature difference T between the evaporator wall temperature and the vapor temperature in the vapor grooves has been obtained. Calculation results have been obtained for two working fluids water and methanol. A comparative analysis of calculated and experimental results for a copper LHP has been carried out. KEYWODS Loop heat pipe,, porous structure, evaporation, heat and mass transfer INTODUCTION A loop heat pipe (LHP) is a two-phase heat-transfer system with a capillary pumping of the working fluid. Detailed descriptions of the LHPs main working principles are presented in [1 3]. The evaporator, a key element of an LHP, determines the serviceability and efficiency of the device. It consists of a body,, vapor grooves and a liquid-passage core. The evaporator is joined to a compensation chamber or a reservoir, into which the liquid from the condenser flows. The heat supplied to the outer surface of the wall penetrates through it and then is transferred through the to evaporating menisci. The generated vapor is collected in the vapor grooves and then is moved off to a condenser by the vapor line. The liquid inflow into the evaporating zone is realized from the reservoir through the. Investigations showed [4 7] that the evaporating menisci, creating a capillary pressure, can be placed both on the groove- surface and inside the. Mathematical models of the heat and mass exchange processes in the evaporation zone take this fact into consideration. But the majority of the models are built on the assumption that the structure is homogeneous [8 14], i.e. they do not take pore size distribution into consideration (Fig. 1), while in actual s pores of different sizes are present. As an instance in Figure 1 the integral and the differential curves of pore size distribution are shown. A porous material has a porosity of 69 %. The pore radius of this varies from 0.5 to 30 µm. Figures et al. [15] have developed a two-dimensional mathematical pore network model for a varying pore-size. In our previous work aimed at the heat and mass exchange processes modeling, the structural characteristics of the were also taken into consideration [16]. This work is a continuation of these investigations. The model is adapted to a new configuration of the evaporation zone. Besides, in the calculating procedure a new specified formulation of the condition for transformation of a liquid pore into a vapor one is used. 79

2 1 p B b А p Fig. 1. Pore size distribution. А differential line, В integral line. 1. PHYSICAL MODEL AND MATHEMATICAL FOMULATION In Fig. a fragment of the LHP s evaporator is presented. According to the applied heat load three different working modes can exist in the evaporation zone. At a low heat flux the evaporating menisci are at the -groove interface (Fig. a). The is completely saturated with liquid and the grooves are filled with vapor. At a high heat flux drying of large pores takes place and a two-phase a b c y y y liquid liquid liquid saturated saturated 8 saturated two-phase vapor vapor vapor region 6 two-phase 6 5 dry region 5 region wall x 1 x 1 x Q Q Q Fig.. Scheme of vaporization modes region where one can find both dry and saturated pores forms (Fig. b). When the heat load increases to a critical value a dry region of the can arise near the hot wall (Fig. c). The thermal resistance of the evaporating zone sharply increases because the two-phase region is separated from the wall by the vapor blanket. Formulas for the full thermal resistance in accordance with the described model of three vaporization modes are presented below. For the first mode: for the second mode: for the third mode: ev = wall + cont + 1f, (1) ev = wall + cont + f, () ev = wall + cont + dry + f. (3) 80

3 In formulas (1) (3) the contact thermal resistance cont is included. It considers the imperfection of the thermal contact between the and the body. According to ef. [16], the value of cont can vary from to m K/W. Pore drying can be caused by two things. Firstly, by the boiling up of the overheated liquid. According to the nucleation evaporation theory, the formation of a viable vapor bubbles of radius r nucl is possible only if the liquid is overheated sufficiently with respect to its equilibrium state T sh. The lower boundary of the overheating T nucl is determined by the formula (4): σts Tnucl =. (4) ρ r h v nucl The second reason for the drying of pores with radius r can be an excessive hydraulic load P lhp on the meniscus, which exceeds its capillary potential P c : σ P lhp,. (5) r where P lhp is the value of the total pressure drop in the LHP. It includes the pressure losses in the region external with respect to the evaporation zone and the pressure losses in the evaporation zone: hv P lhp = Pext + Pev_ zone. (6) Conditions of the transfer from surface evaporation to vaporization in a two-phase region are described by inequalities (7) and (8) and conditions of the vapor region formation by inequalities (9) and (10): Tsh Tnucl ( max ) (7) Plhp Pc ( max ), (8) Tsh Tnucl ( min ) (9) Plhp Pc ( min ). (10) The mathematical model is based on the following assumptions. The evaporation regime in the evaporation zone is stationary and stable. There is a local thermal equilibrium between the porous structure and the working fluid. The motion of the working fluid in the conforms to the Darsy rule. Phase permeabilities for vapor and liquid flows in a two-phase region are determined by the correlation between the number and the size of the pores, which are filled correspondingly with vapor or liquid. The prevailing direction of the liquid and vapor flow is shown in Fig. with arrows. In the evaporation zone the liquid flow is directed along the groove- surface. In the two-phase thermal region the vapor flow moves along the normal to the channel surface. The interfacial equilibrium is maintained by the surface tension forces. The computation model is two-dimensional. The left and right borders of the computation domain are symmetry lines. The convective component of the heat transfer in the is small as compared to the conductive component. The thermal conductivity and effective thermal conductivity are determined by formulas (11) and (1):.1 k = k comp (1 ε )(1 + ε ), (11) k eff = k + εk. (1) l Under these assumptions, the governing equations for vapor and liquid phases are as follows. Liquid and vapor motion in one-phase regions, i.e. where the is saturated with liquid or filled with vapor, are described by the equations: K K ul = P1 f, uv = P1 f. (13) µ l µ v For the two-phase zone with allowance for the phase vapor and liquid permeabilities we have: 81

4 K l ul = P f µ l K, v uv = P f µ v. (14) Phase permeabilities are determined by the equations: K v max K * = * 1 F ( ) max min F d ; F d K l = * F d K min ; * F ( ) max F d min (15) where * is a current value of a boundary meniscus radius. A minimal value of radii determined from the eq. (4) and eq. (5) is used as quantity of the boundary radius *. Pore size distribution is approximated by the equation: ( 1 ) ( ) 1 1 F() = p p exp C1 exp C π χ 1 χ + 1 π χ 1 χ, (16) where 1 p, 1 p are pick pore sizes, χ 1, χ and C 1, C are approximation coefficients. The energy equations for the evaporator wall and the single phase are: The energy equation for the two-phase region is: T wall = 0 T = 0. (17) ' keff T = qev, (18) where q`ev is the volume heat sink. The heat absorption intensity is supposed to be the same at any point of a two-phase region. The boundary conditions, common to all, regimes are: At the boundary 1-: k wall Twall (19) = qin At 1-7 and -9: T wall = 0, T = 0, ul,x = 0, u v,x = 0. (0) x x At 7-9: T = and at 8-9: Tv Q ul, y = ρl hhv N gr Lgr L89. (1) The vapor temperature in the groove is defined as: T v dt dp P = Tv, cond + v, () where T v,cond is the saturation temperature in the condenser. A vapor pressure drop P v includes a pressure drop in the grooves, in the vapor line and in the vapor section of the condenser. The specific boundary conditions are the following. 8

5 At 5-6 and 6-8 for a saturated : T k eff = qev, qev T uv, y =, k eff = qev, hhv ρv x qev uv, x = (3) hhv ρv T At 5-6 for a dry : = 0, u v, y = 0. (4) At 3-4 for a saturated : and for a dry : Twall T kwall = keff, (5) T T k wall k wall =. (6) At the boundary between a single-phase region and a two-phase one: T T keff = k. (7) n n The task was solved by the numerical-analytical method. A results of solving the set equations for each mode is the temperature field in the evaporation zone. The intensity of heat exchange processes was evaluated by the temperature difference T between the wall temperature T wall and vapor temperature in the groove T v. As T wall the average temperature on the external surface of the evaporator body was used, i.e. at the boundary 1-.. ESULTS AND DISCUSSION Numerical results were obtained for three identical copper LHPs with flat evaporators having similar overall dimensions: the length was 80 mm, the width was 40 mm and the thickness was 7 mm. The wall thickness was 0.5 mm, the active zone length was 40 мм. The length of the vapor and the liquid lines amounted to 350 mm and 900 mm respectively. Their internal diameter was 4 mm. The LHP was placed horizontally. The heat sink and the ambient temperatures were 0 C. The geometrical parameters of a typical domain were as follows: L 1- = 1.6 mm, L 1-3 = 0.5 mm, L 3-5 = 0.4 mm, L 5-6 = 0.9 mm, L 5-7 = 1.4 mm. The LHPs had different s and working fluids. The main characteristics of the porous materials and the corresponding working fluids of these LHPs are presented in Table 1. Table 1. The distinctive features of the LHPs Characteristics LHP 1 LHP LHP 3 Porosity ε,% Brake-down radius b, µm Working liquid water methanol methanol The calculation results are presented in Fig. 3 as a dependence of Т on the heat load for three LHPs. For the evaluation of the model quality, the graph contains the experimental data as well. The satisfactory coincidence of calculation and experimental results suggests that the model proposed describes adequately the vaporization processes in the LHP evaporation zone. 83

6 LHP LHP 1 LHP 3 Fig. 3. Temperature difference T dependence on the heat load Q. experimental data, calculated data One should point out different behavior of lines T = f(q) for a water LHP and methanol LHPs. Thus, the line for a water LHP has a linear dependence in the whole range of the heat load change. A monotonous growth of the temperature difference in the evaporation zone indicates the lack of critical changes in the character of heat and mass exchange processes. Calculation results show that the twophase evaporation region formation takes place under a heat load of about 15 W. The vaporization regime in a two-phase thermal region is retained up to 100 W. The overheating value in the whole range of Q turns out to be insufficient for the formation of totally dried areas. It is confirmed by the data in Table, where values of nucl calculated by eq. 4 for some overheat values are presented. Table. A dry pore size (µm) for different values of the superheat for T s = 80 C superheat, C liquid water * 1.87 * 1.50 * methanol As for the results for methanol LHPs, it is obvious that the lines T = f(q) are different in general, although under low heat loads all three lines behave similarly and are close to each other. The temperature differences here are practically the same. Then, starting from W the behavior of the methanol LHP s lines changes and the lines go sharply upward. According to the calculation, the reason for such changes is the dried areas formation in the wall region of the. As Q continues to increase, these areas form a dry blanket between the wall and two-phase evaporation region. The criticality of such a situation is intensified by the fact that the layer of the situated under the vapor line becomes totally dried. As a result a quite large area appears to be excluded from the active evaporation heat exchange. This leads to redistribution of the heat flows, an increase of the thermal load on a fin, where evaporation takes place, and a sharp growth of the temperature difference T between the wall and the vapor. A correlation of the methanol LHPs superheats (see Fig. 3.) with the sizes of pores which are dried during these superheats (see Table ), confirms the conclusions made. It becomes clear that in contrast to the water LHP the transfer to the third evaporation regime exists in methanol LHPs and it starts at quite low heat flows. Thus the obtained results indicate that thermophysical properties of a working fluid influence the vaporization character and the heat exchange intensity in the LHP evaporation zone. 84

7 As the structural characteristics of the investigated LHPs are different, the dynamics of the pores drying process under the effect of a heat load is different too. It is obvious that on the whole methanol lines behavior is similar. At the same time the T sharp growth of T of LHP begins under the lower heat loads. As calculations show, the evaporating zone transformation in LHP occurs with some delay because of the structural features of its. As a result, the overheating value in the evaporation zone of LHP is higher than that of LHP 3 at the same heat load. 3. CONCLUSION A two-dimensional mathematical model of the evaporating zone of an LHP s flat evaporator is developed. Solutions of the heat and mass transfer problem are obtained for three modes of vapor generation evaporation at the -groove interface, evaporation in the two-phase zone, evaporation in the two-phase region over the vapor blanket. Structural characteristics like porosity and a pore size distribution of a porous material are taken into account. This model was used for investigation of the heat-exchange process of a copper LHP with water and methanol as working fluids. The effect of working liquid properties on the evaporation mechanism was found. Simulation and experiment data have been compared. It is shown that the character and the intensity of heat exchange depend on the structural characteristics of capillary porous material. A satisfactory agreement of the results of calculation and experiment shows that the suggested model gives an adequate description of evaporation processes in the LHP s evaporation zone. Acknowledgements This work was supported by the ussian Foundation for Basic esearch, Grant No a. NOMENCLATUE c p specific heat at constant pressure, J/(kg K) k thermal conductivity, W/(m K) K permeability, m h hv latent heat of vaporization, J/kg L length, m Q heat load, W q in applied heat flux, W/m - thermal resistance, K/W, r pore radius, m α heat exchange coefficient, W/(m K) ε porosity µ dynamic viscosity, Pa s ρ density, kg/m 3 Subscripts ext cond cont dry gr q nucl l ll v vl wall 1f f external condensation contact dry vapor groove active zone (heat input zone) nucleation liquid liquid line vapor vapor line evaporator wall (or case) mono-phase (saturated with liquid) two-phase 85

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