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Hysteresis phenomena in loop heat pipes
Applied Thermal Engineering 27 (2007) 962–968 www.elsevier.com/locate/apthermeng
Hysteresis phenomena in loop heat pipes Sergey V. Vershinin, Yury F. Maydanik
*
Institute of Thermal Physics, Ural Branch of the Russian Academy of Sciences, Amundsen st. 106, Ekaterinburg 620016, Russia Received 28 April 2006; accepted 21 August 2006 Available online 24 October 2006
Abstract Testing of loop heat pipes (LHPs) has shown that the heat-load dependence of the operating temperature is not always unambiguous. It may have a hysteresis nature. It has been found that temperature hysteresis is connected with changes in the liquid distribution between the compensation chamber (CC) and the condenser. Analysis makes it possible to distinguish three types of temperature hysteresis. In the first case this redistribution is caused by the change in the amount of the parasitic heat flow that penetrates into the CC, which in its turn is a result of heat-transfer hysteresis in the evaporation zone. In the second, temperature hysteresis is connected with the liquid metastable state, which leads to a delay of formation of the vapor phase in the compensation chamber. The reason for hysteresis of the third type is the change of the initial liquid distribution in an LHP during a start-up. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Loop heat pipe; Capillary structure; Evaporation; Temperature hysteresis
1. Introduction A loop heat pipe is a hermetic closed loop consisting of an evaporator, in which a wick is located, and a condenser connected by separate channels for vapor and liquid (Fig. 1). Temperature hysteresis in an LHP is a phenomenon which under constant external conditions manifests itself as an ambiguous dependence of the operating temperature on the heat load under cyclic changes of the latter. The phenomenon of hysteresis is observed in thermodynamic systems capable of being in metastable states and exposed to the action of periodically changing external conditions. The gist of the phenomenon consists in the fact that the physical quantities characterizing the current state of a system depend not only on the magnitude of the external action, but also on its preceding states, therefore the system reaction to external actions of the same magnitude may be different. The reason for hysteresis is processes which at certain external actions proceed irreversibly.
*
Corresponding author. Tel.: +7 343 267 87 91; fax: +7 343 267 87 99. E-mail address: [email protected] (Y.F. Maydanik).
1359-4311/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2006.08.016
In the heat-exchange sphere the best known and investigated system where hysteresis is observed is a liquid-saturated capillary-porous structure with pores of irregular dimensions under the action of a heat flow. Such an action results in the process of evaporation or boiling, which is investigated, as a rule, at a constant pressure. The hysteresis character has for instance, a dependence of the temperature of the wall through which heat is supplied on the magnitude of the heat load. The reason for heattransfer hysteresis during boiling in this case is capillary hysteresis. As a result of experimental investigations, two main types of hysteresis were distinguished. One of them is connected with the development of boiling in the wall layer of a porous coat (forward loop) [1], the other – with its crisis (reverse loop) [2,3]. Besides, hysteresis was discovered during the boiling-up of a liquid [4]. It turned out that on the same coat, depending on the heat load magnitude, one could observe different types of hysteresis, and the character of their manifestation depended on the size of pores of the capillary structure and the degree of their irregularity [5–7]. Later the results of investigating hysteresis in capillary-porous structures were generalized, in particular, in
S.V. Vershinin, Y.F. Maydanik / Applied Thermal Engineering 27 (2007) 962–968
Fig. 1. Principal scheme of an LHP.
the paper by Poniewski [8], who, in the end, classified six types of hysteresis. From the viewpoint of heat exchange a classical heat pipe is essentially the same device as a chamber for investigating boiling on porous coats. Therefore, it seems reasonable to assume that in heat pipes the dependence of the wall temperature in the evaporation zone on the heat load supplied may also have a hysteresis character. However, attempts to find papers devoted to this problem in classical heat pipes have failed. In loop heat pipes hysteresis was first discovered by Wolf and Bienert [9]. They observed hysteresis not only for the wall temperature in the evaporation zone, but also for the vapor temperature in the vapor line. The latter phenomenon is not evident, but it has not been explained. The hysteresis of operating temperature in an LHP was also discovered by Ku et al. [10,11]. The range of heat loads for the ammonia LHP under test was from 10 to 700 W. At loads above 300 W the heat-load dependence of the vapor temperature was stable and unambiguous. Hysteresis was observed in the range from 10 to 300 W, where the graph of the operating temperature against the heat load passed along one of the two branches that converged at a value of 300 W. If the start-up took place at a low heat load, and the range of its changes was limited by the value of 300 W, the vapor temperature changed only along the low-temperature branch. If the load exceeded 300 W, then on returning into the range from 10 to 300 W the change of the vapor temperature was always realized along the high-temperature branch. The difference between the lowtemperature and the high-temperature branch increased with an increase in the height of lift of the evaporator with respect to the condenser. The reasons for the hysteresis of the vapor temperature in an LHP are explained in the paper [11]. With a decrease in the heat load below 300 W one can observe partial depriming of the secondary wick in the compensation chamber.
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In this case the liquid released moves into the condenser. The enlarged surface of the interface in the secondary wick promotes an increase of heat exchange between the CC and the evaporation zone. As a result, an additional heat inflow into the chamber leads to an increase in the LHP operating temperature. The necessity of investigating temperature hysteresis is of practical interest when LHPs are used, for instance, for the thermal management of objects with a variable heat dissipation. It is evident that in the case of ambiguity of the device operating temperatures a precise control over the object thermal regime becomes problematic. Our aim was to investigate and analyze the general laws of temperature hysteresis in LHPs, and also to elucidate the cause and the mechanism of this phenomenon. Three different LHPs have been investigated in the framework of this work, and by their results three types of temperature hysteresis have been distinguished. One can observe them when operating in a relatively wide range of heat loads. 2. Mechanism of temperature hysteresis in an LHP The mechanism of the temperature hysteresis in an LHP may be presented as follows. The heat load supplied to the evaporator is transferred into the condenser in the form of the latent heat of vaporization, where it is removed by means of condensation and subsequent cooling of the condensate. In this case the vapor operating temperature Tv is set according to the equation T v ¼ T cool þ
Q ; k cond S cond
ð1Þ
where Tcool is the temperature of the heat receiver/cooling medium, Q is the heat load, kcond is the heat-transfer coefficient during condensation, Scond is the condensation surface. It is evident that under invariable external conditions for the same value of heat load Q the change of Tv is possible only as a result of changes in the condensation surface Scond. Part of the heat from the evaporation zone at the expense of the thermal conductivity of the wick and the evaporator body penetrates into the CC, where a certain thermodynamic state determined by temperature and pressure is established under its action. Depending on how the state of the working fluid is correlated with the saturation line, the liquid phase may occupy the CC volume totally or partially. This circumstance has a considerable effect on the temperature level of the LHP operation and the form of the dependence Tv(Q) [12]. In actual conditions the state of the working fluid in the CC is also affected by the heat exchange with the surrounding medium. If a liquid occupies the whole volume of the compensation chamber, the change of Scond may occur mainly at the expense of liquid redistribution between the condenser and the evaporation zone of the wick, for instance, by reason of capillary hysteresis. It is significant to mention that such a
S.V. Vershinin, Y.F. Maydanik / Applied Thermal Engineering 27 (2007) 962–968
type of vapor temperature hysteresis should be observed also in classical heat pipes. If a liquid fills the CC only partially, then changes in its volume will also affect the value of Scond. This is possible under changes in the magnitude of the parasitic heat flow, which determines the thermodynamic state of the working fluid in the CC, i.e., the temperature, the pressure and the relation between the volumes of the liquid and the vapor phase, which are there in dynamic equilibrium. If, for instance, the temperature and the pressure of vapor phase in the CC increase, then for the retention of mechanical equilibrium in an LHP, which ensures the circulation of the working fluid, the vapor pressure and temperature in the vapor line will increase as well. But since the value of the heat load remains the same, there is bound to be a corresponding decrease in the condensation surface. In this case part of the liquid from CC moves into the condenser. If the temperature in the CC decreases the vapor operating temperature decreases together with it, and the liquid partially passes back into the compensation chamber. 3. Testing procedure The main information on the design of the loop heat pipes the results of investigation of which are discussed later is given in Table 1. Fig. 2 presents the LHP schemes. The procedure of tests consisted in measuring temperatures at the characteristic points of the LHPs under cyclic changes of the heat load. Thermocouples were located on the evaporator wall in the heat-supply zone Te, on the vapor line Tv and the wall of the compensation chamber Tcc, and also at several points along the length of the condenser. The heat-load range was limited, on one side, by the minimum value at which a stable LHP start-up was realized, and on the other side, by the maximum value at which its serviceability was retained. Table 1 Main characteristics of the LHPs tested LHP1
LHP2
LHP3
Working fluid
Ammonia
Ammonia
Evaporator (mm)
Diskshaped 30 13 –
Pentane, acetone Cylindrical
Cylindrical
24 – 135
8 – 80
Diameter Thickness Length
2 390
5 500
2 670
Liquid line: (mm) Diameter Length
2 410
4 750
2 620
Condenser: Means of cooling
Coil Cold plate
Pipe-in-pipe Liquid convection +25
Coil Cold plate
+20
The cycle, which consisted of a stepwise increase of the heat load Q" (forward motion) and then its decrease Q# (reverse motion), was repeated at least twice in every experiment. In this case the conditions of cooling of the condenser were maintained constant. The results of measurements were used to determine the heat-transfer coefficient in the evaporation zone a(Q), and also the position of the interface in the condenser. These factors were taken into account in the analysis of cyclograms for Tv = f(Q"#). 4. Hysteresis connected with heat exchange in the evaporation zone This type of hysteresis was discovered in testing LHP1 [13], whose scheme is presented in Fig. 2a. The cyclogram Tv = f(Q"#) during the device operation in the horizontal position is shown in Fig. 3. As is easy to see, one can observe two hysteresis loops on it, with the mutual position of the curves plotted for the forward and reverse motion changing on the hysteresis segments. In the region of low heat loads the graph Tv = f(Q") goes higher than the graph
65
Vapor line: (mm) Diameter Length
Cooling temperature, °C
Fig. 2. Schemes of loop heat pipes: (a) LHP1, (b) LHP2, (c) LHP3; (1) evaporator, (2) wick, (3) compensation chamber, (4) vapor line, (5) liquid line, (6) condenser.
forward motion
Vapor temperature, ºC
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reverse motion
55
45
35
25 0
20, +20, +50
40
80
120
160
Heat load, W
Fig. 3. Cyclogram Tv = f(Q"#) for LHP1.
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Tv = f(Q#), and at high loads – quite the reverse. The cyclogram for the CC temperature has a similar form. The position of the interface in the condenser also corresponds to the hysteresis character of the cyclogram Tv = f(Q"#). In this case on the hysteresis segments at the same heat loads a higher operating temperature of the LHP is established at a similar condensation surface in the condenser. When elucidating the reasons for temperature hysteresis, one may compare it with heat-exchange hysteresis in the evaporation zone. As is seen on the cyclogram a = f(Q"#) presented in Fig. 4, here there are two hysteresis loops. One of them – situated in a region of low heat loads – is a forward loop connected with the development of an evaporating front in the wick, the other – more extended – is a reverse loop caused by a heat-exchange crisis at a maximum heat load. A comparative analysis of both cyclograms makes it possible to conclude that at the same heat-load values lower temperatures are established at higher heat-exchange coefficients in the evaporation zone. It testifies that the heat-exchange hysteresis in the evaporation zone and the hysteresis of the operating temperature in the LHP are interconnected. For the above-mentioned mechanism of temperature hysteresis to adequately reflect the results of experiments, it is reasonable to assume that the amount of the parasitic heat flow penetrating into the CC depends on the heatexchange intensity in the evaporation zone. Indeed, if the temperature of the evaporator wall Te, for instance, in the case of decreasing heat-exchange intensity, increases with respect to the vapor operating temperature, the difference between the value of Te and the temperature of the working fluid in the compensation chamber Tcc will accordingly increase too. In this case, naturally, the amount of the parasitic heat flow penetrating into the CC at the expense of thermal conductivity increases. Thus, the effect of the heat exchange in the wick evaporation zone on the LHP operating temperature was realized through the thermal state of the working fluid in the CC. It is well known that heat-exchange hysteresis during evaporation is caused by capillary hysteresis, which takes
Heat-transfer coef. ×10−3 W/m2 C
25
20
15
10 forward motion
5 reverse motion 0
0
40
80
120
160
Heat load, W
Fig. 4. Cyclogram a = f(Q"#) for LHP1.
200
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place in the wick. Therefore, it is just this hysteresis that is the factor initiating the hysteresis of the vapor operating temperature too. However, a necessary condition for the initiation of the latter is the presence of a vapor phase in the compensation chamber. It is evident that temperature hysteresis is most pronounced in the sections of the heat-load range where the heat-exchange intensity in the evaporation zone is relatively small. In this case the parasitic flows are large enough for heating the liquid entering the CC to the formation of a vapor phase. As a result of intensification of heat exchange in the evaporation zone, the amount of parasitic flows in the CC decreases. Owing to this the difference between their values on the forward and the reverse motion becomes insignificant. Therefore the amount of the liquid transferred between the compensation chamber and the condenser will be small, and the condensation surface is practically unchanged. In this case the vapor phase in the CC may disappear. Thus, temperature hysteresis in this case becomes insignificant or is not observed at all. This may be probably used to explain, for instance, the absence of temperature hysteresis in the range of heat loads from 40 to 100 W (Fig. 3) despite the fact that heatexchange hysteresis is observed here (Fig. 4). As shown by experiments, in this range of heat loads the condensation surface is constant and maximum in magnitude, and the dependence Tv = f(Q"#), as is seen, is linear and unambiguous. These conditions determine the operation of LHP1 in the regime of constant thermal conductance, which is characterized by the absence of a vapor phase in the CC.
5. Hysteresis connected with the formation of a vapor phase in the compensation chamber It is well known that to realize phase transitions it is necessary to have a certain superheat or supercooling of one of the phases with respect to the equilibrium state. The disappearance of the vapor phase takes place, for instance, at a slight vapor supercooling, but for its appearance a much higher liquid superheat is required. Therefore, one might expect that the magnitude of superheat required for the appearance of the vapor phase in the CC is achieved at a value of heat load different from that at which its disappearance is observed. It should be mentioned that, according to the hysteresis mechanism, in the heat-load range where these transitions take place the operating temperature in the case of two-phase state of a working fluid in the chamber has to be higher. The hysteresis of the operating temperature connected with the delay of formation of a vapor phase in the compensation chamber was discovered in testing LHP2, whose scheme is shown in Fig. 2b. The cyclograms Tv = f(Q"#) obtained during the operation of this device with acetone and pentane as working fluids are presented in Fig. 5.
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Heat-transfer coef. ×10−3 W/m2C
100
Vapor temperature, ºC
forward motion reverse motion
80
60
pentane
40
acetone
forward motion reverse motion
10
8
6 pentane
4
acetone
2
20
0
100
200
300
400
500
Head load, W
0
100
200
300
400
500
Head load, W
Fig. 5. Cyclogram Tv = f(Q"#) for LHP2.
Fig. 6. Cyclogram a = f(Q"#) for LHP2.
As is seen, on each cyclogram there is a section with a hysteresis loop, which ends with an abrupt jump of temperature. For LHP2 filled with acetone it lies in the range of heat loads from 150 to 400 W, and with pentane from 25 to 150 W. Judging by the characteristic U-shaped form of the dependence Tv = f(Q") in these sections, in the case of direct motion in the CC there is a vapor phase, and with increasing heat load its volume decreases. On the reverse motion the curve Tv = f(Q#) goes lower, and its linear character indicates that LHP2 operates in the regime of constant conductance when the CC is fully filled with a liquid. Thus, after an increase in the heat load the vapor phase in the CC disappears. For LHP2 with acetone as a working fluid this event occurs at a heat load above 400 W. For the second working fluid the vapor phase is likely to disappear on the reverse motion at a heat load below 200 W. On the whole the LHP operation on the low-temperature branch of the curve Tv = f(Q#) is stable. However, at loads of 25 W (pentane) and 150 W (acetone) the stationary state is retained for no longer than 10–15 min, whereupon one can observe a jump of the operating temperature. A new stationary state of the LHP is established on the high-temperature branch of the cyclogram as at the instant of a jump, as shown by measurements of the condenser temperature field, the degree of its filling with a liquid increases. Such an LHP behavior testifies that the formation of a vapor phase is going on in the compensation chamber at this time. The hysteresis of heat exchange during evaporation in the heat-load range under consideration is only weakly defined (Fig. 6). Therefore here LHP operating temperatures are not explicitly related to the heat exchange in the evaporation zone. In this the present type of operating-temperature hysteresis differs from that described above. Even at the instant of a temperature jump the heat-exchange intensity does not change. Thus, by the peculiarities of manifestation, it is possible to distinguish a second type of temperature hysteresis in LHPs, which is realized at the boundary of segments of the cyclogram Tv = f(Q "#) with constant and variable conductance. The mechanism of its action is also connected
with the liquid redistribution between the compensation chamber and the condenser. The reason for this hysteresis is the liquid metastability, i.e., its temporary stability against superheat, which leads to a delay of the vaporphase formation in the CC with decreasing heat load. On the cyclogram Tv = f(Q"#) for LHP2 (Fig. 5), which operates on pentane, one can observe another hysteresis section lying in a range of higher heat loads from 150 to 350 W. Its origin, as is clear from comparison with the cyclogram a = f(Q"#), is connected with the hysteresis of the heat exchange arising from heat-exchange crisis in the evaporation zone. 6. Hysteresis connected with the initial distribution of liquid in LHPs The two types of hysteresis described above manifest themselves regularly in every cycle of the heat-load change. There also exists another type of hysteresis of the operating temperature, at which the difference of the forward and the reverse motion takes place only once in the first cycle. It is caused by the initial distribution of liquid in the LHP and arises when the LHP start-up takes place at a heat load below a certain critical value. It is evident that in this case the dependence Tv = fst(Q"), which describes the variation of operating temperatures after the start-up, on a certain interval of heat loads will differ from the dependence obtained in subsequent cycles of the heat-load change Tv = f(Q"#). Temperature hysteresis of this type was investigated in testing LHP3 (Fig. 2c) erected vertically when the evaporator was above the condenser. The start-up was realized at a heat load of 1 W. As is seen in Fig. 7, the dependence of the operating temperature after the start-up Tv = fst(Q") to a heat-load value of 80 W goes lower than the main cyclogram Tv = f(Q"#). If the cycle is realized in the range from 1 to 25 W, hysteresis is not observed, and operating temperatures lie on the lower start-up branch Tv = fst(Q") of the cyclogram. But if the critical heat-load value of 80 W is exceeded, on the reverse motion and in subsequent cycles the temperature dependence Tv = f(Q"#) in the range from
S.V. Vershinin, Y.F. Maydanik / Applied Thermal Engineering 27 (2007) 962–968 40
Vapor temperature, ºC
Tcool =20°C 36
32
28 Tv =f(Q ↑↓ ) Tv =fst (Q ↑ )
24
cycle 1-25W
20 0
50
100
150
200
Head load, W
Fig. 7. Cyclogram Tv = f(Q"#) for LHP3.
1 to 80 W always passes along the upper branch, and hysteresis here is absent. To return to the lower branch, it is necessary to restart the LHP on the attainment of thermal equilibrium with the surrounding medium. If the LHP is located horizontally, temperature hysteresis during a start-up is not observed. The effect of the initial liquid distribution on the LHP operating temperature consists in the fact that it determines the warm-up dynamics of the CC and the formation there of a certain thermodynamic state of the working fluid after switching on the heat load. In its turn, the initial distribution depends on both the amount of the working fluid and the LHP orientation, and also on the temperature of the heat receiver Tcool and the surrounding medium Tamb. In Ref. [11] one can observe a similar, in character, type of temperature hysteresis, its dependence on the LHP orientation being mentioned. In our experiments we have managed to establish that this hysteresis type also depends on the condenser cooling temperature Tcool (Fig. 8). Evidently in this case it is the difference between the temperature of the condenser cooling and that of the surrounding medium, which determines the pre-start pressure drop between the CC and the condenser that is of importance. If Tcool is considerably higher than Tamb, the CC is com-
60
Tcool =50°C 20°C -20°C
Vapor temperature, ºC
50 40 30 20
Tv =fst (Q ↑ ) Tv =f(Q ↑↓ )
10
967
pletely filled with a liquid both before a start-up and during the LHP operation. Therefore changes in the heat load do not lead to temperature hysteresis. If Tcool is considerably lower than Tamb, on the contrary, there is as little liquid in the CC initially as possible. When the heat load is switched on, a liquid with a temperature close to Tamb begins to enter the CC. Therefore the start-up and the operation of an LHP in the starting segment of Tv = f(Q") is realized at higher operating temperatures than in subsequent cycles. When Tcool and Tamb are equal, at the instant of start-up a relatively cold CC is filled with a liquid. Therefore here the starting dependence passes below the cyclogram Tv = f(Q"#). But later on the CC is warmed up, and its temperature does not go down to values observed in the starting segment of Tv = fst(Q"). 7. Reasons for hysteresis in an LHP Analyzing the mechanism of different types of hysteresis has shown that for its realization it is necessary to have a vapor phase in the CC. It exists if sufficiently large heat flows penetrate into the CC from the evaporation zone and the surrounding medium. An unfavourable LHP orientation also contributes to the existence of a vapor phase in the CC. If it disappears in some range of heat loads, temperature hysteresis is not observed. In this case, however, one can observe temperature hysteresis of the wall, as a result of heat-exchange hysteresis in the evaporation zone. From the viewpoint of thermodynamics the reason for hysteresis consists in the fact that under certain external actions processes in the system proceed irreversibly. If the operating range of heat loads is limited by values at which physical processes in an LHP proceed in relative equilibrium and are reversible, hysteresis will not be observed. For instance, for LHP1 in a range of heat loads 5–120 W the dependence Tv = f(Q"#) is unambiguous everywhere. The values of operating temperatures lie on the lower branches of the previous cyclogram (Fig. 3). Evidently by reason of capillary hysteresis at heat loads below 5 W there proceeds an irreversible process of degradation of the evaporation front, and above 120 W it irreversibly goes deeper into the wick. Similarly for LHP2 filled with pentane, when operating in the range from 50 to 300 W one does not observe any temperature hysteresis. The dependence Tv = f(Q"#) also passes along the lower branches of the cyclogram (Fig. 5). Beyond the indicated range above 300 W there begins the irreversible process of deepening of the evaporating liquid front in the wick, which causes a heat-exchange crisis, and below 50 W, irreversibly, the process of initiation of a vapor phase in the CC takes place. 8. Conclusion
0 0
50
100
150
200
Heat load, W
Fig. 8. The effect of the cooler temperature Tcool on the type of the startup dependence Tv = fst(Q") and cyclogram Tv = f(Q"#) for LHP3.
Temperature hysteresis is observed in practically all loop heat pipes irrespective of their design, dimensions and the working fluid employed. This phenomenon is connected
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with the presence of a compensation chamber, which is a characteristic element of the LHP design, in which at certain conditions there may exist or be absent a liquid-vapor interface. It has been shown by experiment that in LHPs there are three types of temperature hysteresis. Common to them is the liquid redistribution between the compensation chamber and the condenser, and the difference consists in the reasons that influence the redistribution process. The first type of hysteresis is connected with the phenomenon of capillary hysteresis, which is observed during evaporation in a wick with an irregular capillary structure. The second type is determined by the liquid metastable state which may take place in a filled compensation chamber, and which serves as the reason for a delay of formation here of a vapor–liquid interface. These two types of hysteresis have a regular character. The third type of hysteresis is not regular as it is connected with the initial distribution of a working fluid in the LHP. It manifests itself during a start-up and depends on the magnitude of the starting-up heat load and the initial conditions. Temperature hysteresis may be regarded as a drawback of LHPs when they are to be used for maintaining the temperature of the object being cooled in a relatively narrow range with considerable changes of the heat load. At the same time this phenomenon is not inevitable. As shown by the results of investigations presented in the paper, there is always a sufficiently wide range of heat loads at which hysteresis is not observed or is weakly pronounced.
Acknowledgement The work was supported by the Russian Foundation for Basic Research. Project No. 05-08-01180.
References [1] Ya. Tekhver, Kh. Suy, Hysteresis phenomena in boiling at a porous surface, Izvestiya AN USSR, Ser. Energetika i Transport (4) (1984) 163–167 (in Russian). [2] Ya. Tekhver, A. Tunik, On intralayer heat-exchange crisis in boiling at a surface covered with a porous material, Izvestiya AN, Estonskaya SSR, Ser. Fizika i Matematika 27 (4) (1978) 433–437 (in Russian). [3] A.B. Andrianov, S.P. Malyshenko, Hysteresis and transition phenomena in boiling at surfaces with porous coats, DAN USSR 256 (3) (1981) 591–595 (in Russian). [4] S.P. Malyshenko, A.B. Andrianov, On the initial section of boiling curve at surfaces with porous coats and boiling-up hysteresis, Teplofizika Visokikh Temperatur 25 (3) (1987) 563–572 (in Russian). [5] Ya. Tekhver, Kh. Suy, Transient processes in liquid boiling at a porous surface, Izvestiya AN, Estonskaya SSR, Ser. Fizika i Matematika 34 (3) (1985) 303 (in Russian). [6] Ya. Tekhver, Kh. Suy, R. Liane, On capillary heat-exchange hysteresis in liquid boiling at a surface with a porous coat, Izvestiya AN, Estonskaya SSR, Ser. Fizika i Matematika 30 (4) (1981) 376–380 (in Russian). [7] A.B. Andrianov, S.P. Malyshenko, Effect of characteristics of porous coats on heat-exchange in boiling, Izvestiya AN USSR, Ser. Energetika i Transport (1) (1989) 139–150 (in Russian). [8] M. Poniewski, Peculiarities of boiling heat transfer on capillaryporous coverings, in: Proceedings of the 12th International Heat Pipe Conference, Moscow, Russia, 2002, pp. 41–53. [9] A.D. Wolf, W.B. Bienert, Investigation of temperature control characteristics of LHPs, SAE Pap. 941576, 1994. [10] M.K. Cheng, T.T. Noang, J. Ku, T. Kaya, Thermal performance and operational characteristics of LHP, SAE Pap. 981813, 1998. [11] T. Kaya, J. Ku, Investigation of the temperature hysteresis phenomenon of a loop heat pipe, in: Proceedings of the National Heat Transfer Conference, Albuquerque, NM, USA, 1999. [12] M.A. Chernysheva, Yu.F. Maydanik, Operating temperature of loop heat pipe, in: Proceedings of the 6th Minsk International Seminar ‘‘Heat Pipes, Heat Pumps, Refrigerators’’, Minsk, Belarus, 2005, pp. 122–128. [13] S.V. Vershinin, Yu. F. Maydanik, M.A. Chernysheva, Hysteresis phenomena during evaporation in a loop heat pipe, in: Proceedings of the 3rd Russian National Heat-Exchange Conference, vol. 4, Moscow, Russia, 2002, pp. 245–249 (in Russian).
Hysteresis phenomena in loop heat pipes Sergey V. Vershinin, Yury F. Maydanik
*
Institute of Thermal Physics, Ural Branch of the Russian Academy of Sciences, Amundsen st. 106, Ekaterinburg 620016, Russia Received 28 April 2006; accepted 21 August 2006 Available online 24 October 2006
Abstract Testing of loop heat pipes (LHPs) has shown that the heat-load dependence of the operating temperature is not always unambiguous. It may have a hysteresis nature. It has been found that temperature hysteresis is connected with changes in the liquid distribution between the compensation chamber (CC) and the condenser. Analysis makes it possible to distinguish three types of temperature hysteresis. In the first case this redistribution is caused by the change in the amount of the parasitic heat flow that penetrates into the CC, which in its turn is a result of heat-transfer hysteresis in the evaporation zone. In the second, temperature hysteresis is connected with the liquid metastable state, which leads to a delay of formation of the vapor phase in the compensation chamber. The reason for hysteresis of the third type is the change of the initial liquid distribution in an LHP during a start-up. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Loop heat pipe; Capillary structure; Evaporation; Temperature hysteresis
1. Introduction A loop heat pipe is a hermetic closed loop consisting of an evaporator, in which a wick is located, and a condenser connected by separate channels for vapor and liquid (Fig. 1). Temperature hysteresis in an LHP is a phenomenon which under constant external conditions manifests itself as an ambiguous dependence of the operating temperature on the heat load under cyclic changes of the latter. The phenomenon of hysteresis is observed in thermodynamic systems capable of being in metastable states and exposed to the action of periodically changing external conditions. The gist of the phenomenon consists in the fact that the physical quantities characterizing the current state of a system depend not only on the magnitude of the external action, but also on its preceding states, therefore the system reaction to external actions of the same magnitude may be different. The reason for hysteresis is processes which at certain external actions proceed irreversibly.
*
Corresponding author. Tel.: +7 343 267 87 91; fax: +7 343 267 87 99. E-mail address: [email protected] (Y.F. Maydanik).
1359-4311/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2006.08.016
In the heat-exchange sphere the best known and investigated system where hysteresis is observed is a liquid-saturated capillary-porous structure with pores of irregular dimensions under the action of a heat flow. Such an action results in the process of evaporation or boiling, which is investigated, as a rule, at a constant pressure. The hysteresis character has for instance, a dependence of the temperature of the wall through which heat is supplied on the magnitude of the heat load. The reason for heattransfer hysteresis during boiling in this case is capillary hysteresis. As a result of experimental investigations, two main types of hysteresis were distinguished. One of them is connected with the development of boiling in the wall layer of a porous coat (forward loop) [1], the other – with its crisis (reverse loop) [2,3]. Besides, hysteresis was discovered during the boiling-up of a liquid [4]. It turned out that on the same coat, depending on the heat load magnitude, one could observe different types of hysteresis, and the character of their manifestation depended on the size of pores of the capillary structure and the degree of their irregularity [5–7]. Later the results of investigating hysteresis in capillary-porous structures were generalized, in particular, in
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Fig. 1. Principal scheme of an LHP.
the paper by Poniewski [8], who, in the end, classified six types of hysteresis. From the viewpoint of heat exchange a classical heat pipe is essentially the same device as a chamber for investigating boiling on porous coats. Therefore, it seems reasonable to assume that in heat pipes the dependence of the wall temperature in the evaporation zone on the heat load supplied may also have a hysteresis character. However, attempts to find papers devoted to this problem in classical heat pipes have failed. In loop heat pipes hysteresis was first discovered by Wolf and Bienert [9]. They observed hysteresis not only for the wall temperature in the evaporation zone, but also for the vapor temperature in the vapor line. The latter phenomenon is not evident, but it has not been explained. The hysteresis of operating temperature in an LHP was also discovered by Ku et al. [10,11]. The range of heat loads for the ammonia LHP under test was from 10 to 700 W. At loads above 300 W the heat-load dependence of the vapor temperature was stable and unambiguous. Hysteresis was observed in the range from 10 to 300 W, where the graph of the operating temperature against the heat load passed along one of the two branches that converged at a value of 300 W. If the start-up took place at a low heat load, and the range of its changes was limited by the value of 300 W, the vapor temperature changed only along the low-temperature branch. If the load exceeded 300 W, then on returning into the range from 10 to 300 W the change of the vapor temperature was always realized along the high-temperature branch. The difference between the lowtemperature and the high-temperature branch increased with an increase in the height of lift of the evaporator with respect to the condenser. The reasons for the hysteresis of the vapor temperature in an LHP are explained in the paper [11]. With a decrease in the heat load below 300 W one can observe partial depriming of the secondary wick in the compensation chamber.
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In this case the liquid released moves into the condenser. The enlarged surface of the interface in the secondary wick promotes an increase of heat exchange between the CC and the evaporation zone. As a result, an additional heat inflow into the chamber leads to an increase in the LHP operating temperature. The necessity of investigating temperature hysteresis is of practical interest when LHPs are used, for instance, for the thermal management of objects with a variable heat dissipation. It is evident that in the case of ambiguity of the device operating temperatures a precise control over the object thermal regime becomes problematic. Our aim was to investigate and analyze the general laws of temperature hysteresis in LHPs, and also to elucidate the cause and the mechanism of this phenomenon. Three different LHPs have been investigated in the framework of this work, and by their results three types of temperature hysteresis have been distinguished. One can observe them when operating in a relatively wide range of heat loads. 2. Mechanism of temperature hysteresis in an LHP The mechanism of the temperature hysteresis in an LHP may be presented as follows. The heat load supplied to the evaporator is transferred into the condenser in the form of the latent heat of vaporization, where it is removed by means of condensation and subsequent cooling of the condensate. In this case the vapor operating temperature Tv is set according to the equation T v ¼ T cool þ
Q ; k cond S cond
ð1Þ
where Tcool is the temperature of the heat receiver/cooling medium, Q is the heat load, kcond is the heat-transfer coefficient during condensation, Scond is the condensation surface. It is evident that under invariable external conditions for the same value of heat load Q the change of Tv is possible only as a result of changes in the condensation surface Scond. Part of the heat from the evaporation zone at the expense of the thermal conductivity of the wick and the evaporator body penetrates into the CC, where a certain thermodynamic state determined by temperature and pressure is established under its action. Depending on how the state of the working fluid is correlated with the saturation line, the liquid phase may occupy the CC volume totally or partially. This circumstance has a considerable effect on the temperature level of the LHP operation and the form of the dependence Tv(Q) [12]. In actual conditions the state of the working fluid in the CC is also affected by the heat exchange with the surrounding medium. If a liquid occupies the whole volume of the compensation chamber, the change of Scond may occur mainly at the expense of liquid redistribution between the condenser and the evaporation zone of the wick, for instance, by reason of capillary hysteresis. It is significant to mention that such a
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type of vapor temperature hysteresis should be observed also in classical heat pipes. If a liquid fills the CC only partially, then changes in its volume will also affect the value of Scond. This is possible under changes in the magnitude of the parasitic heat flow, which determines the thermodynamic state of the working fluid in the CC, i.e., the temperature, the pressure and the relation between the volumes of the liquid and the vapor phase, which are there in dynamic equilibrium. If, for instance, the temperature and the pressure of vapor phase in the CC increase, then for the retention of mechanical equilibrium in an LHP, which ensures the circulation of the working fluid, the vapor pressure and temperature in the vapor line will increase as well. But since the value of the heat load remains the same, there is bound to be a corresponding decrease in the condensation surface. In this case part of the liquid from CC moves into the condenser. If the temperature in the CC decreases the vapor operating temperature decreases together with it, and the liquid partially passes back into the compensation chamber. 3. Testing procedure The main information on the design of the loop heat pipes the results of investigation of which are discussed later is given in Table 1. Fig. 2 presents the LHP schemes. The procedure of tests consisted in measuring temperatures at the characteristic points of the LHPs under cyclic changes of the heat load. Thermocouples were located on the evaporator wall in the heat-supply zone Te, on the vapor line Tv and the wall of the compensation chamber Tcc, and also at several points along the length of the condenser. The heat-load range was limited, on one side, by the minimum value at which a stable LHP start-up was realized, and on the other side, by the maximum value at which its serviceability was retained. Table 1 Main characteristics of the LHPs tested LHP1
LHP2
LHP3
Working fluid
Ammonia
Ammonia
Evaporator (mm)
Diskshaped 30 13 –
Pentane, acetone Cylindrical
Cylindrical
24 – 135
8 – 80
Diameter Thickness Length
2 390
5 500
2 670
Liquid line: (mm) Diameter Length
2 410
4 750
2 620
Condenser: Means of cooling
Coil Cold plate
Pipe-in-pipe Liquid convection +25
Coil Cold plate
+20
The cycle, which consisted of a stepwise increase of the heat load Q" (forward motion) and then its decrease Q# (reverse motion), was repeated at least twice in every experiment. In this case the conditions of cooling of the condenser were maintained constant. The results of measurements were used to determine the heat-transfer coefficient in the evaporation zone a(Q), and also the position of the interface in the condenser. These factors were taken into account in the analysis of cyclograms for Tv = f(Q"#). 4. Hysteresis connected with heat exchange in the evaporation zone This type of hysteresis was discovered in testing LHP1 [13], whose scheme is presented in Fig. 2a. The cyclogram Tv = f(Q"#) during the device operation in the horizontal position is shown in Fig. 3. As is easy to see, one can observe two hysteresis loops on it, with the mutual position of the curves plotted for the forward and reverse motion changing on the hysteresis segments. In the region of low heat loads the graph Tv = f(Q") goes higher than the graph
65
Vapor line: (mm) Diameter Length
Cooling temperature, °C
Fig. 2. Schemes of loop heat pipes: (a) LHP1, (b) LHP2, (c) LHP3; (1) evaporator, (2) wick, (3) compensation chamber, (4) vapor line, (5) liquid line, (6) condenser.
forward motion
Vapor temperature, ºC
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reverse motion
55
45
35
25 0
20, +20, +50
40
80
120
160
Heat load, W
Fig. 3. Cyclogram Tv = f(Q"#) for LHP1.
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Tv = f(Q#), and at high loads – quite the reverse. The cyclogram for the CC temperature has a similar form. The position of the interface in the condenser also corresponds to the hysteresis character of the cyclogram Tv = f(Q"#). In this case on the hysteresis segments at the same heat loads a higher operating temperature of the LHP is established at a similar condensation surface in the condenser. When elucidating the reasons for temperature hysteresis, one may compare it with heat-exchange hysteresis in the evaporation zone. As is seen on the cyclogram a = f(Q"#) presented in Fig. 4, here there are two hysteresis loops. One of them – situated in a region of low heat loads – is a forward loop connected with the development of an evaporating front in the wick, the other – more extended – is a reverse loop caused by a heat-exchange crisis at a maximum heat load. A comparative analysis of both cyclograms makes it possible to conclude that at the same heat-load values lower temperatures are established at higher heat-exchange coefficients in the evaporation zone. It testifies that the heat-exchange hysteresis in the evaporation zone and the hysteresis of the operating temperature in the LHP are interconnected. For the above-mentioned mechanism of temperature hysteresis to adequately reflect the results of experiments, it is reasonable to assume that the amount of the parasitic heat flow penetrating into the CC depends on the heatexchange intensity in the evaporation zone. Indeed, if the temperature of the evaporator wall Te, for instance, in the case of decreasing heat-exchange intensity, increases with respect to the vapor operating temperature, the difference between the value of Te and the temperature of the working fluid in the compensation chamber Tcc will accordingly increase too. In this case, naturally, the amount of the parasitic heat flow penetrating into the CC at the expense of thermal conductivity increases. Thus, the effect of the heat exchange in the wick evaporation zone on the LHP operating temperature was realized through the thermal state of the working fluid in the CC. It is well known that heat-exchange hysteresis during evaporation is caused by capillary hysteresis, which takes
Heat-transfer coef. ×10−3 W/m2 C
25
20
15
10 forward motion
5 reverse motion 0
0
40
80
120
160
Heat load, W
Fig. 4. Cyclogram a = f(Q"#) for LHP1.
200
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place in the wick. Therefore, it is just this hysteresis that is the factor initiating the hysteresis of the vapor operating temperature too. However, a necessary condition for the initiation of the latter is the presence of a vapor phase in the compensation chamber. It is evident that temperature hysteresis is most pronounced in the sections of the heat-load range where the heat-exchange intensity in the evaporation zone is relatively small. In this case the parasitic flows are large enough for heating the liquid entering the CC to the formation of a vapor phase. As a result of intensification of heat exchange in the evaporation zone, the amount of parasitic flows in the CC decreases. Owing to this the difference between their values on the forward and the reverse motion becomes insignificant. Therefore the amount of the liquid transferred between the compensation chamber and the condenser will be small, and the condensation surface is practically unchanged. In this case the vapor phase in the CC may disappear. Thus, temperature hysteresis in this case becomes insignificant or is not observed at all. This may be probably used to explain, for instance, the absence of temperature hysteresis in the range of heat loads from 40 to 100 W (Fig. 3) despite the fact that heatexchange hysteresis is observed here (Fig. 4). As shown by experiments, in this range of heat loads the condensation surface is constant and maximum in magnitude, and the dependence Tv = f(Q"#), as is seen, is linear and unambiguous. These conditions determine the operation of LHP1 in the regime of constant thermal conductance, which is characterized by the absence of a vapor phase in the CC.
5. Hysteresis connected with the formation of a vapor phase in the compensation chamber It is well known that to realize phase transitions it is necessary to have a certain superheat or supercooling of one of the phases with respect to the equilibrium state. The disappearance of the vapor phase takes place, for instance, at a slight vapor supercooling, but for its appearance a much higher liquid superheat is required. Therefore, one might expect that the magnitude of superheat required for the appearance of the vapor phase in the CC is achieved at a value of heat load different from that at which its disappearance is observed. It should be mentioned that, according to the hysteresis mechanism, in the heat-load range where these transitions take place the operating temperature in the case of two-phase state of a working fluid in the chamber has to be higher. The hysteresis of the operating temperature connected with the delay of formation of a vapor phase in the compensation chamber was discovered in testing LHP2, whose scheme is shown in Fig. 2b. The cyclograms Tv = f(Q"#) obtained during the operation of this device with acetone and pentane as working fluids are presented in Fig. 5.
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Heat-transfer coef. ×10−3 W/m2C
100
Vapor temperature, ºC
forward motion reverse motion
80
60
pentane
40
acetone
forward motion reverse motion
10
8
6 pentane
4
acetone
2
20
0
100
200
300
400
500
Head load, W
0
100
200
300
400
500
Head load, W
Fig. 5. Cyclogram Tv = f(Q"#) for LHP2.
Fig. 6. Cyclogram a = f(Q"#) for LHP2.
As is seen, on each cyclogram there is a section with a hysteresis loop, which ends with an abrupt jump of temperature. For LHP2 filled with acetone it lies in the range of heat loads from 150 to 400 W, and with pentane from 25 to 150 W. Judging by the characteristic U-shaped form of the dependence Tv = f(Q") in these sections, in the case of direct motion in the CC there is a vapor phase, and with increasing heat load its volume decreases. On the reverse motion the curve Tv = f(Q#) goes lower, and its linear character indicates that LHP2 operates in the regime of constant conductance when the CC is fully filled with a liquid. Thus, after an increase in the heat load the vapor phase in the CC disappears. For LHP2 with acetone as a working fluid this event occurs at a heat load above 400 W. For the second working fluid the vapor phase is likely to disappear on the reverse motion at a heat load below 200 W. On the whole the LHP operation on the low-temperature branch of the curve Tv = f(Q#) is stable. However, at loads of 25 W (pentane) and 150 W (acetone) the stationary state is retained for no longer than 10–15 min, whereupon one can observe a jump of the operating temperature. A new stationary state of the LHP is established on the high-temperature branch of the cyclogram as at the instant of a jump, as shown by measurements of the condenser temperature field, the degree of its filling with a liquid increases. Such an LHP behavior testifies that the formation of a vapor phase is going on in the compensation chamber at this time. The hysteresis of heat exchange during evaporation in the heat-load range under consideration is only weakly defined (Fig. 6). Therefore here LHP operating temperatures are not explicitly related to the heat exchange in the evaporation zone. In this the present type of operating-temperature hysteresis differs from that described above. Even at the instant of a temperature jump the heat-exchange intensity does not change. Thus, by the peculiarities of manifestation, it is possible to distinguish a second type of temperature hysteresis in LHPs, which is realized at the boundary of segments of the cyclogram Tv = f(Q "#) with constant and variable conductance. The mechanism of its action is also connected
with the liquid redistribution between the compensation chamber and the condenser. The reason for this hysteresis is the liquid metastability, i.e., its temporary stability against superheat, which leads to a delay of the vaporphase formation in the CC with decreasing heat load. On the cyclogram Tv = f(Q"#) for LHP2 (Fig. 5), which operates on pentane, one can observe another hysteresis section lying in a range of higher heat loads from 150 to 350 W. Its origin, as is clear from comparison with the cyclogram a = f(Q"#), is connected with the hysteresis of the heat exchange arising from heat-exchange crisis in the evaporation zone. 6. Hysteresis connected with the initial distribution of liquid in LHPs The two types of hysteresis described above manifest themselves regularly in every cycle of the heat-load change. There also exists another type of hysteresis of the operating temperature, at which the difference of the forward and the reverse motion takes place only once in the first cycle. It is caused by the initial distribution of liquid in the LHP and arises when the LHP start-up takes place at a heat load below a certain critical value. It is evident that in this case the dependence Tv = fst(Q"), which describes the variation of operating temperatures after the start-up, on a certain interval of heat loads will differ from the dependence obtained in subsequent cycles of the heat-load change Tv = f(Q"#). Temperature hysteresis of this type was investigated in testing LHP3 (Fig. 2c) erected vertically when the evaporator was above the condenser. The start-up was realized at a heat load of 1 W. As is seen in Fig. 7, the dependence of the operating temperature after the start-up Tv = fst(Q") to a heat-load value of 80 W goes lower than the main cyclogram Tv = f(Q"#). If the cycle is realized in the range from 1 to 25 W, hysteresis is not observed, and operating temperatures lie on the lower start-up branch Tv = fst(Q") of the cyclogram. But if the critical heat-load value of 80 W is exceeded, on the reverse motion and in subsequent cycles the temperature dependence Tv = f(Q"#) in the range from
S.V. Vershinin, Y.F. Maydanik / Applied Thermal Engineering 27 (2007) 962–968 40
Vapor temperature, ºC
Tcool =20°C 36
32
28 Tv =f(Q ↑↓ ) Tv =fst (Q ↑ )
24
cycle 1-25W
20 0
50
100
150
200
Head load, W
Fig. 7. Cyclogram Tv = f(Q"#) for LHP3.
1 to 80 W always passes along the upper branch, and hysteresis here is absent. To return to the lower branch, it is necessary to restart the LHP on the attainment of thermal equilibrium with the surrounding medium. If the LHP is located horizontally, temperature hysteresis during a start-up is not observed. The effect of the initial liquid distribution on the LHP operating temperature consists in the fact that it determines the warm-up dynamics of the CC and the formation there of a certain thermodynamic state of the working fluid after switching on the heat load. In its turn, the initial distribution depends on both the amount of the working fluid and the LHP orientation, and also on the temperature of the heat receiver Tcool and the surrounding medium Tamb. In Ref. [11] one can observe a similar, in character, type of temperature hysteresis, its dependence on the LHP orientation being mentioned. In our experiments we have managed to establish that this hysteresis type also depends on the condenser cooling temperature Tcool (Fig. 8). Evidently in this case it is the difference between the temperature of the condenser cooling and that of the surrounding medium, which determines the pre-start pressure drop between the CC and the condenser that is of importance. If Tcool is considerably higher than Tamb, the CC is com-
60
Tcool =50°C 20°C -20°C
Vapor temperature, ºC
50 40 30 20
Tv =fst (Q ↑ ) Tv =f(Q ↑↓ )
10
967
pletely filled with a liquid both before a start-up and during the LHP operation. Therefore changes in the heat load do not lead to temperature hysteresis. If Tcool is considerably lower than Tamb, on the contrary, there is as little liquid in the CC initially as possible. When the heat load is switched on, a liquid with a temperature close to Tamb begins to enter the CC. Therefore the start-up and the operation of an LHP in the starting segment of Tv = f(Q") is realized at higher operating temperatures than in subsequent cycles. When Tcool and Tamb are equal, at the instant of start-up a relatively cold CC is filled with a liquid. Therefore here the starting dependence passes below the cyclogram Tv = f(Q"#). But later on the CC is warmed up, and its temperature does not go down to values observed in the starting segment of Tv = fst(Q"). 7. Reasons for hysteresis in an LHP Analyzing the mechanism of different types of hysteresis has shown that for its realization it is necessary to have a vapor phase in the CC. It exists if sufficiently large heat flows penetrate into the CC from the evaporation zone and the surrounding medium. An unfavourable LHP orientation also contributes to the existence of a vapor phase in the CC. If it disappears in some range of heat loads, temperature hysteresis is not observed. In this case, however, one can observe temperature hysteresis of the wall, as a result of heat-exchange hysteresis in the evaporation zone. From the viewpoint of thermodynamics the reason for hysteresis consists in the fact that under certain external actions processes in the system proceed irreversibly. If the operating range of heat loads is limited by values at which physical processes in an LHP proceed in relative equilibrium and are reversible, hysteresis will not be observed. For instance, for LHP1 in a range of heat loads 5–120 W the dependence Tv = f(Q"#) is unambiguous everywhere. The values of operating temperatures lie on the lower branches of the previous cyclogram (Fig. 3). Evidently by reason of capillary hysteresis at heat loads below 5 W there proceeds an irreversible process of degradation of the evaporation front, and above 120 W it irreversibly goes deeper into the wick. Similarly for LHP2 filled with pentane, when operating in the range from 50 to 300 W one does not observe any temperature hysteresis. The dependence Tv = f(Q"#) also passes along the lower branches of the cyclogram (Fig. 5). Beyond the indicated range above 300 W there begins the irreversible process of deepening of the evaporating liquid front in the wick, which causes a heat-exchange crisis, and below 50 W, irreversibly, the process of initiation of a vapor phase in the CC takes place. 8. Conclusion
0 0
50
100
150
200
Heat load, W
Fig. 8. The effect of the cooler temperature Tcool on the type of the startup dependence Tv = fst(Q") and cyclogram Tv = f(Q"#) for LHP3.
Temperature hysteresis is observed in practically all loop heat pipes irrespective of their design, dimensions and the working fluid employed. This phenomenon is connected
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with the presence of a compensation chamber, which is a characteristic element of the LHP design, in which at certain conditions there may exist or be absent a liquid-vapor interface. It has been shown by experiment that in LHPs there are three types of temperature hysteresis. Common to them is the liquid redistribution between the compensation chamber and the condenser, and the difference consists in the reasons that influence the redistribution process. The first type of hysteresis is connected with the phenomenon of capillary hysteresis, which is observed during evaporation in a wick with an irregular capillary structure. The second type is determined by the liquid metastable state which may take place in a filled compensation chamber, and which serves as the reason for a delay of formation here of a vapor–liquid interface. These two types of hysteresis have a regular character. The third type of hysteresis is not regular as it is connected with the initial distribution of a working fluid in the LHP. It manifests itself during a start-up and depends on the magnitude of the starting-up heat load and the initial conditions. Temperature hysteresis may be regarded as a drawback of LHPs when they are to be used for maintaining the temperature of the object being cooled in a relatively narrow range with considerable changes of the heat load. At the same time this phenomenon is not inevitable. As shown by the results of investigations presented in the paper, there is always a sufficiently wide range of heat loads at which hysteresis is not observed or is weakly pronounced.
Acknowledgement The work was supported by the Russian Foundation for Basic Research. Project No. 05-08-01180.
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