An Advanced Numerical Model of a Loop Heat Pipe

XXVII UIT CONGRESS 2009 - 019

An Advanced Numerical Model of a Loop Heat Pipe for Space Applications Claudio Ferrandi, Marco Marengo University of Bergamo, Engineering Faculty, viale Marconi 5, 24044 Dalmine, Italy

Stefano Zinna Uniheat S.r.l., Viale Marconi, 5 - c/o University of Bergamo, Engineering Labs, 24044 Dalmine, Italy

Copyright © 2009 U.I.T. Unione Italiana Termofluidodinamica

ABSTRACT The paper proposed an advanced numerical code, developed by SINDA/FLUINT, of a particular Loop Heat Pipe (LHP) for space applications, based on the optimization of the subroutines scheme in order to complete full simulations with CPU time even four times faster than the real work time, on a pc with standard performances. The SINDA/FLUINT thermal network, made by a thermal model (representing the solid part of the LHP) interfaced with a fluidic one (representing the fluid inside the LHP), also presents the novel possibility to switch off the fluidic part according to the incoming power into the LHP, in order to be able to test also those situations in which the incoming power is too low, when namely the pumping force is not sufficient to maintain the fluid circulation in the loop and the heat transfer in the device is just made by thermal conduction.

INTRODUCTION The LHP is a two-phase heat transfer device which has large application potentialities in spacecraft thermal control due to its high efficiency, long distance in heat transfer, good performance in thermal control and flexibility and convenience in installation. LHP is a heat transport devices that use capillary forces to circulate a two-phase working fluid. It consists of a heat-accepting evaporator, a heat rejecting condenser, a fluid reservoir and tubing to connect the components. Internal to the evaporator is a porous wick, which provides capillary pumping of the fluid in the loop (see Fig. 1 LHP scheme).

Since the simulation time is strongly reduced, sensitivity analysis are then possible with a larger number of parameters, and, as the sake of example, a parametrical analysis, based on the influence on the temperature profiles of the ratio of the heat incoming in the LHP evaporator (for fluid evaporation) and the heat coming back to the compensation chamber, is presented. Even if the model is built around a precise LHP application, it is now possible, just changing the input data and the boundary conditions, to use the present numerical tool for a generic LHP device employed in other fields.

Fig. 1 LHP scheme

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The Alpha Magnetic Spectrometer (AMS) is an experiment to search for dark, missing and antimatter on the space Shuttle and the International Space Station Alpha (Fig. 2).

Fig. 2 The AMS detector For this reason several detectors and sub-detectors operate in a magnetic field, which is generated by a super-conductive Helium-cooled magnet. Before starting the AMS experiment, it is necessary to charge the magnet. This will be done by the CAB, which is mounted to the USS upper trunnion bridge on the WAKE side of the experiment (shown in Fig. 3).

The condenser of upper LHP is glues on the upper radiative side of Main WAKE radiator and the other is on the lower section (shown in Fig. 3). The material of the entire LHPs are stainless steel, except the evaporator saddle and the condenser saddles, which are made in 6061 aluminium alloy. The LHP evaporator saddles are directly screwed on the CAB base-plate plate, with an estimated contact area of 100 mm x 245 mm each; the corresponding condenser fluid lines are routed to the WAKE radiative side of the AMS main radiator, above some embedded HPs, used to equalize the radiator temperature. The condenser tubes are soldered to an aluminium saddle, which in turn is permanently glued (with a thermally conductive glue) to the Main WAKE radiator. The saddle is secured to the WAKE radiator aluminium skin by some rivets to prevent that the saddle/condenser assembly becomes loose. Both LHPs have the same size both for the evaporator saddles and the condenser lines. We can consider the nominal and the failure modes of AMS working: - the nominal operative mode is characterized by all the 6 CCS converters and both the LHPs mounted on the CAB base plate working. - the failure mode can be considered the failure of one of the LHPs mounted on the CAB base plate or the failure of one of the CCS CS converters

Fig. 3 CAB and 2 sets of LHPs, the USS and the WAKE Main radiator

Also three main operational modes are defined for the CAB: Steady state, Ramp-up and Ramp-down. For each of this operative mode we can consider the nominal and the failure modes. The Ramp-up process is the most critical case because of a relative large amount of internal heat dissipation to deal with, maximum 750 W with a duration of 30 minutes for 6 CCS CS converter working and 827 W for the case of one CCS CS failure (shown in Fig. 5).

CAB LHP system consists of 2 sets of LHPs, one is the upper LHP and the other is the lower (corresponding to their location), with the carrier is same as high-purity ammonia, and they are distinguished by their different condenser line locations, as is shown in Fig. 4:

Fig. 5 CAB power profile during charging the magnet Fig. 4 CAB LHP fluid line routing on WAKE radiator

As hinted by CGS a maximum of 5 orbits will be run before the Ramp-up is starting: precisely, 3 under hot environment and 5 under cold one. In this paper just the Ramp-up mode will be considered.

NUMERICAL MODEL As said in the introduction, two sets of LHPs are implemented to service the CAB and they are distinguished by the different position of the condenser lines (the “upper” and “lower” LHP). The latter LHP will be analyzed in this work. Some geometric characteristics are provided from CGS [3] while other data, like the compensation chamber length or the wick properties, are unknown. The starting points of this project activity are two reference models: the first one was the ‘prebuilt model’ of a LHP, developed by Cullimore and Ring in which the researchers considered precise choices of the geometric and heat transfer parameters according to the description presented in [4]. The second reference was an interesting research of Zinna [5], just on CGS LHP, whose results are used in this work as an element of comparison for all tests performed. Nevertheless from Zinna’s papers we can notice that, a part from the results, the CPU time of the simulations is around 170 h on a standard machine (CPU 3.4 GHz and RAM 3.4 GHz – 2 GB); this period of run is certainly too high for a parametrical analysis, but also for repetitive runs. So the purpose of the study was to try to obtain a different LHP model, that simulates the CGS LHP with lower CPU time, and compare the new results with Zinna’s ones. For this reason a modified C&R ‘prebuilt model’ was developed, in order to take into account all known parameters (liquid and vapour lines, condenser) provided by CGS, supplied by the boundary conditions corresponding to those of the CAB in which the LHP will be installed, but maintaining the same values for the evaporator (geometry and heat transfer coefficients) chosen by C&R. All the design LHP data are provided in the Appendix; some data in the table (yellow color) follow from C&R [4]; the remaining data listed in the table (white background) are provided from CGS and they are considered certain. By using a numerical lumped parameters code (SINDA/FLUINT, 1) a global loop model has been designed that consists of a set of four different objects 2: (1) the Cryo-cooler, which transfer parasitic heat from one of the thermal protection shields to the LHP evaporator; (2) the Evaporator where the power is put in to attain the evaporation; (3) a Radiator panel in which the power is rejected to the outer ambient; (4) the Lines constituted by a vapour line that came out from the evaporator, a condenser line that cross the radiator panel to which reject the power and a liquid line that carries back the condensed liquid to the evaporator. By the model the user poses a heat transfer problem by creating an arbitrary network of temperature points (nodes) connected by heat flow paths (conductors). FLUINT is a network-style fluid flow simulator. It can also be combined with SINDA thermal networks to simulate combined thermal/ hydraulic systems. The user poses a problem by creating an arbitrary network of thermodynamic points (lumps) connected by fluid flow

passages (paths). The user may also define heat transfer routes (ties) between SINDA nodes and FLUINT lumps to simulate convection. The heat power and the conductances to the ambient are time varying elements simulating different orbital periods defined through previous flight conditions supplied by Carlo Gavazzi Space. A complete new scheme of the LHP was created by using the SINDA/FLUINT tool [4]. The model considers 5 nodes to discretize the liquid and vapour lines and 23 (just 9 nodes indicated in the image, for clearance motivation) for the condenser [Fig. 6]:

Fig. 6 Novel SINDA/FLUINT model of the LHP The number of nodes is based on a compromise for good numerical resolution and the reduction of the CPU time. CONDENSER The condenser is attached to the Wake radiator as showed in Fig. 7:

Fig. 7 Condenser nodes attached to the radiator

The condenser nodes are linked to the WAKE radiator as showed in Fig. 8:

theoretical investigations are therefore necessary to better understand condensation in space applications and must be conducted before effective two-phase heat transport systems for thermal management of the microgravity environments can be validated. For the reasons explained above, the common gravity models will be considered here. In particular the Rohsenow correlation will be the input in the SINDA/FLUINT model:

 ρl g ( ρl − ρv ) h fg L3  Nu = 0,943    µl kl (Tsat − Ts ) 

1/ 4

Fig. 8 Section of the condenser and the WAKE radiator As it is visible the footprint width is 12.5 mm. The heat transfer coefficient from condenser line to radiator panels 2 is set to a constant value of 800 W/m K [6]. The process of vapour condensation results physically from the interaction of high-energy vapour phase molecules with the interface molecules of a bulk subcooled liquid phase, with the outcome of coalescence or “rebound”. It is commonly thought that fundamentally the process of condensation does not depend on the gravity level [7]. Condensation may be classified into two different process: homogeneous condensation and inhomogeneous condensation. Homogeneous condensation occurs in the bulk phase of a vapour when molecules of sufficiently low energy coalesce to form microscopic liquid phase particles. Although this process is of interest in certain technology applications, homogeneous nucleation does not play any role in condensation occurring in equipment and therefore is not very relevant here. Inhomogeneous condensation occurs either as filmwise or dropwise. Filmwise condensation occurs when the liquid phase wets the solid surface, otherwise dropwise condensation happens. Filmwise condensation occurs with most metal surface and working fluids. Dropwise condensation occurs only for specially treated surfaces, although any non-wetting surface/fluid combination will produce this phenomena. Shear-driven condensation within an externally cooled tube of constant diameter can be considered as a form of film condensation, as likely inside a LHP condenser. Vapour enters the tube at saturation conditions, condenses on the cool wall, wets the surface, and forms an annular liquid film. This type of condensation process is basically inertia dominated, in which the effects of gravity are minimal [7]. Energy is transferred due to the temperature difference between the phases, resulting in vapour condensing into liquid at the interface. The condensation heat transfer coefficient in the filmwise process depends on the thickness of the liquid layer. Some theoretical investigations of condensation in space or reduced-gravity environment has been carried out [8][9]. However, given the difficulty and expense of conducting extensive space-based experiments, experimental data are still scarce, and the mechanisms of condensation in the absence of gravity are not adequately understood. Additional experimental and

(1)

where ρl and ρv are respectively the liquid and the vapour density, g is the gravity constant, hfg the latent heat, L the condenser length, µl and kl respectively the liquid viscosity and conductivity, Tsat and Ts the saturation and the solid temperature. Such empirical correlation is oversimplified, but it provides a robust estimation and is valid also for the transition between the single phase and the two-phase mode. EVAPORATOR In the SINDA/FLUINT model the fluid contained in the evaporator is shared into 4 nodes [4]: one that accounts for the two-phase reservoir, one for the liquid in the wick and two for the vapour in the grooves. To simulate the solid part five temperature-varying capacitance nodes are inserted: the reservoir wall, the solid wick, the evaporator wall, the saddle and the equipment. All these solid nodes are diffusion type, hence in transient mode some of the power absorbed from the cryo-cooler

& (Q CRYO ) can be stored or released in the saddle while in steady state mode the overall power comes in the

& ) (Fig. 6). In normal LHP steadyevaporator wall ( Q SW state mode, heat is conducted from the evaporator body (evaporator wall) to the wick and is transferred to

& ) or it is leaked by backevaporate the fluid ( Q W & ). The remaining part of the power conduction ( Q back arriving in the evaporator wall can be considered negligible and it is transferred to the solid nodes of the

& ), to superheat the vapour in the grooves vapour line ( Q V & ), and is exchanged with the reservoir by an axial (Q G

& ). In the liquid control volume a heat conductance ( Q ER flux is considered arriving from the liquid lines ( H& RL ) and one heat flux is transferred to the vapour line ( H& RV ).

Gback =

Fig. 9 Heat exchanges inside the evaporator

Fig. 10 Conductances inside the evaporator SINDA/FLUINT model Majority of the heat input goes into vaporizing liquid or it is leaked in the compensation chamber. The ratio between those two heat links depends on the ratio between their conductances (Fig. 10, UWb=UW/Gback). The other heat patterns coming away from the evaporator wall transfer only a little portion of the overall power, hence this ratio assumes a crucial importance in the LHP working. The correlations used to account for the UW and the Gback are explained in the following, and they are based on the assumptions made by C&R [4]: ● Back conduction (Gback) Wick back conduction is comprised of two terms; the radial conduction through the wick, and film heat transfer on the core-side surface of the wick as shown in the equation below. For the purposes of this model, the core side film heat transfer is assumed to be very high in comparison to the radial conduction term [4]. In other words, the back conduction is dominated by the radial conduction term, therefore only the radial conductance is modeled:

Gback

 1 1  = +   Gradial G film 

2π K wick Levap D  ln  e , w  D   i,w 

(3)

where Kwick is the conductivity of the wick, Di,w and De,w respectively its internal and external diameter and Levap the length of the evaporator. Actually, the above term is corrected to account for the fact that the wick is wet and the temperature profile within the wick is not as simple as the above formula implies. Rather, the influx of slightly subcooled liquid (relative to the saturation condition at the outer diameter of the wick) and the heat exchange of this fluid with the wick material causes a nonlinear profile. A correction for this heat exchange effect, which is normally rather small, is made as a function of the current flow rate, liquid conductivity, etc. If Kwick represents the conductivity of the dry wick material instead of the whole (wet wick) conductivity, the effective conductance of the wet wick can be calculated by using the following Dunn and Reay correlation for sintered wicks where γ = Kliq/Kwick and ε = porosity:

 2 + γ − 2ε (1 − γ )  keff = kwick    2 + γ + ε (1 − γ ) 

(4)

The secondary wick, another component of the evaporator can, to a first order, be neglected as its primary purpose during steady state conditions is to ensure liquid is supplied to the wick. ● Heat transfer coefficient to the wick (Uw) For the understanding of the C&R choice of the heat transfer coefficient it is useful to propose the scheme that represents the complete evaporator model used in the SINDA/FLUINT code; the image is a detail description of all nodes employed to discretized the fluid and solid part of the LHP and the connectors used to link each part:

−1

(2)

If the flow rate were zero, the Gback would be defined in the equation below:

Fig. 11 Correlation between solid and fluid nodes

In the scheme we can see the node #10 (lines.10) to represent the solid wall of the evaporator; the convective heat transfer from evaporator wall to saturation (Gww) is calculated using the traditional heat transfer convective formula defined by Uevap (the evaporator internal heat transfer coefficient)

Gww = π U evap Di , w Levap

(5)

A junction is used to tie the saturation with the wick fluid in the fluid submodel with a conductance, expressed by:

U w = R * Gww

(6)

with R an empirical constant chosen by C&R to guarantee Uw to be in general 10 times more than Gww. In fact the temperature drop for the vaporization is actually modeled within the thermal model by this conductor (#10); a large value Uw is applied to make sure that vaporization does not generate a significant temperature drop. This method then assures that node #2 of solid model (lines.2) represents saturation and can therefore be used as a source of back conduction. In other words, at the saturation condition the in-flowing energy splits into evaporation and back-conduction into the compensation chamber (no attempt is made to change this modeling method during reflux mode when the evaporator floods, although the physics of the problem will be slightly different in that circumstance). Because of the uncertainty in some geometric data the resulting Uw and Gback values belong to a reasonable range and are not fixed to such precise values like C&R decided to choose, probably motivated by the attempt to guarantee no failure in the simulation run. In fact, in a common LHP most of the heat input goes into vaporizing liquid or it is leaked in the compensation chamber (back conduction). The ratio between those two heat links depends on the ratio between their conductances (UWb=UW/Gback). If an high value of Gback is imposed, the back conduction is influenced, in the sense that the power coming by back conduction is heavily forced to be zero but it is not physical; at the same time for a lower value of UWb (for example by imposing R values less than 10) the model run could fail in the case when the power coming in the LHP is close to zero since the LHP evaporator cannot supply the capillary force. For this reason a parametrical analysis was carried out, in order to understand the effects of the UWb rate on simulation results and running failures.

NUMERICAL RESULTS Since one of the main purpose of the research was to create a model running faster as possible for what concerns the CPU time, not all possible situations will be presented here but, as a sake of shortness, just the HOT

environment with Ramp-up failure (5 CCS modules) profile with transient conditions. A very important issue is that all simulations presented in this chapter involved a CPU time of about 11 – 12 h; so 14 times less than the previous Zinna’s model; that’s good result permitted to obtain fast runs, and so the possibility to conduce a parametrical analysis for the understanding of the model behavior at varying the UWb value. The numerical investigation starts from the UWb maximum value obtained using the C&R choice, which is fixed around 85, and will end with the minimum value used in the Zinna’s model around 11.5, considering also UWb = 65, 45 and 28 in sequence; such UWb values are obtained by changing the value of the R coefficient (eq. (6)). The control variables are the CAB base plate temperatures (ID from 200 to 219) and the temperature evolution at the end of the liquid line (subcooling temperature, T_CON_IN), at the beginning of the condenser (T_CON_OUT), in the compensation chamber (T_CC), in the evaporator wall (T_EVAP_WALL) and in the saddle (T_PAYLOAD). The first results refer to a simulation with the highest value of UWb = 85, compared with the same ones obtained by Zinna, using the lowest value of UWb = 11.5:

Fig. 12 CAB base-plate node temperatures, RAMPUP, UWb = 85

Fig. 13 CAB base-plate node temperatures, RAMPUP, UWb = 11.5 (Zinna’s model) and:

Fig. 14 LHP main temperatures, RAMP-UP, UWb = 85

Fig. 15 LHP main temperatures, RAMP-UP, UWb = 11.5 (Zinna’s model) We can notice:

The other diagrams, derivable after simulations conduced for UWb = 65 and 45, will be omitted since the temperature curve envelopments are the same to those reported for UWb = 85, reflecting the fact that we are in the presence of an ‘asymptotic’ behavior of the model, i.e. any variation of the conductances rate cannot affect sensibly the simulation results. Reducing the rate till UWb = 28 (omitted too), we notice an increasing of all temperatures and a remarkable gradient between the inlet and the outlet of the condenser. Unfortunately any other reduction in the value of the UWb ratio traduces in a running crash during the simulation, since under the level proposed the LHP can’t maintain the sufficient capillary pumping effect. Since we showed that in all simulations, in which the power is quite low, the decreasing of the UWb may reach a threshold under which the capillary pressure is not enough for the LHP running, we want now present the results obtained turning off the fluidic model for the first part of the simulation (about 45000 s) and concluding the process with the complete thermal and fluidic model. This assumption should not be too restrictive since the power off of the fluid model is made when the incoming power is very low; so even if in fact we vary the global conductance of the LHP, the total effect on the temperature is limited to less degrees. It’s useful to propose the results refer to a simulation with a high value of UWb = 85, for a comparison with the ones obtained with the same value of UWb but with fluidic part turned on:

- the temperature in Zinna’s model are higher, and this can be attributed (excluding the differences in the models linked to the evaporator geometric parameters) to the choice of UWb = 85 against 11.5. Increasing the value, in fact, the global conductance of the LHP increases since the power coming back to the compensation chamber by the wick is almost zero and all power goes into the fluid evaporation, as shown in the scheme below: Power

Saddle

Vapour grooves

Wall node

Saturation Node

QW

Fig. 17 CAB base-plate node temperatures, RAMPUP, UWb = 85 (fluidic part turned off until 45000 s)

Wick Fluid

Qback Compensation Chamber

Two-phase reservoir

Fig. 16 Negligible power in the evaporator for UWb = 85 - also the temperature inside the condenser are quite close each other, so the gradient from the input to the output is negligible compared to Zinna’s one.

Fig. 18 LHP temperatures, RAMP-UP, UWb = 85 (fluidic model turned off until 45000 s)

The temperature of the solid nodes of the CAB (Fig. 17) are now slightly higher until the fluidic part is turned off (< 45000 s), since the global conductance of the LHP is lower than in the complete model. But when both thermal and fluidic models are active (> 45000 s) the curve are exactly the same than those presented in Fig. 12; the model is then independent from the initial condition and the user could switch on or off the fluidic part at any instant time without problems about the effects on results. The temperatures of some thermal and fluidic nodes presents until 45000 s a ‘strange’ behavior since the fluid part is not active; the only range of interest is over 45000 s in which again we notice precisely the same trace than in Fig. 14. The last step of the analysis presented in this paper is a model that can turn on/off the fluidic part of the LHP model according to a precise value of the incoming power, thus, as said before, the critical element for the crash running because strictly length to the capillary pump limits. The following figures represent the simulation for a value of UWb = 11.5 (the same of Zinna’s model) and with an incoming power limit of 23 W:

Fig. 19 CAB base-plate node temperatures, RAMPUP, UWb = 11.5 (fluidic part turned off below 23 W of incoming power)

Fig. 20 LHP temperatures, RAMP-UP, UWb = 11.5 (fluidic model turned off below 23 W incoming power) In this case the trend of the temperature for CAB (Fig. 19) seems to be quite similar to Zinna’s one (Fig. 13) since the UWb ratio is the same and because, for low incoming power (before the rump), the absence of the

fluid model is not so relevant to effect noteworthy the temperature profile. Also Fig. 20 shows a raise in the picks of the temperature during the Rump-up and an increasing gradient of the temperatures between the two extremes of the condenser, since the T_CON_IN and T_CON_OUT curves are significantly far-between. Besides, since in some moments of the simulation the fluidic part is turned off, the solid part is the only that runs on the pc; then we can notice an additional reduction of the CPU time of about 5 - 6 h.

CONCLUSION This document defines the working of the Magnetic avionic box (CAB). Just one operational mode is analyzed for the CAB: Ramp-up for the failure mode with 5 CCS modules. The LHP model has been realized by using the lumped parameter code SINDA/FLUINT. The results proposed in the previous sections bring to the following conclusions: -

The ratio UWb between the heat transfer coefficient between the evaporator body and the primary wick (Uw) and from the wick to the compensation chamber (Gback) has a noteworthy influence on the temperature profiles. Increasing its value, in fact, the global conductance of the LHP increases since the power coming back to the compensation chamber by the wick is almost zero and the whole thermal power goes into the fluid vaporization; the temperature peaks tend to decrease

-

an high value of Gback influences the back conduction, in the sense that the power coming by back conduction will be negligible, hence the model run could fail in the case when the power coming in the LHP is close to zero since the LHP evaporator cannot supply the necessary capillary force,

-

if the fluidic model is turned off under some critical value of the incoming power (23 W), the failure problems may be by-passed. Even if the LHP global conductances vary, the total effect on the temperature is limited to few degrees,

-

the CPU time is around 11 - 12 h for the complete thermal and fluid model and 5 - 6 h for the model with the turning on/off of the fluid submodel; so a good decreasing in the execution time it has been obtained respect to the reference point of this research, represented by Zinna’s model.

In conclusion the present research supplies a quite flexible and fast model for LHP simulations; such numerical tool could be thought as a reference for any kind of LHP even changing the CAB conditions in which the device will be considered for cooling.

ACKNOWLEDGMENTS This work was conducted also with the economical and technical helps of the Carlo Gavazzi Space company, to which our particular acknowledges are addressed. Specially we want to thank Ing. Ivan Corradino and Ing. Paolo Ruzza for their technical support and Ing. Marco Molina for his important ‘experience’ in LHP research.

REFERENCES 1. C&R technologies, SINDA/FLUINT user’s manual. March 2004, version 4.6. 2. G.E. Cossali, M. Marengo, S. Zinna, 2005. Response of a loop heat pipe subjected to various heat load transient, XXIV Congresso Nazionale UIT sulla Trasmissione del Calore, Parma. 3. AMS-02 CAB Loop Heat Pipe Specification, CGS, 11/11/2005. 4. Cullimore and Ring Technologies, Inc., Loop Heat Pipe Prebuilt Model, 2004, User documentation. 5. Stefano Zinna, Numerical analysis of a loop heat pipe for the thermal control of a cryo-cooler on the international space station. 2007, Thesis in Industrial engineering. 6. Franzoso A. (DT/MT) , Du W.(SDU), Vettore C., CAB THERMAL CONTROL SYSTEM DESIGN AND ANALYSIS REPORT, CGS, 22/05/2006 7. Basil N. Antar and Vappu S. Nuotio-Antar. Fundamentals of Low Gravity Fluid Dynamics and Heat Transfer. CRC Press, Boca Raton, Florida, 1993. 8. Ryan M. MacGillivray, Kamiel S. Gabriel. A STUDY OF ANNULAR FLOW FILM CHARACTERISTICS IN MICROGRAVITY AND HYPERGRAVITY CONDITIONS, Acta Astronautica, 53 (2003) 289297, Canada 9. NASA/CR—2006-214085 Two Phase Flow Modeling: Summary of Flow Regimes and Pressure Drop Correlations in Reduced and Partial Gravity 10. A.K. Goncharov, V.L. Barantsevich, A.A. Orlov, Experience of development of heat pipes applied in Russian spacecrafts, in: Proc. Fifth Minsk Int. Sem. Heat Pipes, Heat Pumps, Refrigerators, Minsk, Belarus, September 8–11, 2003. 11. D.T. Swanson, Thermal control technologies for complex spacecraft systems, Proc. 13th Int. Heat Pipe Conf. Shanghai, China, China Astronautic Publishing House, Beijing (2004). 12. M. Molina, C. Vettore, M. Cova, Progress in the Alpha Magnetic Spectrometer (AMS-02) Thermal

Control System (TCS) Design, Operations Scenarios and Verification Approach, SAE 2005-01-2987 13. B. Cullimore and Jane Baumann, Steady-State and Transient Loop Heat Pipe Modeling, ICES 2000.

DEFINITIONS, ACRONYMS, ABBREVIATIONS Variable Gback [W/K] Uw [W/K] hfg [J/Kg] µl [kg/ms] kl [W/mK] NU L [m] 2 g [m/s ] hfg [J/Kg] ρ [kg/m3] Tsat [K] Ts [K] Levap [m] Di,w [m] De,w [m] Kwick [W/mK] Keff [W/mK]

ε Uevap [W/K] Gww [W/K]

Description Back conductance Heat transfer inside the wick Latent heat Liquid dynamic viscosity Liquid thermal conductivity Nusselt number Condenser length Gravity acceleration Latent heat Fluid density Saturation temperature Evaporator wall temperature Evaporator length Internal diameter of the wick External diameter of the wick Conductivity of dry wick material Effective wick conductivity Wick porosity Evaporator internal heat transfer coefficient Conductance from evaporator wall to saturation

USS: Unique support structure CCS: electronic converters to charge the magnet CAB: Magnet Avionic Box LHP: Loop heat pipe AMS: Alpha Magnetic Spectrometer C&R: Cullimore and Ring CGS: Carlo Gavazzi Space

APPENDIX Description Capillary Pump Wick material Wick external diameter Wick Wick internal diameter properties Wick pore radius Wick permeability Wick porosity Number of axial grooves Axial groove depth Axial Grooves Axial groove width Groove Shape Evaporator material Evaporator Evaporator heated length Evaporator wide Contact conductance between CAB panel and saddle Contact area between CAB panel and saddle CAB Power distribution on the baseplate Power distribution on the other walls of the CAB

Saddle material

Saddle material Saddle mass Saddle dimensions (length/width/height) Contact conductance between saddle and evaporator Contact area between saddle and evaporator

Compensation Chamber Internal fluid volume in the compensation chamber Compensation Chamber material Conductance from evaporator to reservoir wall

Value

Units

Nickel 0.022 m 0.0076 m 1.2E-06 m 4.0E-14 m2 0.6 (0-1) 6 1.50E-03 m 2.50E-03 m Rectangular Stainless steel 0.152 m 0.0381 m 2500

2

W/m *K 2

0.0229 m They are already in the submodel of CAB. it is stable for steady state. for RAMP-UP a new profile will be provided AI 6061 0.485 kg 3

Fig. 7

Mm

5000

W/m *K

0.00579

2

m

2

3

113.6E-06 m Stainless steel 0.053 W/K

Vapour Line Vapour line mass

Size

Bending Thermal

Vapour Line Material Vapour Line Wall Thickness Vapour Line Length Vapour Line Hydraulic Diameter Total number of bends Angle of bend number 1-7 Bending radius of bend number 1-7 ISOLATED

4.14873E06 Stainless steel 0.0005 0.755 0.003 7 90° 0.015

Kg m m m º m K

2

Environment

m W

Liquid Line

Size

Bending

Liquid line mass Liquid Line Material Liquid Line Wall Thickness Liquid Line Length Liquid Line Hydraulic Diameter Total number of bends Angle of bend number 1-4 Bending radius of bend number 1-4

Thermal Environment

2.89273E06 Stainless steel 0.0005 0.737 0.002 5 90° 0.015

ISOLATED

kg m m m º m K 2 m W

Condenser Line Condenser line mass

Size

Bending

Condenser Line Material Condenser Line Wall Thickness Condenser Line Length Condenser Line Hydraulic Diameter Total number of bends Angle of bend number 1-11 Bending radius of bend number 1-11

9.26049E05 Stainless steel 0.001 7.373

kg m m

0.003 11 90°

m º

0.015

m

Radiator Condenser saddle material

AL6061

Conductance between condenser saddle and condenser tube N/A Conductance between condenser saddle and radiator plate N/A Condenser saddle mass Thickness of condenser saddle 0.02 Conductance between condenser tube and radiator plate 800 Contact area between condenser tube and radiator plate 0.0125*7.373 Material of radiator plate AL6061 Thickness of radiator plate 0.0005

2

W/m K m

2

m

Fluid Total mass of fluid in the LHP

0.055

kg