Numerical Simulation of Flow Inside Grooves of

a Loop Heat Pipe Evaporator

Pierre-Yves FRAVALLO1,3, Marc Prat1, Vincent Platel2, Guillaume Boudier3, Benjamin Lagier4

1 Institut de Mécanique des Fluides de Toulouse 2 Laboratoire de Thermique, Energétique et Procédés 3 Centre National d’Etudes Spatiales 4Airbus Defence and Space

13th to 15th November 2019 Journées CNES Jeunes Chercheurs 2019

Context: As satellite can be submitted to a wide range of temperature differences, it is necessary to keep their

electronic components inside their working temperature range. One of the devices used to ensure a good thermal

control of those equipments are the Loop Heat Pipes (LHP). Yet the accurate prediction of their behavior is still a

challenge.

State of art: In a previous work [1], a Pore Network Model (PNM) was developed with success and permitted to

study the thermal and fluid behavior within a LHP's unit cell (fig.2) (fig.3). However some assumptions

(temperature inside the vapor grooves, thermal exchange between vapor and casing and the wick...) have to be

checked. Only a few study are devoted to what happens in the vapour grooves [2].

Objective: Check the validity of previous assumptions and study their impact on the LHP's evaporator.

Method: In a first approach the maximal temperature of the casing and the flow rate produced by the unit cell for

each heat flux applied are extracted from the PNM (fig.4). These data are inputs for a Comsol Multiphysics model

which solves the thermal and fluid flow inside one groove. It is then possible to compare the fluid temperature and

the exchange coefficients inside the groove with the correlation usually used.

Introduction

Figure 1 – Loop heat pipe

Hypothesis:

§ Gravity is neglected,

§ Vapour flow is incompressible

§ Wick interface is in saturated state

§ Constant thermophysical properties

Heat transfer:

§ Casing: !. k"!T = 0

§ Groove: (#$%&'$%)*%. !T = !. (+$%!T*

Flow in groove:

§ Continuity equation: !. ,- = 0

§ Momentum equation:

# )%. ! ) = %!. /'1 2 %3 !) 2% !) 4 /%5

63 !. ) 1

Main boundary conditions: (fig.5)

§ 1: Top of casing : 7 = 789:;9<>?@

§ 2: Casing part in contact with Compensation

Chamber (CC/Tank) :

k"!T . A = %k"%(7BCD / 7*

&CBEAF%DGEH+AIBB%EA%HJADCHD%KEDG%&&%LM

§ 3 – 8: Symmetry on lateral faces:% k"!T . N = 0 and )%. N = 0

§ 4: Wick-groove interface: 7 = 7BCD and ) = O>?P. N

§ 5 – 7: Outflow conditions and no stress :

k"!T . N = 0 and

/'1 2 %3 !) 2% !) 4 /%5

63 !. ) 1 . N = 0

§ 6: Wick-casing interface: 7 = 7BCD

Mathematical model

Figure 2 – Cross section of evaporator and 3D unit cell [1]

Pressure drops inside the groove: The pressure drop in a pipe can be written as: QR = %S%

U%V%WX

X%YZ%, based on

Poiseuille law where : S =[\

]^ and applying mass conservation W =

_`ab%U

cdeeW^fg^`hZi. Then it is possible to plot the

computed pressure drop inside the groove versus the Poiseuille pressure drop: QR = %jX%l%_`ab%U

X

%cdeeW^fZ^`hZi%YZX %%(fig.6).

As the pressure differences are not significant except for the highest value tested, the Poiseuille correlation

can be considered as a good first approach.

Temperature inside the groove: The average temperature inside the groove is based on a mixing

approach: mn`U`ah o = %p m%q%rss

s_ with: A=cross section of the groove and t = p q%rs

s.

In fig.7 the difference between the assumed and the computed temperature when the wick is unsaturated

reaches 3K and raises to 8K when a vapor pocket occurs. For detailed evaporator modelling the groove

temperature cannot be assumed as equal to the saturation temperature when the wick is unsaturated.

Heat Transfer coefficient: (fig. 8)

§The local heat transfer coefficient at each surface is computed as: Zuqdv%wexyw(o* = %zwexyw

mn`U`ah o {mwexyw, with:

|}~;9} = +$�7. N for the top and side faces and |}~;9} = +$�7. N 2 #$&'$� T��� / T��� . N for the injection side.

Then the average heat transfer coefficient is: Zuqdv o =p Zuqdv%wexyw o ru�qdv%�`riZ�

�qdv�`riZ.

§The difference between the correlation used in [1], [3] and the one computed on each surface, illustrates the

heterogeneity and under or over estimation of the heat transfer coefficient on the surfaces.

Results:

Figure 3 – Evaporator behaviour under a heat flux range. [1]

Grooves inside the casing with vapour phase in contact with casing is in light grey.

The assumptions and correlations used previously underestimate the heat transfers

which occur within the groove inside the evaporator.

Current work: Study of the impact of these observations on the conductance and

mass flow rate of the evaporator with the PNM model.

Conclusions and prospects

[1] Mottet L. (2016) Simulations of heat and mass transfer

within the capillary evaporator of a two-phase loop. I.N.P.T.

Ph.D. Thesis

[2] Jesuthasan N. (2011) Modeling of Thermofluid

Phenomena in Segmented Network Simulations of Loop Heat

Pipes. McGill University PH.D Thesis

[3] C. Sleicher and M. Rouse, "A convenient correlation for

heat transfer to constant and variable property fluids in

turbulent pipe flow," International Journal of Heat and Mass

Transfer, vol. 18, pp. 677-683, 1975

Figure 5 – Geometry in Comsol and boundary

conditions

In order to ensure thermal

control and to limit the

maximum temperature of any

devices, the evaporator’s

conductance : �����%[W/K/cm²]

!

Is the ratio that is usually used

to represent its performances.

����� =����%����%(

���5*

T���"����� / T<9�

Figure 4 – Injection velocity and Tmax casing from PNM with grooves in casing

Figure 6 – Difference between pressure drop in

Comsol (color) and corresponding Poiseuille

correlation (black).

Figure 7 – Difference between mixing

temperature and saturation temperature

Figure 8 – Heat transfer coefficients

Va

po

ur

po

cke

t U

nsa

tura

ted

Sa

tura

ted

Increase

Tmax casing

Increase

Tmax casing

Increase

Tmax casing

Increase

Tmax casing

Increase

Tmax casing