impact of fluid flow pressure drop on temperature of
TRANSCRIPT
48th International Conference on Environmental Systems ICES-2018-25 8-12 July 2018, Albuquerque, New Mexico
Copyright © 2018 Jet Propulsion Laboratory
Impact of Fluid Flow Pressure drop on Temperature of
Components Controlled by Mechanically Pumped Fluid
Loop Thermal Control System
Pradeep Bhandari1, Jenny Hua2, Razmig Kandilian3, and Arthur J. Mastropietro3
Jet Propulsion Laboratory, California Institute of Technology
4800 Oak Grove Dr., Pasadena, CA 91109
In a typical thermal control system that employs a mechanically pumped fluid loop to
control component temperatures, fluid flow pressure drop is minimized to ensure that
adequate fluid flow can be provided by the pump. Engineers often are overly concerned about
violating a maximum pressure drop, almost treating it as a “wall” that should not be crossed.
The true “wall” is the control of the temperatures of the components served by the loop to
ensure that their temperatures do not violate their allowed limits. As a case study, for
assessing this “constraint,” sensitivity analyses were undertaken to understand if this is truly
a major constraint, and to assess the impact of pressure drop exceedance on the controlled
components’ temperatures. The flow impedance is varied as a parameter to understand how
it affects the controlled components’ temperatures. One key finding was that the
temperatures of the controlled components is relatively insensitive to the flow impedance
increases. This finding is obviously most relevant to this particular case study; however, this
also provides the process and guidance for assessing the performance of other pump/loop
combinations in terms of their sensitivity to pressure drop impedances.
V. Nomenclature
CFC-11 = Trichlorofluoromethane (Freon-11)
HRS = Heat Rejection System
IPA = Integrated Pump Assembly
LC = Lower Cylinder
MLI = Multi-layer Insulation
MPF = Mars Pathfinder
MPFL = Mechanically Pumped Fluid Loop
MSL = Mars Science Laboratory
NASA = National Aeronautics and Space Administration
PM = Propulsion Module
RHB = Replacement Heater Block
REM = Rocket Engine Module
RF = Radio Frequency
RW = Reaction Wheel
UC = Upper Cylinder
WCH = Worst Case Hot
WCC = Worst Case Cold
1 Principal Thermal Engineer, Propulsion, Thermal & Materials Engineering Section 2 Thermal Engineer, Instrument and Payload Thermal Engineering 3 Thermal Engineer, Spacecraft Thermal Engineering
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I. Introduction
ECHANICALLY pumped fluid loops (MPFLs) have been utilized for temperature control of spacecraft
designed for interplanetary missions like the Mars Pathfinder, Mars Exploration Rovers, Mars Science
Laboratory (Curiosity Rover) and are slated for future missions like the Mars 2020, Europa Clipper and Parker Solar
Probe. Additionally, they have been utilized in the Space Shuttle and the international Space Station [1]. Besides the
fluid pump, the loop employs long lengths of metal tubing bonded to various interfaces to transfer heat from the heat
sources to the heat sinks. In addition, there are various components in the flow path such as mechanical fittings, flex
lines, bends, tees, elbows, filters, and heat exchangers that impede the flow of the fluid and contribute to the drop in
the fluid pressure (ΔP). All these contribute to the fluid’s pressure drop for the desired flow rate to achieve the requisite
heat transfer coefficient and thermal performance. Each pump has a performance curve that determines the flow rate
in the system based on the pressure drop. The system also has a flow rate dependent pressure drop. The intersection
of these two curves determines the operating point, i.e., the flow rate and the pressure drop, of the system. In general,
as system pressure drop increases the resultant fluid flow rate decreases. The flow rate is the key driver of the thermal
performance of the fluid loop because it determines both the fluid flow thermal capacity, �̇�𝐶𝑝, and the heat transfer
coefficient h between the fluid and the tubing in contact with the thermally controlled surfaces. These two factors
determine the temperature gradients in the fluid flow and between the fluid and the temperature-controlled surface.
A typical fluid loop can be divided into components that are characterized by major and minor pressure losses.
The former include straight tubing while the latter is comprised of fittings, tees, elbows, and various other small
components. The so-called “minor” components can potentially be the major causes of pressure drop rather than the
“major” components. Accounting for straight length ΔPs is relatively simple and accurate using correlations2.
However, accounting for “minor” losses by analytical means is not precise and large variances exist in the estimating
methods1. The only way to be accurate is to measure these in test setups to simulate the flight system configuration.
These tests are performed much later in the design flow and the configuration typically evolves during the design
process. Therefore, the ΔP estimates could have large uncertainty in estimation and due to the incompleteness of the
spacecraft and heat rejection system (HRS) layout design. Hence, the concern is that if there were large errors in the
ΔP estimates, they could lead to temperature violations at the key interfaces.
This paper presents a methodology to determine the sensitivity of controlled interface temperatures to pressure
drop. First, overall system pressure drop as a function of flow rate was estimated to obtain the system operation point.
Then, the heat transfer coefficient and the fluid heat capacity were estimated based on the operating flow rate. Key
interface temperatures were then estimated for the nominal system pressure drop as well as considering errors of up
to 90% in the estimated pressure drop. Finally, the methodology was applied to the Europa Clipper heat rejection
system (EC-HRS) to determine the sensitivity of interface temperatures to pressure drop.
II. Methodology for estimating interface temperature sensitivity to pressure drop
HRS controlled interface temperatures depend on the heat capacity of the fluid and the flow rate of the fluid as the
latter determines the heat transfer coefficient between the fluid and the interface. Moreover, the flow rate of the fluid
depends on the pressure drop in the system. Therefore, higher-pressure drops would lead to warmer interface
temperatures. If thermally controlled interfaces are already close to their allowable limits, larger ΔPs could potentially
lead to maximum allowable flight temperature (AFT) violations. This paper presents the methodology for performing
sensitivity analysis of interface temperatures on pressure losses in the system. The process consists of three steps: A)
estimating fluid flow rate in the system and B) performing thermal analysis to determine fluid and interface
temperatures, and C) performing sensitivity analysis to determine the effect of pressure drop increase on interface
temperatures.
A. Process for Estimating Flow Rate
The basic process of estimating the flow rate in the fluid loop consists of three parts:
1) Determination of the fluid loop system curve: flow impedance of every component in the fluid flow should
be estimated as well as the pressure drop in the flow path as a function of flow rate. The flow impedance is
the pressure drop per unit flow rate for any component. The typical components comprise of straight and
curved tubing, fittings such as mechanical connectors, joints, tees, elbows, bends, flexible lines, filters, etc.
The system curve is approximately parabolic in shape for turbulent flow. Then, the total pressure drop in the
system is estimated as the sum of the pressure drops of the sum of all the components1
M
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∆𝑷 = −𝝆𝑽𝟐
𝟐(𝒇
𝑳
𝑫+ 𝑲) 1
Here, 𝑓 is the friction factor, 𝐿 and 𝐷 are the length and diameter of the pipe respectively, and 𝐾 is the so-
called loss coefficient. Table 1 presents 𝐿/𝐷 and 𝐾 factors for various components of the fluid loop in equation
1. In general, standard components and shapes have simple relationships for estimating flow impedances. For
other unique configurations, like flexible lines, mechanical fittings, filters, etc., experimental data are the only
means to estimate the flow impedances. Moreover, the friction factor 𝑓 for laminar flow (Re<4000) can be
expressed as2
𝒇 =𝟔𝟒
𝑹𝒆 2
Where 𝑅𝑒 is the Reynold’s number.
The friction factor 𝑓 for Turbulent flow (104 < 𝑅𝑒 < 107 ) is given by3
𝒇 =𝟏
[𝟏.𝟓𝟖𝟏 𝐥𝐧(𝑹𝒆)−𝟑.𝟐𝟖]𝟐 3
2) Pump curve: This is a characteristic of the pump, which describes the relationship between the pump pressure
produced and the flow rate through the pump. This is typically provided by the pump vendor using pump fluid
models that are corrected by test data.
3) The two curves are cross-plotted (ΔP vs. flow rate) with the intersection representing the operating point of
the overall system. The operating point describes the flow rate produced and the corresponding pressure drop
(or pressure head) in the system.
Table 1: Flow pressure drop impedances for some example components in fluid flow path [1]
Minor Components K Factor L/D
90o street elbow 1.85 47
90 o standard elbow 1 26
90 o standard elbow: screwed R/a = 2 1.820 47
90 o standard elbow: Long Radius R/a = 3 0.993 25
90 o smooth bend in circular pipe 0.340 9
180 o bends 3.7 95
180 o standard elbow: Long Radius R/a = 3 1.448 37
180 o standard elbow: screwed R/a = 2 2.688 69
180 o smooth bends in circular pipe 0.521 13
Tee Fittings - line flow 0.8 20
Tee Fittings - branch 2.35 60
Mechanical Fittings 0.8 20
B. Process for Estimating Temperatures
The estimated flow rate in the system can then be used to compute fluid temperature distribution in the HRS at all
key temperature controlled modules for the worst-case hot (WCH) and worst-case cold (WCC) operating conditions
by knowing the heat flow (Q in W) into or out of each module as follows:
�̇�𝒄𝒑(𝑻𝒇,𝒐𝒖𝒕 − 𝑻𝒇,𝒊𝒏) = 𝐐 4
Where 𝑇𝑓,𝑜𝑢𝑡 and 𝑇𝑓,𝑖𝑛 are the fluid inlet and outlet temperatures. A radiator (coupled to the flowing fluid) is employed
to reject excess heat from the system. The heat rejection rate for the radiator can be estimated as
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𝐐 = 𝛆𝛔𝐀𝒔𝐓𝟒 5
Where ε is the emissivity of the radiator, 𝐴𝑠 (in m2) is the radiating area, T is the average absolute temperature of the
radiator in K, and σ is the Stefan-Boltzman constant equal to 5.67 x 10-8 (W.m−2.K−4). The interface temperatures can
be estimated based on the fluid temperature Tf, the heat transfer conductance between fluid and interface and the heat
transfer rate Q in or out of the module as
𝑻𝒊 = 𝑻𝒇,𝒐𝒖𝒕 + 𝑸 𝑮⁄ 6
Where 𝑇𝑖 (in oC) is the interface temperature for each module while G (in W/K) is the thermal conductance G between the fluid and the interface. The latter is estimated as the sum of the conductance between the fluid and the tube wall ℎ𝐴 and the tube wall to the interface 𝐺𝑡𝑢𝑏𝑒
𝑮 =𝟏
𝑹= (
𝟏
𝒉𝑨+
𝟏
𝑮𝒕𝒖𝒃𝒆)
−𝟏
7
Here, A is the surface area of the tube. The heat transfer coefficient h can be determined based on the Nusselt number Nu
𝒉 =𝑵𝒖𝒌𝒇
𝑫𝒉 8
where 𝑘𝑓 (in W/m.K)is the thermal conductivity of the fluid and 𝐷ℎ (in m) is the hydraulic diameter of the
tube. For laminar flow where Re<4000, the Nusselt number has a constant value2 𝑵𝒖 = 𝟒 9
For turbulent flow where 104<Re<5x106 and 0.5<Pr<200, the Nusselt number is expressed as2
𝑵𝒖 = (𝒇
𝟖)
(𝑹𝒆𝑷𝒓)
𝟏. 𝟎𝟕 + 𝟏𝟐. 𝟕(𝑷𝒓𝟐/𝟑 − 𝟏)(𝒇 𝟖⁄ )𝟎.𝟓
Here, the flow regime is assumed to be laminar for Re<4000 and turbulent when Re>4000. In reality, the flow is
fully laminar when Re<2300 and fully turbulent for Re>10,000, and in transition in between those two limits. For
this study, for simplicity and conservatism, it was assumed that the flow was laminar for Re<4000 and turbulent for
Re>4000. Note that the Nusselt number is equal to 4 for laminar flow and significantly smaller than that for turbulent
flow. As a result, the conductance between the fluid to the interface will be much smaller for laminar compared to
turbulent flows, therefore will cause a larger temperature gradient between the fluid and interface. Therefore, the first
metric for maximum allowable ΔP is to avoid low conductance by ensuring that the flow does not transition to laminar
at low flow rates.
C. Process for Deriving Sensitivity of Operating points to Changes in Flow Impedances
To understand the sensitivity of interface temperatures to the reference ΔP values, an error is added to the latter as
a variable between 10% to 100% of the nominal ΔP in incremental steps and tabulated. Following this, families of
system of plots of ΔP vs. flow rate are cross-plotted with the pump curve to create a family of operating points that
represent the sensitivity of resultant flow rates as a function of flow pressure drop impedance errors.
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III. Application of the methodology to the Europa Clipper HRS
Figure 1: Europa Clipper spacecraft model showing the major modules and thermal control components.
The Europa Clipper mission is a deep space planetary exploration mission with an objective to evaluate the
potential habitability of Jupiter’s icy moon Europa. Specifically, it aims to 1) characterize the icy shell of Europa and
the properties of the subsurface water including ocean salinity and ice sheet thickness, 2) determine the chemical
composition of the surface matter and the atmosphere including potential plumes, and 3) characterize the geology of
the moon to aid with the selection of future landing sites as well as to understand the formation of magmatic, tectonic,
and impact landforms3. Figure 1 illustrates the Europa Clipper spacecraft showing the Vault, Radio Frequency (RF),
and Propulsion Modules (PM) as well as thermal control components such as the replacement heater block and the
radiator.
Figure 2: HRS loop diagram illustrating the three cases investigated, (a) serial flow in all modules with low
flow rate pump, (b) parallel flow in the propulsion module using the high flow rate pump, and (c) parallel
flow in the propulsion module and the radiator using the high flow rate pump.
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Figure 2 shows a schematic of the Europa Clipper HRS loop servicing the following modules and components:
a) Avionics Vault module where the electronic components reside
b) Radio Frequency (RF) Module
c) Replacement heater block (RHB), used to supply supplemental heat to the loop
d) Rocket engine modules (REMs) each housing six reaction control system (RCS) thrusters
e) Upper cylinder (UC) and lower cylinder (UC) of propulsion module
f) Thermal control radiator used to reject excess heat
The REMs, RW, UC, and LC can be grouped together into the propulsion module (PM). The thermal control valve
(TCV) functions to control the vault inlet temperature by modulating the flow rate to the radiator4. The details of the
TCV operation were described by Birur et.al.4 but are outside of the scope of this study. The valve was assumed to be
fully open, i.e., 99.86% flow to radiator in the hot case, and fully closed, i.e., 0.16% flow to the radiator in the cold
case. The three cases investigated were (a) serial flow through all spacecraft modules using the low flow pump, (b)
parallel flow in the propulsion module using the high flow rate pump, and (c) parallel flow in the propulsion module
and radiator using the high flow rate pump. The low flow rate and the high flow rate pumps are two of the proposed
Europa Clipper HRS pumps. The former can supply 68.9 kPa (10 psid) of pressure to CFC-11 flowing at 0.75 LPM
while the latter can provide 151.6 kPa (22 psid) at 1.5 LPM.
IV. Operating Flow Rate and thermal conductance Estimates
Figure 2a and 2b show the pressure drop vs flow rate respectively for the high flow rate pump with parallel flow in
the PM (Figure 2b) system and low flow rate pump with serial flow (Figure 2a). The figure also shows the pump
curves with the intersection point of the two curve marking the operating point for the HRS. Additionally, the system
curve was plotted with various pressure drop errors ranging from 20% to 75% and the operating flow rate for those
cases were obtained from the plots. Table 2 summarizes the correspondence between the pressure drop error and the
operating point flow rate. Three different configurations or cases were investigated: a) low flow rate pump with serial
flow through all the modules, b) high flow rate pump with split flow in propulsion module, and c) high flow rate pump
with split flow in propulsion module and radiator.
Figures 3a and 3b show the fluid flow rate and conductance as a function of pressure drop error for the three cases
analyzed. The nominal pressure drop for Cases 1 to 3 were 53.7 kPa (7.8 psid), 141.9 kPa (20.6 psid), and 129.5 kPa
(18.8 psid), respectively. These corresponded to flow rates equal to 0.89 LPM, 1.53 LPM, and 1.59 LPM, respectively.
A pressure drop estimation error of 90% in Case (a) led to only a 30% drop in resultant flow rate. The resulting flow
rate of 0.63 LPM remained in the turbulent regime. Note that as stated previously, fluid to interface conductance is
Figure 3: Pump and system curves for Europa Clipper (a) high and (b) low flow rate pumps
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significantly larger for turbulent flow than laminar. Moreover, the fluid to interface conductance decreased from 11.6
to 8.8 W/m.K. For Case (b), a 60% error in the pressure drop caused the flow rate to decrease from 1.53 LPM to 1.25
LPM. Note that, the flow rate was 0.63 LPM in the propulsion module where the flow was split. The corresponding
conductance 𝐺 decreased from 18.6 W/m.K to 15.5 W/m.K due to the decrease in the flow rate. Similarly, this resulted
in a reduction in the conductance of 13% in the PM compared to its nominal value of 10.1 W/m.K at 1.5 LPM. Finally,
for Case (c) a 70% pressure drop error led to a 20% reduction in flow rate reducing conductance value from 19.2 to
15.7 W/m.K. All these cases illustrate the relatively small impact of the pressure drop error on the resultant flow rate
and the fluid to interface thermal conductance. This suggests the Europa Clipper HRS design is robust with respect to
future changes in design and errors in the pressure drop estimates.
Table 2: Example impacts of Pressure drop error on flow rates & Tube thermal conductances
Operating Cases % ΔP Error Flow Rate V Conductance G
a Low flow rate pump 0% 0.89 LPM 11.6 W/m-C
90% 0.63 LPM 8.8 W/m-C
b High Flow rate pump with split PM 0% 1.53 LPM 18.6 W/m-C
60% 1.25 LPM 15.5 W/m-C
c High flow rate pump with split PM
and radiator
0% 1.59 LPM 19.2 W/m-C
70% 1.27 LPM 15.7 W/m-C
Figure 4: (a) Fluid to interface conductance and (b) flow rate as a function of pressure drop error for low flow
rate pump, high flow rate pump with split flow in the PM, and high flow rate pump with split flow in PM and
radiator.
V. Spreadsheet for computing ΔP, Flow Rate & Thermal Conductances
To facilitate rapid calculations of the various parameters like ΔP, flow rate, and thermal conductances, a Microsoft
Excel® spreadsheet was created with built in macros to automatically estimate pressure drop, flow rate, and thermal
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conductance for high and low flow rate pump, different ΔP errors, as well as different fluid routing. A macro button
starts the calculations after inserting above parameters in the appropriate cells. All relevant ΔPs, flow rates and thermal
conductances are tabulated and plotted (as delineated before) as outputs. Flags are provided to warn the user of laminar
flow, which would lead to low thermal conductances for large pressure drop errors.
VI. Estimating Interface Temperature Sensitivity to Pressure Drop
Once the flow rates were determined, the fluid heat capacity, �̇�𝐶𝑝 and module total thermal conductances G were
used to perform a detailed thermal model of the overall system. For each component module the fluid inlet and outlet
temperatures as well as the average interface temperature was estimated based on the heat transfer rate Q and the
total conductance G. Two thermally bounding cases were analyzed for Case b (Figure 2b), a worst case hot at 0.65
AU and a worst case cold at 5.6 AU. Figure 5 and Figure 6 respectively present the block diagrams of HRS for WCH
and WCC conditions along with the heat inputs and outputs for each module as well as fluid and interface temperatures
for Case (b) with nominal pressure drop. The fluid temperature range was between 0.2 oC and 25.9 oC and the PM
interfaces were maintained within their allowable flight temperatures of 0 oC and 35 oC in both WCH and WCC.
Moreover, the radiator was maintained 15 oC above the CFC-11 freezing point at -95 oC in WCC to limit heat loss
through the radiator to less than 10 W. Finally, the Vault was maintained within its allowable flight temperature range
of -15 oC to 45 oC.
Figure 5: Schematic of heat balance and temperature for Case (b) for worst-case hot conditions
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Figure 6: Schematic of heat balance and temperature for Case (b) for worst-case cold conditions
VII. Assessing Worst Case Conditions at different pressure drop errors
Figure 7a and 7b show increase in WCH interface temperatures and WCC heater power as a function of increasing
pressure drop error. They illustrate that Europa Clipper HRS design is robust with respect to pressure drop. Indeed, a
75% error in ΔP for Case (b), i.e., high flow rate pump with spit PM, resulted in less than 2 oC increase in interface
temperatures compared to the nominal interface temperatures. Moreover, a 90% error in ΔP for Case (a), low flow
rate pump with serial flow through the system, resulted in less than 5 oC increase in interface temperatures compared
to the nominal values. In addition, a linear increase in ΔT vs. pressure drop was observed when the flow was in
turbulent regime. However, a sharp increase in interface temperatures was observed when flow became laminar in
both Case (a) and Case (c) due to the smaller fluid to interface heat transfer conductance associated with laminar flow
compared to turbulent regime.
Survival heater power needed to maintain the HRS controlled interfaces at their minimum AFTs increased linearly
with increasing pressure drop error. This was due to two different effects: 1) smaller fluid to interface conductance,
i.e., higher average fluid loop temperature was necessary to maintain minimum AFTs resulting in additional heat loss
and 2) the HRS operated at higher temperature and with a larger temperature gradient across the loop due to the smaller
heat capacity of the fluid �̇�𝐶𝑝 in the system with larger pressure drop.
On the other hand, low flow rate system (Case a) required more heater power compared to high flow rate system
(Case b and c) for the same ΔP error. The increase in survival heater power as a function of ΔP error is smaller for
high flow rate Cases than for low flow rate Case regardless of radiator routing. Indeed, in WCC the radiator is bypassed
completely and has no impact on loop performance. Indeed, heater power 𝑄ℎ𝑒𝑎𝑡𝑒𝑟 increased by less than 3 W (<2.5%)
due to 75% increase in pressure drop.
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VII. Conclusions
A comprehensive case study of the effect of pressure drop increases on the overall thermal performance of a
mechanically pumped fluid loop was conducted on the Clipper HRS, and the key finding was that it was very robust
to accommodating significant pressure drop increases above the nominal estimated values. Pressure drop increases
of as much as 60% to 90% above the most conservative values lead to relatively small reductions in margins against
max allowable temperature limits. For cold conditions, this would also translate to relatively small increases in
required survival heater powers to maintain component temperatures above their minimum allowable limits. Hence,
this study gives confidence in the robustness of the fluid loop’s thermal performance to pressure drop increases either
due to the fidelity of the estimating process or due to the inevitable changes in the spacecraft configuration as the
design matures. It also dispels the notion that pressure drop is a “wall” which is impermeable or cannot be crossed
without very adverse impacts. The consequent flow regime being laminar - because of excessive pressure drops
leading to smaller flow rates - is more drastic in consequence (more of a “wall”) due to the much lower heat transfer
coefficients (thermal coupling between fluid and tubing walls) that could lead to large increases in controlled interface
temperatures. Even though this was a case study for a specific configuration (Europa Clipper), the methodology
presented in this paper and the general conclusions can be utilized for different configurations that utilize single phase
mechanically pumped fluid loops for their thermal control.
VIII. Acknowledgments
The development described in this paper was carried out at the Jet Propulsion Laboratory, California Institute of
Technology, under a contract with the National Aeronautics and Space Administration. The authors express their
thanks to Brian Carroll at JPL for data provided on measured pressure drop impedances for miscellaneous
components (mechanical fittings, flex lines, etc.) from past and current missions. Reference herein to any specific
commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not constitute or
imply its endorsement by the United States Government or the Jet Propulsion Laboratory, California Institute of
Technology. Copyright 2018 California Institute of Technology. Government sponsorship acknowledged.
Figure 7: Effect of pressure drop error on (a) maximum interface temperature increase in WCH
conditions and (b) increase in survival heat for WCC conditions for Europa Clipper HRS controlled
component
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IX. References 1
T. T. Lam, G. Birur and P. Bhandari, "Pumped Fluid Loops," in Spacecraft Thermal Control Handbook, El
Segundo, CA, The Aerospace Press, 2002, pp. 405-472. 2 A. Mills and C. Coimbra, Heat Transfer, San Diego, CA: Temporal Publishing, 2016. 3 R. Pappalardo, D. Senske, H. Korth, R. Klima, S. Vance and K. Craft, "The Europa Clipper Mission: Exploring
The Habilatbility of A Unique Icy World," in European Planetary Science Congress, Berlin, Germany, 2017. 4 G. Birur, M. Prina, P. Bhandari, P. Karlman, B. Hernandez, B. Kinter, P. Wilson, D. Bame and Ganapathi,
"Applications, Development of Passively Actuated Thermal Control Valves for Passive Control of Mechanically
Pumped Single-Phase Fluid Loops for Space," in International Conference on Environmental Systems, San
Francisco, CA, 2008.