1. Aerospace Thermal Control Workshop 2005
FDM/FEM System-level Analysis of Heat Pipes and LHPs in Modern CAD Environments
Aerospace Thermal Control Workshop 2005
Brent Cullimore, Jane Baumann

2. The Need for Analysis
The user’s confidence in any technology is based in part on its predictability
The ability to model predictable behavior
The ability to bound unpredictable behavior
Must have compatibility with industry standard thermal analysis tools, including radiation/orbital analyzers
Should be able to integrate with concurrent engineering methods such as CAD and structural/FEM

3. How Not to Model a Heat Pipe: Common Misconceptions
“Full two-phase thermohydraulic modeling is required”
Overkill with respect to heat pipe modeling at the system level
Applicable thermohydraulic solvers are available for detailed modeling, but uncertainties in inputs can be quite large
“Heat pipes can be represented by solid bars with an artificially high thermal conductivity”
Disruptive to the numerical solution (especially in transient analyses)
Unlike a highly conductive bar, a heat pipe’s axial resistance is independent of transport length: not even anisotropic materials approximate this behavior
No information is gleaned regarding limits, design margin
“Heat pipes can be modeled as a large conductor”
Analyst shouldn’t assume which sections will absorb heat and which will reject it
Heat pipes can exhibit up to a two-fold difference in convection coefficients between evaporation and condensation

4. Typical System-Level Approach
Targeted toward users (vs. developers) of heat pipes:
Given simple vendor-supplied or test-correlated data …
How will the heat pipe behave? (Predict temps accurately)
How far is it operating from design limits?
From this perspective, no need to model what happens past these limits!!
Network-style “Vapor node, conductor fan” approach:
Gi = 1/Ri = Hi*P*DLi
where: Hi = Hevap (Ti > Tvapor) Hi = Hcond (Ti < Tvapor)

5. Next Level: QLeff Checking Power-Length Product Limits
Sum energies along pipe, looking for peak capacity:
QLeff = maxi | [ Si( Qi/2 + Sj=0,i-1Qj ) DLi ] |
Can be compared with vendor-supplied QLeff as a function of temperature, tilt
What matters is verifying margin, not modeling deprime
Exception: start-up of liquid metal pipes (methods available)

6. Noncondensible Gas Gas Front Modeling (VCHP or gas-blocked CCHP)
Amount of gas (in gmol, kmol, or lbmol) must be known or guessed (can be a variable for automated correlation)
Gas front modeled in 1D: “flat front”
Iteratively find the location of the gas front
Sum gas masses from reservoir end (or cold end). For a perfect gas:* mgas = Si {(P-Psat,i)*DLi*Apipe/(Rgas*Ti)}
Block condensation in proportion to the gas content for each section
Provides sizing verification for VCHP, degradation for CCHP
____________ * Real gases may be used with full FLUINT FPROP blocks

7. Gas Blockage in CCHPs
Parametric Study of Heat Pipe Degradation from Zero NCG (left) to 8.5e-9 kg-mole (right)

8. VCHP rejecting heat through a remote radiator
VCHP Modeling
Requires reservoir volume and gas charge (sized by heat pipe vender)
Model axial conduction along pipe to capture heat leak through adiabatic section of pipe
Accurately capture reservoir parasitics through system model
Easy to integrate 1D or 2D Peltier device (TEC), proportional heater, etc. for reservoir (or remote payload) temperature control
VCHP rejecting heat through a remote radiator

9. 2D Wall Models Condenser Section
Relatively straightforward to extend methods to 2D walls
Example: top half can condense while bottom half evaporates
However:
QLeff remains a 1D concept
Gas blockage remains flat front (1D, across cross-section)
This can complicate vapor chamber fin modeling
Condenser Section

10. The Old Meets the New Proven Heat Pipe Routines New CAD-based methods
VCHPDA SINDA subroutine
1D Modeling of VCHP gas front
Vapor node as boundary node for stability
SINDA/FLUINT Heat Pipe routines (HEATPIPE, HEATPIPE2)
Modeling of CCHP with or w/out NCG present
Modeling of VCHP gas front
1D or 2D wall models available
QLeff reported
Vapor node as boundary node optionally
Implicit within-SINDA solution used for improved stability
New CAD-based methods
CAD based model generation
New 1D piping methods within 2D/3D CAD models

11. Heat Pipes Embedded in a Honeycomb Panel
New CAD Methods
Modeling heat pipes in FloCAD
Import CAD geometry
Quickly convert CAD lines and polylines to “pipes”
Generates HEATPIPE and HEATPIPE2 calls automatically
without heat pipes
with heat pipes
Heat Pipes Embedded in a Honeycomb Panel

12. Heat Pipe Data Input
User-defined heat pipe options and inputs

13. CAD-based Centerlines and Arbitrary Cross Sections

14. Attach to 2D/3D Objects (contact), radiate off walls …

15. What’s Missing? Future Heat Pipe Modeling Efforts
Currently heat pipe walls are limited to 1D or 2D finite difference modeling (FDM)
Other FloCAD objects (like LHP condenser lines) allow walls to be unstructured FEM meshes, collections of other surfaces, etc.
But a detailed model can conflict with common assumptions such as heat transfer at the “vapor core diameter”
Vapor Chamber Fins
2D “power-length” capacity checks
2D gas front modeling (not currently a user concern)

16. A little about Loop Heat Pipes (LHPs)
CCHPs and VCHPs are “SINDA only” (thermal networks)
Can access complex fluid properties, but FLUINT is not required
LHPs require more complex solutions (two-phase thermohydraulics: fluid networks)
Condenser can be quickly modeled using FloCAD’s pipe component.
Walls can be FEM meshes, Thermal Desktop surfaces, or plain tubes (piping schedule available)
Easy to connect or disconnect pipes
Manifolds, etc.

17. LHP Condenser Modeling
Must accurately predict subcooling production and minor liquid line heat leaks
Import CAD geometry for condenser layout
Requires sufficient resolution to capture thermal gradients
Capture variable heat transfer coefficient in the condenser line based on flow regime
Model flow splits in parallel leg condenser
Model flow regulators

18. Conclusions
Heat pipes and LHPs are can be easily modeled at the system-level
Heat pipes: using modern incarnations of “trusted” methods
LHPs: using off-the-shelf, validated thermohydraulic solutions
New CAD methods permit models to be developed in a fraction of the time compared with traditional techniques