FDM/FEM System-level Analysis of Heat Pipes and LHPs in Modern CAD Environments

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

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 • Musthave compatibility with industry standard thermal analysis tools, including radiation/orbital analyzers • Shouldbe 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 ofHeat Pipe Degradationfrom Zero NCG (left)to 8.5e-9 kg-mole (right)

8. 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 • 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 • 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. 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 with heat pipes without 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 quicklymodeled using FloCAD’spipe component. • Walls can be FEM meshes,Thermal Desktop surfaces,or plain tubes (piping scheduleavailable) • 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