1. www.crtech.com C&R Technologies, Inc. Phone 303.971.0292 Fax 303.971.0035 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 l The users confidence in any technology is based in part on its predictability The ability to model predictable behavior The ability to bound unpredictable behavior l Must have compatibility with industry standard thermal analysis tools, including radiation/orbital analyzers l 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 l 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 l 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 pipes axial resistance is independent of transport length: not even anisotropic materials approximate this behavior No information is gleaned regarding limits, design margin l Heat pipes can be modeled as a large conductor Analyst shouldnt 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 l 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!! l Network-style Vapor node, conductor fan approach: G i = 1/R i = H i *P* L i where: H i = H evap (T i > T vapor ) H i = H cond (T i < T vapor )

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

6. Noncondensible Gas l 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:* m gas = i {(P-P sat,i )* L i *A pipe /(R gas *T i )} 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 Modeling l Requires reservoir volume and gas charge (sized by heat pipe vender) l Model axial conduction along pipe to capture heat leak through adiabatic section of pipe l Accurately capture reservoir parasitics through system model l 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 l Relatively straightforward to extend methods to 2D walls Example: top half can condense while bottom half evaporates l However: QL eff 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 l 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 QL eff reported Vapor node as boundary node optionally Implicit within-SINDA solution used for improved stability l New CAD-based methods CAD based model generation New 1D piping methods within 2D/3D CAD models

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

12. Heat Pipe Data Input l 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. Whats Missing? Future Heat Pipe Modeling Efforts l 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 l 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) l CCHPs and VCHPs are SINDA only (thermal networks) Can access complex fluid properties, but FLUINT is not required l LHPs require more complex solutions (two-phase thermohydraulics: fluid networks) l Condenser can be quickly modeled using FloCADs pipe component. Walls can be FEM meshes, Thermal Desktop surfaces, or plain tubes (piping schedule available) l Easy to connect or disconnect pipes Manifolds, etc.

17. l 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 LHP Condenser Modeling

18. Conclusions l 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 l New CAD methods permit models to be developed in a fraction of the time compared with traditional techniques