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FDM/FEM System-level Analysis of Heat Pipes and LHPs in Modern CAD Environments Aerospace Thermal 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 C&R Technologies, Inc. www. crtech. com 9 Red Fox Lane Littleton CO 80127 -5710 USA Phone 303. 971. 0292 Fax 303. 971. 0035

The Need for Analysis l The user’s confidence in any technology is based in The Need for Analysis l The user’s confidence in any technology is based in part on its predictability ü The ability to model predictable behavior ü The ability to bound unpredictable behavior l l 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

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

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

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

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

Gas Blockage in CCHPs Parametric Study of Heat Pipe Degradation from Zero NCG (left) Gas Blockage in CCHPs Parametric Study of Heat Pipe Degradation from Zero NCG (left) to 8. 5 e-9 kg-mole (right)

VCHP Modeling l Requires reservoir volume and gas charge (sized by heat pipe vender) 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 1 D or 2 D Peltier device (TEC), proportional heater, etc. for reservoir (or remote payload) temperature control VCHP rejecting heat through a remote radiator

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

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

New CAD Methods l Modeling heat pipes in Flo. CAD ü Import CAD geometry New CAD Methods l Modeling heat pipes in Flo. CAD ü Import CAD geometry ü Quickly convert CAD lines and polylines to “pipes” ü Generates HEATPIPE and HEATPIPE 2 calls automatically without heat pipes Heat Pipes Embedded in a Honeycomb Panel with heat pipes

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

CAD-based Centerlines and Arbitrary Cross Sections CAD-based Centerlines and Arbitrary Cross Sections

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

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

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

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

Conclusions l Heat pipes and LHPs are can be easily modeled at the system-level Conclusions l Heat pipes and LHPs are can be easily modeled at the system-level ü Heat pipes: using modern incarnations of “trusted” methods ü 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