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.

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

[email protected]

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

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

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*Li

where:Hi = Hevap (Ti > Tvapor)Hi = Hcond (Ti < Tvapor)

Next Level: QLeff

Checking Power-Length Product Limits Sum energies along pipe, looking for peak capacity:

QLeff = maxi | [ i( Qi/2 + j=0,i-1Qj ) Li ] |

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)

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 = i {(P-Psat,i)*Li*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

Gas Blockage in CCHPs

Parametric Study ofHeat Pipe Degradationfrom Zero NCG (left)

to 8.5e-9 kg-mole (right)

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

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

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

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

Heat Pipes Embedded in a Honeycomb Panel

without heat pipes with heat pipes

Heat Pipe Data Input

User-defined heat pipe options and inputs

CAD-based Centerlines and Arbitrary Cross Sections

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

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)

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.

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

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