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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]
C&R Technologies, Inc.
www.crtech.com
Phone 303.971.0292
Fax 303.971.0035
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*DLi
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 | [ 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)
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
Gas Blockage in CCHPs
Parametric Study of
Heat Pipe Degradation
from 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
without heat pipes
Heat Pipes Embedded in a Honeycomb Panel
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 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.
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
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