TFAWS Paper Session
Benchmarking of NX Space Systems
Thermal (TMG) for use in
Determining Specular Radiant Flux
Distributions
Carl Poplawsky (Maya Simulation Technologies)
Dr. Chris Jackson (Maya Heat Transfer Technologies)
Chris Blake (Maya Heat Transfer Technologies)
Thermal & Fluids Analysis Workshop
TFAWS 2011
August 15-19, 2011
NASA Langley Research Center
Newport News, VA
Agenda
• Summary of NX Space Systems Thermal (NXSST)
radiation calculation methods
– Monte Carlo
– Deterministic
– Hemiview
• Deterministic Benchmark for compound parabolic
concentrator (CPC) Specular Reflection
– Monte Carlo – reference solution
– Deterministic - test analysis
• Summary of diffuse/specular QA test results
– Monte Carlo – reference solution
– Deterministic - test analysis
TFAWS 2011 – August 15-19, 2011
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NXSST Radiation Calculation Methods
• NX Space Systems Thermal (NXSST) includes three approaches for
view factor calculations
– Monte Carlo
• Suitable for both diffuse and specular problems
– Deterministic
• Suitable for both diffuse and specular problems
– Hemiview
• Suitable only for diffuse problems
• NXSST also has several choices for radiative conductance
calculations
– Monte Carlo
– Gebhardt’s
– Openheim’s
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NXSST Radiation Calculation Methods
FEM
Deterministic
Ray Tracing/
Semi-Analytic
Hemicube
Monte Carlo
Geometric/Ray-Traced View Factors
Gebhardt’s
Method
Monte Carlo
Radiosity
(or Oppenheim’s)
Method
Radiative couplings (RAD-K’s)
Numerical Model
Other inputs (heat loads
other conductances,
etc.)
Nonlinear outer
iterations,
linear solver
Temperatures
NXSST Ray Tracing

Ray tracing enables treatment of optical properties beyond simple diffuse
(Lambertian) emission and reflection

More complicated reflection and transmission optical properties can be
supported if ray tracing is also introduced

Specular reflection from curved surfaces can be captured through use of
parabolic shell elements

Ray tracing can be used in two ways:


With the Monte Carlo method, to compute heat loads and radiative exchange
factors directly
To produce Ray-traced view factors with the Deterministic Method
which can be used together with the view factor method
Ray Tracing With Monte Carlo

Monte Carlo ray-tracing can be used to compute view factors

More powerful is the application of Monte Carlo to compute radiative
conductances and radiative heat loads directly
 This is the default behavior
 Works by following the actual path of the radiation as it goes through
the model

Instead of computing View Factors, MC computes the Gray Body View
Factor: it is the fraction of energy leaving element i, absorbed by element
j, including all intermediate reflections

Instead of computing radiative heat load view factors, Monte Carlo
computes heat loads directly
NXSST Deterministic View Factor Method
For each element pair (i,j):
1. Determine if elements i,j are potentially shadowed
2. If not shadowed and target is diffuse
i. Compute view factor with exact contour integral method
3. If shadowed or target has specular or transmissive properties
i. Subdivide elements according to element subdivision criterion
ii. Determine shadowing between sub-elements
iii. For unshadowed sub-element pairs, determine view factor contribution
using Nusselt sphere method
iv. if target element is specular or transparent, ray trace the reflected or
transmitted component through the model
v. Add view factor contributions of sub-elements
Deterministic Ray-tracing for view factor correction

Ray-tracing corrects the geometric view factors to account for specular
reflections and transmission

Rays are launched from every element which has a direct view of an element
with specular reflectivity or transmissivity

Ray density is controlled by the user through the subdivision or error control
 Default is 256 rays per element pair

With the Deterministic option, ray distribution is deterministic, not random
 Elements are subdivided and rays are launched between the subelements

Diffuse reflections are still accounted for through Oppenheim’s or Gebhardt’s
method
 Effective radiating areas and optical properties are modified after ray
tracing to account for effects which have already been ray-traced
NX SST Hemicube Method



With the Hemicube method, a half cube is situated around the “emitter”
element.
Each face of the cube is divided into pixels, each pixel having a known
view factor contribution.
The image of the surrounding “receiver” elements is projected onto the
hemicube.
(a) Projection of two elements onto the hemicube
(b) Pixel-resolution image of the elements
on the hemicube faces.
NX SST Hemicube Method

The hemicube algorithm in NX Thermal uses the Open Graphics
Library (OGL) to render scenes (either on GPU or CPU)

During the solve, the hemicube engine draws the scene of elements as
seen from each element in the Radiation Request
 The software post processes these images to determine the view
factors

Potentially very fast

Accuracy depends upon:
 The number of pixels used to draw the images
 Resolution limit associated with the minimum view factor
contribution of one pixel
 Error due to sampling from discrete locations of the viewing
element (addressed with subdivision criteria)

Supports only diffuse (Lambertian) optical properties
NXSST Comparison of Methods
Optical Properties
ε(T)?
Speed vs.
accuracy
Computation of
Heat Loads
Monte Carlo
(direct computation)
Deterministic
Hemicube
Can potentially
support any optical
property model.
Supports diffuse,
specular, and
transmissive
properties.
Supports diffuse
properties.
NO, must repeat
ray-tracing
YES, if used with
Oppenheim
YES, if used with
Oppenheim
Slow for diffuse
properties.
Competitive with
specular/
transmissive optical
properties.
Good. Competitive
with Hemiview if
surfaces are planar.
Fast.
Direct calculation, no
Yes. Diffuse
view factors
reflections calculated
necessary
using geometric view
factors.
N/A. Only used to
compute geometric view
factors for diffuse
reflections.
NXSST Radiative Conductances
 Radiative couplings (RAD-K’s) take into account all
reflections including diffuse reflections
 Radiosity (Oppenheim’s) method:
– Additional radiosity nodes are introduced into the model, view
factors can be used directly to calculate radiative couplings
 Gebhardt’s method:
– Radiative couplings are computed by solving a linear system
involving the view factors and the optical properties
 Monte Carlo
– Radiative couplings are computed directly by tracing rays
through the model
• Ray behaviour statistically follows exactly the (non-wave) behaviour
of the light travelling through the system
NXSST Radiative Conductances
Gebhardt’s
Radiosity /
(Oppenheim’s)
Speed
Monte Carlo
Mediocre,
requires matrix
solve
Good, no matrix solve
necessary
Slow for diffuse
properties. More
competitive with
specular / transmisisve
surfaces
NO, must re-solve
matrix
YES, goes right into
numerical model
NO, must repeat ray
tracing
NO
NO
YES, easy to do
Limited support
Accuracy (within
limitations)
Uniform
illumination
approximation
Uniform illumination
approximation
Depends on number of
rays
Intuitive results?
YES
Need heat map tools
YES
ε(T)?
BRDF, ε(θ,φ)?
Deterministic Ray Tracing

In computing solar view factors, NXSST automatically uses ray-tracing to model
specular reflections and transmissions.

The ray-tracing operations are carried out after computing the solar view factors
for all elements.

Rays are launched from all elements which have a non-zero solar view factor
and a specular reflectivity or transmissivity component defined.
 ray density is controlled by the element subdivision parameter.
 anti-aliasing algorithm automatically increases the subdivision parameter
for specular and/or transmissive elements

When used with the View Factor Method:

Rays are traced through the enclosure until one of the following conditions
is satisfied:
 the ray impinges a fully diffuse element
 the ray’s magnitude is reduced to less than 0.1% of its original value
 the ray has been traced through 100 reflections

Diffusely reflected fluxes are distributed through the model using the view
factors
Deterministic Benchmark for CPC Specular Reflection
• The CPC is a good test for specular reflectivity
– Concentrates light at the CPC exit (detector location) when within the
acceptance angle (ө)
• Essentially traps all incoming light
– Light distribution at detector varies with light incidence angle (ø)
Incidence Angle (ø)
TFAWS 2011 – August 15-19, 2011
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Deterministic Benchmark for CPC Specular Reflection
• The CPC is defined with an off-axis revolved parabola
– The focal point moves with light incidence angle (ø)
• Focal point is beyond the detector when ø = 0
• Focal point is at the detector edge when ø = ө/2
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Deterministic Benchmark for CPC Specular Reflection
• 5mm exit diameter CPC chosen for benchmark
– 45 degree acceptance angle
– 25 degree acceptance angle
25 degrees
45 degrees
(same scale)
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Deterministic Benchmark for CPC Specular Reflection
• Mesh size held constant
– 1mm parabolic triangular shells for the reflector
– .5mm parabolic triangular shells for the detector
• Linear elements are unsuitable for curved surface specularity
25 degrees
45 degrees
(same scale)
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Deterministic Benchmark for CPC Specular Reflection
• Monte Carlo used for reference solution
– Studies at ø = 0° shows little sensitivity of average flux value at
the detector to the number of rays/element for this example
• Higher sensitivity may be observed with other optical geometries
– 2000 rays/element chosen for reference solution
MONTE CARLO
RAYS/ELEMENT
1000
2000
3000
AVERAGE
DETECTOR
FLUX (W/mm2)
1.773e-2 (45°)
6.372e-2 (25°)
1.773e-2 (45°)
6.373e-2 (25°)
1.773e-2 (45°)
6.373e-2 (25°)
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Deterministic Benchmark for CPC Specular Reflection
• Deterministic test analysis average detector flux
correlates well with reference solution
– ø = 0 degrees
– Little sensitivity to number of subdivisions for this example
• Higher sensitivity may be observed with other optical geometries
– Deterministic subdivision factor = 3 used for all subsequent
analysis solutions
DETERMINISTIC
ELEMENT
SUBDIVISIONS
1
3
5
AVERAGE
DETECTOR
FLUX % ERROR
0.00% (45°)
0.00% (25°)
0.00% (45°)
0.00% (25°)
0.00% (45°)
0.00% (25°)
TFAWS 2011 – August 15-19, 2011
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Deterministic Benchmark for CPC Specular Reflection
• Deterministic test analysis detector flux distribution
correlates well with reference solution
– 25 degree CPC
– ø = 0 degrees
REFERENCE
TFAWS 2011 – August 15-19, 2011
DETERMINISTIC
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Deterministic Benchmark for CPC Specular Reflection
• Deterministic test analysis detector flux distribution
correlates well with reference solution
– 45 degree CPC
– ø = 0 degrees
REFERENCE
DETERMINISTIC
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Deterministic Benchmark for CPC Specular Reflection
• Deterministic test analysis average detector flux over a range of
incidence angles correlates well with reference solution
– ø = 0 to 30 degrees
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Deterministic Benchmark for CPC Specular Reflection
• Deterministic test analysis detector flux distribution correlates well
with reference solution
– 25 degree CPC and ø = 15°
REFERENCE
DETERMINISTIC
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Deterministic Benchmark for CPC Specular Reflection
• Deterministic test analysis detector flux distribution correlates well
with reference solution
– 45 degree CPC and ø = 30°
REFERENCE
DETERMINISTIC
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Deterministic Benchmark for CPC Specular Reflection
• The Deterministic method provided a slight advantage in terms of
computer resource for this example
– CPU times are for the full solve through temperatures
– Both CPC’s solved in the same solution
– Results will vary depending on subdivision factor (DT) or rays/element (MC)
• Reasonable values were used for this benchmark
2000
1800
1600
1400
1200
DT
1000
MC
800
600
400
200
0
0
5
10
15
20
Incidence
Angle 25
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35
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Deterministic Benchmark for CPC Specular Reflection
• Deterministic method specular results are
indistinguishable from those for the Monte Carlo
reference solution
• For the settings chosen for this benchmark, Deterministic
provides a slight advantage in reduced computer
resource
• Monte Carlo and Deterministic approaches are equally
recommended for specularity
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Summary of diffuse/specular QA test results
• Over 30 test cases for specular/diffuse radiation models
are exercised during QA testing for all NXSST releases
– Temperature results differences between Monte Carlo,
Deterministic are routinely tabulated
• Using MC as the reference solution and the latest
software revision, the maximum difference in local
temperature was tabulated for each case, and then
normalized
– Deterministic models run with default view factor error criterion
• Element view factor sum +/- 2%
• Average normalized maximum temperature difference
between DT and MC was .79%
– Well within the default view factor error criterion
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NX Space Systems Thermal
THANK YOU
(www.mayahtt.com)
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CPC with Specular and Diffuse Properties
• Mesh size held constant
– 1mm linear triangular shells for the reflector
– .5mm linear triangular shells for the detector
• Linear elements chosen for the sake of speed
25 degrees
Reflector Surface Properties
εIR = 0.5
ρIR,d = 0.5
αS= 0
ρS,d = 0.5
ρS,s = 0.5
Detector Surface Properties
εIR = 1
αS= 1
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CPC with Specular and Diffuse Properties
• Radiation problem setup
– Conductive properties set to null; radiative problem only
– Collimated solar flux of 1000 W/m2 parallel to CPC axis
– Radiative heat exchange within the CPC and to the environment.
No external radiation.
• Two analysis types
– Monte Carlo to compute RadKs and to compute heat loads
– Deterministic to compute view factors with ray tracing;
Oppenheim method for “RadKs”. Error criterion of 2%.
• Parameters varied
– Monte Carlo: # rays per element; same for radiation request and
solar load calculations
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CPC with Specular and Diffuse Properties
• As number of rays per element increases, detector
temperatures level off and approach temperatures
obtained by deterministic method with error criterion of
2% (dotted line)
Detector Temperatures
500
450
400
Temperature (C)
350
300
250
Min T
200
Max T
Ave T
150
100
50
0
0
2000
4000
6000
8000
10000
12000
14000
Rays Per Element
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CPC with Specular and Diffuse Properties
• Detector temperature distribution for deterministic case (error
criterion 2%) correlates with Monte Carlo case (15000 rays/element)
– Deterministic results are ~2.5% warmer
MONTE CARLO
DETERMINISTIC
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CPC with Specular and Diffuse Properties
• Detector flux distribution for deterministic case (error criterion 2%)
correlates well with Monte Carlo case (15000 rays/element)
MONTE CARLO
DETERMINISTIC
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