1. 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

2. 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
This presentation is separated into 3 parts:
First, I will present a summary of the radiation calculation methods used in NX Space Systems Thermal.
Then, we will review the results of small benchmark problem, comparing the deterministic and Monte Carlo methods. The model is of a Compound Parabolic Concentrator
Finally, I have a short summary of the results validating the deterministic method against the Monte Carlo method. Models from MAYA’s QA test suite are used for this validation.
TFAWS 2011 – August 15-19, 2011

3. 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
Hemiview
Suitable only for diffuse problems
NXSST also has several choices for radiative conductance calculations
Gebhardt’s
Openheim’s
There are three methods for calculating view factors, or “form factors”: MC, DT, and HV. Each is applicable for different situations: MC for diffuse, specular, and complex surface properties; DT for diffuse and specular; HV for diffuse.
There are three methods for calculating radiative conductances.
TFAWS 2011 – August 15-19, 2011

4. NXSST Radiation Calculation Methods
FEM
Deterministic Ray Tracing/
Semi-Analytic
Hemicube
Monte Carlo
Monte Carlo
Geometric/Ray-Traced View Factors
Radiosity
(or Oppenheim’s)
Method
Gebhardt’s
Method
Radiative couplings (RAD-K’s)
This is shown schematically on this slide. The deterministic and Hemicube methods will produce view factors, whether geometric or ray-traced. These are then turned into radiative conductances. The Monte Carlo method can also produce view factors, but can also produced classical “Radk”s directly. The radiative conductances are incorporated into the solution matrix, which ends up being a function of temperature (hence a non-linear system). The system is solved iteratively for temperatures; for each iteration, a linear solver solves the GT=Q problem.
Numerical Model
Other inputs (heat loads
other conductances,
etc.)
Nonlinear outer iterations,
linear solver
Temperatures

5. 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
(...) Images show diffuse reflections, specular reflection, and an example of a BRDF. Ray tracing enables the more complex reflections to be simulated. Both the Monte Carlo method and the Deterministic methods involve ray tracing.

6. 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
MC can be used to compute view factors only. In the diffuse case, rays are launched randomly from each element. The quantity of rays that fall directly on another element, determines the VF.
However, MC is more powerful when used to compute RadKs and radiative heat loads directly. A ray is considered the path of a photon. Rays are launched randomly from each element and the path they follow throughout the model is tracked. When a ray falls on an element, a probability function , arising from the surface properties, is sampled, and that determines what happens to the ray. So, if an element has an emissivity of 0.5, the ray has a 50% chance of being absorbed. In this fashion, MC computes the GBVF, which is the fraction of energy leaving one element and falling on another, through all intermediate reflections. The same process is used when the rays originate from a radiative source.

7. NXSST Monte Carlo Method
For radiation enclosures with simple diffuse properties of emission and diffuse reflection, Monte Carlo is inferior in terms of performance / accuracy tradeoff when compared to the Hemicube and Deterministic methods
Useful for advanced optical properties:
Specular transmissive optical properties: handled by the Deterministic method, but experiments show MC results can converge faster for some test cases.
BRDF’s and direction-dependent emissivity: only handled by BRDF (limited support in NXSST)
Does not suffer from uniform illumination approximation which is troublesome for coarse meshes
Based on this description you can see how Monte Carlo is not as accurate for a model containing only diffuse surface properties. Deterministic methods based on geometric VFs are “exact”, and in order to match that, a lot of rays have to be launched. MC is useful for advanced optical properties, and is needed for BRDFs and direction-dependent emissivity. VF methods suffer from the uniform illumination problem when a mesh is quite coarse: radiation absorbed by only a portion of an element is reradiated by the entire surface area of the element. MC doesn’t encounter this.
(BRDF: ray strikes the element at a given incidence angle (spherical), and the reflected portion can go off in a number of different directions (spherical), each with different intensity. BRDF is the proportion in that direction).
Element 2
Element 1
Element 2
VF Method
Element 1

8. NXSST Deterministic View Factor Method
For each element pair (i,j):
Determine if elements i,j are potentially shadowed
If not shadowed and target is diffuse
Compute view factor with exact contour integral method
If shadowed or target has specular or transmissive properties
Subdivide elements according to element subdivision criterion
Determine shadowing between sub-elements
For unshadowed sub-element pairs, determine view factor contribution using Nusselt sphere method
if target element is specular or transparent, ray trace the reflected or transmitted component through the model
Add view factor contributions of sub-elements
With DT, BBVFs are computed between each pair of elements in the model. (...) If target is specular/transparent, rays are launched from subelement to subelement.

9. 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
Ray density is determined by user-controlled subdivision parameter. Geometric VFs are adjusted accordingly. Think of a mirror example.

10. 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.
(...) The emitter element is subdivided. For each subelement, the scene is rendered. VF contributions are summed up.

11. 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

12. NXSST Comparison of Methods
Monte Carlo
(direct computation)
Deterministic
Hemicube
Optical Properties
Can potentially support any optical property model.
Supports diffuse, specular, and transmissive properties.
Supports diffuse properties.
ε(T)?
NO, must repeat ray-tracing
YES, if used with Oppenheim
Speed vs. accuracy
Slow for diffuse properties. Competitive with specular/ transmissive optical properties.
Good. Competitive with Hemiview if surfaces are planar.
Fast.
Computation of Heat Loads
Direct calculation, no view factors necessary
Yes. Diffuse reflections calculated using geometric view factors.
N/A. Only used to compute geometric view factors for diffuse reflections.
(...) When a model is illuminated by a radiative source (like the sun), diffuse reflections of that source energy are accounted for using the geometric VFs. (Describe an example.)

13. 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
Radiative couplings take into account all the energy leaving one element and falling on another, including the diffuse reflections. Gebhardt’s method solves a matrix equation involving the VFs. MC, we saw computes these RadKs directly. The radiosity method is slightly different. Additional calculation points called “Oppenheim elements” are added to the model. The so-called radiative conductances between O-elements are functions of the BBVF and the surface area. Between the O-element and the original element, f(e,A,T). It’s a direct substitution, no solving, no iteration.

14. NXSST Radiative Conductances
Gebhardt’s
Radiosity /
(Oppenheim’s)
Monte Carlo
Speed
Mediocre, requires matrix solve
Good, no matrix solve necessary
Slow for diffuse properties. More competitive with specular / transmisisve surfaces
ε(T)?
NO, must re-solve matrix
YES, goes right into numerical model
NO, must repeat ray tracing
BRDF, ε(θ,φ)? NO
YES, easy to do
Limited support
Accuracy (within limitations)
Uniform illumination approximation
Depends on number of rays
Intuitive results?
YES
Need heat map tools

15. 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
Ray-tracing is performed automatically when computing environmental view factors (i.e. the amount of incoming source radiation falling on an element) and there are specular properties in the model. This is done after direct source view factors are computed. Any source radiation that is reflected diffusely is distributed throughout the model based on the BBVFs. (These BBVFs should also be raytraced if there are specular properties in the model).

16. 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)
CPC = compound parabolic concentrator. All light within the acceptance angle is trapped by the CPC
Incidence Angle (ø)
TFAWS 2011 – August 15-19, 2011

17. 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
CPC shape is formed by rotating an inclined parabola about an offset axis. As a result, when the incoming light has an incidence angle of 0, it is concentrated on a focal ring. That focal ring moves as the incidence angle increases. Beyond half the acceptance angle, any incoming radiation escapes.
TFAWS 2011 – August 15-19, 2011

18. 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)
TFAWS 2011 – August 15-19, 2011

19. 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
A mesh sensitivity study was conducted, and these element sizes were selected.
(same scale)
TFAWS 2011 – August 15-19, 2011

20. 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°)
6.373e-2 (25°)
Little sensitivity to the number of rays. Notice that the average flux at the detector is different for the acceptance angles, because the aperture size is different. Rays=2000 selected
TFAWS 2011 – August 15-19, 2011

21. 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°)
No discrepancy between the MC results and the DT results for this geometry. SUBDIV=3 selected.
TFAWS 2011 – August 15-19, 2011

22. Deterministic Benchmark for CPC Specular Reflection
Deterministic test analysis detector flux distribution correlates well with reference solution
25 degree CPC
ø = 0 degrees
REFERENCE DETERMINISTIC
TFAWS 2011 – August 15-19, 2011

23. 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
Lower flux and wider focal ring.
TFAWS 2011 – August 15-19, 2011

24. 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
Here, the incidence angle was increased, and the average flux between MC and DT compared. Notice, no discrepancy. The average flux starts to drop off when the incidence angle reaches half the acceptance angle
TFAWS 2011 – August 15-19, 2011

25. 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
TFAWS 2011 – August 15-19, 2011

26. 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
TFAWS 2011 – August 15-19, 2011

27. 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
CPU Seconds
Comparable calculation times, with a slight advantage going to the DT method. The time increases once the incidence angle moves beyond half the acceptance angle because now all incoming radiation undergoes multiple reflections
Incidence Angle
TFAWS 2011 – August 15-19, 2011

28. 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
TFAWS 2011 – August 15-19, 2011

29. 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
(...). Subdivision of the elements increased in order for VF Sum errors to be less than 2% (i.e. VF Sums are within 0.98 and 1.02).
TFAWS 2011 – August 15-19, 2011

30. NX Space Systems Thermal
THANK YOU (
TFAWS 2011 – August 15-19, 2011

31. 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
A mesh sensitivity study was conducted, and these element sizes were selected.
TFAWS 2011 – August 15-19, 2011

32. 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
TFAWS 2011 – August 15-19, 2011

33. 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)
TFAWS 2011 – August 15-19, 2011

34. 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
TFAWS 2011 – August 15-19, 2011

35. 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
TFAWS 2011 – August 15-19, 2011