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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). - PowerPoint PPT Presentation
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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 WorkshopTFAWS 2011August 15-19, 2011NASA Langley Research CenterNewport News, VA
TFAWS Paper Session
TFAWS 2011 – August 15-19, 2011 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– Monte Carlo – reference solution– Deterministic - test analysis
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
• 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
NXSST Radiation Calculation Methods
FEM
Monte Carlo
Radiative couplings (RAD-K’s)
Radiosity(or Oppenheim’s)
Method
Geometric/Ray-Traced View Factors
Numerical ModelOther inputs (heat loads
other conductances,etc.)
Gebhardt’sMethod
Deterministic Ray Tracing/
Semi-Analytic
Hemicube Monte Carlo
TemperaturesNonlinear outer iterations,
linear solver
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 shadowed2. If not shadowed and target is diffuse
i. Compute view factor with exact contour integral method3. If shadowed or target has specular or transmissive properties
i. Subdivide elements according to element subdivision criterionii. Determine shadowing between sub-elementsiii. For unshadowed sub-element pairs, determine view factor contribution
using Nusselt sphere methodiv. if target element is specular or transparent, ray trace the reflected or
transmitted component through the modelv. 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
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
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
necessaryYes. Diffuse reflections
calculated 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)
Monte Carlo
SpeedMediocre,
requires matrix solve
Good, no matrix solve necessary
Slow for diffuse properties. More competitive with
specular / transmisisve
surfaces ε(T)? NO, must re-
solve matrixYES, goes right into
numerical modelNO, must repeat ray
tracing
BRDF, ε(θ,φ)? NO NO YES, easy to doLimited support
Accuracy (within limitations)
Uniform illumination
approximationUniform
illumination approximation
Depends on number of rays
Intuitive results? YES Need heat map tools
YES
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
TFAWS 2011 – August 15-19, 2011 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)
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
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
(same scale)
25 degrees 45 degrees
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
(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 CARLORAYS/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°)
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
DETERMINISTICELEMENT
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 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
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
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
0 5 10 15 20 25 30 350
200
400
600
800
1000
1200
1400
1600
1800
2000
DTMC
Incidence Angle
CPU
Seconds
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 28
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
TFAWS 2011 – August 15-19, 2011 29
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 degreesReflector Surface Properties
εIR = 0.5ρIR,d = 0.5
αS= 0ρS,d = 0.5ρS,s = 0.5
Detector Surface PropertiesεIR = 1αS= 1
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 32
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 33
0
50
100
150
200
250
300
350
400
450
500
0 2000 4000 6000 8000 10000 12000 14000
Tem
pera
ture
(C)
Rays Per Element
Detector Temperatures
Min TMax TAve T
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
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