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

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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

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

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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)

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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

(same scale)

25 degrees 45 degrees

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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 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°)

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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

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°)

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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 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

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

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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)

TFAWS 2011 – August 15-19, 2011 30

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

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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)

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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

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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