Ray tracing enhancement for space thermal analysis: isocell method

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R

AY TRACING ENHANCEMENT FOR SPACE

THERMAL ANALYSIS

: I

SOCELL METHOD

Lionel Jacques,

Luc Masset, Gaetan Kerschen

Space Structures and Systems Laboratory University of Liège

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F

INITE

E

LEMENT VS

. L

UMPED

P

ARAMETER

2

MTG IRS BTA: strong thermal

requirements

Detailed GMM and TMM

necessary

Finite Element method

Automatic meshing & conductive links

Thermo-mechanical analyses straightforward

Error-prone manual inputs: geometry &

conductive links

Thermo-mechanical: map the T° on the FEM

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3

Radiative exchange factors: proportional to (# of elements)²

×

wavelength bands (infrared, visible, multispectral)

×

orbit positions & geometrical configurations

Computed mostly through Monte-Carlo ray-tracing:

∝

seed 1

seed 2

Theoretical value

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4

1. Decrease the number of rays:

isocell ray direction sampling

2. Decrease the number of faces:

super-faces

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Based on Nusselt’s analogy

And Malley’s method:

1 point on the unit disc defines the ray direction

Sampling of the unit disc

Number of rays emitted by facet i, hitting j

total number of rays emitted by facet i

5 P normal unit hemisphere unit disc ray

&

_'

(

Facet j Point )

&

_'

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More uniform ray direction sampling:

Divide the unit disc into cells of equal area

and aspect ratio

*+

*,

~1

Fire one ray per cell

6

Random (classic) sampling Isocell sampling

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7 0 0.5 1 1.5 2 2.5 3 0 50 100 150 200 250 300 350 n u m b e r o f V o ro n o i c e ll s Random: σ = 0.53 Isocell: σ = 0.25 Number of Voronoi cells

C

ONFIRMATION

:

UNIT DISC

V

ORONOI CELL AREA

Relative Voronoi cell area

Isocell more

uniform

. 0.25

. 0.53

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102 103 104 105 106 10-4 10-3 10-2 10-1 100 Number of rays R e la ti v e e rr o r ∆ F /F 8

Isocell:

∝

4

5

6.78

random sampling (ESARAD):

∝

4

5

6.8

P

OINT

-

WISE

VF: I

SOCELL REQUIRES LESS RAYS

Relative error Δ /

;

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S

URFACE

&

DIRECTION SAMPLING

9

=&

>

&

_>

=&

>

Ray direction sampling over hemisphere

Ray origin sampling over surface

&

_>

2 alternatives:

Local direction sampling at each origin

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0.7 0.8 0.9 1 1.1 1.2 1.3 ζ η -1 1 -1 1 10

Uniform sampling

Gauss sampling

Random sampling

(a) Uni form i n nat ural coordi nat es, 120 ori gi ns

(b) Gauss poi nt s i n

(c) Random i coordi nat es, 1 ori gi ns

Problem: concentration due to non area-preserving mapping of the face

Solution: each origin is weighted by the Jacobian of the mapping (origins in

denser regions less weighted and vice-versa)

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G

AUSS SAMPLING

:

GAUSS WEIGHTS

11

Constant # of rays per origin

→

@ A

4 B →

4

5

_CDEF

4GH

Uniform & random sampling:

A

₄

1 ∀

Gauss sampling:

A

₄

Gauss-Legendre quadrature weights

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12 104 105 106 10-4 10-3 Number of rays R M S a b s o lu te e rr o r [-] ESARAD 10 origins 20 origins 50 origins 100 origins 104 105 106 10-4 10-3 Number of rays R M S a b s o lu te e rr o r [-] ESARAD 10 origins 20 origins 50 origins 100 origins

Uniform origin sampling &

Local Isocell direction sampling

S

URFACE SAMPLING IS CRITICAL

Random origin sampling &

Local Isocell direction sampling

&

_<

&

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104 105 106 10-4 10-3 Number of rays R M S a b s o lu te e rr o r [-] ESARAD

local, 10 origins (Gauss) global isocell, halton origins

104 105 106 10-4 10-3 Number of rays R M S a b s o lu te e rr o r [-] ESARAD 10 origins 20 origins 50 origins 100 origins 13

Gauss origin sampling &

Local Isocell direction sampling

G

AUSS SAMPLING GIVES BETTER RESULTS

Random origin sampling &

Global Isocell direction sampling

Nb rays = Nb origins

random

Global direction sampling:

- Still ~2x better than ESARAD

- Does not need to specify a number of origins

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14

EUI

ENTRANCE BAFFLE ON

S

OLAR

O

RBITER

0.28 AU perihelion: 17.5kW/m²

Coated CFRP entrance baffle and filter to

reject unwanted light

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R

ADIATIVE EXCHANGE FACTORS GLOBAL ERROR

15 104 105 106 10-4 10-3 10-2 Number of rays L in e s u m e rr o r [-] ESARAD

Local, 10 origins (Gauss) Global isocell, random origins

KLM

NOP

1 @ KLM

Q

1 @ 1 R @

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C

ONVERGENCE ON

T

EMPERATURES

Benchmark: pure radiative equilibrium

3K environment, 293K boundary

16

-225°C

20°C

104 105 106 10-2 10-1 100 Number of rays R M S a b s o lu te e rr o r [K ] ESARAD

Local, 10 origins (Gauss) Global isocell, random origins

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C

ONCLUSIONS

Isocell direction sampling offers significant improvement

Surface sampling is critical

50% reduction of number of rays with global direction sampling

Same performances on simple case and real-life space structure

First step to bridge the gap between structural and thermal analysis

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Thank you for your attention…

Any question?

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[1] T.D. Panczak, The failure of finite element codes for spacecraft thermal analysis, Proceedings of the International Conference on Environmental Systems, Monterey, USA, 1996.

[2] J.-P. Halain, P. Rochus, T. Appourchaux, D. Berghmans, L. Harra, U. Schühle, F. Auchere, A. Zhukov, E. Renotte, J.-M. Defise, L. Rossi, K. Fleury-Frenette, L. Jacques, J.-F. Hochedez, and A. Ben Moussa, The technical challenges of the Solar-Orbiter EUI instrument, Proceedings of the SPIE, Vol. 7732, 2010, 77320R-77320R-10.

[3] L. Masset. “Thermal Model Reduction Using the Super-Face Concept.” presented at the 25th European Workshop on Thermal and ECLS Software, ESA ESTEC, August 11, 2011.

[4] L. Masset, O. Brüls, and G. Kerschen. Partition of the Circle in Cells of Equal Area and Shape. University of Liège, 2012. http://orbi.ulg.ac.be/handle/2268/91953.

[5] T. Malley. A shading method for computer generated images. Master's thesis, University of Utah, June 1988

R

EFERENCES

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