Post on 21-Jan-2023
1
09/29/2020
PuMA and Multiscale ModelingFederico Semeraro
Krishnan Swaminathan Gopalan
Presenters:
Project contributors: Joseph C. Ferguson, Marcos Acin, Arnaud Borner, John Thornton Francesco Panerai, Nagi N. Mansour
Advanced Modeling & Simulation (AMS) Seminar SeriesNASA Ames Research Center, September 29th, 2020
2
Content
• Motivation
• Overview of PuMA
• Effective properties for fibrous mediav Fiber orientationv Thermal conductivityv Elasticity
• Surface chemistryv Molecular beamv Oxidation model
4
Ablative TPS
=+
Carbon preform Phenolic Resin PICA
Stardust Capsule Mars Science Laboratory
Stackpoole et al., AIAA 2008-1202
5
Modeling TPS
Simulation of surface temperaturefor MSL heatshield
Macroscale ModelingFull scale material response solvers, using
volume-averaged techniques to solve conservation equations for ablation
Lachaud and Mansour, JTHT 2013
Microscale ModelingUsed to inform material properties and material response parameters used in
macro-scale modeling
6
X-Ray Microtomography
Collect X-ray images of the sample as you rotate it through 180°
Use this series of images to reconstruct the 3D object
Multiple anglesPenetrating power Courtesy of D. Parkinson (ALS)
7
Porous Microstructure Analysis (PuMA)New features in Version 3:
• Modular C++ library
• Redesigned GUI
• Wrapped as Python module
• Linux and Mac compatibility
CT Reconstruction of FiberForm
Material PropertiesØ Volume Fraction and Surface Area
Ø Pore Diameter Estimation and FillingØ Tortuosity (continuum and rarefied)
Ø PermeabilityØ Computation of Material Orientation
Ø Conductivity (isotropic and anisotropic)Ø Elasticity and Stress Analysis
Domain Generation
Ø Artificial Materials:Ø WeavesØ Random FibersØ FoamsØ Analytical shapes
Ø Micro-CT Import and FilteringØ
Shared UtilitiesØ Matrix and Vector data
structures/operations
Ø Linear solversØ Iso-surface extraction
Ø Input/Output to binary, TIFF, STL, VTK formats
8
Transport Properties in PuMAEffective Thermal Conductivity
Permeability Considering Anisotropy
Tortuosity / Diffusivity
Low KnudsenHigh Knudsen
Ray casting orientation
Heat flux orientation
Pressure driven flow through 2D fibrous material
Pressure driven flow through 3D triply periodic material
Woven materials considering anisotropy
Conductivity of fibrous materials
12
An Anisotropic and Multiscale Problem
6-ply weave
1000 vox
450 vox
390
vox
Porous Tow100 vox 50 vox
Sub-tow sample120 vox
120
vox
Fiber
5.2µm
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Effective properties for fibrous media
0.05 0.050.05
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0.15
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0.2 0.3
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0.3 0.45
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Tem
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NumericalAnalytical
Semeraro, F., Ferguson , J.C, Acin, M., Panerai, F. and Mansour, N.N., Anisotropic analysis of fibrous and woven materials part 2: Computation of effective conductivity. Computational Materials Science, 186, p.109956. (2021)
Semeraro, F., Ferguson, J.C., Panerai, F., King, R.J. and Mansour, N.N., Anisotropic analysis of fibrous and woven materials part 1: Estimation of local orientation. Computational Materials Science, 178, p.109631. (2020)
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Fiber Orientation Methods
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Structure Tensor
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Artificial Flux Ray Casting
CGLS
15
Workflow for Weave Orientation
Individual tow segmentation and tracking
Mean Filtering
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q =⇥R�1k00R
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<latexit sha1_base64="i4QZX0XovBwEwrDv4wn00zSWGQ4=">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</latexit><latexit sha1_base64="i4QZX0XovBwEwrDv4wn00zSWGQ4=">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</latexit><latexit sha1_base64="i4QZX0XovBwEwrDv4wn00zSWGQ4=">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</latexit><latexit sha1_base64="i4QZX0XovBwEwrDv4wn00zSWGQ4=">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</latexit>
16
Effective Thermal Conductivity
CGLSkeff = qx · Lx
<latexit sha1_base64="Q0zXVUzK7W85k9ztsoEQsGBXg2I=">AAACDHicbVC7TsMwFHXKq5RXgZHFokJiqhKEBAtSJRYGhiLRh9SUyHGc1qpjB9tBraJ8AAu/wsIAQqx8ABt/g9NmgJYrWT4651zde48fM6q0bX9bpaXlldW18nplY3Nre6e6u9dWIpGYtLBgQnZ9pAijnLQ01Yx0Y0lQ5DPS8UeXud55IFJRwW/1JCb9CA04DSlG2lBeteb6ggVqEpkvHWVeSsIwgxfw/m7s4kBoeO2Njcuu29OCi8ApQA0U1fSqX24gcBIRrjFDSvUcO9b9FElNMSNZxU0UiREeoQHpGchRRFQ/nR6TwSPDBDAU0jyu4ZT93ZGiSOX7GmeE9FDNazn5n9ZLdHjeTymPE004ng0KEwa1gHkyMKCSYM0mBiAsqdkV4iGSCGuTX8WE4MyfvAjaJ3XHrjs3p7WGXcRRBgfgEBwDB5yBBrgCTdACGDyCZ/AK3qwn68V6tz5m1pJV9OyDP2V9/gAHJZuC</latexit><latexit sha1_base64="Q0zXVUzK7W85k9ztsoEQsGBXg2I=">AAACDHicbVC7TsMwFHXKq5RXgZHFokJiqhKEBAtSJRYGhiLRh9SUyHGc1qpjB9tBraJ8AAu/wsIAQqx8ABt/g9NmgJYrWT4651zde48fM6q0bX9bpaXlldW18nplY3Nre6e6u9dWIpGYtLBgQnZ9pAijnLQ01Yx0Y0lQ5DPS8UeXud55IFJRwW/1JCb9CA04DSlG2lBeteb6ggVqEpkvHWVeSsIwgxfw/m7s4kBoeO2Njcuu29OCi8ApQA0U1fSqX24gcBIRrjFDSvUcO9b9FElNMSNZxU0UiREeoQHpGchRRFQ/nR6TwSPDBDAU0jyu4ZT93ZGiSOX7GmeE9FDNazn5n9ZLdHjeTymPE004ng0KEwa1gHkyMKCSYM0mBiAsqdkV4iGSCGuTX8WE4MyfvAjaJ3XHrjs3p7WGXcRRBgfgEBwDB5yBBrgCTdACGDyCZ/AK3qwn68V6tz5m1pJV9OyDP2V9/gAHJZuC</latexit><latexit sha1_base64="Q0zXVUzK7W85k9ztsoEQsGBXg2I=">AAACDHicbVC7TsMwFHXKq5RXgZHFokJiqhKEBAtSJRYGhiLRh9SUyHGc1qpjB9tBraJ8AAu/wsIAQqx8ABt/g9NmgJYrWT4651zde48fM6q0bX9bpaXlldW18nplY3Nre6e6u9dWIpGYtLBgQnZ9pAijnLQ01Yx0Y0lQ5DPS8UeXud55IFJRwW/1JCb9CA04DSlG2lBeteb6ggVqEpkvHWVeSsIwgxfw/m7s4kBoeO2Njcuu29OCi8ApQA0U1fSqX24gcBIRrjFDSvUcO9b9FElNMSNZxU0UiREeoQHpGchRRFQ/nR6TwSPDBDAU0jyu4ZT93ZGiSOX7GmeE9FDNazn5n9ZLdHjeTymPE004ng0KEwa1gHkyMKCSYM0mBiAsqdkV4iGSCGuTX8WE4MyfvAjaJ3XHrjs3p7WGXcRRBgfgEBwDB5yBBrgCTdACGDyCZ/AK3qwn68V6tz5m1pJV9OyDP2V9/gAHJZuC</latexit><latexit sha1_base64="Q0zXVUzK7W85k9ztsoEQsGBXg2I=">AAACDHicbVC7TsMwFHXKq5RXgZHFokJiqhKEBAtSJRYGhiLRh9SUyHGc1qpjB9tBraJ8AAu/wsIAQqx8ABt/g9NmgJYrWT4651zde48fM6q0bX9bpaXlldW18nplY3Nre6e6u9dWIpGYtLBgQnZ9pAijnLQ01Yx0Y0lQ5DPS8UeXud55IFJRwW/1JCb9CA04DSlG2lBeteb6ggVqEpkvHWVeSsIwgxfw/m7s4kBoeO2Njcuu29OCi8ApQA0U1fSqX24gcBIRrjFDSvUcO9b9FElNMSNZxU0UiREeoQHpGchRRFQ/nR6TwSPDBDAU0jyu4ZT93ZGiSOX7GmeE9FDNazn5n9ZLdHjeTymPE004ng0KEwa1gHkyMKCSYM0mBiAsqdkV4iGSCGuTX8WE4MyfvAjaJ3XHrjs3p7WGXcRRBgfgEBwDB5yBBrgCTdACGDyCZ/AK3qwn68V6tz5m1pJV9OyDP2V9/gAHJZuC</latexit>
Multi-Point Flux Approximation (MPFA):
r · q = 0<latexit sha1_base64="XEpR7tZYfebJ/c5LXDi9mvj0cxE=">AAACCHicbVDLSgMxFM3UV62vUZcuDBbBVZmpgiIIBTcuK9gHdIaSyWTa0EwyJhmhDF268VfcuFDErZ/gzr8x085CWw+EHM65l3vvCRJGlXacb6u0tLyyulZer2xsbm3v2Lt7bSVSiUkLCyZkN0CKMMpJS1PNSDeRBMUBI51gdJ37nQciFRX8To8T4sdowGlEMdJG6tuHHkcBQ9DDodDQCwQL1Tg2X3Y/gVfQ6dtVp+ZMAReJW5AqKNDs219eKHAaE64xQ0r1XCfRfoakppiRScVLFUkQHqEB6RnKUUyUn00PmcBjo4QwEtI8ruFU/d2RoVjl65nKGOmhmvdy8T+vl+rows8oT1JNOJ4NilIGtYB5KjCkkmDNxoYgLKnZFeIhkghrk13FhODOn7xI2vWae1qr355VG5dFHGVwAI7ACXDBOWiAG9AELYDBI3gGr+DNerJerHfrY1ZasoqeffAH1ucPyYiZJg==</latexit>
q(x, t) = E(x)TN (x, t)<latexit sha1_base64="olOgWaDsFtrqhUqxqIZH+lO3/Nc=">AAACKXicbZBLS8NAEMc3Pmt9RT16WSxCC6UkIuhFKIrgSSr0BU0tm+22XbrZxN2NWEK+jhe/ihcFRb36RdymOfThwLJ/fjPDzPzdgFGpLOvbWFpeWV1bz2xkN7e2d3bNvf269EOBSQ37zBdNF0nCKCc1RRUjzUAQ5LmMNNzh1TjfeCRCUp9X1SggbQ/1Oe1RjJRGHbPsuD7rypGnv+ghzj8VVQFewGl6rWkBOsUZWI3vb5PijpmzSlYScFHYqciBNCod893p+jj0CFeYISlbthWodoSEopiROOuEkgQID1GftLTkyCOyHSWXxvBYky7s+UI/rmBCpzsi5MnxhrrSQ2og53Nj+F+uFareeTuiPAgV4XgyqBcyqHw4tg12qSBYsZEWCAuqd4V4gATCSpub1SbY8ycvivpJybZK9t1prnyZ2pEBh+AI5IENzkAZ3IAKqAEMnsEr+ACfxovxZnwZP5PSJSPtOQAzYfz+Ae7MpmI=</latexit><latexit sha1_base64="olOgWaDsFtrqhUqxqIZH+lO3/Nc=">AAACKXicbZBLS8NAEMc3Pmt9RT16WSxCC6UkIuhFKIrgSSr0BU0tm+22XbrZxN2NWEK+jhe/ihcFRb36RdymOfThwLJ/fjPDzPzdgFGpLOvbWFpeWV1bz2xkN7e2d3bNvf269EOBSQ37zBdNF0nCKCc1RRUjzUAQ5LmMNNzh1TjfeCRCUp9X1SggbQ/1Oe1RjJRGHbPsuD7rypGnv+ghzj8VVQFewGl6rWkBOsUZWI3vb5PijpmzSlYScFHYqciBNCod893p+jj0CFeYISlbthWodoSEopiROOuEkgQID1GftLTkyCOyHSWXxvBYky7s+UI/rmBCpzsi5MnxhrrSQ2og53Nj+F+uFareeTuiPAgV4XgyqBcyqHw4tg12qSBYsZEWCAuqd4V4gATCSpub1SbY8ycvivpJybZK9t1prnyZ2pEBh+AI5IENzkAZ3IAKqAEMnsEr+ACfxovxZnwZP5PSJSPtOQAzYfz+Ae7MpmI=</latexit><latexit sha1_base64="olOgWaDsFtrqhUqxqIZH+lO3/Nc=">AAACKXicbZBLS8NAEMc3Pmt9RT16WSxCC6UkIuhFKIrgSSr0BU0tm+22XbrZxN2NWEK+jhe/ihcFRb36RdymOfThwLJ/fjPDzPzdgFGpLOvbWFpeWV1bz2xkN7e2d3bNvf269EOBSQ37zBdNF0nCKCc1RRUjzUAQ5LmMNNzh1TjfeCRCUp9X1SggbQ/1Oe1RjJRGHbPsuD7rypGnv+ghzj8VVQFewGl6rWkBOsUZWI3vb5PijpmzSlYScFHYqciBNCod893p+jj0CFeYISlbthWodoSEopiROOuEkgQID1GftLTkyCOyHSWXxvBYky7s+UI/rmBCpzsi5MnxhrrSQ2og53Nj+F+uFareeTuiPAgV4XgyqBcyqHw4tg12qSBYsZEWCAuqd4V4gATCSpub1SbY8ycvivpJybZK9t1prnyZ2pEBh+AI5IENzkAZ3IAKqAEMnsEr+ACfxovxZnwZP5PSJSPtOQAzYfz+Ae7MpmI=</latexit><latexit sha1_base64="olOgWaDsFtrqhUqxqIZH+lO3/Nc=">AAACKXicbZBLS8NAEMc3Pmt9RT16WSxCC6UkIuhFKIrgSSr0BU0tm+22XbrZxN2NWEK+jhe/ihcFRb36RdymOfThwLJ/fjPDzPzdgFGpLOvbWFpeWV1bz2xkN7e2d3bNvf269EOBSQ37zBdNF0nCKCc1RRUjzUAQ5LmMNNzh1TjfeCRCUp9X1SggbQ/1Oe1RjJRGHbPsuD7rypGnv+ghzj8VVQFewGl6rWkBOsUZWI3vb5PijpmzSlYScFHYqciBNCod893p+jj0CFeYISlbthWodoSEopiROOuEkgQID1GftLTkyCOyHSWXxvBYky7s+UI/rmBCpzsi5MnxhrrSQ2og53Nj+F+uFareeTuiPAgV4XgyqBcyqHw4tg12qSBYsZEWCAuqd4V4gATCSpub1SbY8ycvivpJybZK9t1prnyZ2pEBh+AI5IENzkAZ3IAKqAEMnsEr+ACfxovxZnwZP5PSJSPtOQAzYfz+Ae7MpmI=</latexit>
0.1
0.1
0.10.1
0.1
0.1
0.10.1
0.10.1
0.1 0.2
0.2
0.2
0.20.2
0.20.2
0.20.2
0.2
0.2
0.2 0.2 0.2 0.2
0.3
0.3
0.3
0.3
0.3 0.30.3
0.3
0.3
0.30.3
0.3
0.3
0.3
0.4
0.4
0.4
0.4
0.4
0.40.4
0.4
0.40.4
0.4
0.4
0.4
0.4
-100 -80 -60 -40 -20 0 20 40 60 80 100x dimension
-20
-15
-10
-5
0
5
10
15
20
y di
men
sion
0
0.2
0.4
0.6
0.8
1
Tem
pera
ture
(K)
NumericalAnalytical
ki,j =
1 0.75
0.75 1
�W
mK<latexit sha1_base64="1AT9h5kecQ30OoDV9ulge4IKWzQ=">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</latexit>
ki,j =
20.8 18.118.1 83.6
�W
mK<latexit sha1_base64="CbCYd2AiwCQi4cuybLkC4eA6TPU=">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</latexit>
ki,j =
52.7 20.620.6 76.5
�W
mK<latexit sha1_base64="SEAGxyV0SshqvrwhOCvpisaKbRY=">AAACX3icbZFPa9swGMZl7087t+u87jR2EQsLOwxjZ2vTy6Cwy2CXDpamEIUgy69TNbJsJLk0CH3J3Qa77JtMds3Y2j0g9ON59aJXj/JGcG3S9EcQPnj46PHO7pNob//pwbP4+eG5rlvFYMZqUauLnGoQXMLMcCPgolFAq1zAPN986urza1Ca1/Kb2TawrOha8pIzary1iq9JXotCbyu/2Y1bWf7uyuGPOCI5rLm0eUWN4jcuwl5Hk2SKx3iSJseYkN7qeYynx8lRZxGQxZ8eTEpFmSUGboydOzdQ9cW5VTxKk7QXvg/ZACM06GwVfydFzdoKpGGCar3I0sYsLVWGMwEuIq2GhrINXcPCo6QV6KXt83H4jXcKXNbKL2lw7/7dYWmluwj8ST/6pb5b68z/1RatKU+WlsumNSDZ7UVlK7CpcRc2LrgCZsTWA2WK+1kxu6Q+FOO/JPIhZHeffB/OJ0n2Ppl8/TA6HQ9x7KJX6DV6izI0RafoMzpDM8TQzyAM9oL94Fe4Ex6E8e3RMBh6XqB/FL78DQ9lsOY=</latexit>
Verification against analytical solutions
18
Single Fiber Conductivity Estimation
korthoeff =
2
42.342 � �� 1.766 �� � 0.305
3
5 k12plyeff =
2
42.184 � �� 1.980 �� � 0.394
3
5
<latexit sha1_base64="HDkOlA+Of71vKSTkL/MMUhoPHy4=">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</latexit>
[kweft// , kweft
? ] = [5.4, 1.8] and [kwarp// , kwarp
? ] = [7.7, 2.7]W
mK<latexit sha1_base64="8DvU60PhJqEJVjiwzDU3jToOXGk=">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</latexit>
k4plyeff =
2
41.750 �0.032 �0.024
�0.093 1.490 0.0020.039 0.001 0.193
3
5 W
mK<latexit sha1_base64="vKzWdwjpQ3VJncP2NJQFQYKBqo4=">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</latexit>
k6plyeff =
2
41.740 �0.141 �0.020
�0.105 1.710 �0.0050.091 �0.023 0.200
3
5 W
mK<latexit sha1_base64="ZdUOdrGyfs6z1KmuFn/JzfYbcs4=">AAACz3icbVLLbhMxFPUMrzI8msKSjUVExaYjTxpaWCBVYoMEi1YiTaU4RB6PJ7Fie0a2BxoZI7b8Hjt+gO/Akw7QplzJ8tG55/heXzuvBTcWoZ9RfOPmrdt3tu4m9+4/eLjd23l0aqpGUzailaj0WU4ME1yxkeVWsLNaMyJzwcb58k2bH39i2vBKfbCrmk0lmSteckpsoGa9XzivRGFWMmxu6T+6g1qs/MyxsvRw9zVMcM7mXLlcEqv5uU9gCFwviLKVdHs+Sw+HCO5CuIfSbJh1CA0QxHitbXn0ouWvurI/LhSynfaSIvCv/p22v+FH6QCtK2Cmir+9QVxqQh227Ny6sfcdku+8n/X6baU24HWQdaAPujie9X7goqKNZMpSQYyZZKi2U0e05VQwn+DGsJrQJZmzSYCKSGambv0eHj4LTAHLSoelLFyzlx2OSNOOPChD6wuzmWvJ/+UmjS1fTh1XdWOZoheFykZAW8H2cWHBNaNWrAIgVPPQK6QLEoZiwxdIwhCyzStfB6eDNNtPByfD/hHqxrEFnoCn4DnIwCE4Am/BMRgBGr2PdOSiL/FJ/Dn+Gn+7kMZR53kMrkT8/Tfx4NJ1</latexit>
k8plyeff =
2
41.830 �0.244 0.016
�0.192 1.510 0.0050.039 0.000 0.231
3
5 W
mK<latexit sha1_base64="KwjiWT0OOkXOvexKK9425HwMa7o=">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</latexit>
k12plyeff =
2
42.310 �0.414 0.000
�0.524 2.030 0.0710.007 0.005 0.504
3
5 W
mK<latexit sha1_base64="hBNZj+RuGDxi3LK72zyLLAxa6F4=">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</latexit>
[k//, k?] = [9.7, 5.5]W
mK<latexit sha1_base64="aD/Zo0ssgR3s7Q2ThmbNWNTCdxI=">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</latexit>
Two experimental values at Room Temperature:
19
Semeraro, F., Acin, M., Panerai, and Mansour, N.N., Anisotropic analysis of fibrous and woven materials part 3: Computation of effective elasticity. Computational Materials Science, (work in progress)
BiCGStabConverged
stressesCeff = �x · Lx
<latexit sha1_base64="9aybYf8j3gMqG2ajit+Foa79W1g=">AAACHnicbVDLSsNAFJ34rPVVdelmsAiuSlIVXSgUunHhooJ9QBPDZDJph04yYWYiLSFf4sZfceNCEcGV/o3TNovaemCYwzn3cu89XsyoVKb5Yywtr6yurRc2iptb2zu7pb39luSJwKSJOeOi4yFJGI1IU1HFSCcWBIUeI21vUB/77UciJOXRvRrFxAlRL6IBxUhpyS2d2x5nvhyF+kvrmZuSIMjgNZyVbUl7Icoehjb2uYK37tAtlc2KOQFcJFZOyiBHwy192T7HSUgihRmSsmuZsXJSJBTFjGRFO5EkRniAeqSraYRCIp10cl4Gj7Xiw4AL/SIFJ+psR4pCOV5VV4ZI9eW8Nxb/87qJCi6dlEZxokiEp4OChEHF4Tgr6FNBsGIjTRAWVO8KcR8JhJVOtKhDsOZPXiStasU6rVTvzsq1qzyOAjgER+AEWOAC1MANaIAmwOAJvIA38G48G6/Gh/E5LV0y8p4D8AfG9y8OKqOl</latexit>
Verification against analytical solution
�xx<latexit sha1_base64="WIgE5P+Lp0yF8EqUrErHPCmyWuo=">AAAB8nicbVDLSgNBEJz1GeMr6tHLYBA8hd0o6MFDwIvHCOYByRJmJ7PJkHksM72SsOQzvHhQxKtf482/cZLsQRMLGoqqbrq7okRwC77/7a2tb2xubRd2irt7+weHpaPjptWpoaxBtdCmHRHLBFesARwEayeGERkJ1opGdzO/9cSM5Vo9wiRhoSQDxWNOCTip07V8IEkvG4+nvVLZr/hz4FUS5KSMctR7pa9uX9NUMgVUEGs7gZ9AmBEDnAo2LXZTyxJCR2TAOo4qIpkNs/nJU3zulD6OtXGlAM/V3xMZkdZOZOQ6JYGhXfZm4n9eJ4X4Jsy4SlJgii4WxanAoPHsf9znhlEQE0cINdzdiumQGELBpVR0IQTLL6+SZrUSXFaqD1fl2m0eRwGdojN0gQJ0jWroHtVRA1Gk0TN6RW8eeC/eu/exaF3z8pkT9Afe5w/Y55Ga</latexit>
�yy<latexit sha1_base64="ggkeb/cWr4wKcMxmZ+zWeUw6nmk=">AAAB8nicbVDLSgNBEOz1GeMr6tHLYBA8hd0o6MFDwIvHCOYByRJmJ7PJkHksM7PCsuQzvHhQxKtf482/cZLsQRMLGoqqbrq7ooQzY33/21tb39jc2i7tlHf39g8OK0fHbaNSTWiLKK50N8KGciZpyzLLaTfRFIuI0040uZv5nSeqDVPy0WYJDQUeSRYzgq2Ten3DRgIP8iybDipVv+bPgVZJUJAqFGgOKl/9oSKpoNISjo3pBX5iwxxrywin03I/NTTBZIJHtOeoxIKaMJ+fPEXnThmiWGlX0qK5+nsix8KYTESuU2A7NsveTPzP66U2vglzJpPUUkkWi+KUI6vQ7H80ZJoSyzNHMNHM3YrIGGtMrEup7EIIll9eJe16Lbis1R+uqo3bIo4SnMIZXEAA19CAe2hCCwgoeIZXePOs9+K9ex+L1jWvmDmBP/A+fwDb8pGc</latexit>
Multi-Point Stress Approximation (MPSA)
Effective Elasticity
r · � = r · (C") = 0<latexit sha1_base64="KI00QEAvJJcqb+1/XNkjBhx5Fd0=">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</latexit>
Validation on fibrous and woven media
�(x, t) = E(x)DN (x, t)<latexit sha1_base64="JNlE19NTkgFWGWCBBBtPnqkCpBI=">AAACK3icbVDLSgMxFM3UV62vUZdugkVoQcpMFRRBKD7AlVSwD+jUkknTNjTzIMmIZZj/ceOvuNCFD9z6H2ams+jDCyGHc87l3ntsn1EhDeNLyywsLi2vZFdza+sbm1v69k5deAHHpIY95vGmjQRh1CU1SSUjTZ8T5NiMNOzhZaw3HgkX1HPv5cgnbQf1XdqjGElFdfQLy/ZYV4wc9YWWoH0HRYWnQ1mE53BSulZscYq5ih5uE2dHzxslIyk4D8wU5EFa1Y7+ZnU9HDjElZghIVqm4ct2iLikmJEoZwWC+AgPUZ+0FHSRQ0Q7TG6N4IFiurDncfVcCRN2siNEjog3VE4HyYGY1WLyP60VyN5pO6SuH0ji4vGgXsCg9GAcHOxSTrBkIwUQ5lTtCvEAcYSlijenQjBnT54H9XLJPCqV747zlbM0jizYA/ugAExwAirgBlRBDWDwDF7BB/jUXrR37Vv7GVszWtqzC6ZK+/0DZ4qntg==</latexit>
21
Application motivation
Vitreous carbonPreform carbonSPI SuppliesImage courtesy: Prof. Panerai
Objectives:
• Characterize recession/ablation of carbon surface coated with NuSil due to oxidation
• Develop a predictive model for use in microscopic (DSMC, PuMA) and macroscopic (CFD, MRC) solvers
NuSil-coated FiberForm
Image courtesy: Dr. Bessire
Murray, V J., et al. The Journal of Physical Chemistry C 119.26 (2015): 14780-14796.
22
Surface chemistry framework • Methodology to represent surface sites similar to Marschall, Maclean and Driver for CFD.
• Particles adsorbed (deleted) and desorbed (created), surface element stores adsorbed particle concentration.
• Surface reactions based on concentration within surface element.
• Multiple triangulated elements (like cells) on surfaces
• Langmuir model for surface sites.
taken from Marschall and Maclean.
Marschall, J., & MacLean, M. (2011). Finite-rate surface chemistry model, I: Formulation and reaction system examples. AIAA Paper, 3783, 2011.
24
Molecular Beam Experimental Setup
Thermally desorbed (TD) prompt- MB distribution
Impulsively scattered (IS)/non-thermal
LH Slow desorbing
Murray, V J., et al. The Journal of Physical Chemistry C 119.26 (2015): 14780-14796.
Murray et al
25
TD
TD
TD
Carbon Oxidation Model
K. Swaminathan-Gopalan et al., "Development and validation of a finite-rate model for carbon oxidation by atomic oxygen." Carbon 137 (2018): 313-332.
Fast TD reactions
Slow formation reactions
Desorption reactions
27
Effective model for macroscopic solvers
Real model Rates → k
Effective model Rates → keff
Image credit: NASA
29
FiberForm – Varying Porosity
Effective model Rates → keff(T,𝝐)
Effective Rates → keff(T)
Real model Rates → k
Effective Rates → keff(T) Effective Rates → keff(T)
31
FiberForm-NuSil oxidation model
2 phase model
Preform carbonNuSil
• SiO additional product with NuSil.
• O mainly scatters non-reactively from NuSil.
• NuSil starts burning off ~ 1400 K.
• Higher fluxes of O and lower fluxes of CO on NuSil surfaces at lower temperatures.
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SiO reactions
• SiO TOF has a fast TD and slow desorption component.
SiO TOF T = 1800K
ExpFast TD
Time (s)
Arb
. uni
ts
New reaction mechanisms for SiO
33
Reaction Rate Constants Fitting Method
No
Better initial guesses for k based on error
Yes, the rates are obtained.
Initial guess for keff
Keep track of the changing surface conditions
Perform reactions based on instantaneous probabilities
Compare final products with the experimental data
Solution converged ?
K. Swaminathan Gopalan and K. A. Stephani. In 47th AIAA Thermophysics Conference, p. 4347. 2017.
Systematic procedure Particle Swarm
algorithm
• Error = || fluxcalc – fluxexp ||• Find values for keff to
minimize this error.
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FiberForm-NuSil oxidation model
• New 2 phase model for FiberForm-NuSil
ØPhase 1: FiberForm – same rates as preform carbon model.
ØPhase 2: NuSil – new reactions and rates.
• Newly developed FiberForm-NuSil model agrees well with the experiments.
35
Summary
• Detailed surface chemistry framework was implemented in PuMA.
• The vitreous carbon (VC) oxidation model was developed and extended to FiberForm.
• Effective oxidation model for use in CFD was developed as a function of porosity keff (T,𝜖).
• Effective model was extended to NuSil-coated FiberForm.
• Future Work: extend to NuSil-coated PICA
36
09/29/2020
Questions?Federico Semeraro (federico.semeraro@nasa.gov)
Krishnan Swaminathan Gopalan (krishnan.swaminathan-gopalan@nasa.gov)