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

3

Thermal Protection Systems (TPS)

NASA TM 101055, 1989

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

9

Material Response - Oxidation

10

Advanced Domain Generation

Fiber StructuresPacked Sphere Beds Periodic Foams

11

Fibers and Weaves Generator

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

13

Effective properties for fibrous media

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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)

14

Fiber Orientation Methods

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Structure Tensor

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Artificial Flux Ray Casting

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15

Workflow for Weave Orientation

Individual tow segmentation and tracking

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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=">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</latexit>

Verification against analytical solutions

17

ADEPT Validation

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=">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</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

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Verification against analytical solution

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�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

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Validation on fibrous and woven media

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20

Conclusion

Work in progress

Already available

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.

23

PuMA simulation

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

26

Vitreous carbon

FiberFormcarbon

Vitreous and Preform Carbon model

27

Effective model for macroscopic solvers

Real model Rates → k

Effective model Rates → keff

Image credit: NASA

28

FiberForm – Varying Porosity

𝜖 = 0.84 𝜖 = 0.96𝜖 = 0.90

Varying porosity

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)

30

Effective model as a function of porosity

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.

32

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.

34

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)