Modeling Pyrolyzing Ablative Materials with COMSOL Multiphysics®

Tim RischDeputy Branch Chief

Aerostructures BranchNASA Armstrong Flight Research Center

COMSOL Day Los AngelesMarch 21, 2019

1

https://ntrs.nasa.gov/search.jsp?R=20190001958 2020-03-03T09:39:37+00:00Z

Outline

• Definition and Applications

• General Pyrolyzing Ablator Problem

• Solution Example Using Finite Element Model

• Summary and Conclusions

2

Definitions

• Ablation is removal of material from the surface of an object by melting, vaporization, chipping, or other erosive processes.

• Pyrolysis is the decomposition of a material brought about by high temperatures

• Pyrolyzing Ablator is a material that undergoes sub-surface decomposition when heated and when becomes sufficiently hot, loses surface mass loss through melting or vaporization

3

4

Applications of Pyrolyzing Ablator

Modeling

Rocket Nozzles

Laser Machining

Reentry Heat Shields

Plasma Heating

Wood Combustion

Heated Pyrolyzing Ablator

5

From Başkaya, A. O. “CFD Analysis of The Cork-Phenolic Heat Shield Of A Reentry Cubesat In Arc-Jet Conditions Including Ablation And Pyrolysis”, 15th International Planetary Probe Workshop

Virgin MaterialChar Material

General Problem Illustration

6

RadiationOut

RadiationIn

In-DepthConduction

ConvectionIn

AblationProducts

Chemical SpeciesDiffusion

External Flow

Char or Residue

Pyrolysis Zone

Virgin Material

Pyrolysis Gasy

s

Backface

Frontface

Modeling Requirements for Pyrolyzing Ablators

• Non-linear heat conduction in solids

• Non-linear, thermal boundary conditions

• Moving boundaries

• Non-linear, time-dependent quasi-solid in-depth reactions

• Transport and thermal properties as a function of material state as well as temperature

• Inclusion of the thermal effects of gas flow within the solid material

• In-depth pore pressure due to pyrolysis gas transport (not always employed)

7

Material Pyrolysis

8

10 K/min

• Material consists of three constituents (although the number could be increased)

• Components A and B decompose according to:

• Material properties are a function not only of temperature, but also material state

Decomposition Model

𝜕𝜌𝑖𝜕𝑡

𝑦

= −𝐴𝑖exp −𝐸𝑖𝑅𝑇

𝜌𝑜,𝑖𝜌𝑖 − 𝜌𝑟,𝑖𝜌𝑜,𝑖

𝜓𝑖

9

𝜌 = Γ 𝜌𝐴 + 𝜌𝐵 + 1 − Γ 𝜌𝐶

• In-depth temperature time history can come from:– Thermogravimetric Analysis (TGA)

– Steady-State energy balance (1-D transformed coordinate)

– Transient energy balance (1-D transformed coordinate)

– Transient Energy Balance (1- and 2-D fixed coordinate)

In-Depth Temperature History

𝜌𝐶𝑝𝜕𝑇

𝜕𝑡𝑦

=1

𝐴

𝜕

𝜕𝑦𝑘𝐴

𝜕𝑇

𝜕𝑦𝑡

− തℎ 𝑇𝜕𝜌

𝜕𝑡𝑦

+ ሶ𝑠𝜌𝐶𝑝𝜕𝑇

𝜕𝑦𝑡

+1

𝐴

𝜕 ሶ𝑚𝑔ℎ𝑔𝐴

𝜕𝑦𝑡

10

𝜕

𝜕𝑦𝑘𝜕𝑇

𝜕𝑦+

𝜕 ሶ𝑚𝑔ℎ𝑔

𝜕𝑦+ ሶ𝑠

𝜕𝜌ℎ𝑠𝜕𝑦

= 0

𝑇 = 𝛽𝑡 + 𝑇0

𝜌𝐶𝑝𝜕𝑇

𝜕𝑡=1

𝐴𝛻 𝑘𝐴𝛻𝑇 − തℎ(𝑇)

𝜕𝜌

𝜕𝑡+1

𝐴𝛻 ∙ ሶ𝒎𝒈ℎ𝑔𝐴

Surface Energy Balance and Pyrolysis Gas Flow

11

𝛼𝐼 +𝜌𝑒 𝑢𝑒𝐶𝐻 ℎ𝑟 − ℎ𝑤 + 𝑘𝜕𝑇

𝜕𝑦− 𝐹𝜎𝜀 𝑇𝑤

4 − 𝑇∞4 − ሶ𝑚𝑤ℎ𝑤 − ሶ𝑚𝑐ℎ𝑐 − ሶ𝑚𝑔ℎ𝑔 = 0

𝛼𝐼 𝜌𝑒𝑢𝑒𝐶𝐻 ℎ𝑟 − ℎ𝑤

−𝑘𝜕𝑇

𝜕𝑦

ሶ𝑚𝑤ℎ𝑤

ሶ𝑚𝑐ℎ𝑐ሶ𝑚𝑐ℎ𝑐

𝐹𝜎𝜀 𝑇𝑤4 − 𝑇∞

4

𝛻2Φ =𝜕𝜌

𝜕𝑡

ሶ𝒎𝒈 = 𝛻Φሶ𝑚𝑔

Surface Thermochemistry – Normalized Mass Loss

Surface thermochemistry conditions computed from equilibrium thermochemistry in terms of normalized mass fluxes.

12

0.01

0.1

1

10

100

0 1000 2000 3000 4000

B'c

Temperature (K)

B'g = 10

B'g = 7.5

B'g = 5.5

B'g = 4

B'g = 3

B'g = 2.4

B'g = 1.9

B'g = 1.5

B'g = 1.2

B'g = 1

B'g = 0.9

B'g = 0.8

B'g = 0.7

B'g = 0.6

B'g = 0.5

B'g = 0.4

B'g = 0.32

B'g = 0.25

B'g = 0.2

B'g = 0.15

B'g = 0.1

B'g = 0.07

B'g = 0.04

B'g = 0.02

B'g = 0

P = 1 atm

Increasing B'g

𝐵𝑐′ = ሶ𝑚𝑐/𝜌𝑒𝑢𝑒𝐶𝑀

𝐵𝑔′ = ሶ𝑚𝑔/𝜌𝑒𝑢𝑒𝐶𝑀

𝐵𝑐′ = 𝐵𝑐

′(𝑝, 𝐵𝑔′ , 𝑇𝑠)

Implementation

13

In-Depth Conduction and Surface Energy Balance

Decomposition Reactions

In-Depth Pyrolysis Gas Flow

Moving Boundary

Surface Thermochemistry

Two-Dimensional Transient Example

• Problem is for a two-dimensional, axisymmetric puck

• Top of puck heated with Gaussian flux profile

• Pyrolysis gas flow calculated from potential flow

• Full surface thermochemistry with recession

• 2-D COMSOL Multiphysics

results compared to a series of 1-D results

14

𝐼𝑜

𝑟

𝐼 = 𝐼𝑜 ∙ exp −𝐶 𝑟/𝑟02

𝐼𝑜 = 1 × 107 W/m2 : 𝐶 = 5

2-D Problem Animation

15

Animation is twice actual speed

Original and Deformed Mesh

16

Summary

• COMSOL is a suitable tool for modeling pyrolyzing ablative materials

• General capabilities of COMSOL Multiphysics allow for a wide variety of geometries and problems to modeled

• COMSOL allows for modifications to model to be made quickly and easily

• Solution algorithms are efficient and stable

• Integrated environment provides a very user friendly and powerful system for modeling

• Multiphysical modeling capability allows for structural and external flow to be incorporated into analysis (in progress)

17

For Additional Information

Risch, T., “Verification of a Finite-Element Model for PyrolyzingAblative Materials”, presented at the AIAA 47th AIAA Thermophysics Conference, Denver CO, June 5-9, 2017.

18

QUESTIONS?

19

Final Recession Profile at 30 s

20

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.010

0 0.002 0.004 0.006 0.008 0.01

Hei

ght,

m

Radius, m

2-D

1-D

Quasi 1-D

Example Problems

• Look at four examples solved with COMSOL

– Thermogravimetric Analysis (TGA)

– Steady-state one-dimensional thermal and density profile

– One-dimensional transient temperature and recession history

– Two-dimensional transient temperature and recession history

21

Thermogravimetric Analysis (TGA) Example

22

Thermogravimetric Analysis (TGA) Example

• Three component TACOT model

• Linear ramp increase in temperature at 10 K/min

• First-order time integration, not a spatial problem

• Results provide density and reaction rate for three components as a function of time

• COMSOL Multiphysics results compared to independent fourth-order Runge-Kutta calculation

23

TGA Results - I

24

0.00%

0.02%

0.04%

0.06%

0.08%

0.10%

0.12%

0.14%

0.16%

210

220

230

240

250

260

270

280

290

300 400 500 600 700 800 900 1000 1100 1200

Dif

fere

nce

Den

sity

, kg

/m3

Temperature, K

COMSOL

Runge-Kutta

Difference

= 10 K/min

TGA Results - II

25

-0.05%

-0.03%

-0.01%

0.01%

0.03%

0.05%

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

300 400 500 600 700 800 900 1000 1100 1200

Dif

fere

nce

Dec

om

po

siti

on

Rat

e, k

g/m

3-s

Temperature, K

COMSOL

Runge-Kutta

Difference

= 10 K/min

Steady-State Profile Example

26

Steady-State Profile Example

• After long times in an infinite sample with a fixed surface temperature and recession, temperature and density profile will reach a steady state

• Problem solution becomes independent of time

• Specified surface temperature (3000 K) and steady recession rate (110-4 m/s)

• COMSOL Multiphysics results compared to independent second order finite difference calculation and results from the Fully Implicit Ablation and Thermal Analysis Program (FIAT)

27

Finite Difference Temperature Profile Comparison

28

-0.25%

-0.20%

-0.15%

-0.10%

-0.05%

0.00%

0.05%

0

500

1000

1500

2000

2500

3000

3500

0 0.02 0.04 0.06 0.08 0.1

Rel

ativ

e D

iffe

ren

ce

Tem

per

atu

re, K

Distance, m

Finite Difference

COMSOL

Solution Difference

110-4 m/s

Finite Difference Density Profile Comparison

29

-0.14%

-0.12%

-0.10%

-0.08%

-0.06%

-0.04%

-0.02%

0.00%

0.02%

0.04%

220

230

240

250

260

270

280

290

0 0.02 0.04 0.06 0.08 0.1

Rel

ativ

e D

iffe

ren

ce

Den

sity

, kg

/m3

Distance, m

Finite Difference

COMSOL

Solution Difference

110-4 m/s

FIAT Temperature Profile Comparison

30

-4.0%

-3.5%

-3.0%

-2.5%

-2.0%

-1.5%

-1.0%

-0.5%

0.0%

0

500

1000

1500

2000

2500

3000

3500

0 0.02 0.04 0.06 0.08 0.1

Rel

ativ

e D

iffe

ren

ce

Tem

pe

ratu

re,

K

Distance, m

FIAT

COMSOL SS

Difference

110-4 m/s

FIAT Density Profile Comparison

31

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

200

210

220

230

240

250

260

270

280

290

0 0.02 0.04 0.06 0.08 0.1

Rel

ativ

e D

iffe

ren

ce

Den

sity

, kg

/m3

Distance, m

FIAT

COMSOL SS

Difference

110-4 m/s

One-Dimensional Transient Example

32

One-Dimensional Transient Example

• Problem is for a planar, finite width slab heated on one surface

• Frontface free stream enthalpy of 40 MJ/kg, a heat transfer coefficient of 0.1 kg/m2-s, and reradiation

• Backface is adiabatic

• Full surface thermochemistry

• Thermocouples located at 0.001, 0.002, 0.004, 0.008, 0.016, 0.024, and 0.050 m

• COMSOL Multiphysics results compared to FIAT results

33

FIAT Surface Temperature Comparison

34

0.0%

0.5%

1.0%

1.5%

2.0%

0

500

1,000

1,500

2,000

2,500

3,000

0 10 20 30 40 50 60

Rel

ativ

e D

iffe

ren

ce

Tem

per

atu

re, K

Time, s

COMSOL

FIAT

Difference

FIAT Recession Comparison

35

0.0%

0.5%

1.0%

1.5%

2.0%

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035

0.0040

0.0045

0 10 20 30 40 50 60

Rel

aive

Dif

fere

nce

Rec

essi

on

, m

Time, s

COMSOL

FIAT

Difference

Char and Pyrolysis Surface Mass Loss Rates

36

-4%

-3%

-2%

-1%

0%

1%

2%

3%

4%

5%

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0 10 20 30 40 50 60

Rel

ativ

e D

iffe

ren

ce

Mas

s Lo

ss R

ate,

kg

/m2-s

Time, s

COMSOL mc

COMSOL mg

FIAT mc

FIAT mg

Difference mc

Difference mg

FIAT In-Depth Temperature Comparison

37

0

500

1000

1500

2000

2500

3000

0 20 40 60

Tem

per

atu

re, K

Time, s

COMSOL Surface

COMSOL TC1 - 0.001 m

COMSOL TC2 - 0.002 m

COMSOL TC3 - 0.004 m

COMSOL TC4 - 0.008 m

COMSOL TC5 - 0.016 m

COMSOL TC6 - 0.024 m

COMSOL TC7 - 0.050 m

FIAT Surface

FIAT TC1 - 0.001 m

FIAT TC2 - 0.002 m

FIAT TC3 - 0.004 m

FIAT TC4 - 0.008 m

FIAT TC5 - 0.016 m

FIAT TC6 - 0.024 m

FIAT TC7 - 0.050 m

FIAT Temperature Profile Comparison after 60 s

38

-0.5%

0.0%

0.5%

1.0%

1.5%

2.0%

0

500

1000

1500

2000

2500

3000

0 0.01 0.02 0.03 0.04 0.05

Rel

ativ

e D

iffe

ren

ce

Tem

per

atu

re, K

Distance, m

COMSOLFIATDifference

FIAT Density Profile Comparison after 60 s

39

-1.0%

-0.9%

-0.8%

-0.7%

-0.6%

-0.5%

-0.4%

-0.3%

-0.2%

-0.1%

0.0%

210

220

230

240

250

260

270

280

290

0 0.01 0.02 0.03 0.04 0.05

Rel

ativ

e D

iffe

ren

ce

Den

sity

, kg

/m3

Distance, m

COMSOL Density

FIAT Density

Difference

Two-Dimensional Transient Example

40

BACKUP

41

Density Comparison 1-D vs 2-D

42

1-D 2-D

Pyrolysis Gas Flowrate

43

Thermophysical properties defined separately for virgin and char constituents. Composite properties determined by mixing rule based on mass.

Thermophysical Properties

𝑘 = 𝑥𝑘𝑣 + (1 − 𝑥)𝑘𝑐

𝐶𝑝 = 𝑥𝐶𝑝,𝑣 + (1 − 𝑥)𝐶𝑝,𝑐

44

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0

500

1,000

1,500

2,000

2,500

0 1,000 2,000 3,000 4,000

Ther

mal

Co

nd

uct

ivit

y, W

/m-K

Spec

ific

Hea

t, J

/g-K

Temperature, K

Virgin Specific Heat

Char Specific Heat

Virgin Thermal Conductivity

Char Thermal Conductivity𝑥 =𝜌𝑣

𝜌𝑣 − 𝜌𝑐1 −

𝜌𝑐𝜌

Material Enthalpy

Virgin and char enthalpies computed from integration of specific heats.

ℎ = න𝑇0

𝑇

𝐶𝑝𝑑𝑇 + ℎ0

ℎ = 𝑥ℎ𝑣 + (1 − 𝑥)ℎ𝑐

45

-1,000

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

0 1,000 2,000 3,000 4,000

Enth

alp

y, k

J/kg

Temperature, K

Virgin

Char

Pyrolysis Gas Enthalpy

Pyrolysis gas enthalpy computed from equilibrium thermochemistry as a function of temperature and pressure.

ℎ𝑝𝑔 = ℎ𝑝𝑔 𝑝, 𝑇

46

-20,000

-10,000

0

10,000

20,000

30,000

40,000

50,000

60,000

0 1,000 2,000 3,000 4,000

Enth

alp

y, k

J/kg

Temperature, K

0.01 atm0.1 atm1 atm

Surface Thermochemistry – Normalized Mass Loss

Surface thermochemistry conditions computed from equilibrium thermochemistry in terms of normalized mass fluxes.

47

0.01

0.1

1

10

100

0 1000 2000 3000 4000

B'c

Temperature (K)

B'g = 10

B'g = 7.5

B'g = 5.5

B'g = 4

B'g = 3

B'g = 2.4

B'g = 1.9

B'g = 1.5

B'g = 1.2

B'g = 1

B'g = 0.9

B'g = 0.8

B'g = 0.7

B'g = 0.6

B'g = 0.5

B'g = 0.4

B'g = 0.32

B'g = 0.25

B'g = 0.2

B'g = 0.15

B'g = 0.1

B'g = 0.07

B'g = 0.04

B'g = 0.02

B'g = 0

P = 1 atm

Increasing B'g

𝐵𝑐′ = ሶ𝑚𝑐/𝜌𝑒𝑢𝑒𝐶𝑀

𝐵𝑔′ = ሶ𝑚𝑔/𝜌𝑒𝑢𝑒𝐶𝑀

𝐵𝑐′ = 𝐵𝑐

′(𝑝, 𝐵𝑔′ , 𝑇𝑠)

Surface Thermochemistry –Gas Phase Enthalpy

Enthalpy of gases at the wall computed similarly from equilibrium thermochemistry.

ℎ𝑤 = ℎ𝑤(𝑝, 𝐵𝑔′ , 𝑇𝑠)

48

-15000

-10000

-5000

0

5000

10000

15000

20000

25000

30000

35000

0 1000 2000 3000 4000

Enth

alp

y (J

/g)

Temperature (K)

B'g = 10

B'g = 7.5

B'g = 5.5

B'g = 4

B'g = 3

B'g = 2.4

B'g = 1.9

B'g = 1.5

B'g = 1.2

B'g = 1

B'g = 0.9

B'g = 0.8

B'g = 0.7

B'g = 0.6

B'g = 0.5

B'g = 0.4

B'g = 0.32

B'g = 0.25

B'g = 0.2

B'g = 0.15

B'g = 0.1

B'g = 0.07

B'g = 0.04

B'g = 0.02

B'g = 0

P = 1 atm

Increasing B'g

COMSOL Multiphysics User Interface

49

Example Uses of Pyrolyzing Ablator

50

Objective

• NASA primarily relies on custom written codes to analyze ablation and design TPS systems

• The basic modeling methodology was developed

50 years ago

• Through the years, CFD, thermal, and structural mechanics calculations have migrated from custom, user-written programs to commercial software packages

• Objective is to determine that a commercial finite element code can accurately and efficiently solve pyrolyzing ablation problems

51

Advantages of Commercial Codes

• Usability (e.g. GUI)• Built–in pre- and post-processing • Built-in grid generation• Efficient solution algorithms• Multi-dimensional capability (planar, cylindrical, 1-D,

2-D, & 3-D)• Built in function capability (predefined, analytic, and tabular)• Validated by a wide user base• Reduced life cycle cost • Regular upgrades and maintenance• Modeling flexibility• Better documentation

52

Material Selection

• For comparisons, utilize Theoretical Ablative Composite for Open Testing (TACOT) Material Properties

• Open, simulated pyrolyzing ablator that has been used a baseline test case for modeling ablation and comparing various predictive models

• Properties Required– Solid virgin and char specific heat, enthalpy, thermal

conductivity, absorptivity and emissivity– Pyrolysis gas enthalpy– Surface thermochemistry mass loss and gas phase

enthalpy

53