Upload
others
View
4
Download
0
Embed Size (px)
Citation preview
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