Abstract

This article describes a finite-volume fully implicit solver that simulates the transient thermal response and pyrolysis gas transport inside orthotropic charring ablators. Due to surface recession of ablators in the aeroheating environments, an arbitrary Lagrangian–Eulerian (ALE) formulation of the problem is presented. The governing equations (which consist of solid phase continuity, gas phase continuity, unsteady form of Darcy's law as gas momentum, and gas–solid mixture energy) are solved with an unstructured moving grid system. The boundary condition at the ablated surface is characterized by integrating the equilibrium thermochemical tables into the surface energy balance under assumption of a unity Lewis number. The developed computational scheme is verified using both analytical solution and code-to-code comparison. The simulations are performed on both cylindrical and iso-q shaped samples. The results show that the pyrolysis gas movement significantly influences the thermal response of the ablator. As the hot pyrolysis gas travels inside the porous ablator, it carries a great deal of energy, which enhances the solid temperature in the downstream region. Also, blowing the gas into the freestream has reduced the net convective heat flux, resulted in a decrease in the heat penetration area inside the ablator and char depth in the vicinity of permeable boundaries.

References

1.
Chen
,
Y.
, and
Milos
,
F.
,
2013
, “
Effects of Nonequilibrium Chemistry and Darcy-Forchheimer Pyrolysis Flow for Charring Ablator
,”
J. Spacecr. Rockets
,
50
(
2
), pp.
256
269
.10.2514/1.A32289
2.
Lin
,
W.
,
2007
, “
Quasi-Steady Solutions for the Ablation of Charring Materials
,”
Int. J. Heat Mass Transfer
,
50
(
5–6
), pp.
1196
1201
.10.1016/j.ijheatmasstransfer.2006.11.011
3.
Tahmasbi
,
V.
, and
Noori
,
S.
,
2018
, “
Thermal Analysis of Honeycomb Sandwich Panels as Substrate of Ablative Heat Shield
,”
J. Thermophys. Heat Transfer
,
32
(
1
), pp.
129
140
.10.2514/1.T5051
4.
Martin
,
A.
, and
Boyd
,
I.
,
2008
, “
Simulation of Pyrolysis Gas Within a Thermal Protection System
,”
AIAA
Paper No. 2008-3805.10.2514/6.2008-3805
5.
Milos
,
F. S.
, and
Chen
,
Y.-K.
,
2009
, “
Two-Dimensional Ablation, Thermal Response, and Sizing Program for Charring Ablators
,”
J. Spacecr. Rockets
,
46
(
6
), pp.
1089
1099
.10.2514/1.36575
6.
Mazaheri
,
A.
,
Bruce
,
W. E.
, III
,
Mesick
,
N. J.
, and
Sutton
,
K.
,
2014
, “
Methodology for Flight Relevant Arc Jet Testing of Flexible Thermal Protection Systems
,”
J. Spacecr. Rockets
,
51
(
3
), pp.
789
800
.10.2514/1.A32721
7.
Weng
,
H.
,
Bailey
,
S.
, and
Martin
,
A.
,
2015
, “
Numerical Study of Iso-Q Sample Geometric Effects on Charring Ablative Materials
,”
Int. J. Heat Mass Transfer
,
80
(
5
), pp.
570
596
.10.1016/j.ijheatmasstransfer.2014.09.040
8.
Weng
,
H.
, and
Martin
,
A.
,
2014
, “
Multi-Dimensional Modeling of Pyrolysis Gas Transport Inside Charring Ablative Materials
,”
J. Thermophys. Heat Transfer
,
28
(
4
), pp.
583
597
.10.2514/1.T4434
9.
Hogan
,
R.
,
Blackwell
,
B.
, and
Cochran
,
R.
,
1996
, “
Application of Moving Grid Control Volume Finite Element Method to Ablation Problems
,”
J. Thermophys. Heat Transfer
,
10
(
2
), pp.
312
319
.10.2514/3.789
10.
Suzuki
,
T.
,
Sawada
,
K.
,
Yamada
,
T.
, and
Inatani
,
Y.
,
2004
, “
Thermal Response of Ablative Test Piece in Arc-Heated Wind Tunnel
,”
AIAA
Paper No. 2004-341.10.2514/6.2004-341
11.
Suzuki
,
T.
,
Sakai
,
T.
, and
Yamada
,
T.
,
2007
, “
Calculation of Thermal Response of Ablator Under Arc Jet Flow Condition
,”
J. Thermophys. Heat Transfer
,
21
(
2
), pp.
257
266
.10.2514/1.25499
12.
Suzuki
,
T.
,
Fujita
,
K.
, and
Sakai
,
T.
,
2010
, “
Experimental Study of Graphite Ablation in Nitrogen Flow, Part II: Further Numerical Analysis
,”
J. Thermophys. Heat Transfer
,
24
(
3
), pp.
589
597
.10.2514/1.43264
13.
Milos
,
F.
, and
Chen
,
Y.
,
2013
, “
Ablation, Thermal Response, and Chemistry Program for Analysis of Thermal Protection Systems
,”
J. Spacecr. Rockets
,
50
(
1
), pp.
137
149
.10.2514/1.A32302
14.
Chen
,
Y.
, and
Milos
,
F.
,
2001
, “
Two-Dimensional Implicit Thermal Response and Ablation Program for Charring Materials
,”
J. Spacecr. Rockets
,
38
(
4
), pp.
473
481
.10.2514/2.3724
15.
Chen
,
Y.-K.
, and
Milos
,
F. S.
,
2005
, “
Three-Dimensional Ablation and Thermal Response Simulation System
,”
AIAA
Paper No. 2005-5064.10.2514/6.2005-5064
16.
Chen
,
Y.-K.
,
Milos
,
F. S.
, and
Gokcen
,
T.
,
2010
, “
Validation of a Three-Dimensional Ablation and Thermal Response Simulation Code
,”
AIAA
Paper No. 2010-4645.10.2514/6.2010-4645
17.
Schulz
,
J. C.
,
Stern
,
E. C.
,
Muppidi
,
S.
,
Palmer
,
G. E.
,
Schroeder
,
O.
, and
Martin
,
A.
,
2017
, “
Development of a Three-Dimensional, Unstructured Material Response Design Tool
,”
AIAA
Paper No. 2017-0667.10.2514/6.2017-0667
18.
Chen
,
Y.
, and
Milos
,
F.
,
2018
, “
Multidimensional Finite Volume Fully Implicit Ablation and Thermal Response Code
,”
J. Spacecr. Rockets
,
55
(
4
), pp.
914
927
.10.2514/1.A34184
19.
Chen
,
Y.-K.
,
Gökçen
,
T.
, and
Edquist
,
K. T.
,
2009
, “
Two-Dimensional Ablation and Thermal Response Analyses for Mars Science Laboratory Heatshield
,”
AIAA
Paper No. 2009-4235.10.2514/1.A32868
20.
Howard
,
M.
, and
Blackwell
,
B.
,
2015
, “
A Multi-Dimensional Finite Element Based Solver for Decomposing and Non-Decomposing Thermal Protection Systems
,”
AIAA
. Paper No. 2015-250610.2514/6.2015-2506
21.
Amar
,
A.
,
Oliver
,
B.
,
Kirk
,
B.
,
Salazar
,
G.
, and
Droba
,
J.
,
2016
, “
Overview of the CHarring Ablator Response (CHAR) Code
,”
AIAA
Paper No. 2016-3385.10.2514/6.2016-3385
22.
Weng
,
H.
, and
Martin
,
A.
,
2015
, “
Numerical Investigation of Thermal Response Using Orthotropic Charring Ablative Material
,”
J. Thermophys. Heat Transfer.
,
29
(
3
), pp.
429
438
.10.2514/1.T4576
23.
Zeng
,
D.
, and
Ethier
,
C.
,
2005
, “
A Semi-Torsional Spring Analogy Model for Updating Unstructured Meshes in 3D Moving Domains
,”
Finite Elem. Anal. Des.
,
41
(
11–12
), pp.
1118
1139
.10.1016/j.finel.2005.01.003
24.
Liou
,
M.
,
2006
, “
A Sequel to AUSM, Part II: AUSM+-Up for All Speeds
,”
J. Comput. Phys.
,
214
(
1
), pp.
137
170
.10.1016/j.jcp.2005.09.020
25.
Ganesh
,
S.
, and
Prasad
,
B.
,
2012
, “
Iterative Inverse Design Method With AUSM+-Up Scheme Implemented on Unstructured Grids
,”
J. Propul. Power
,
28
(
1
), pp.
16
26
.10.2514/1.B34216
26.
Moyer
,
C. B.
, and
Rindal
,
R. A.
,
1968
, “
An Analysis of the Coupled Chemically Reacting Boundary Layer and Charring Ablator—Part II: Finite Difference Solution for the in-Depth Response of Charring Materials Considering Surface Chemical and Energy Balances
,” NASA, Washington, DC, Report No. NASA CR-1061.
27.
van Eekelen
,
T.
,
Martin
,
A.
,
Lachaud
,
J.
, and
Bianchi
,
D.
,
2014
, “
Ablation Test-Case Series #3
,” Sixth Ablation Workshop,
Urbana Champaign, IL
, Apr. 10.
28.
Ahn
,
H.
,
Park
,
C.
, and
Sawada
,
K.
,
2002
, “
Response of Heatshield Material at Stagnation Point of Pioneer-Venus Probes
,”
J. Thermophys. Heat Transfer
,
16
(
3
), pp.
432
439
.10.2514/2.6697
29.
Douglas
,
J.
,
Paes-Leme
,
P. J.
, and
Giorgi
,
T.
,
1993
, “
Generalized Forchheimer Flow in Porous Media
,”
Purdue University
,
West Lafayette, IN
, Report No. 205.
30.
Martin
,
A.
, and
Boyd
,
I.
,
2010
, “
Non-Darcian Behavior of Pyrolysis Gas in a Thermal Protection System
,”
J. Thermophys. Heat Transfer
,
24
(
1
), pp.
60
68
.10.2514/1.44103
31.
Marschall
,
J.
, and
Milos
,
F.
,
1998
, “
Gas Permeability of Rigid Fibrous Refractory Insulations
,”
J. Thermophys. Heat Transfer
,
12
(
4
), pp.
528
535
.10.2514/2.6372
32.
Cross
,
P.
, and
Boyd
,
I.
,
2017
, “
Two-Dimensional Modeling of Ablation and Pyrolysis With Application to Rocket Nozzles
,”
J. Spacecr. Rockets
,
54
(
1
), pp.
212
224
.10.2514/1.A33656
33.
Suzuki
,
T.
,
Sawada
,
K.
,
Yamada
,
T.
, and
Inatani
,
Y.
,
2004
, “
Gas Permeability of Oblique-Layered Carbon-Cloth Ablator
,”
J. Thermophys. Heat Transfer
,
18
(
4
), pp.
548
550
.10.2514/1.6242
34.
Saad
,
Y.
,
2003
,
Iterative Methods for Sparse Linear Systems
, 2nd ed.,
Society for Industrial and Applied Mathematics
,
Philadelphia, PA
, pp.
301
321
.
35.
Rauch
,
R. D.
,
Batira
,
J. T.
, and
Yang
,
N. T. Y.
,
1991
, “
Spatial Adaption Procedures on Unstructured Meshes for Accurate Unsteady Aerodynamic Flow Computations
,”
AIAA J.
, 30(5), p.
1243
.10.2514/3.11057
36.
Kays
,
W. M.
,
Crawford
,
M. E.
, and
Weigand
,
B.
,
2005
,
Convective Heat and Mass Transfer
, 4th ed.,
McGraw-Hill
,
New York
.
37.
Anon
.,
1981
, “
User's Manual Aerotherm Chemical Equilibrium Program
,” Acurex Corp., Aerotherm Division, Mountain View, CA, Report No. UM-81-11/ATD.
38.
Zhang
,
H.
,
Reggio
,
M.
,
Trépanier
,
J.
, and
Camarero
,
R.
,
1993
, “
Discrete Form of the GCL for Moving Meshes and Its Implementation in CFD Schemes
,”
Comput. Fluids
,
22
(
1
), pp.
9
23
.10.1016/0045-7930(93)90003-R
39.
Tran
,
H. K.
,
Johnson
,
C. E.
,
Rasky
,
D. J.
,
Hui
,
F. C. L.
,
Hsu
,
M.-T.
,
Chen
,
T.
,
Chen
,
Y. K.
,
Paragas
,
D.
, and
Kobayashi
,
L.
,
1997
, “
Phenolic Impregnated Carbon Ablators (PICA) as Thermal Protection Systems for Discovery Missions
,” NASA Ames Research Center; Moffett Field, CA, Report No. TR-110440.
40.
Amar
,
A.
,
Calvert
,
N.
, and
Kirk
,
B.
,
2011
, “
Development and Verification of the Charring Ablating Thermal Protection Implicit System Solver
,”
AIAA
Paper No. 2011-144.10.2514/6.2011-144
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