A viscous shock-layer analysis is for calculating high energy equilibrium flow fields about blunt axisymmetric bodies is applied to the problem of massive ablation injection with radiation transport. A nongray radiation model is used that accounts for both line and continuum radiation. The solution method is direct and provides both stagnation and downstream solutions. Results for shock heated air show that phenolic-nylon injection is substantially more effective in reducing the wall radiant flux than air injection. Also, for large included body angles, the wall radiative flux and the coupled phenolic-nylon injection rate do not continue to decrease with increasing distance downstream

Moss, J. N.

English

NASA Technical Reports Server

NASA TECHNICAL NASA TM X-71976
MEMORANDUM COPY NO.
C,
I-
I--
THE EFFECT OF ABLATION INJECTION ON
RADIATIVE AND CONVECTIVE HEATING
By James N. Moss
Langley Research Center
Hampton, Virginia 131 q
Presented at the 10th Anniversary Meeting of
the Society of Engineering Science, 1973 i. 1A
This informal documentation medium is used to provide accelerated or
special release of technical information to selected users. The contents
may not meet NASA formal editing and publication standards, may be re-
vised, or may be incorporated in another publication.
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
LANGLEY RESEARCH CENTER, HAMPTON, VIRGINIA 23665
(NASA-TM-X-71976) THE EFFECT OF ABLATION N74-284241
IVJECTION CN RADIATIVE AND CONVECTIVE
HEATING (NASA) - p HC $3.©00 CSCL 2~8
Unclas
G3/33 43167\
https://ntrs.nasa.gov/search.jsp?R=19740020311 2020-03-23T05:52:03+00:00Z
1. Report No. 2. Government Accession No. 3. Recipient's Catalog No.
. TM X-71976
4. Title and Subtitle 5. Report Date
THE EFFECT OF ABLATION INJECTION ON RADIATIVE AND June 1974
CONVECTIVE HEATING 6. Performing Organization Code
7. Author(s) 8. Performing Organization Report No.
James N. Moss
10. Work Unit No.
9. Performing Organization Name and Address
Langley Research Center 11. Contract or Grant No.
Hampton, VA 23665
13. Type of Report and Period Covered
12. Sponsoring Agency Name and Address Technical Memorandum
NASA Langley Research Center 14. Sponsoring Agency Code
Hampton, VA 23665
15. Supplementary Notes
Article proposed for publication in the Proceedings of the 10th Anniversary
Meeting of the Society of Engineering Science, 1974
16. Abstract
A viscous shock-layer analysis for calculating high energy equilibrium
flow fields about blunt axisymmetric bodies is applied to the problem of
massive ablation injection with radiation transport. A nongray radiation model
is used that accounts for both line and continuum radiation. The solution
method is direct and provides both stagnation and downstream solutions.
Results for shock heated air show that phenolic-nylon injection is substantially
more effective in reducing the wall radiant flux than air injection. Also,
for large included body angles, the wall radiative flux and the coupled
phenolic-nylon injection rate do not continue to decrease with increasing
distance downstream.
17. Key Words (Suggested by Author(s)) (STAR category underlined) 18. Distribution Statement
Radiative viscous flows Mass injectionAblation Shock layerContinuum radiation Unclassified - unlimited
Line radiation
Equilibrium
19. Security Cassif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price-
Unclassified Unclassified 7 $3.00
The National Technical Information Service, Springfield, Virginia 22151
Available from
STIF/NASA Scientific and Technical Information Facility, P.O. Box 33, College Park, MD 20740
/
THE EFFECT OF ABLATION INJECTION ON RADIATIVE
AND CONVECTIVE HEATING
James N. Moss
NASA Langley Research Center, Hampton, Va., 23365
ABSTRACT
A viscous shock-layer analysis for calculating high energy
equilibrium flow fields about blunt axisymmetric bodies is
applied to the problem of massive ablation injection with radia-
tion transport. A nongray radiation model is used that accounts
for both line and continuum radiation. The solution method is
direct and provides both stagnation and downstream solutions.
Results for shock heated air show that phenolic-nylon injection
is substantially more effective in reducing the wall radiant flux
than air injection. Also, for large included body angles, the
wall radiative flux and the coupled phenolic-nylon injection rate
do not continue to decrease with increasing distance downstream.
INTRODUCTION
The flow field about planetary entry vehicles is very com-
plex because of the many interactions that occur between ablation
injection, radiation transfer, and viscous and diffusion effects.
In addition, no experimental data exist which fully duplicate the
thermodynamic environment for planetary entry regimes or how the
environment interacts with the thermal protection material. Con-
sequently, rigorous numerical analysis of high energy flow fields
is essential; essential to the understanding of the basic mecha-
nisms involved in energy transport and to the design of adequate
thermal protection systems.
Almost all existing radiative viscous flow analyses are
limited to stagnation solutions. However, Sutton (Ref. [1]) and
Chou (Ref. [2]) have recently presented downstream solutions for
viscous radiating flows. Sutton's analysis is a direct method
and is applicable for zero to moderate mass injection while
Chou's analysis accounts for massive blowing but is an indirect
method.
A rigorous viscous shock-layer analysis for calculating high
energy equilibrium flow fields about blunt axisymmetric bodies at
zero degree angle of attack is presented herein. The present
analysis, based on the analysis developed by Davis (Ref. [3]) for
a perfect gas, includes mass injection, radiation transfer, dif-
fusion, and viscous effects. The analysis is direct and provides
both stagnation and downstream solution for all levels of blow-
ing. Radiation transfer is calculated with a nongray radiation
model that accounts for line and continuum radiation. Results
are presented for earth entry conditions to demonstrate the
L-9183 I
\
essential features of this analysis. Particular emphasis is
given to the effects of mass injection on the stagnation and
downstream flow. Results for both specified and coupled mass
injection are presented. The injectants considered are the spe-
cies for both air and a phenolic-nylon ablator. This is the
first direct analysis that provides nonsimilar downstream solu-
tions for radiative viscous flows for all levels of blowing.
ANALYSIS
The viscous shock-layer equations for an equilibrium multi-
component gas mixture are developed in References [4] and [5].
The same viscous shock-layer equations are solved in the present
study with the addition of radiation transport. The nondimen-
sional equations in a body oriented coordinate system (Fig. 1)
are:
00
cuIly- u U*
JI IVVnI
n*
U* -N
Figure 1. Coordinate system.
Global continuity:
(r + n cos 9)pu] + [(1 + n)(r + n cos K )jpv] =
s-momentum:
u u u UVK 1 up 2 = u UK
P + nK _ +v 3 +1v+nKT + n
+ 2K + j COs 0 /6U UK (2)
nmmn 1 + nK r +n cos D n +nK
u av av U 20 (3)
P( +nK +v s  1+nK +7 -= O 
(
Energy:
u H 6H 6p PKU 2  j cos 6+ nK CO
v f j n Q ( 1 + cose ~ )K -s + v - +n+ r+ n cos (4)
2,
Elemental continuity:
p + V = (+nK)(r+ncos)
(1 + nK)(r + n cos8)
NSc n
State:
p = pTR*/rM*C* (6)
where
ref u2
*=J Hh + , CV
Pri= i=
N KU
NP  n + (NLeP- r)i=l hi
+ (Npr - 1) u N-i + n1
and Q is the divergence of the radiative flux (Q*R/p*u*3). The
superscript * denotes dimensional quantities while j has a
value of one for an axisymmetric body and zero for a two-
dimensional body. The bar denotes mixture values while the sub-
scripts i and I denote species and elements, respectively. The
quantity h is the static enthalpy (h*/p u*2 ), p the density
p*/p*), p the pressure (p*/p*u*), i the viscosity (~*/P*ef),
C2 the elemental mass fraction, Ci the species mass fraction,
M* the molecular weight, bil the number of atoms of element I
in species i, N the total number of species, R* the universal
gas constant, Cp the specific heat, and Npr, NLe, and NSc the
Prandtl, Lewis, and Schmidt numbers, respectively. The reference
viscosity is the viscosity evaluated at the reference temperature
u*2/Cpm.
The boundary conditions at the shock are calculated by using
the Rankine-Hugoniot relations. At the wall, the no slip and no
temperature jump boundary conditions are used; consequently,
uw = 0. The wall temperature and mass injection rate are either
specified or calculated. For the calculated conditions, the mass
injection rate is determined from an energy balance at the flow-
field-ablator interface. The coupled mass injection rate and
surface temperature are calculated by iterating the solution of
the governing flow-field equations and the boundary conditions.
The total heat transferred to the surface boundary is given,
in nondimensional form, as
qT = q + qr (8a)
where
2 T N N
q = (K , [(  - Jhi) w + i [(Cihi)
- 
(Cihi)w ]  (8b)
i=l i=l
3
The quantity K is the mixture frozen thermal conductivity
(K*/*e C* ), Ji the diffusion mass flux of secies i(JiRN* ref ,and i  the mass injection rate [(p v*)w/(p*u*)).
The sub scripts w and - denote quantities at the surface boundary
and adjacent but below the surface boundary, respectively. The radi-
ative flux, qr = q*/p*u*3, and the divergence of the radiative flux, Q,
are calculated with the radiation transport model LRAD - 3, as pre-
sented in Reference [6]. The radiation transport model is an extended
version of a coupled line and continuum model that was originally
developed by Wilson (Ref. [7]). The LRAD - 3 radiation model accounts
for the effects of nongray self-absorption, radiative cooling, and the
contribution of atomic line radiation. Twelve continuum frequency
bands and nine line bands are used. The species considered for deter-
mining the radiation transport are: C, H, N, and O for both con-
tinuum and lines and CO, C2, C3, 02, H2 , C2H, and e- for con-
tinuum. Details of the radiation transport analysis are given in
References [6] and [7] and, therefore, will not be reproduced here.
The equilibrium composition is determined by a free energy
minimization calculation as developed in Reference [8]. Thermo-
dynamic and transport properties are calculated for each species.
In this study, the binary diffusion coefficient is set equal to
the diffusion coefficient for atomic carbon diffusing into atomic
nitrogen.
The method of solving the governing equations and boundary
conditions is discussed in detail in Reference [5]; therefore,
only a brief overview of the solution procedure is presented.
The governing equations are written in finite-difference form by
using Taylor's series expansions. A variable grid spacing is
used in both the tangential and normal directions to the surface
so that the grid spacing can be made small in the region of large
gradients. The order of the truncation terms neglected are As
and either 6AAjnIn- or (Ain - Arn-l), where T = n/ns. The
governing equations are uncoupled and the dependent variables are
solved one at a time at any body station in the following
sequence: Rankine-Hugoniot equations to obtain the shock condi-
tions, material response for Tw and mw, elemental equations
Cz, radiation transport for Q, energy equation for H, equilib-
rium chemistry for Ci and T, s-momentum for u, global contin-
uity for ns and v, n-momentum for p, and the equation of
state for p. The solution is iterated until convergence is
achieved. The solution advances to the next body station and
uses the previous converged solution profiles as initial values
for starting the solution at the new body station. This proce-
dure is repeated until a solution pass is obtained. In the first
solution pass, it is necessary to make some approximations (see
Ref. [5]). These approximations are then removed by iterating
the global solution. Two solution passes are generally suffi-
cient. This solution procedure is programed for the CDC 6600
computer.
4
/
RESULTS AND DISCUSSION
To demonstrate the essential features of the analysis,
results are presented for the following earth entry conditions:
velocity = 15.24 km/s and altitude = 62.2 km. The body is a
hyperboloid with a total included angle of 1200 and a nose radius
of 0.305 m. For these conditions, the free-stream Reynolds num-
ber is 67,850 and the stagnation shock pressure and temperature
are 0.5 atm and 14,700 K, respectively. Mass injection rates, i,
from 0. to 0.60 are considered. Results for both air and
phenolic-nylon injection are presented. For air, seven chemical
species are used: 0, 02, 0+, N, N2 , N+, and e-. For phenolic-
nylon, 20 chemical species are used; the seven used for air plu:;
C, C2, C3 , CO, CN, C2H, C3H, C4fH, C2112, C+, H, H2, and HCN. The
present analysis can be easily modified for planetary atmospheres
other than earth by including thermodynamic, transport, and radia-
tive property data for the necessary species that are not pres-
ently accounted for.
/ HEATING RATE
s  I -- 0. 1361 2395J- .12 113 2010
.4 / l .12b  32 1581
/ / .30 4 1361
I --- . .60 0 1311
aAIR INJECTION
bCOIJPLED ABLATION
INJECTION
6I 1 IS .01 .02 .03 .0(1 .05 .06 .07 .08
nYIR'N
Figure 2. Stagnation temperature profiles
for various injection rates.
Figure 2 shows the effect of' mass injection on stagnation
temperature profiles. Both coupled and arbitrary injection are
considered. The injection rate of 0.12 is the coupled mass
injection rate for a phenolic-nylon ablator. At this point in
the trajectory, the mass injection is sufficient to cause a 98%
reduction in q* and a 34% reduction in q*. For phenolic-nylon
injection, the specific heat of the gas is much greater near the
wall and the radiation flux toward the wall is attenuated much
more than for the corresponding air injection rate. Consequently,
the phenolic-nylon injection has a much larger effect on tempera-
ture profile and surface heating than air injection, as shown in
Figure 2. For air injection of 0.12, the heating reduction is 92%
for q* and 16% f'or qr. For phenolic-nylon injection rates in
excess of' the coupled injection value, only -;mall additional
reductions in heating occur.
5
For large injection rates, the problem of numerical insta-
bilities is characteristic of most, if not all, analyses that
have been developed. For example, the analysis described in
Reference [9] was unable to obtain a converged solution to the
energy equation for an injection rate of 0.2. However, with the
present analysis, a converged solution is obtained for injection
rates substantially in excess of 0.2, as shown in Figure 2.
Figure 3 presents the surface heating rate and mass injec-
tion distributions where the mass injection from a phenolic-nylon
ablator is coupled with the radiating flow-field solution. For
the body shape considered and because the shock thickens with
distance downstream, the radiative heating and mass injection do
not continue to decrease with increasing distance downstream.
Figure 4 shows the tangential velocity profiles for the stagna-
tion and downstream locations. These results show very clearly
20 11.00 
2
.8 - SoIR 3.0-
1.6 
- N
W/cm2 10 - /.
5 -- i (PHENOLIC-NYLONI .05 2
0 1 2 SR 3 4 0 .2 .4 n .6 .8 1.0
Figure 3. Shock-layer results with Figure 4. Tangential velocity
coupled ablation injection. profiles for coupled abla-
tion injection.
the nonsimilar behavior of the flow field. Also, note that the
viscous effects along the stagnation streamline are evident
throughout the shock layer. Downstream, however, the viscous
effects are confined to a small segment of the shock-layer
thickness.
The spectral details of the radiation flux at the wall are
shown for the continuum and line radiation in Figure 5. A com-
parison of the surface spectral flux with and without injection
are made. The results show that for both continuum and line
radiation, the phenolic-nylon injection causes a large attenua-
tion of the ultraviolet radiation.
6
x 102 5-x 102 - 0
--- n 0.12 PHENOLIC-NYLON
- n--- 0.12 PHENOLIC-NYLON
3 3-
W/cm 2 -eV W/cm2 -eV
2- 2 -
I L
0 4 8 1 16 20 4 12 16 20
PHOTON ENERGY, eV PHOTON ENERGY, eV
(a) Continuum. (b) Line.
Figure 5. Comparison of wall radiation with and
without mass injection.
REFERENCES
[1]Kenneth Sutton, "Fully Coupled Nongray Radiating Gas Flows
with Ablation Product Effects About Planetary Entry Bodies,"
AIAA Paper No. 73-672, July 1973.
[2]Y. S. Chou, "Effect of Downstream Massive Blowing on Jovian
Entry Heating," AIAA Paper No. 73-717, July 1973.
[3]R. T. Davis, "Numerical Solution of the Hypersonic Viscous
Shock-Layer Equations," AIAA J., Vol. 8, May 1970, pp. 843-
851.
[4]James N. Moss, "Solutions for Reacting and Nonreacting Viscous
Shock Layers with Multicomponent Diffusion and Mass Injection,"
Ph.D. Thesis, Virginia Polytechnic Institute and State
University, 1971.
[5]James N. Moss, "Reacting Viscous Shock-Layer Solutions with
Multicomponent Diffusion and Mass Injection," NASA TR R-411
(to be published).
[6 ]Carl D. Engel, Richard C. Farmer, and Ralph W. Pike, "Abla-
tion and Radiation Coupled Viscous Hypersonic Shock Layers,"
NASA CR-112306, 1971.
[7]K. H. Wilson, "Stagnation Point Analysis of Coupled Viscous-
Radiating Flow with Massive Blowing," NASA CR-1548, 1970.
[8C. W. Stroud and Kay L. Brinkley, "Chemical Equilibrium of
Ablation Materials Including Condensed Species. NASA TN
D-5391, 1969.
[9]L. B. Garrett, G. L. Smith, and J. N. Perkins, "An Implicit
Finite-Difference Solution to the Viscous Shock Layer
Including the Effects of Radiation and Strong Blowing,"
NASA TR R-388, 1972.
7


The effect of ablation injection on radiative and convective heating

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