A method is presented for calculating the heating and erosion of blunt bodies made of graphite in a high-enthalpy flow of dissociated air, assuming chemical equilibrium on the surface and taking account of the thermal effects of combustion and sublimation of graphite. The analysis involves the use of a finite difference scheme to solve an equation of unsteady heat conduction. Attention is given to the equilibrium vaporization of C, C2 and C3 molecules. The calculations agree well with experimental data for a wide range of temperatures and stagnation pressures

Bovina, T. A.

Chudetskiy, Y. V.

Markelov, N. V.

Zviagin, Y. V.

English

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NASA TECHNICAL MEMORANDUM NASA TM-78000
S
THEORETICAL AND EXPERIMENTAL INVESTIGATION OF THE
DESTRUCTION OF GRAPHITES IN A FLOW OF DISSOCIATED AIR
T. A. Bovina, Yu. V.
N. V. Markelov, Yu. V.
Translation of "Teoreticheskoye i eksperimental"noye
issledovaniye razrusheniya grafitov v potoke dissotsiirovannogo
vozdukha," in Heat and Mass Transfer V: Ail-Union Conference
on Heat and Mass Transfer/ 5th, Minsk, Belorussian SSR, May
17-20, 1976, Proceedings, vol. 2, pp. 85-90.
THEORETICAL AND 1XPEEIHENTAL INVESTIGATION N86-21632
'OF THE DESTRUCTION OF GBAPHI1IS IN A FLOW OF
DISSOCIATED AIE {National Aeronautics and
I Space Administration) 10 p HC AQ2/HF A01 Unclas
CSCL 07D G3/25 05718.
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
WASHINGTON, D.C. 20546 FEBRUARY 1986
https://ntrs.nasa.gov/search.jsp?R=19860012161 2020-03-20T14:59:10+00:00Z
S T A N D A R D 1 17 LE P A C E
I . Ripon No
TM-78000
2. Cc No. 3. Rec ip ien t ' s Cotclop No.
Till, one! Subti t le
Theoretical and Experimental Investigation of
the Destruction of Graphites.in a Flow of
Dissociated Air '
5. R.poii Dot.
February 1986
6. P.rloiminp Otponilotion Coo**
7. Aothor(s)
T. Pr, Bovina, Yu. V. Zviagin, N. V. Markelov,
Yu. V. Chudetskiy
8. P.rfotminp Orporti i otion Repor t No.
10. tfo.k Unit No.
9. Perfoiminp Of (oni lotion Nome on^ Ac'c'rcit
The Corporate Word
1102 Arrott Building
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11. ConltoC' o« Cionl No.
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13. T yp« of Rcpor l end Pct io i f
Translation
12. Sponsoring Apency Nome ond A<ioi**B
ixiATIONAL AERONAUTICS AND SPACE ADMINISTRATION
WASHINGTON, DC 20546
^ . Sponi oi inp A.c*ncy CocJ«
15. Supplemenlory Kotcs
Translation o£:""Teoreticheskoye i eksperimental'noye issledovaniye
razrucheniya grafitov v potoke dissotsiirovannogo vozdukha," IN: Heat and
Mass Transfer V: Ail-Union Conference on Heat and Mass Transfer, 5th, Minsk,
Belorussian SSR, May 17-20, 1976, Proceedings, Vol. 2, pp. 85-90
(A77-43935)
. Ab»troc1
A method is presented for claculating the heating and erosion of blunt
bodies made of graphite in a high-enthalpy flow of dissociate air, assuming
thermal effects of combustion and sublimation of graphite. The analysis
involves the use of a finite difference sfaheme to solve anaequation of un- .
steady heat conduction.• • Attention is given to the equilibrium vaporization
of C, Q.., and C molecules. The calculations,agree well with experimental
data for a wide range of temperatures and stagnation pressures.
17. Key Wordi (Selected by Author(i))
aerothermochemistry/blkunt bodies/
graphite/high.-temperature air/
pyrolysis/thermal dissociation
IE. Dillribution Slol.m.nl
Unclassified - Unlimited
19. Security Cloitlf. (of ihis f.porl)
unclassified
JO. S.cunlr Clcl.lf. (c( thi» p.p.)
Unclassified
21. He. «f P.O.
10
22. Prie."".
ORIGINAL PAGE !3
OF POOR QUALITY
2
NASA-HQ
THEORETICAL AND EXPERIMENTAL INVESTIGATION OF THE
DESTRUCTION OF GRAPHITES IN A FLOW OF DISSOCIATED AIR
T. A. Bovina, Yu. V. Vziagin,
N. V. Markelov, Yu. V. Chudestkiy
Authors in this country and abroad have devoted a whole /85:
series of experimental and theoretical studies to combustion of
carbon materials in high-enthalpy air flows. However, the
results of different researchers' calculations correlate quite
poorly because of the difference in approaches to identifying
definitive physico-chemical processes on the carbon's surface
at high temperatures. Existing experimental relationships
between carbon material gasification rate and surface
temperature are also extremely contradictory.
Ablation of carbon material in a low-temperature air flow
results basically from two processes: chemical interaction
with the components of the air (accompanied by heat release)
and sublimation of carbon (with heat absorption). While it is
not difficult to follow the first process at rather high
temperatures (2,500 K + ) , there is no consensus on the
description of the second regarding either the kinetics of
carbon sublimation or the composition of the sublimating gas.
Disagreements in interpretation of the carbon sublimation
mechanism result in considerable discrepancies in results in
terms of carbon material gasification rate and temperatures of
the surface being destroyed.
When the analytical procedure presented below was being
developed, the authors' goal was to account as much as possible
for all basic features of the process by which carbon material
interacts with an air flow at high temperatures. In contrast
to most existing studies, the problem of unstable heating and
Numbers in the margin indicate pagination in the foreign text.
PRECEDING PAGE BLANK NOT FILMED
erosion of a blunted graphite body immersed in a dissociated
air flow was also solved.
The proposed analytical procedure is used to solve the
equation for unstable heat conductivity
3 (i)
which is considered in finite-difference form with regard for
dependency of the material's thermophysical properties on /86
temperature for the given temperature profile and with the
following boundary conditions:
• Heat insulation on the cold surface
(2)
The energy balance on the surface where the carbon material
interacts with the air flow is preserved in the form
(3)
M v i r 1 <T~? 1 r
where
For h., the study used approximations of tabular data
from [2] in the form
The solution to the thermal conductivity equation requires
that the "mobility" of the surface where the material interacts
with the flow be taken into account.
To close system of equations (l)-(3) given known
relationships between the enthalpies of the subject components
and temperature, one must know the relationships between the
gas mixture's composition and carbon ablation velocity, as well
as pressure, temperature, and the coefficient of heat and
mass exchange on the material's surface.
The carbon composition and ablation velocity at the
material's surface can be determined only by defining the
physico-mechanical interaction between the carbon material and
the high-temperature flow of dissociated air.
The following physical model was used for the process by
which carbon material interacts with a high-enthalpy air flow.
Just as in [3], the compositions of the gas in the flow and
at the material's surface were regarded as equiponderant. On
the "catalytic" surface of the carbon material, all chemical
reactions proceed at an infinitely high speed.
Profiles for complete enthalpy and for the concentrations
of all subject components are similar in the boundary layer.
Five components are considered on the outer edge of the
boundary layer: 0, N, 0~, N?, NO; eleven on the carbon's
surface: C^, C2, C3/ CO, N2/ CN, CO2/ N, NO, 02, O.
Carbon vaporizes in the form of C, C?, and C,
molecules. Saturating vapor pressures for these components
also satisfy conditions for chemical equilibrium at surface
temperature.
It is not difficult to calculate the equilibrium
composition of air at the outer edge of the boundary layer for
the assigned temperature and pressure.
The following relationships are considered in determining
composition at the surface.
• Equations for the law of mass action for molecular
component (CO, CO , NO, 0 , C_, C_) atomization
reactions in the form
(of the seven equations, one can be replaced by Dalton's law
- Equations for mass balance at the material's surface for
atoms of
- nitrogen
• — -* C ' i — \ O)
- oxygen
- and carbon
Mass balance for carbon vaporization
^ n, (8)
where " 'oT ^  Vl '&, Uc ~ /C V/Om /^ is the speed of
vaporization for carbon in the form of C molecules, where
HAC _ HAC n,
PCn " (PC1 } /KCn
To solve system of equations (4)-(8) relative to G and
C. (which are functions of T ), static pressure and thein w .
factor for heat-mass exchange '( &fcn) must be set.
Fey-Riddel's formula [4] was used to calculate i/Cp, for
immersion of a blunted body.
If solid carbon gasification is intense, .... must be
calculated with a correction for blowing (cf. e.g. [51]).
Approximations of tabular data from [2] in the form
Ig K = A + B/T + C Ig T.
below were used for the temperature dependence of molecular
component atomization constants and carbon vapor saturating
pressure.
/88
Thus, this system of basic equations (l)-(8) is closed, and
its solution makes it possible, generally speaking, to
determine flow parameters which are variable over time (P'nf
T'Q, <L/Cp,), ablation velocity, gas composition at the
surface, and temperature profiles deep in the material, at any
time.
The algorithm for numerical solution of this system of
equations has been compiled in ALGOL-60 for the BESM-4M
computer.
A specially designed high-temperature setup (described in
detail in [6]) was used to test cylindrical graphite samples 14
mm in diameter and 40 mm long in a supersonic flow of
dissociated air. Flow parameters and test results are
presented in the table below (tests 1-4).
Test
No.
1
2
3
4
5
6
Graphite
density
g/cm^
1.94
1.65
1.65
1.80
2.2
2.2
P'O' ata
5.5
6.0
5.75
17.0
1.2
1.0
T'0, K
5,600
4,500
5,900
4,800
6,310
8,100
W, mm/sec
0,17
0.20
0.36
0.4
0.078
0.31
Tw, K
3,100
3,100
3,000
3,200
3,100
4,000
Results of tests 5 and 6 are presented in [7] and pertain
to pyrographite.
Results of calculation using the proposed procedure and the
experimental data presented here are shown in the figure.
The arrangement of points on the figure close to the ray
running at a 45° angle to the x-axis indicates a completely
satisfactoy correlation between results of calculation and
experimental data for the range of temperatures and pressures
studied.
Wexp
Wcal
w-exp
CM
„ .
*
V-
0.1
.-
- -
\
1
• •
f
1/J
/*
\" n
X
i i}1} />
1 . "1
1 ' / .. •1
 . ,- i VM.V
ii
f
'~ '!
• - i
!>000
2000
,__..! j '000
i i
j
' /•
•- —
'
/
/
/
^
•'
i •
*
' ~ i
x* |
**•
- ,•? *
/
. — _ ,
•
--
• 1
, /,/, u loan aw xno woo •
w-exp
Fig. Comparison of calculated and experimental data on
the linear velocity of ablation (W, mm/sec) and surface
temperature (T , K).
W
A good correspondence of calculation results and
experimental data for G and T indicates that elementary
1W
processes occurring during interaction of carbon materials and
a high-temperature air flow have been correctly taken into
account.
Symbols
. - heat and mass exchange coefficient; cL - vaporization
Nfactor; £ - emissivity factor; V. - number of N atoms in
a molecule of the i-th component; A - thermal conductivity
factor; Q - graphite density; CT' - Stephen-Boltzmann constant;
C. - weight concentration of the i-th component; G - carbon
ablation velocity; h - specific chemical enthalpy; J - total
chemical enthalpy of the gas mixture; K - equilibrium
f\D
constant for the reaction AB ^  A + B; M - molecular weight;
HACP' - pressure behind a straight shock wave; P
saturation pressure of C ; R - universal gas constant; T ' „
- temperature behind a shock wave.
REFERENCES
1. Landell, Dikki, Raketnaya tekhnika i kosmonavtika, 1973,
11, No. 2, pp. 111-119.
2. Glushko, V. P., ed., Termodinamicheskiye svoystva
individual'nykh veshchestv [Thermodynamic Properties of
Individual Substances], AN SSSR Press, 1962.
3. Zavelevich, F. S., Mekhanika zhidkostey i gazov, 1966, No.
1, pp. 161-167.
4. Fey, Riddel, Problemy dvizheniya golovnoy chasti raket
dal'nego deystviya [Problems of the Motion of a Long-Range
Rocket Nose Cone], Moscow, Inostrannaya Literature Press,
1959, pp. 217-256.
5. Mugalev, V. I., Izvestiya AN SSSR, Mekhanika [Proceedings
of the USSR Academy of Sciences, Mechanics], 1965, No. 1,
pp. 57-68.
6. Shirokov, N. N., Chudetskiy, Yu. V., Teplo i massoperenos
[Heat and Mass Transfer], vol. 2, Minsk, "Nauka i tekhnika"
Press, 1968, pp. 162-171.
7. Metsger, Engel1, Diakonio, Raketnaya tekhnika i
kosmonavtika, 1967, vol. 5, No. 3, pp. 81-92.
10


Theoretical and experimental investigation of the destruction of graphites in a flow of dissociated air

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