Effect of Pressure and Propellant Composition
on Graphite Rocket Nozzle Erosion Rate
Ragini Acharya
*
and Kenneth K. Kuo
†
The Pennsylvania State University, University Park, Pennsylvania 16802
DOI: 10.2514/1.24011
The objective of this work is to study the nozzle erosion rates at a broad range of pressures from 7 to 55 MPa with
two baseline propellants: one is a nonmetallized propellant and the other is a metallized propellant, called propellants
S and M, respectively. A comprehensive model for graphite nozzle erosion minimization and a numerical code has
been advanced to predict the nozzle throat recession rates at high pressures. Four different kinetic schemes for
heterogeneous graphite oxidation reactions were compared. The recession rate was found to increase almost linearly
with pressure. The magnitudes of recession rates depend on the chemical kinetic scheme and the propellant
composition. Contrary to popular belief, at lower pressures (P < 14 MPa), the heterogeneous kinetic rates showed a
pronounced effect on the erosion rates, though at higher pressures, the nozzle throat erosion is mainly diffusion
controlled. This observation stresses the importance of more accurate and definitive kinetic parameters for graphite
oxidation reactions, especially at lower pressures. It was also observed that, besides H
2
O, the OH species affects the
nozzle recession rate greatly. For the metallized propellant, the concentrations of major oxidizing species such as
H
2
O, OH, and CO
2
are substantially reduced in comparison with the nonmetallized propellant, resulting in
significant reduction of the erosion rates. A comparison of experimental data and predicted results from the graphite
nozzle erosion minimization code shows excellent agreement especially for the nonmetallized propellant. To
substantially reduce the throat recession rates at high pressures, it is suggested that the boundary-layer control at the
throat region could be an effective method for future nozzle design considerations.
Nomenclature
A = cross-sectional area at the nozzle throat
A
s
= preexponential factor in the Arrhenius reaction-rate
expression
A
s;j
= preexponential factor in the Arrhenius reaction-rate
expression for jth reaction
C
c
= thermal capacity of graphite
C
1
= constant in k–" model
C
2
= constant in k–" model
C
3
= constant in k–" model
C
4
= constant in k–" model
C
= constant in k–" model
E
a;s
= activation energy in the Arrhenius reaction-rate
expression
E
a;s;j
= activation energy in the Arrhenius reaction-rate
expression for jth reaction
D = binary mass diffusivity of gas-phase species
Da = Damköhler number
D
i
= binary mass diffusivity of ith gas-phase species
F = ratio of the overall erosion rate to diffusion-limited
erosion rate
H = total enthalpy of the mixture
P
N
i1
Y
i
h
i
1
2
u
2
v
2
h
i
= sensible enthalpy of ith gas-phase species
k = turbulent kinetic energy
Ma = Mach number
Ma
c
L
= Mach number at the centerline of nozzle
Mw = molecular weight
Mw
c
= molecular weight of carbon
Mw
i
= molecular weight of ith gas-phase species
m = number
_ m
00
= total mass rate of reaction with graphite per unit
surface area
_ m
00
i
= mass rate of chemical reaction of ith gas-phase
species with graphite per unit surface area
N = number of gas-phase oxidizing species at the solid–
gas interface
P = pressure
Pr = Prandtl number
Pr
t
= turbulent Prandtl number
Prod
j
= jth component of product species
P
i
= partial pressure of ith gas-phase species (H
2
O or
CO
2
)
q
00
= heat flux
q
00
rad;net
= net radiation heat flux to the nozzle throat surface
r = radial coordinate
_ r
c
= net recession rate
_ r
c;ch
= kinetic-limited recession rate
_ r
c;d
= diffusion-limited recession rate
_ r
i
= recession rate due to chemical reaction of ith gas-
phase species (H
2
O or CO
2
) with graphite
R
o
= outer radius of graphite nozzle
R
u
= universal gas constant
S = surface area
Sc = Schmidt number
Sc
t
= turbulent Schmidt number
S
1
= interfacial surface area at the graphite-gas interface
T = temperature
T
c
= temperature of graphite
T
c
L
= temperature at centerline
T
c
0
= initial temperature of graphite
T
s
= surface temperature at the nozzle throat
T
t;c
L
= total temperature at centerline ()
t = time
U
b
= bulk gas velocity component in axial direction
U
c
L
= centerline gas velocity component in axial direction
u = gas velocity component in axial direction
v = gas velocity component in radial direction
x = axial coordinate
Y = mass fraction
Presented as Paper 0363 at the 44th AIAA Aerospace Sciences Meeting
and Exhibit, Reno, Nevada, 9–12 January 2006; received 18 March 2006;
revision received 19 April 2007; accepted for publication 23 April 2007.
Copyright © 2007 by the American Institute of Aeronautics and Astronautics,
Inc. All rights reserved. Copies of this paper may be made for personal or
internal use, on condition that the copier pay the $10.00 per-copy fee to the
Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA
01923; include the code 0748-4658/07 $10.00 in correspondence with the
CCC.
*
Ph.D. Candidate, Department of Mechanical and Nuclear Engineering,
137 Research Building East. Member AIAA.
†
Distinguished Professor, Department of Mechanical and Nuclear
Engineering, 140 Research Building East. Fellow AIAA.
JOURNAL OF PROPULSION AND POWER
Vol. 23, No. 6, November–December 2007
1242
Downloaded by UNITED TECHNOLOGIES CORP on August 2, 2013 | http://arc.aiaa.org | DOI: 10.2514/1.24011