-
a
:
-
pre exponent in strand-burning rate law, (0.245 × 10−2 (m/s)/(Mpa)n)
-
A
:
-
cross-sectional flow area
-
A
s
:
-
Arrhenius frequency factor in propellant surface decomposition, (5.65 m/s)
-
A
+
:
-
damping constant in van Driest’s hypothesis (26)
-
C
1 → C
4,C
μ, C
ω
:
-
constants in turbulence models (C
1 = 1, C
2 = 1.3, C
3 = 1.57, C
4 = 2, C
ω = 0.18, C
μ = 0.09)
-
C
p
:
-
\({\sum\limits_k {Y_{k}}}{C_{pk}}\) average heat capacity of reacting gases, (1.254 kJ/kg K)
-
C
pk
:
-
heat capacity of kth species (kJ/kg K)
-
C
s
:
-
heat capacity of solid propellant, (1.59 kJ/kg-K)
-
d
Ap
:
-
average diameter of ammonium per-chlorate particles
-
D
:
-
port diameter of rocket motor (m)
-
D
f
:
-
diffusion coefficient in Fick’s law (m2/s)
-
E
as
:
-
activation energy in propellant surface decomposition, (62.7 kJ/kmole)
- Δh
o
f,k
:
-
heat of formation of kth species, (233.662 kJ/kg for fuel, −3937.56 kJ/kg for oxidizer, −4753.914 kJ/kg for products)
-
k
:
-
von Karman’s constant (0.41)
-
K
:
-
\(\overline{{u_{i}^{\prime} u_{i}^{\prime}}}/2,\) turbulent kinetic energy (m2/s2)
- ℓ:
-
mixing length (m)
-
n
:
-
exponent in strand-burning rate law (0.41)
-
P
:
-
pressure (Pa)
- Pr:
-
C
p
μ/λ, Prandtl number based upon molecular properties of fluid
- Pr
t
:
-
Prandtl number for turbulent flow (0.9)
-
r
:
-
coordinate in radial direction (m)
-
r
b
:
-
total burning rate of a solid propellant (m/s)
-
r
bo
:
-
ap
n strand burning rate of a solid propellant (mm/s)
- R:
-
port radius of rocket motor (m)
-
R
h
:
-
roughness height (m)
-
R
u
:
-
universal gas constant (J/kmol k)
-
Sc
:
-
\(\mu /\bar{\rho}D_{i},\) Schmidt number based upon molecular properties of fluid
-
Sc
t
:
-
Schmidt number for turbulent flow
-
T
:
-
temperature (K)
-
T
ci
:
-
initial centerline temperature (K)
-
T
o
:
-
reference temperature, 298.14 K
-
Q
s,ref
:
-
surface heat release due to pyrolysis at reference temperature (J/kg)
-
T
p
:
-
propellant temperature (K)
-
T
pi
:
-
propellant initial temperature, (298 K)
-
T
ps
:
-
propellant surface temperature, (800 K)
-
T
oi
:
-
initial stagnation temperature (K)
-
\(\bar{T}_{ps}\)
:
-
reference surface temperature of propellant (K)
-
u
:
-
gas velocity in x-direction (m/s)
-
U
:
-
axial velocity outside boundary layer (m/s)
-
U
ci
:
-
initial centerline velocity (m/s)
-
u
*
:
-
\({\sqrt \frac{\tau_{w}}{{\rho_{\infty}}}},\) friction velocity (m/s)
-
v
:
-
gas velocity in y-direction (m/s)
-
W
:
-
\({\left({{\sum\limits_k {Y_{k}}}/W} \right)}^{{- 1}} \) average molecular weight of gases (kg/kmol)
-
W
k
:
-
molecular weight of kth species, kg/kmol (30 kg/kmol for fuel, 27.9 kg/kmol for oxidizer, 20.4 kg/kmol for products)
-
x
:
-
coordinate in axial direction (m)
-
y
:
-
coordinate normal to propellant surface (m)
-
Y
k
:
-
mass fraction of k-th species
-
Y
FS
:
-
mass fraction of fuel in a composite solid propellant (0.25)
-
Y
OS
:
-
mass fraction of oxidizer in a composite solid propellant (0.75)
-
\(\overline{{{\left({} \right)}}}\)
:
-
time-averaged quantity
-
\((^{\tilde{}})\)
:
-
Favre averaged quantity
-
\({\left({} \right)}^{\prime}\)
:
-
fluctuating quantity
- δ:
-
boundary-layer thickness (m)
- ɛ:
-
\(\mu \overline{{u^{\prime}_{{ij}} u^{\prime}_{{ij}}}}/\overline{\rho},\) turbulent dissipation (m2/s3)
- γ:
-
constant-pressure to constant-volume specific heat ratio (1.26)
- λ:
-
thermal conductivity of gas (kJ/m s K)
- λ
s
:
-
thermal conductivity of solid propellant (kJ/m s K)
- μ:
-
gas viscosity (kg/m s)
- μ
eff
:
-
μ + μ
t
, effective viscosity (kg/m s)
- μ
t
:
-
turbulent viscosity (kg/m s)
- (μ/Pr )
eff
:
-
μ/Pr + μ
t
/Pr
t
(kg/m s)
- (μ/Sc )
eff
:
-
μ/Sc + μ
t
/Sc
t
(kg/m s)
- ν
k
:
-
number of moles of kth species (1 kmol for fuel, 3.23 kmol for oxidizer, 5.9 kmol for products)
- ρ:
-
gas density (kg/m3)
- ρ
s
:
-
solid propellant density (1600 kg/m3)
- τ:
-
\(\mu_{{eff}} \partial \overline{u}/\partial y,\) local shear stress (N/m2)
- ω
k
:
-
rate of production of species k due to chemical reactions (kg/m3 s)
-
b
:
-
bulk or averaged variable
-
c
:
-
centerline condition
-
k
:
-
species index representing fuel gas [F], oxidizer gas [O], and product gas [P].
- ∞:
-
free stream condition
-
w
:
-
wall (propellant surface) condition