ABSTRACT
Artificial compressibility method is extended to solve the low Mach variable density Navier–Stokes equations for the simulation of axisymmetric laminar radiative diffusion flames. A combustion model based on the generalized state relationships for species mass fractions and temperature is adopted and the radiation heat loss is estimated as a fraction of heat of combustion. Conventional finite difference method along with a total variation diminishing scheme is used for the spatial discretization on nonuniform half-staggered grid layouts. To reach the steady-state condition, a three-step low-storage explicit Runge–Kutta method is used. The accuracy of the proposed method is reported for confined and unconfined diffusion flames.
Nomenclature
c | = | artificial sound speed (m/s) |
D | = | mixture mass diffusion coefficient (m2/s) |
gz | = | gravitational acceleration (m/s2) |
h | = | absolute enthalpy of the mixture, kJ/(kg · K) |
= | enthalpy of formation, kJ/(kg · K) | |
hk | = | kth species absolute enthalpy, kJ/(kg · K) |
p | = | dynamic pressure (Pa) |
P0 | = | thermodynamic pressure (Pa) |
Pr | = | Prandtl number |
qr | = | radiative heat loss fraction |
Qr | = | radiative heat loss, kJ/(kg · K) |
R | = | universal gas constant, 8314.32 Pa/(mol · K) |
r | = | radial coordinate (m) |
t | = | time or pseudo-time (s) |
T0 | = | reference temperature, 298 K |
U | = | vector of primitive variables |
ur | = | radial velocity (m/s) |
uz | = | axial velocity (m/s) |
= | mixture molecular weight (kg/kmol) | |
Wk | = | kth species molecular weight (kg/kmol) |
Yk | = | kth species mass fractions |
z | = | axial coordinate (m) |
Greek symbols | = | |
β | = | compressibility parameter |
μ | = | mixture dynamic viscosity, kg/(ms) |
= | reference viscosity, | |
ρ | = | density (kg/m3) |
= | density of still air (kg/m3) | |
χ | = | ratio of two consecutive variations |
ψ | = | Van Leer flux limiter |
Nomenclature
c | = | artificial sound speed (m/s) |
D | = | mixture mass diffusion coefficient (m2/s) |
gz | = | gravitational acceleration (m/s2) |
h | = | absolute enthalpy of the mixture, kJ/(kg · K) |
= | enthalpy of formation, kJ/(kg · K) | |
hk | = | kth species absolute enthalpy, kJ/(kg · K) |
p | = | dynamic pressure (Pa) |
P0 | = | thermodynamic pressure (Pa) |
Pr | = | Prandtl number |
qr | = | radiative heat loss fraction |
Qr | = | radiative heat loss, kJ/(kg · K) |
R | = | universal gas constant, 8314.32 Pa/(mol · K) |
r | = | radial coordinate (m) |
t | = | time or pseudo-time (s) |
T0 | = | reference temperature, 298 K |
U | = | vector of primitive variables |
ur | = | radial velocity (m/s) |
uz | = | axial velocity (m/s) |
= | mixture molecular weight (kg/kmol) | |
Wk | = | kth species molecular weight (kg/kmol) |
Yk | = | kth species mass fractions |
z | = | axial coordinate (m) |
Greek symbols | = | |
β | = | compressibility parameter |
μ | = | mixture dynamic viscosity, kg/(ms) |
= | reference viscosity, | |
ρ | = | density (kg/m3) |
= | density of still air (kg/m3) | |
χ | = | ratio of two consecutive variations |
ψ | = | Van Leer flux limiter |