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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 |