A three-dimensional unsteady, viscous aerodynamic analysis has been developed for the ow inside a transonic, high-through-ow, single-stage compressor. The compressor stage is comprised of a low-aspectratio rotor and a closely coupled stator. The analysis is based on a numerical method for solving the three-dimensional Navier -Stokes equation for unsteady viscous ow through multiple turbomachinery blade rows. The method solves the fully three-dimensional Navier -Stokes equation with an implicit scheme. A two-equation turbulence model with a low Reynolds number modi cation is applied for the turbulence closure. A third-order accurate upwinding scheme is used to approximate convection terms, whereas a second-order-accurate central difference scheme is used for the discretization of the viscous terms. A second-order accurate scheme is employed for the temporal discretization. The numerical method is applied to study the unsteady ow eld inside a transonic, high-through-ow, axial compressor stage. The numerical results are compared with available experimental data.
Nomenclatureconstants in turbulence closure models e = total energy F = body force k = turbulent kinetic energy M = Mach number Pr = Prandtl number p = pressure R = gas constant T = temperature t = time U, V, W = mean velocity components u, v, w = uctuating velocity components dij = Kronecker delta « = turbulence dissipation rate « ijk = permutation symbol m = viscosity n = kinematic viscosity r = density s k , s « = constants in turbulence closure models f = any time-dependent term V = angular velocity Subscript eff = effective value