Unsteady Aerodynamic Flow Phenomena in a Transonic Compressor Stage

Abstract

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

Experimental and Computational Study of the Unsteady Flow in a 1.5 Stage Axial Turbine With Emphasis on the Secondary Flow in the Second Stator

“…During the last five years, several computational studies of flow associated with blade row interaction have been carried out e.g. by Hah et al (1993), Valkov and Tan (1993), Gallus et al (1994), Dawes (1994), Eulitz et al (1996), He (1996), and Hall (1997. Looking at the complex pattern of the flow in multi-blade row machines it becomes obvious that a numerical method to accurately predict the time-dependent secondary flow in multi-blade row environment has to account for the three-dimensionality as well as the unsteadiness of the flow.…”

Numerical Simulation of the Shock-Tip Leakage Vortex Interaction in a HPC Front Stage

“…The 3D steady approach is complemented by unsteady viscous simulations, see e.g. Hah et al (1997), Puterbaugh and Brendel (1997) and Dorney and Sharma (1996).…”

Filtered chorochronic interface as a capability for 3-D unsteady throughflow analysis of multistage turbomachinery

“…Rotor/stator interaction (Sharma, Picket, and Ni 1992;Gallus, Zeschky, and Hah 1995;Hah, Puterbaugh, and Copenhaver 1997) and multistage matching (Cumpsty 1989) are fundamental issues in the analysis and design of modern turbomachinery, both with respect to the timeaveraged flow and to the unsteady phenomena. The mixingplane steady 3-D analysis approach, introduced by Denton (1992) and Dawes (1992), has become the standard tool of analysis used in the design process, the key element in this approach being the capability of coupled multistage computations.…”

“…Starting with the work of Erdos, Alzner, and McNally (1977), unsteady nonlinear CFD methods were developed and applied to the computation of rotor/stator interaction (Hah et al 1997;Chen et al 2001;Gerolymos, Michon, and Neubauer 2002a). There are mainly two different approaches for the computation of time-periodic unsteady flows in turbomachinery (He 2010), the time-marching methods (Erdos et al 1977), which time-integrate the flow equations, and the nonlinear harmonic (Chen et al 2001;He 2008;McMullen, Jameson, and Alonso 2006) and harmonic-balance (Hall et al 2002;Hall 2007, 2008) methods, which solve a coupled set of timeindependent problems to determine the Fourier coefficients of the decomposition of the flow into harmonics, eventually with multiple fundamental frequencies (He 1992;Li and He 2002;Ekici and Hall 2008).…”