TIME SPECTRAL CALCULATION OF A CASING TREATMENT CONFIGURATION FOR A HIGH PRESSURE COMPRESSOR

The accurate and reliable prediction of transonic high pressure compressor with slot-type casing treatments needs costly unsteady simulations . In order to reduce the CPU-time to engineering requirements, the Time Spectral Method dedicated to periodic flow analysis is investigated. This approach is based on an unsteady representation of the flow variables in time Fourier series. This leads to a harmonic balan ce form of the Navier-Stokes equations which casts a time periodic unsteady problem to a s et of several coupled steady calculations solved with conventional RANS methods. A validation of the TSM is done by comparisons with the classical Unsteady RANS approach. The objectives are to assess its capabili ty to estimate the slot impact on the compressor performances and to compute correctly th e strongly non-linear flows due to the casing treatment. In comparison to the Unsteady RAN S approach, results obtained with the TSM show an encouraging agreement with only a few n umbers of harmonics applied, leading to a reduction of the CPU-time. NOMENCLATURE Dt Spectral time derivative operator h Radial position E Energy Η Compressor span N Number of Harmonic Pref Reference pressure Pt1 Upstream stagnation pressure PSBC Static pressure for the boundary condition Q Massflow Qpe Massflow at peak efficiency Qstall Massflow at stall inception T Time period of the rotor ( ω π 2 ) Tref Reference temperature Tt1 Upstream stagnation temperature V Volume of a cell Vx y,z Components of the relative velocity Wn Vector of the conservative and turbulent variables ρ Density η Isentropic efficiency λ Throttle parameter; spectral radius ω Rotational speed of the rotor