Accurate Numerical Simulation of Compressible Transitional Flows in Turbomachinery

Abstract

An accurate and efe cient methodology is provided for computing turbulent and transitional e ows by solving the compressible Reynolds-averaged Navier ‐Stokes equations with an explicit algebraic stress model and k‐! turbulence closure. The space discretization is based on a e nite volume method with Roe’ s approximate Riemann solver and formally second-order-accurate MUSCL extrapolation. Second-order accuracy in time is achieved using a dual time-stepping technique combined with an explicit Runge ‐Kutta scheme and multigrid acceleration to converge the false transient at each physical time level. The turbulence model has been validated computing the vortex shedding behind a two-dimensional turbine cascade. Furthermore, the transition model of Mayle for separated e ow has been combined with such a turbulence model; this methodology has been validated computing thee owthroughtheT106low-pressureturbinecascadewithseparated-e owtransitionatthesuction-sideboundary layer.Finally,thethree-dimensionale owthroughtheT106linearcascadehasbeencomputedprovidingtheanalysis of the loss-coefe cient distribution downstream of the cascade and the description of the interaction between the secondary e ow pattern and the suction-side separation bubble.