A Direct Numerical Simulation of Transition and Turbulence in a Turbine Stage

Abstract

A direct numerical simulation (DNS) of transitional/turbulent flow in a lowspeed axial turbine stage is presented here. The non-conservative form of the Navier-Stokes equations for compressible flows is utilized in this simulation. A high-order accurate, upwind-biased, iterative-implicit, finite difference method developed earlier for DNS of airfoil flows is used to solve the governing differential equations. Unlike flows over airfoils in isolation, flows through a turbine stage are characterized by complex interactions such as wake-blade, vortex-blade, shock-blade and wakewake interactions in addition to the potential effect caused by the relative motion between the stator and rotor rows. Earlier computational efforts have focused on wake-blade interaction where a simulated wake possessing the characteristics of the far wake but with appropriate intensity levels is injected into the computational domain via appropriate boundary conditions. Here we simulate the flow through the entire stage. The wakes of the stator and the rotor are computed along with the rest of the flow and thus the computed wake-blade interaction is closer to reality. The results provided here include flow visualization that shows the evolution of the stator wake as it convects through the rotor passage and, flow transition on the rotor suction surface caused by wake-blade interaction. Time-averaged pressure and heat transfer, and, fluctuating pressure amplitudes, on the airfoils surfaces are also provided. Velocity and temperature statistics both in the transitional and turbulent regions on the suction side of the stator and rotor airfoils are included. The computed results are compared with experimental data where possible. The results indicate that some of the essential features of transition and turbulence in a turbine stage have been captured.