Three-dimensional unsteady Navier-Stokes analysis of stator-rotor interaction in axial-flow turbines

A three-dimensional full Navier-Stokes method is developed and applied to calculations of unsteady flows through multiple blade rows in axial-flow turbomachinery, The solver adopts the cell-centred finite volume discretization and the four-stage Runge-Kutta time-marching scheme. Unsteady calculations are effectively accelerated by using a time-consistent multi-grid technique, resulting in a speed-up by a factor of 10-20 with adequate temporal accuracy. The computational efficiency and validity of the present multi-grid technique are illustrated by comparisons with the results of the conventional dual time-stepping scheme. Calculated unsteady pressures on blade surfaces for a turbine stage test rig compare well with the corresponding experimental data. A computational study of turbine stage performances at different stator-rotor axial gaps reveals a marked three-dimensional behaviour of the interaction between incoming wakes and rotor passage-vortex structures. The time-averaged losses from unsteady calculations show a noticeable spanwise redistribution compared with the steady results. Two dimensional and three-dimensional calculations: indicate opposite trends in stage efficiency variation when the stator-rotor gap is reduced.