The modelling of three-dimensional transonic flows in turbomachines using time-marching techniques

For the efficient design of transonic turbomachinery systems, understanding of the complex flow phenomena inherent in the flow passages is essential. In the present study, a computational technique is adopted to meet this formidable goal. A code using a time-marching technique has been developed first for quasi three-dimensional cascades (that is two-dimensional computation with the varying streamtube height in the third dimension taken into consideration) and then extended to fully three-dimensional flows within the rotating flow passages. Each code has a built-in switch for in viscid and viscous flows. The basis of the codes is the conservative form of the Reynolds- averaged Navier-Stokes equations in a rotating framework. This is supplemented by either the Baldwin-Lomax (algebraic) or the k-e (two-equation) turbulence model. For solving the hyperbolic type governing equations, spatial derivatives are first discretized on the easily-constructed H-type grid system using a central-difference finite-volume approximation with the flow variables stored at the cell centre. An explicit multistage Runge-Kutta scheme is then employed for the time integration o f the resulting ordinary differential equations. The accuracy of the quasi three-dimensional code is initially evaluated by predicting the flows through cascades with simple geometry. Its robustness is then confirmed by two realistic configurations with a wide range o f operating conditions. Finally the fully three-dimensional code is applied to two highly loaded transonic rotors with complicated geometry at peak efficiency and near stall operating conditions. An extensive comparison in terms of detailed flowfield and overall performance between the predictions and experiments with laser anemometry and conventional probes shows the accuracy o f the codes and also indicates that the present study has great potential to be a viable aerodynamic design and analysis tool in the development of transonic turbomachinery systems.