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A three-dimensional compressible flow model is presented to study the occurrence of weak rotating waves in unparallel wall vaneless diffusers in centrifugal compressors. The model extends the three-dimensional compressible flow model for parallel wall diffusers recently developed by present authors. Linearised three-dimensional compressible Euler equations casted on a rotating frame of reference travelling at the same speeds as the waves are employed and the viscous effects are ignored. Complex functions of the solutions to the linearised Euler equations are then obtained by a second-order finite difference method and the singular value decomposition technique. Undisturbed flow is assumed potential and first solved by numerical method of strongly implicit procedure. Critical inlet flow rate and rotating wave speed of diffusers of three different shroud wall shapes, namely, convergent, convergent then divergent and constant area tapered, are studied for three different diffuser outlet-to-inlet radius ratios and for different inlet Mach numbers, and results compared with those from diffusers with parallel walls. The results show suppression effects on rotating stall by the contracting walls and the suppression effects vary with wall contraction rate, wall shape, inlet Mach number and the diffuser radius ratio. Further, the effects of diffuser inlet contraction are studied and prediction of the model is compared with experimental result.

Numerical simulation of three-dimensional flow field and film cooling effectiveness in film-cooled turbine rotor and stationary turbine cascade were carried out by using the k- εturbulence model, and the predictions of the three-dimensional velocities were compared with the measured results by Laser-Doppler Velocimetry (LDV). Results reveal the secondary flow near the blade surface in the wake region behind the jet hole. Compared with the stationary cascade, there are the centrifugal force and Coriolis force existing in the flow field of the turbine rotor, and these forces make the three-dimensional flow field change in the turbine rotor, especially for the radial velocity. The effect of rotation on the flow field and the film cooling effectiveness on the pressure side is more apparent than that on the suction side as is shown in the computational and measured results, and the low film cooling effectiveness appears on the pressure surface of the turbine rotor blade compared with that of the stationary cascade.