Modeling for tip clearance effects on stall-onset condition in transonic axial compressors

Rotating stall is a primary limit to compressor performance, and the reasonable estimation of stall-onset point is very useful in compressor design. Extensive investigations have been conducted in the past few decades to develop analytical models and numerical methods for stall-onset prediction, and much progress has been made in the understanding of flow mechanism for rotating stall. In spite of the robust prediction ability of stall-onset condition, the unsteady 3-D computations are still time-consuming for industrial applications. Analytical models are able to provide a fast estimation of compressor stall onset. However, empirical correlations are usually needed in the analytical models, which leads to a decrement in the accuracy and application scope of the models. Especially for high speed compressors, tip clearance effects hasn't been evaluated reasonably in the previous analytical models, which actually plays a very important role in determining the stall-onset point. Therefore, new analytical models accounting for tip clearance effects will be promising in estimating the stall-onset more precisely. It's the requirement for a new analytical model that motivates the present work. In the present work, the unsteady flow simulation of a transonic compressor rotor at near stall condition was performed to clarify the relations between tip clearance flow oscillations and compressor stall-onset in transonic axial compressor rotors. The interaction between tip clearance and incoming flow is simplified to a 2-D analogy of free-stream and counter-flow wall jet interaction. Momentum balance analysis is applied to identify the position of tip clearance/incoming flow interface, together with a prediction method of tip leakage vortex core trajectory. The effects of the in-passage shock on tip clearance/incoming flow interaction is taken into account by applying an upstream deflection of the interface, and this deflection is also observed in the computational flow field at near stall conditions. As a combination of the above-mentioned aspects, a model is proposed to define the critical point for tip clearance flow spillage from blade leading edge, which corresponds to the stall-onset point on compressor performance curves. Validations against numerical results prove that the model is capable of including tip clearance effects on stall-onset point. Parametric study of the model shows that blade tip offloads with increasing tip clearance, reducing the inverse momentum flux of tip clearance flow. As a result, the stalling flow coefficient appears to be less sensitive to tip clearance variation, which accords with the published experimental results.