Reynolds number effect on nonlinear aerodynamic characteristics of compressors and model predictions

The widespread use of unmanned aerial vehicles has increasingly drawn attention to the operating conditions of compressors at low Reynolds number conditions. The nonlinear aerodynamic characteristics of compressors vary significantly under different Reynolds numbers, making the prediction of these variations and the associated instability boundaries a critical issue. This paper starts with the bistable equilibrium surface equation of the compressor system and proposes a novel quantitative prediction method for the nonlinear aerodynamic characteristics of compressors at different Reynolds numbers. The method is based on the nonlinear characteristics of state and control parameters, combined with the principle of topological invariance and the radial basis function neural network. The establishment of the prediction method and its results indicate that the “bistable” nature observed in real compressor operating conditions shares the same topological properties as the equilibrium surface equation described by the cusp catastrophe model, which accounts for the multi-parameter influences on the state changes of the compressor system. The established equilibrium surface equation can conveniently characterize the different hysteretic behaviors of compressor rotational stall under multi-parameter influences and assess the size of hysteresis loops. By developing a high-precision topological mapping method, a topological mapping relationship between the compressor equilibrium surface equation and the nonlinear aerodynamic characteristics of real compressors has been constructed, allowing the theoretical compressor characteristics to predict unknown nonlinear aerodynamic features at various Reynolds numbers, with model prediction errors within 5%.