| High efficiency and wide stable operating range are the goals pursued by modern centrifugal compressors.Deeply exploring the unsteady flow characteristics of centrifugal compressors is an important foundation for improving their aerodynamic performance and flow stability.In order to reveal the unsteady flow mechanism from a dynamic point of view and clarify the key factors that affect the flow stability,this paper introduces the modified mode decomposition method into the exploration of the unsteady flow field of the centrifugal compressor.Based on the analysis of the flow field characteristics of the centrifugal compressor and the deficiencies of the traditional decomposition methods,the Proper Orthogonal Decomposition(POD)method is modified and the single-frequency mode decomposition method(F-POD)is proposed.Based mainly on the single-frequency mode decomposition as well as a variety of flow field analysis methods,the mode characteristics and physical interpretations of unsteady disturbances such as rotor-stator interaction,tip leakage flow effect,shock wave,etc.,in the flow field of centrifugal compressor are analyzed layer by layer.Those methods are further combined with the energy transfer analysis of the main modes for the unsteady flow field,as a result,the disturbance modes related to the stability of the compressor are refined and the internal driving force of their development and evolution is clarified.Firstly,the mathematical properties and physical interpretations of POD and dynamic mode decomposition method(DMD)are studied with analytical functions with certain physical characteristics such as discrete frequency and growth rate.It is concluded that the POD method decomposes the flow field into structures with different energy levels from the perspective of energy,and each mode shows multiple frequencies.DMD method can obtain the single-frequency mode structures of the flow field,but there is a deviation in the fitting of the mode growth rate information.In order to accurately extract the single frequency structure and growth rate characteristics of the unsteady flow field of the compressor,the POD method is modified by two steps in combination with the Fourier transform(DFT)and its inverse operation.In the preliminary modification,the single-frequency mode decomposition method is obtained through the single-frequency decomposition and reconstruction of the POD mode.In the further modification,the reconstruction method of the main frequency neighbourhood is proposed,which can accurately extract the growth rate information of the single-frequency mode.Eventually the F-POD method is proposed.The F-POD method is verified in detail by analytical functions with different growth rates and multiple frequencies,and also by classic cylinder wake case,showing that the F-POD method can accurately extract the single-frequency mode structures and the growth rate information from the discrete frequency flow field.F-POD provides an effective new method for analyzing complex and unsteady flow field from the perspective of dynamics.The highest efficiency operating condition of the compressor which has better flow stability and the clearer flow field structures is chosen as the start point to conduct mode decomposition.By decomposing the single frequency mode of the three-dimensional pulsating flow field in the blade channel,and combining with the flow field contours of the main parameters,the distribution of the full-field vortex structures,the spectral characteristics of the monitoring points,the modes characteristics and their physical interpretations of the compressor flow field under different tip clearances and rotating speeds are clarified.It is found that: 1)The mode of BPF/n BPF corresponding to rotorstator interaction disturbances is always the first-order main frequency of the flow field under stable condition,and with the participation of other disturbance factors such as tip leakage vortices and shock waves,the energy proportion of the main frequency mode gradually decreases;2)The upstream tip leakage vortex corresponds to the0.05 BPF mode,and the main mode of the downstream tip leakage vortex and wake region is 0.2BPF;3)The interactions of shock wave/tip leakage vortex,shock wave/boundary layer have enhanced the pulsation of the flow field,resulting in the break of the tip leakage vortex(0.2BPF,0.4BPF mode)and the decrease of the boundary layer flow stability after the wave(0.05 BPF mode).The single-frequency mode decomposition method of the three-dimensional unsteady flow field provides a new perspective for exploring the new phenomenon and analyzing the unsteady dynamic characteristics in the centrifugal compressor.On the basis of clarifying the physical interpretations of the dominant modes of the highest efficiency condition,the single-frequency mode decomposition is further carried out on the three-dimensional unsteady flow field under the off-design conditions(highest pressure ratio and small flow rate conditions)for different tip clearances and different rotating speeds.According to the energy transfer characteristics of the main modes under varying operating conditions,it is found that the decrease of the compressor flow stability(flow rate reduction process)is always accompanied by the energy transfer from the rotor-stator interaction disturbance modes(BPF/n BPF)to the low-frequency disturbance modes.Therefore,the change process of each lowfrequency mode can reflect the internal driving factors of mode development and evolution related to compressor stability: 1)The decrease in the flow stability of the shrouded centrifugal compressor is mainly due to the increased pulsation in the boundary layer area of the suction surface,and the corresponding “unstable” mode is0.4BPF;2)The flow stability of the unshrouded impeller is mainly related to the tip leakage vortex(0.05 BPF mode)and the “high” frequency modes of 0.4BPF and 0.7BPF produced by continuous vortex breaking;3)The interaction between shock waves,tip leakage vortices,and boundary layer in the transonic compressor is enhanced,as a result,the flow field shows a multi-peak broadband mode characteristic with lower frequency,which means that the flow stability of the compressor is weakened.The method of exploring the flow stability of compressors using mode energy transfer and mode structure evolution features provides a new idea for studying the mechanism of compressor instability.Based on the modified mode decomposition method,the mode characteristics of the centrifugal compressor at different rotating speeds,different tip clearances and various operating conditions are well investigated.The results reveal the flow dynamic mechanism of the compressor and provide theoretical support for the design of centrifugal compressor with high-performance and wide operating range. |
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