A dual-time method is introduced to calculate the unsteady flow in a certain vibrating flat cascade. An implicit lower-upper symmetric-gauss-seidel scheme（LU-SGS） is applied for time stepping in pseudo time domains, and the convection items are discretized with the spatial three-order weighted non-oscillatory and non-free-parameter dissipation difference （WNND） scheme. The turbulence model adopts q-co low-Reynolds-number model. The frequency specmuns of lift coefficients and the unsteady pressure-difference coefficients at different spanwise heights as well as the entropy contours at blade tips on different vibrating instants, are obtained. By the analysis of frequency specmuns of lift coefficients at three spanwise heights, it is considered that there exist obvious non-linear perturbations in the flow induced by the vibrating, and the perturbation frequencies are higher than the basic frequency. The entropy contours at blade tips at different times display an intensively unsteady attribute of the flow under large amplitudes.
Casing treatment is a widely employed technique to increase the stall margins of turbomachineries. In the last several decades, many researches on casing treatment have been carded out. However, the mechanism of its expanding stall margins is still not very clear. Till now, most casing teatment schemes are designed for axial compressors, while the investigations on casing treatments in centrifugal compressors are rarely reported. Moreover, current investigation methods mainly focus on experiments, and perfect theoretic al analysis is not yet feasible. In order to study the effectiveness and further the mechanism of casing treatments in centrifugal compressors, in this paper, a computationally based investigation of the impact of the self-recireulating casing treatment on the performance of a radial compressor is carried out. The results indicate that, by casing bleed and injection, the casing treatment with inclined blades in the cavity expands the stall margin most. At low mass flows, the reversed flow through the cavity with inclined blades develops the counter swirl flow in front of the impeller inlet, which is considered to benefit increasing the pressure rise from the injection port to the bleed port and thereby augment the recirculating flow. At 120% design speed, the stall margin is larger than that at the design speed. However, the cost of extending the stall margin is the reduction of isentropic efficiency. A mended casing treatment by shifting the bleed port upstream is also studied. It is demonstrated that, relative to the original casing treatment, this mend can improve the efficiency evidently notwithstanding a little narrowing of the flow range.
As demonstrated by former work,the holed casing treatment can be used to expand the stall margin of a centrifugal compressor with unshrouded impeller.In addition,the choked margin can also be expanded as experimental results indicated.Moreover,the compressor performance,especially the efficiency,on the whole working range is improved.As shown by experiments,the stall margin and choked margin of the compressor are extended,and the maximum efficiency improvement is 14%at the large flowrate of 1.386.Numerical simulations were carried out to analyze the flow in the impeller and in the holes in the case of large flowrate.The results indicate that in large flowrate conditions,there is a low-pressure region on the throat part of the impeller passage,leading to the bypass flows appearing in the holes,which means the flow area at the inlet of the impeller is increased.The bypass flow can also contribute to the decrease of the Mach number at the throat part near the shroud end-wall which implies that the choked margin is expanded.Besides,as the bypass flow would inhibit the development of the vertexes in the tip clearance and suppress the flow recirculation in the shroud end-wall region,both the pressure ratio and efficiency of the compressor are improved,which agrees well with the experiments.
