Investigation of non-uniform leading-edge tubercles in compressor cascade:Based on multi-objective optimization and data mining

Corner stall receives noticeable attention in the aeroengine field as an important phenomenon in highly-load compressors.Non-uniform leading-edge tubercles,as an effective method to delay stall,are introduced into the compressor.In this paper,the shape of leading-edge tubercles was controlled by a third-order Fourier function.To judge corner stall,a more precise stall indicator for compressor cascade with flow control methods was defined.Besides,the total kinetic energy of the secondary flow at large incidence was adopted as a parameter for stall evaluation to save computing resources.The results of multiobjective optimization reveal that the loss coefficient exhibited negligible variation at design incidence,while the total kinetic energy of secondary flow showed a significant reduction at large incidence,resulting in a substantial increase in stall incidence.In the optimal profiling cases,the stall incidencewas delayed from 7.9°to 11.6°.The major purpose of the research is to provide proper design guidelines for nonuniformleading-edge tubercles and uncover the flow controlmechanisms of leading-edge profiling.Hence,the geometric features that meet different optimization objectives were extracted through geometric analysis near the Pareto Front and through Self-OrganizingMap(SOM)dataminingmethods in the optimization database.Besides,flow field analysis reveals the flow control mechanism of leading-edge tubercles.The convex-concave-convex structure at the 0%-70%blade height region can form two branches of leading-edge vortex pairs that are opposite in the rotation direction to the passage vortex.The two branches of leading-edge vortex pairs mixed with the leading-edge separation vortex to form two stronger mixed vortices,which can effectively suppress the development of passage vortex and delay stall incidence.

Unstable Dynamical Properties of Spiral Cloud Bands in Tropical Cyclones

A nondivergent barotropic model （Model 1） and a barotropic primitive equation vortex model （Model 2） are linearized respectively in this paper. Then their perturbation wave spectrums are computed with a normal mode approach to study the instability problem on an appointed tropical cyclone （TC）-like vortex, thereby, the dynamic instability properties of spiral cloud bands of TCs are discussed. The results show that the unstable mode of both models exhibits a spiral band-like structure that propagates away from the vortex outside the radius of maximum winds. The discrete modal instability of the pure vortex Rossby wave can account for the generation of the eyewall and the inner spiral band. The unstable mode in Model 2 has three parts, i.e., eyewall, inner and outer spiral bands. This mode can be interpreted as a mixed vortex Rossby-inertia gravitational wave. The unbalanced property of the wave outside the stagnation radius of the vortex Rossby wave is one of the important reasons for the formation of the outer spiral band in TCs. Accordingly, the outer spiral band can be identified to possess properties of an inertial-gravitational wave. When the formation of unstable inner and outer spiral bands is studied, a barotropic vortex model shall be used. In this model, the most unstable perturbation bears the attributes of either the vortex Rossby wave or the inertial-gravitational wave, depending on the vortex radius. So such perturbations shall be viewed as an unbalanced and unstable mixed wave of these two kinds of waves.