Effective end wall profiling rules for a highly loaded compressor cascade

This paper presents a numerical study of a linear compressor cascade to investigate the effective end wall profiling rules for highly-loaded axial compressors. The first step in the research applies a correlation analysis for the different flow field parameters by a data mining over 600 profiling samples to quantify how variations of loss, secondary flow and passage vortex interact with each other under the influence of a profiled end wall. The result identifies the dominant role of corner separation for control of total pressure loss, providing a principle that only in the flow field with serious corner separation does the does the profiled end wall change total pressure loss, secondary flow and passage vortex in the same direction. Then in the second step, a multi-objective optimization of a profiled end wall is performed to reduce loss at design point and near stall point. The development of effective end wall profiling rules is based on the manner of secondary flow control rather than the geometry features of the end wall. Using the optimum end wall cases from the Pareto front, a quantitative tool for analyzing secondary flow control is employed. The driving force induced by a profiled end wall on different regions of end wall flow are subjected to a detailed analysis and identified for their positive/negative influences in relieving corner separation, from which the effective profiling rules are further confirmed. It is found that the profiling rules on a cascade show distinct differences at design point and near stall point, thus loss control of different operating points is generally independent.

Constant wall heat flux boundary conditions in micro-channels filled with porous material with internal heat generation under local thermal non-equilibrium conditions

Forced convection heat transfer in a micro-channel filled with a porous material saturated with rarefied gas with internal heat generation is studied analytically in this work. The study is performed by analysing the boundary conditions for constant wall heat flux under local thermal non-equilibrium (LTNE) conditions. Invoking the velocity slip and temperature jump, the thermal behaviour of the porous-fluid system is studied by considering thermally and hydrodynamically fully-developed conditions. The flow inside the porous material is modelled by the Darcy–Brinkman equation. Exact solutions are obtained for both the fluid and solid temperature distributions for two primary approaches models A and B using constant wall heat flux boundary conditions. The temperature distributions and Nusselt numbers for models A and B are compared, and the limiting cases resulting in the convergence or divergence of the two models are also discussed. The effects of pertinent parameters such as fluid to solid effective thermal conductivity ratio, Biot number, Darcy number, velocity slip and temperature jump coefficients, and fluid and solid internal heat generations are also discussed. The results indicate that the Nusselt number decreases with the increase of thermal conductivity ratio for both models. This contrasts results from previous studies which for model A reported that the Nusselt number increases with the increase of thermal conductivity ratio. The Biot number and thermal conductivity ratio are found to have substantial effects on the role of temperature jump coefficient in controlling the Nusselt number for models A and B. The Nusselt numbers calculated using model A change drastically with the variation of solid internal heat generation. In contrast, the Nusselt numbers obtained for model B show a weak dependency on the variation of internal heat generation. The velocity slip coefficient has no noticeable effect on the Nusselt numbers for both models. The difference between the Nusselt numbers calculated using the two models decreases with an increase of the temperature jump coefficient.