Engine operating range and efficiency are of increasing importance in modern compressor design for heavy duty gas turbines and aircraft engines. These highly challenging objectives can only be met if all components provide high aerodynamic performance and stability. The aerodynamic losses of highly loaded axial compressors are mainly influenced by the leakage flow through clearance gaps. Especially the leakage flow due to the radial clearances of rotor blades affects negatively both, the efficiency and the operating range of the engine. Recent publications showed that the clearance flow and the clearance vortex can be influenced by an additional static pressure gradient at the outer casing, which is created by an axisymmetric wavy casing shape. A notable performance increase of up to 0.4% stage efficiency at design point conditions was reported for high pressure stages with large tip clearance heights  as well as for a transonic stage with a relatively small radial clearance gap . An analytic approach to predict the effects of axisymmetric casing contouring has been developed at DLR, Institute of Propulsion Technology, and is outlined in the first part of this work. The characteristic behavior of the clearance vortex in an adverse pressure gradient is discussed by means of an inviscid vortex model . The critical vortex parameters are isolated and related to the static pressure increase due to the casing contour. The second part illustrates the application of an axisymmetric endwall contour. A three dimensional optimization of the outer casing and the corresponding blade tip airfoil section of a typical gas turbine high pressure compressor stage with a high number of free variables is presented. The optimization led to a significant increase in aerodynamic performance of about 0.8% stage efficiency and to a notable reduction of the endwall blockage at ADP conditions. Furthermore, an improved off-design performance was found and a simple design rule is given to transfer both, the casing contour and the blade tip section modification on similar high pressure compressor blades. Based on these design rules the results of the optimized stages were applied to the rear stages of a Siemens gas turbine compressor CFD model. An increase of 0.3% full compressor performance was reached at design point conditions.
Theory and Application of Axisymmetric Endwall Contouring for Compressors
Kro¨ger, G, Voß, C, Nicke, E, & Cornelius, C. "Theory and Application of Axisymmetric Endwall Contouring for Compressors." Proceedings of the ASME 2011 Turbo Expo: Turbine Technical Conference and Exposition. Volume 7: Turbomachinery, Parts A, B, and C. Vancouver, British Columbia, Canada. June 6–10, 2011. pp. 125-137. ASME. https://doi.org/10.1115/GT2011-45624
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