Static pressure redistribution mechanism of non-axisymmetric endwall based on radial equilibrium

Non-axisymmetric endwall contouring has been proved to be an effective flow control technique in turbomachinery. Several different flow control mechanisms and qualitative design strategies have been proposed. The endwall contouring mechanism based on the flow governing equations is significant for exploring the quantitative design strategies of the non-axisymmetric endwall contouring. In this paper, the static pressure redistribution mechanism of endwall contouring was explained based on the radial equilibrium equation. A quantified expression of the static pressure redistribution mechanism was proposed. Compressor cascades were simulated using an experimentally validated numerical method to validate the static pressure redistribution mechanism. A geometric parameter named meridional curvature (C_me) is defined to quantify the concave and convex features of the endwall. Results indicate that the contoured endwall changes the streamline curvature, inducing a centrifugal acceleration. Consequently, the radial pressure gradient is reformed to maintain the radial equilibrium. The convex endwall represented by positive C_me increases the radial pressure gradient, decreasing the endwall static pressure, while the concave endwall represented by negative C_me increases the endwall static pressure. The C_me helps to establish the quantified relation between the change in the endwall radial pressure gradient and the endwall geometry. Besides, there is a great correlation between the distributions of the C_me and the change in the endwall static pressure. It can be concluded that the parameter C_me can be considered as a significant parameter to parameterize the endwall surface and to explore the quantitative design strategies of the non-axisymmetric endwall contouring.