A new boundary layer equation and its application to the flow in turbo-machinery


Coraddress to: Kaitai Li, Department of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China, (e-mail: ktli@mail.xjtu.edu.cn)


In this article, a new boundary layer equation (BLE) in turbomachinery flow is established using semigeodesic coordinate system (S-coordinate) on the curved two-dimensional surface of the blade. BLE are a nonlinear partial differential equations for unknown normal gradient of the velocity and pressure on the blade, which could be applied in the blade shape optimal control. Furthermore the existence of solution of BLE and a finite element algorithm based on approximate inertial manifold are provided and numerical example of flow in a centrifugal impeller is also presented. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1455–1483, 2014