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A new boundary layer equation and its application to the flow in turbo‐machinery
Author(s) -
Li Kaitai,
Chen Hao,
Zhang Yin,
Wang Shangjin
Publication year - 2014
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21844
Subject(s) - turbomachinery , partial differential equation , mathematics , coordinate system , impeller , flow (mathematics) , partial derivative , blade (archaeology) , finite element method , mathematical analysis , boundary layer , geometry , mechanics , mechanical engineering , engineering , physics , structural engineering
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