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

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 pressu...

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Bibliographic Details
Published in:Numerical methods for partial differential equations 2014-09, Vol.30 (5), p.1455-1483
Main Authors: Li, Kaitai, Chen, Hao, Zhang, Yin, Wang, Shangjin
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Blades
boundary layer equation
Boundary layer equations
Impellers
Mathematical analysis
Mathematical models
Navier-Stokes equations
normal stress tensor
Partial differential equations
semi-geodesic coordinate system
two-dimensional manifold
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Summary: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
ISSN:0749-159X
1098-2426
DOI:10.1002/num.21844