1. A novel variational method for 3D viscous flow in flow channel of turbomachines based on differential geometry.
- Author
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Ju, Guoliang, Li, Jingzhi, and Li, Kaitai
- Subjects
- *
CHANNEL flow , *NAVIER-Stokes equations , *OPERATOR equations , *TURBOMACHINES , *COORDINATES , *DIFFERENTIAL geometry , *VISCOUS flow - Abstract
This paper presents a novel variational method for treating three-dimensional rotational Navier-Stokes equations in flow channel of turbomachines. The proposed method establishes a new semi-geodesic coordinate system on the central surface of blades. From the perspective of differential geometry, the system under concern is split into a set of membrane operator equations on two-dimensional manifolds and bending operator equations along hub circle. The third variable of the new coordinate system is approximated by the central difference scheme. We derive a new formulation of two-dimensional Navier-Stokes equations with three components on the manifolds in the variational sense. The well-posedness of the proposed variational formulation is rigorously justified. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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