A novel variational method for 3D viscous flow in flow channel of turbomachines based on differential geometry

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.

KEYWORDS:

• Rotational Navier-Stokes equation
• differential geometry
• semi-geodesic coordinate system
• two-scale parallel algorithm

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 65N30
• 76U05
• 76M05

Disclosure statement

No potential conflict of interest was reported by the authors.