A novel variational method for 3D viscous flow in flow channel of turbomachines based on differential geometry. Issue 13 (2nd October 2020)

• Record Type: Journal Article
• Authors: Ju, Guoliang; Li, Jingzhi; Li, Kaitai
• Is Part Of: Applicable analysis. Volume 99:Issue 13(2020)
• Page Start: 2322
• Page End: 2338
• Publication Date: 2020-10-02
• Subjects: Rotational Navier-Stokes equation -- differential geometry -- semi-geodesic coordinate system -- two-scale parallel algorithm; 65N30 -- 76U05 -- 76M05; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1559304
• Languages: English
• ISSNs: 0003-6811

Abstract

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.