A Quasi-Generalized-Coordinate Approach for Numerical Simulation of Complex Flows

[+] Author and Article Information
Donghyun You1

Center for Turbulence Research, Stanford University, Stanford, CA 94305dyou@stanford.edu

Meng Wang

Department of Mechanical and Aerospace Engineering, George Washington University, Washington, DC 20052 and Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556

Rajat Mittal

Department of Mechanical and Aerospace Engineering, George Washington University, Washington, DC 20052

Parviz Moin

Center for Turbulence Research, Stanford University, Stanford, CA 94305


Corresponding author.

J. Fluids Eng 128(6), 1394-1399 (Apr 11, 2006) (6 pages) doi:10.1115/1.2354533 History: Received October 11, 2005; Revised April 11, 2006

A novel structured grid approach which provides an efficient way of treating a class of complex geometries is proposed. The incompressible Navier-Stokes equations are formulated in a two-dimensional, generalized curvilinear coordinate system complemented by a third quasi-curvilinear coordinate. By keeping all two-dimensional planes defined by constant third coordinate values parallel to one another, the proposed approach significantly reduces the memory requirement in fully three-dimensional geometries, and makes the computation more cost effective. The formulation can be easily adapted to an existing flow solver based on a two-dimensional generalized coordinate system coupled with a Cartesian third direction, with only a small increase in computational cost. The feasibility and efficiency of the present method have been assessed in a simulation of flow over a tapered cylinder.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Schematic diagram of coordinate transformation from Cartesian coordinates to curvilinear coordinates. Planes perpendicular to η3 are required to be parallel in the quasi-generalized coordinates.

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Figure 2

Examples of algebraic functions used in the proposed transformation: (a) shift; (b) magnification/contraction; (c) rotation; (d) skewing to x1 direction; (e) skewing to x2 direction

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Figure 3

A twisted compressor blade generated by mesh rotation and skewing: (a) compressor blade; (b) mesh around the blade

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Figure 4

An airplane wing generated by contraction and shift: (a) airplane wing; (b) mesh around the wing

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Figure 5

(a) Flow configuration and computational domain, and (b) computational grid in a base x-y plane used for numerical simulation of flow over a tapered circular cylinder

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Figure 6

Instantaneous vortical structures behind a tapered circular cylinder: (a) water tunnel flow visualization (11); (b)λ2 vortex identification from computational results

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Figure 7

(a) Time history and (b) frequency energy spectrum of the vertical velocity at x∕D2=1, y∕D2=0, z∕D2=13.5



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