Application of an Angular Momentum Balance Method for Investigating Numerical Accuracy in Swirling Flow

[+] Author and Article Information
H. Nilsson, L. Davidson

Department of Thermo and Fluid Dynamics, Chalmers, SE-412 96 Göteborg, Sweden

J. Fluids Eng 125(4), 723-730 (Aug 27, 2003) (8 pages) doi:10.1115/1.1595673 History: Received November 15, 2001; Revised February 23, 2003; Online August 27, 2003
Copyright © 2003 by ASME
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Circumferentially averaged velocity coefficients above and below a Kaplan runner (Kaplan 1). Solid lines: tangential velocity; dashed lines: axial velocity. Markers: ▵: first-order hybrid scheme; ○: second-order Van Leer scheme. The velocities are normalized by the runner radius and the runner angular velocity. (a) Above the runner, (b) below the runner.
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Angular momentum distributions at the inlet and a section before the runner of a Kaplan runner (Kaplan 1). The distribution at the inlet should be approximately conserved at the section before the runner in a correct solution, i.e., the curves should coincide. Markers: □: inlet distribution; ▵: first-order hybrid scheme, before the runner; ○: second-order Van Leer scheme, before the runner. The angular momentum is normalized by the runner radius and the runner angular velocity.
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The three geometries studied in this work. In all cases the flow is swirling radially inwards at the top and axially downwards at the bottom. (a) The simplified geometry, (b) Kaplan 1, (c) Kaplan 2.
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Meridional view of the coarse (left) and fine (right) grid of the simplified geometry. The grid densities and distributions differ mainly in the through-flow direction.
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Definitions of the cross-flow axisymmetric surfaces. The numbered surfaces (represented by thin lines) are grid surfaces for the simplified case and general control surfaces for the Kaplan cases. (a) The simplified geometry with numbered axisymmetric cross-flow grid surfaces corresponding to the coarse grid. (b) The meridional contour of the Kaplan 1 runner (thick lines). The dashed lines show the computational domain. (c) The meridional contour of the Kaplan 2 runner (thick lines). The dashed lines show the computational domain.
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Local and cumulative error distributions from inlet to outlet of the simplified geometry. Dashed line: Van-Leer, local error; dotted line: hybrid, local error; solid line: Van-Leer, cumulative error; dashed-dotted line: hybrid, cumulative error. (a) Coarse grid, (b) fine grid.
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Cumulative error distributions from inlet to outlet of the Kaplan cases. Dashed line: Van-Leer, Kaplan 1; dashed-dotted line: hybrid, Kaplan 1; solid line: Van-Leer, Kaplan 2; dotted line: hybrid, Kaplan 2.
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Iso-surfaces of the absolute value of the computational control volume angular momentum balance indicating where the largest errors are located. The Kaplan 2 case with the Van Leer scheme.




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