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Research Papers: Multiphase Flows

Modeling the Unsteady Cavitating Flow in a Cross-Flow Water Turbine

[+] Author and Article Information
E. Sansone

 Laboratoire des Ecoulements Géophysiques et Industriels (LEGI), 38000 Grenoble, France

C. Pellone

 Centre National de la Recherche Scientifique (CNRS), 38042 Grenoble, France

T. Maitre

 Institut National Polytechnique de Grenoble (INPG), 38031 Grenoble, France

J. Fluids Eng 132(7), 071302 (Jul 08, 2010) (13 pages) doi:10.1115/1.4001966 History: Received February 14, 2008; Revised May 28, 2010; Published July 08, 2010; Online July 08, 2010

The noncavitating and cavitating flows over a cross-flow water turbine are simulated by using an unsteady Navier–Stokes formulation. For the cavitating flow case, a homogeneous mixture with a varying density is considered and one additional transport equation is explicitly solved in time for the liquid volume fraction. The instantaneous rate of vapor production and absorption appearing as a source term is governed by a hydrodynamic model based on a simplified bubble dynamic equation. The spatial discretization is achieved by a 2D multiblock technique consisting of fixed and rotating blocks, which were especially adapted for Darrieus geometry. Several test cases corresponding to experiments performed on fixed and rotating blades are selected to compare the numerical results with experimental data. Finally, a calculation of a monobladed cavitating cross-flow turbine is presented. The effect of cavitation on the dynamic stall phenomenon and on the turbine performance is analyzed. In particular, it is shown that cavitation earlier reveals the stall phenomenon on the blades and magnifies the size of the shedding vortex structures in the turbine.

Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic cross section of a one-bladed Darrieus turbine

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Figure 2

Angle of attack versus the azimuthal angle for different tip speed ratios λ

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Figure 3

Meshes for a fixed domain and for a rotating domain

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Figure 4

Lift coefficient CL versus the angle of attack β (NACA0012)

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Figure 5

Drag coefficient CD versus the angle of attack β (NACA0012)

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Figure 6

Pressure coefficient on the NACA66(mod)-312 foil, noncavitating flow, β=6 deg, Re=8.0×105

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Figure 7

Tangential force coefficient CT versus the azimuthal angle θ, one-bladed Darrieus turbine, ReΩ=6.7×104, λ=2.5. Effect of the outer iterations.

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Figure 8

Tangential force coefficient CT versus the azimuthal angle θ, one-bladed Darrieus turbine, ReΩ=6.7×104, λ=2.5. Effect of the revolutions number.

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Figure 9

Tangential force coefficient CT versus the azimuthal angle θ, one-bladed Darrieus turbine, ReΩ=6.7×104, λ=2.5

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Figure 10

Normal force coefficient CN versus the azimuthal angle θ, one-bladed Darrieus turbine, ReΩ=6.7×104, λ=2.5

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Figure 11

Relative streamlines, comparison with the Cebeci-Smith results (53), one-bladed Darrieus turbine, ReΩ=6.7×104, λ=2.5

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Figure 12

Transitional curve between dynamics 1 and 2, cloud cavitation regime, experiments from Leroux (51), β0=−2.35 deg, U∞=5.33 m/s

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Figure 13

Lift coefficient, NACA66(mod)-312, cavitating regime, Re=8.0×105, β=6 deg

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Figure 14

Drag coefficient, NACA66(mod)-312, cavitating regime, Re=8.0×105, β=6 deg

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Figure 15

Lift coefficient, NACA66(mod)-312, cavitating regime, Re=8.0×105, β=6 deg. Maximum relative residual for the velocity.

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Figure 16

Drag coefficient, NACA66(mod)-312, cavitating regime, Re=8.0×105, β=6 deg. Maximum relative residual for the pressure.

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Figure 17

Pressure coefficient, NACA66(mod)-312, unsteady cavitating regime, n0=108 nuclei/m3, Re=8.0×105, β=6 deg

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Figure 18

Results obtained with IZ (34) and CAVKA codes, comparison with the Leroux experimental results (51), foil NACA66(mod)-312, Re=8.0×105, β=6 deg. The color map indicates the water volume fraction αL for numerical calculations and vapor volume fraction αV for Leroux experiences (51).

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Figure 19

Results obtained with IZ (34) and CAVKA codes, comparison with the Leroux experimental results (51), foil NACA66(mod)-312, Re=8.0×105, β=6 deg (continuation of Fig. 1)

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Figure 20

Noncavitating and cavitating regimes, one-bladed Darrieus turbine, blade foil: NACA0015, tangential force coefficient, λ=2.5, σλ=3, ReΩ=1.9×105

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Figure 21

Noncavitating and cavitating regimes, one-bladed Darrieus turbine, blade foil: NACA0015, normal force coefficient, λ=2.5, σλ=3, ReΩ=1.9×105

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Figure 22

Cavitating regime, one-bladed Darrieus turbine, blade foil: NACA0015, normal force coefficient, λ=2.5, σλ=3, ReΩ=1.9×105. Effect of the revolutions number.

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Figure 23

Cavitating regime, one-bladed Darrieus turbine, blade foil: NACA0015, relative streamlines and liquid fraction αL for various azimuthal angles θ. λ=2.5, ReΩ=1.9×105.

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Figure 24

Noncavitating (left figures) and cavitating (center and right figures) regime (second revolution), one-bladed Darrieus turbine, blade foil: NACA0015, vorticity and streamlines (left and center figures), liquid fraction and streamlines (right figures), λ=2.5, σλ=3, ReΩ=1.9×105

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