Numerical Prediction of Cavitating Flow on a Two-Dimensional Symmetrical Hydrofoil and Comparison to Experiments

[+] Author and Article Information
Olivier Coutier-Delgosha1

 ENSAM Lille/LML Laboratory, 8 bld Louis XIV, 59046 Lille Cedex, Franceolivier.coutier@lille.ensam.fr

François Deniset

Institut de Recherche, l’Ecole Navale – EA3634, BP 600, 29240 Brest Naval, Francedeniset@ecole-navale.fr

Jacques André Astolfi

Institut de Recherche, l’Ecole Navale – EA3634, BP 600, 29240 Brest Naval, Franceastolfi@ecole-navale.fr

Jean-Baptiste Leroux2

Institut de Recherche, l’Ecole Navale – EA3634, BP 600, 29240 Brest Naval, Francejean-baptiste.leroux@ensieta.fr


Corresponding author.


Now at ENSIETA - Laboratoire MSN, 2 rue François Verny, 29806 Brest Cedex 9, France.

J. Fluids Eng 129(3), 279-292 (Aug 04, 2006) (14 pages) doi:10.1115/1.2427079 History: Received August 11, 2005; Revised August 04, 2006

This paper presents comparisons between two-dimensional (2D) CFD simulations and experimental investigations of the cavitating flow around a symmetrical 2D hydrofoil. This configuration was proposed as a test case in the “Workshop on physical models and CFD tools for computation of cavitating flows” at the 5th International Symposium on cavitation, which was held in Osaka in November 2003. The calculations were carried out in the ENSTA laboratory (Palaiseau, France), and the experimental visualizations and measurements were performed in the IRENav cavitation tunnel (Brest, France). The calculations are based on a single-fluid approach of the cavitating flow: the liquid/vapor mixture is treated as a homogeneous fluid whose density is controlled by a barotropic state law. Results presented in the paper focus on cavitation inception, the shape and the general behavior of the sheet cavity, lift and drag forces without and with cavitation, wall pressure signals around the foil, and the frequency of the oscillations in the case of unsteady sheet cavitation. The ability of the numerical model to predict successively the noncavitating flow field, nearly steady sheet cavitation, unsteady cloud cavitation, and finally nearly supercavitating flow is discussed. It is shown that the unsteady features of the flow are correctly predicted by the model, while some subtle arrangements of the two-phase flow during the condensation process are not reproduced. A comparison between the peer numerical results obtained by several authors in the same flow configuration is also performed. Not only the cavitation model and the turbulence model, but also the numerical treatment of the equations, are found to have a strong influence on the results.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 8

Conditions of cavitation inception and desinence

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Figure 14

Comparison between the experiments and the simulations, Vref=6m∕s, α=7deg. (a) Maximum cavity length l∕lref (b) Strouhal number Stc based on the chord lref (c) Strouhal number Stl based on the maximum cavity length l.

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Figure 15

Time evolution of large cavity (Vref=6m∕s,α=7deg,σ=0.55): (a) on the foil pressure side, (b) on the foil suction side

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Figure 18

Vorticity field at T∕Tref=30(Vref=6m∕s,α=7deg,σ=0.55)

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Figure 19

Evolution of the vorticity at x∕lref=1.3, y=0(Vref=6m∕s,α=7deg,σ=0.55)

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Figure 1

Flow configuration proposed in the Workshop on physical models and CFD tools for computation of cavitating flows

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Figure 2

Barotropic state law ρ(P). Water 20°C.

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Figure 3

(a) Computational domain, (b) Zoom at the foil leading edge

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Figure 4

Measurement of the cavity length, from the distance between the inception point and the closure of the cavity, both projected on the chord. (Here, σ=2.0 and l∕lref=0.175).

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Figure 5

Pressure fields around the foil in non-cavitating conditions. (Velocity vectors drawn only 1 cell over 5 along the foil, and 1 cell over 3 perpendicularly to the foil.)

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Figure 6

Velocity magnitude obtained by simulation (top view) and PIV measurements (bottom view), α=7 deg, Vref=6m∕s, σ=4

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Figure 7

Size of sheet cavitation for (a) σ=3.5, (b) σ=3, Vref=6m∕s, α=7°. From top to bottom: general view of the foil (experiment), side view at the leading edge (simulation), side view at the leading edge (experiment).

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Figure 9

Cloud cavitation (Vref=6m∕s,α=7deg,σ=0.9). (a) Time evolution of the cavity length: the time is reported in abscissa, and the X position in the cavitation tunnel is graduated in ordinate. The grey levels represent the density values, as indicated under the figure (pure liquid and pure vapor are both in white). At a given point in time and position, the grey level indicates the minimum density in the corresponding cross section of the cavitation tunnel. (b) Time evolution of the vapor volume.

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Figure 10

One cycle of cloud cavitation (14ms between two pictures, Vref=6m∕s, α=7deg, σ=0.9, pure liquid and pure vapor both in white)

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Figure 11

Step 6 of the cloud cavitation cycle. Comparison between the experiment (top view) and the simulation (bottom view).

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Figure 12

Evolution of (a), (b) the lift and drag coefficients and (c), (d), (e) the pressure coefficients on the foil suction side at stations x∕c=0.1, 0.5, 0.9. (Numerical result, Vref=6m∕s, α=7deg, σ=0.9). The dashed lines delimit one sequence “1” (cavity growth) and one sequence “2” (convection of the vapor cloud).

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Figure 13

Reverse flow during the cavity break-off. (Numerical result, Vref=6m∕s, α=7deg, σ=0.9.)

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Figure 16

Fluctuations of the cavity shape (Vref=6m∕s,α=7deg,σ=0.55). (30<T∕Tref<32, 0.5Tref between two pictures.)

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Figure 17

Time evolutions of the lift and drag coefficients, the pressure coefficient at x∕lref=1, and the vapor volume (Vref=6m∕s,α=7deg,σ=0.55)

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Figure 20

Spectral analysis of the pressure fluctuations sampled at 6.5 chords downstream the foil trailing edge (a) σ∕2α=3.5, (b) σ∕2α=4.1

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Figure 21

Sheet cavity for σdownstream=0.4



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