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Research Papers: Multiphase Flows

# Large Eddy Simulation of Turbulent-Cavitation Interactions in a Venturi Nozzle

[+] Author and Article Information
Nagendra Dittakavi

Advanced Dynamics Inc., Lexington, KY 40511nagendra.dittakavi@gmail.com

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-2088achuneka@purdue.edu

Steven Frankel1

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-2088frankel@purdue.edu

1

Corresponding author.

J. Fluids Eng 132(12), 121301 (Dec 03, 2010) (11 pages) doi:10.1115/1.4001971 History: Received August 04, 2009; Revised June 10, 2010; Published December 03, 2010; Online December 03, 2010

## Abstract

Large eddy simulation of turbulent cavitating flow in a venturi nozzle is conducted. The fully compressible Favre-filtered Navier–Stokes equations are coupled with a homogeneous equilibrium cavitation model. The dynamic Smagorinsky subgrid-scale turbulence model is employed to close the filtered nonlinear convection terms. The equations are numerically integrated in the context of a generalized curvilinear coordinate system to facilitate geometric complexities. A sixth-order compact finite difference scheme is employed for the Navier–Stokes equations with the $AUSM+-up$ scheme to handle convective terms in the presence of large density gradients. The stiffness of the system due to the incompressibility of the liquid phase is addressed through an artificial increase in the Mach number. The simulation predicts the formation of a vapor cavity at the venturi throat with an irregular shedding of the small scale vapor structures near the turbulent cavity closure region. The vapor formation at the throat is observed to suppress the velocity fluctuations due to turbulence. The collapse of the vapor structures in the downstream region is a major source of vorticity production, resulting into formation of hair-pin vortices. A detailed analysis of the vorticity transport equation shows a decrease in the vortex-stretching term due to cavitation. A substantial increase in the baroclinic torque is observed in the regions where the vapor structures collapse. A spectra of the pressure fluctuations in the far-field downstream region show an increase in the acoustic noise at high frequencies due to cavitation.

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## Figures

Figure 2

Water hammer: pressure history at valve location—(a) water and (b) water with modified speed of sound

Figure 3

Computational domain with boundary conditions: cross-sectional mesh and three axial locations

Figure 4

Turbulent pressure spectrum downstream of the throat for the noncavitating case

Figure 5

Instantaneous contours of nondimensionalized: (a) streamwise velocity and (b) pressure for noncavitating flow

Figure 12

Instantaneous vortex-stretching magnitude contours: (a) σ=18.0 and (b) σ=10.0

Figure 13

Instantaneous isosurfaces of baroclinic torque (isolevel =0.03) at T∗=25: (a) σ=12.0 and (b) σ=10.0

Figure 14

Reynolds stress component ⟨u′u′⟩/Uref2 profiles: noncavitating flow (solid line), σ=12.0 (dashed dotted line), and σ=10.0 (dashed line). (a) x∗=3.2, (b) x∗=6.2, and (c) x∗=9.2.

Figure 17

Turbulent kinetic energy contours: (a) noncavitating, (b) σ=12.0, and (c) σ=10.0

Figure 18

Power spectral densities of pressure fluctuations at x∗=16.4 (far downstream): (a) noncavitating and (b) σ=10.0

Figure 1

Variation in speed of sound with void fraction (α): original equation of state (solid line) and modified equation of state (dashed line)

Figure 9

Instantaneous isosurfaces of vorticity magnitude for σ=12.0 indicating the formation of hairpin vortices from LES simulations

Figure 10

Formation of hairpin vortices at the trailing edge of the vapor cavity as viewed from the top. The flow is from right to left (image source: Gopalan and Katz (10)).

Figure 11

Instantaneous isosurfaces of vorticity magnitude for: (a) noncavitating case and (b) σ=10.0

Figure 15

Reynolds stress component ⟨v′v′⟩/Uref2 profiles: noncavitating flow (solid line), σ=12.0 (dashed dotted line), and σ=10.0 (dashed line). (a) x∗=3.2,, (b) x∗=6.2, and (c) x∗=9.2

Figure 16

Reynolds stress component ⟨u′v′⟩/Uref2 profiles: noncavitating flow (solid line), σ=12.0 (dashed dotted line), and σ=10.0 (dashed line). (a) x∗=3.2, (b) x∗=6.2, and (c) x∗=9.2

Figure 6

Instantaneous isosurfaces of vorticity magnitude for noncavitating flow

Figure 7

Left: evolution of isosurfaces of void fraction from T∗=26.00 to T∗=27.00 for σ=12.0. Right: high-speed photos of vapor cavity evolution from experiments by Gopalan and Katz (10). The flow is from right to left.

Figure 8

Instantaneous void fraction contours superimposed by velocity vectors showing the re-entrant jet formation at σ=12.0

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