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Research Papers: Multiphase Flows

# Prediction of Small-Scale Cavitation in a High Speed Flow Over an Open Cavity Using Large-Eddy Simulation

[+] Author and Article Information
Ehsan Shams

Computational Flow Physics Laboratory, School of Mechanical Industrial and Manufacturing Engineering, Oregon State University, 204 Rogers Hall, Corvallis, OR 97331

Sourabh V. Apte1

Computational Flow Physics Laboratory, School of Mechanical Industrial and Manufacturing Engineering, Oregon State University, 204 Rogers Hall, Corvallis, OR 97331sva@engr.orst.edu

1

Corresponding author.

J. Fluids Eng 132(11), 111301 (Nov 09, 2010) (14 pages) doi:10.1115/1.4002744 History: Received September 09, 2009; Revised October 04, 2010; Published November 09, 2010; Online November 09, 2010

## Abstract

Large-eddy simulation of flow over an open cavity corresponding to the experimental setup of Liu and Katz (2008, “Cavitation Phenomena Occurring Due to Interaction of Shear Layer Vortices With the Trailing Corner of a Two-Dimensional Open Cavity,” Phys. Fluids, 20(4), p. 041702) is performed. The filtered, incompressible Navier–Stokes equations are solved using a co-located grid finite-volume solver with the dynamic Smagorinsky model for a subgrid-scale closure. The computational grid consists of around $7×106$ grid points with $3×106$ points clustered around the shear layer, and the boundary layer over the leading edge is resolved. The only input from the experimental data is the mean velocity profile at the inlet condition. The mean flow is superimposed with turbulent velocity fluctuations generated by solving a forced periodic duct flow at a freestream Reynolds number. The flow statistics, including mean and rms velocity fields and pressure coefficients, are compared with the experimental data to show reasonable agreement. The dynamic interactions between traveling vortices in the shear layer and the trailing edge affect the value and location of the pressure minima. Cavitation inception is investigated using two approaches: (i) a discrete bubble model wherein the bubble dynamics is computed by solving the Rayleigh–Plesset and the bubble motion equations using an adaptive time-stepping procedure and (ii) a scalar transport model for the liquid volume fraction with source and sink terms for phase change. Large-eddy simulation, together with the cavitation models, predicts that inception occurs near the trailing edge similar to that observed in the experiments. The bubble transport model captures the subgrid dynamics of the vapor better, whereas the scalar model captures the large-scale features more accurately. A hybrid approach combining the bubble model with the scalar transport is needed to capture the broad range of scales observed in cavitation.

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## Figures

Figure 1

Computational domain and grid: (a) three-dimensional domain with Cartesian grid; (b) refined grids (dimensions shown are in mm) used in the shear layer and near the cavity leading and trailing edges. A zoomed-in view of the grid near the trailing edge is shown in wall coordinates.

Figure 2

Comparison of mean and rms axial velocity variations in the vertical direction with experimental data of LK2008: Results from fine (solid lines), base (dotted lines), coarse grid (dashed lines), and experiment (symbols) are shown. Inlet fluctuations are enforced only in the base and fine grids.

Figure 3

Contours of mean velocity and Cp fields near the trailing edge compared with corresponding PIV data of LK2008

Figure 4

Contours of axial and vertical rms velocity fields as well as Reynolds stress compared with PIV data of LK2008 near the trailing edge

Figure 5

Vertical variations of normalized rms velocity (urms/U∞) and Reynolds stress (u′v′¯/U∞2) near the trailing edge: fine grid (solid lines), base grid (dotted lines), coarse grid (dashed lines), and experiment data (symbols)

Figure 6

Probability distribution functions for Cp′ at the eight probe locations (p1–p8) shown in contour plot of C¯p

Figure 7

Instantaneous pressure contours and stream traces (based on removing 0.5U∞ from the streamwise velocity): (a) t=53 ms (high pressure above the trailing edge), (b) t=55 ms (low pressure above the trailing edge), (c) t=65 ms, and (d) power-spectral density of Cp at a probe near the vertical wall of the trailing edge (x/L=0.98,y/L=−0.26,z/L=0)

Figure 8

Time evolution of vapor fraction and Cp near the trailing edge: (a) for σi=0.9 at x=(38.0,0.3,0.0) and (b) for σi=0.4 at x=(38.1,0.01,0.0); (c) power-spectral density of Cp and (d) power-spectral density of ϕ for σi=0.4

Figure 9

Temporal evolution of bubble distribution (initial size of 50 μm) on the shear layer for σi=0.4 during the initial stages: (a) side view showing entire shear layer and trailing edge and (b) top view above the trailing edge

Figure 10

Effect of cavitation index σi on the PDFs and average number of bubbles (Nb) sampled based on the growth ratio (d/dinitial) and pressure coefficient Cp for cases C2 (σi=0.4, triangle symbols), C4 (σi=0.9, diamond symbols), C5 (σi=1.4, filled circles), and C6 (σi=0.1, filled square): ((a) and (b)) PDF of all bubbles over the region of interest, ((c) and (d)) bubbles in zone 1, ((e) and (f)) bubbles in zone 2, and ((g) and (h)) bubbles in zone 3

Figure 11

Average number of conditionally sampled bubbles based on pressure coefficient at bubble location for cases C1 (square), C2 (triangle), and C3 (circle): (a) medium size group (0.8<d/dinitial<1.25) and (b) large size group (1.25<d/dinitial)

Figure 12

Average expansion ratio from scalar transport model (solid lines) and bubble cavitation model (dashed line) above the trailing edge for upstream pressure corresponding to σi=0.4

Figure 13

Instantaneous isosurfaces of Cp=−0.25 (left panel), ϕ=0.25 (middle panel), and bubble scatter plot (right panel) for three time levels corresponding to the expansion ratio signal in Fig. 1: time level A (top panels), time level B (middle panel), and time level C (bottom panels). Scatter symbols are scaled to bubble size relative to the grid.

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