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TECHNICAL PAPERS

Vortex Dynamics and Low-Pressure Fluctuations in the Tip-Clearance Flow

[+] Author and Article Information
Donghyun You1

Center for Turbulence Research, Stanford University, Stanford, CA 94305dyou@stanford.edu

Meng Wang

Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556

Parviz Moin

Center for Turbulence Research, Stanford University, Stanford, CA 94305

Rajat Mittal

Department of Mechanical and Aerospace Engineering, George Washington University, Washington, DC 20052

1

Corresponding author.

J. Fluids Eng 129(8), 1002-1014 (Jan 24, 2007) (13 pages) doi:10.1115/1.2746911 History: Received May 22, 2006; Revised January 24, 2007

The tip-clearance flow in axial turbomachines is studied using large-eddy simulation with particular emphasis on understanding the unsteady characteristics of the tip-leakage vortical structures and the underlying mechanisms for cavitation-inducing low-pressure fluctuations. A systematic and detailed analysis of the velocity and pressure fields has been made in a linear cascade with a moving end-wall. The generation and evolution of the tip-leakage vortical structures have been investigated throughout the cascade using mean streamlines and λ2 contours. An analysis of the energy spectra and space-time correlations of the velocity fluctuations suggests that the tip-leakage vortex is subject to a pitchwise low frequency wandering motion. Detailed statistics of the pressure fields has been analyzed to draw inferences on cavitation. The regions of low pressure relative to the mean values coincide with regions of strong pressure fluctuations, and the regions are found to be highly correlated with the vortical structures in the tip-leakage flow, particularly in the tip-leakage and tip-separation vortices.

Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

(a) Flow configuration and coordinate system for the tip-clearance flow and (b) measurement planes for investigating the flow field and definitions of velocity coordinates

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Figure 2

Surface pressure coefficient at z∕Ca=0.916. —, LES; •, experiment (15)

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Figure 3

Resolution in Kolmogorov units (η) in a y-z plane at x∕Ca=0.7. (a)Δx∕η; (b)Δy∕η; (c)Δz∕η

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Figure 4

Mean velocity U∕U∞ profiles on the suction surface. —, 897×701×16 mesh; - - - -, 449×351×8 mesh. The profiles at x∕Ca=0.50 and 0.99 are shifted by 1 and 2, respectively.

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Figure 5

Time-histories of the streamwise velocity at x∕Ca=0.7, y∕Ca=1.3, and z∕Ca=0.1 using different CFL numbers. —, CFL=1.5; - - - -, CFL=4; ⋯⋯, CFL=5.

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Figure 6

(a) Mean streamlines and (b) contour plot of CFL number distribution in a y-z plane at x∕Ca=0.7. In (a), every third and second points are shown in y- and z-directions, respectively.

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Figure 7

Profiles of Reynolds shear stresses along the spanwise direction at (x∕Ca,y∕Ca)=(0.6,1.51). —, total stress; - - - -, resolved stress. The profiles of u′w′¯∕U∞2 and v′w′¯∕U∞2 are shifted by 0.025 and 0.05, respectively.

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Figure 8

Locations of the end-wall normal planes in which the mean streamlines in Fig. 9 are visualized

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Figure 9

Mean streamlines showing vortical structures in the end-wall region in y*-z planes

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Figure 10

Generation and evolution of end-wall vortical structures along the streamwise direction visualized using the λ2 vortex identification method (31)

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Figure 11

Contour plot of the mean streamwise velocity in a y-z plane at x∕Ca=1.51 and location where the energy spectra in Fig. 1 and space-time correlations in Fig. 1 are measured. ywake denotes the location of peak deficit in the blade wake.

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Figure 12

Profiles of the mean streamwise velocity (U∕U∞) and Reynolds normal stresses ((u′u′¯,v′v′¯,w′w′¯)∕U∞2×102) along the spanwise direction at (x∕Ca,y∕Ca)=(1.51,1.35). —, LES; •, experiment (16). The profiles of u′u′¯∕U∞2×102, v′v′¯∕U∞2×102, and w′w′¯∕U∞2×102 are shifted by 1, 2, and 3, respectively.

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Figure 13

One-dimensional frequency spectra of velocity fluctuations at the location A in Fig. 1. (a)Euu; (b)Evv; (c)Eww. —, LES; •, experiment (16).

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Figure 14

One-dimensional frequency spectra of velocity fluctuations in the blade wake at x∕Ca=1.51, y∕Ca=2.2 and z∕Ca=0.9. (a)Euu; (b)Evv; (c)Eww. —, LES; •, experiment (15).

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Figure 15

Contour plot of two-point correlations of the pitchwise velocity fluctuations as a function of the pitchwise spatial and temporal separations in the location A in Fig. 1. Contours are from −1 to 1 with increments of 0.1.

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Figure 16

Instantaneous low-pressure (p∕ρU∞2=−0.2) iso-surfaces showing a low-frequency wandering motion of the tip-leakage vortex. (a)t0; (b)t0+0.33C∕U∞.

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Figure 17

Contour plots of mean pressure in x-y planes along the z-direction. (a)z∕Ca=0.01; (b)z∕Ca=0.025; (c)z∕Ca=0.1; (d)z∕Ca=0.5.

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Figure 18

Contour plots of p′p′¯ in x-y planes along the z-direction. (a)z∕Ca=0.01; (b)z∕Ca=0.025; (c)z∕Ca=0.1; (d)z∕Ca=0.5.

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Figure 19

Contour plots of mean pressure in y-z planes along the x-direction. (a)x∕Ca=0.1; (b)x∕Ca=0.3; (c)x∕Ca=0.5; (d)x∕Ca=0.7; (e)x∕Ca=0.9.

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Figure 20

Contour plots of p′p′¯ in y-z planes along the x-direction. (a)x∕Ca=0.1; (b)x∕Ca=0.3; (c)x∕Ca=0.5; (d)x∕Ca=0.7; (e)x∕Ca=0.9.

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Figure 21

Contours of (a) instantaneous and (b) time-averaged cavitation criterion, B=1∕3(B11+B22+B33), in a plane inside the tip-gap at z∕Ca=0.01

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