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Research Papers: Flows in Complex Systems

Experimental and Numerical Study of Flow Structures Associated With Low Aspect Ratio Elliptical Cavities

[+] Author and Article Information
Taravat Khadivi

e-mail: tkhadivi@alumni.uwo.ca

Eric Savory

e-mail: esavory@eng.uwo.ca
Department of Mechanical and Materials
Engineering,
University of Western Ontario,
London, ON, N6A 5B9, Canada

Manuscript received October 1, 2012; final manuscript received January 28, 2013; published online March 21, 2013. Assoc. Editor: Francine Battaglia.

J. Fluids Eng 135(4), 041104 (Mar 21, 2013) (14 pages) Paper No: FE-12-1488; doi: 10.1115/1.4023652 History: Received October 01, 2012; Revised January 28, 2013

The flow regimes associated with 2:1 aspect ratio elliptical planform cavities of varying depth immersed in a turbulent boundary layer at a Reynolds number of 8.7 × 104, based on the minor axis of the cavity, have been quantified from particle image velocimetry measurements and three-dimensional steady computational fluid dynamics simulations (Reynolds stress model closure). Although these elliptical cavity flows have some similarities with nominally two-dimensional and rectangular cases, three-dimensional effects due to the low aspect ratio and curvature of the walls give rise to features exclusive to low aspect ratio elliptical cavities, including formation of cellular structures at intermediate depths and vortex structures within and downstream of the cavity.

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Figures

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Fig. 1

Geometry and boundary types

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Fig. 2

Dimensionless (a) velocity, (b) u'u'¯, (c) v'v'¯, (d) u'v'¯ Reynolds stress profiles at the inlet

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Fig. 3

Computational grid in the cavity and the surroundings

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Fig. 4

Comparison of (a) Cp on cavity base, (b) vertical profile of u¯/Uinf at cavity center, and (c) vertical profile of u'u'¯/Uinf2 at cavity center for h/D = 1.0 with three different grids

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Fig. 5

Comparison of Cp profiles on the centerline of the cavity base for h/D = 0.1, 0.5, and 1.0

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Fig. 6

Schematic representation of the experimental setup (not to scale)

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Fig. 7

Schematic diagram showing the velocity profile at x/D = 0, contours of ∂u/∂y, shear layer (dashed line), and Uref vector

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Fig. 8

Comparison of numerical and experimental values of u¯ and u'u'¯ profiles for h/D = 1.0

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Fig. 9

(a) Vortex core position; pressure coefficient contours on cavity base, ground plane, and side walls for h/D = 1.0, (b) experiment [33], and (c) numerical simulation

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Fig. 10

Variation of shear layer thickness with streamwise distance across the cavity opening

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Fig. 11

Variation of the location of shear layer center with h/D

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Fig. 12

Schematic representation of the flow structure in an elliptical cavity in the symmetric-deep flow regime

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Fig. 13

Vortex core positions and Cp contours for h/D = 0.5

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Fig. 14

Schematic representation of the flow structure in an elliptical cavity in the symmetric-cellular structure flow regime

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Fig. 15

Vortex core positions and Cp contours for h/D = 0.1

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Fig. 16

Schematic representation of the flow structure in an elliptical cavity in the symmetric-shallow flow regime

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Fig. 17

Comparison of drag coefficient increment. (The lines are added to visualize the general trend for each planform shape qualitatively. Solid line: elliptical cavity, dashed line: rectangular cavity, and dashed-dotted line: circular cavity.)

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Fig. 18

Velocity deficit contours based on PIV measurements in a horizontal plane. The circular arc is due to masking of the imaging area by the joint between the base plate enclosing the cavity and the ground plate.

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Fig. 19

Quantitative comparison of velocity deficit

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