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A study of a 3-D double backward-facing step

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Abstract

An investigation of the flow over a three-dimensional (3-D) double backward-facing step is presented using a combination of both quantitative measurements from a particle image velocimetry (PIV) system and qualitative oil-flow visualizations. The arrangement of the PIV instrument allows for snap-shots of the (x, y) and (y, z) planes at various axial and spanwise positions. The measurements illustrate characteristics that are found in both two-dimensional (2-D) backward-facing steps and 3-D flows around wall mounted cubes. In particular, the development of a horseshoe vortex is found after each step alongside other vortical motions introduced by the geometry of the model. Large turbulence levels are found to be confined to a region in the center of the backstep; their mean square levels being much larger than what has been observed in 2-D backward-facing steps. The large turbulent fluctuations are attributed to a quasi-periodic shedding of the horseshoe vortex as it continuously draws energy from the spiral nodes of separation, which form to create the base of the horseshoe vortex. A combination of effects including the shedding of the first horseshoe vortex, the horizontal entrainment of air and the presence of two counter rotating vortices initiated at reattachment, are shown to cause the steering vector of the flow to jettison away from the surface in the first redeveloping region and along the center at z/h = 0. Oil-flow visualizations confirm these observations.

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Notes

  1. The interested reader will find a comprehensive mathematical description of the technique by Berkooz et al. (1993).

Abbreviations

\(\tilde{u_{\rm i}}\) :

Instantaneous velocity

U ∞ :

Free-stream velocity

U c :

Convection velocity

t :

Time

f :

Frequency

ν :

Kinematic viscosity

h :

Step-height

St h :

Strouhal number based on step height (\(St_{{{\rm h}}}=\frac{f{h}} {U_{\infty}}\))

Re h :

Reynolds number based on step height (\(Re_{{\rm h}}=\frac{U_{\infty}{h}} {\nu}\))

τ+ :

Non-dimensional time (\(\tau^+=\frac{tU_{\infty}} {h}\))

κ:

Turbulent kinetic energy: \(\kappa=\frac{1}{2}(\langle{uu}\rangle+\langle{vv}\rangle)\)

R ij :

Two-point correlation

n :

POD mode number

Φ:

POD eigenfunction

Λ:

POD eigenvalue

\({\bf x}\) :

Position vector

<>:

Ensemble averaging operation

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Acknowledgments

The authors would like to thank the United States Naval Air Warfare Center—Aircraft Division (NAWCAD) for supporting this research endeavor through a Phase 1 STTR with CRAFT Tech. (contract number N00014-07-M-0401), S. Arunajatesan from CRAFT Tech for technical interactions and performing numerical simulations on this model and P. Khambatta for helping with the arrangement of the PIV system’s optics.

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Authors and Affiliations

  1. Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, 1 University Station, C0600, Austin, TX, 78712, USA

    C. E. Tinney

  2. Department of Mechanical and Aerospace Engineering, Research and Engineering Education Facility, The University of Florida, 1350 N. Poquito Rd, Shalimar, FL, 32579, USA

    L. S. Ukeiley

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  1. C. E. Tinney
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  2. L. S. Ukeiley
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Correspondence to C. E. Tinney.

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Tinney, C.E., Ukeiley, L.S. A study of a 3-D double backward-facing step. Exp Fluids 47, 427–438 (2009). https://doi.org/10.1007/s00348-009-0675-9

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