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Assessment of the organization of a turbulent separated and reattaching flow by measuring wall pressure fluctuations

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Abstract

The effect of local forcing on the organization of a turbulent separated and reattaching flow was assessed by measuring wall pressure fluctuations. Multi-arrayed microphones were installed on the surface to measure the simultaneous spatial and temporal wall pressure fluctuations. Local forcing at the separation edge was applied to the separated flow over a backward-facing step through a thin slit. The organization of the separated and reattaching flow was found to be greatest at the effective forcing frequency. The flow structure was diagnosed by analyzing several characteristics of the wall pressure fluctuations: the wall pressure fluctuation coefficients, wall pressure spectrum, wavenumber-frequency spectrum, coherence, cross-correlation, and multi-resolution autocorrelations of pressure fluctuations using the maximum overlap discrete wavelet transform and continuous wavelet transform. Features indicative of the amalgamation of vortices under the local forcing were observed; this amalgamation process accounted for the observed reduction of the reattachment length. Examination of the wall pressure fluctuations revealed that introduction of local forcing enhanced flapping motion as well as the streamwise and spanwise dispersions of vortical structures.

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Abbreviations

AR:

Aspect ratio

MODWT:

Maximum overlap discrete wavelet transform

CWT:

Continuous wavelet transform

\(C_{p\prime } \) :

Wall pressure fluctuation coefficient, p′/0.5ρU 2∞

H :

Step height of backward-facing step (mm)

Re H :

Reynolds number (U∞H/ν)

St :

The reduced frequency (fH/U∞)

St f :

Normalized forcing frequency by unsteady wake (f p H/U∞)

U ∞ :

Free-stream velocity (m/s)

f :

Frequency (Hz)

k x :

Streamwise wavenumber (1/m)

k z :

Spanwise wavenumber (1/m)

p′:

Instantaneous wall pressure (Pa)

p′rms:

Root-mean-square of wall pressure (Pa)

p ′ f :

Reconstructed multi-resolution pressure at central frequency f (Pa)

q :

Dynamic pressure, 0.5ρ U 2∞ (Pa)

u c :

Convection velocity (m/s)

v rms :

Root-mean-square of total velocity (m/s)

x R :

Time-mean reattachment length (mm)

x R0 :

Time-mean reattachment length at St f =0 (mm)

x 0 :

Streamwise position of reference point (mm)

z 0 :

Spanwise position of reference point (mm) (z0=0)

A 0 :

Forcing amplitude (Chun and Sung 1996)

a :

Timescale dilation parameter (s)

b :

Time transition parameter (s)

w (b, a):

Continuous wavelet transform coefficient (pa)

wc (a, τ):

Auto-correlation of continuous wavelet transform coefficients

ξ :

Streamwise separation interval from x0 (m)

ζ :

Spanwise separation interval from z0 (m)

γ p :

Forward-flow time fraction

δ :

Boundary layer thickness (mm)

δ * :

Displacement thickness (mm)

θ :

Momentum thickness (mm)

ρpp (τ; x0):

Auto-correlation of pressure at x0

ρpp (x0, τ, f):

Multi-resolution auto-correlation of pressure at x0 and f

τ :

Time delay (s)

ω :

Frequency (rad/s)

Φp (f; x0):

Autospectrum of pressure measured at x0 (Pa2 s)

Φpp (ζ, ω; x0):

Spanwise cross spectrum of pressure at x0 (Pa2 s)

Φpp (k x , ω; x0):

Streamwise wavenumber-frequency spectrum of pressure at x0 (Pa2 s)

Φpp (k z , ω; x0):

Spanwise wavenumber-frequency spectrum of pressure at x0 (Pa2 s)

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Authors and Affiliations

  1. School of Mechanical Engineering, Shanghai Jiao Tong University, 1954, Huashan Road, Shanghai, 200030, China

    Ying Zheng Liu

  2. Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 373-1, Guseong-dong Yuseong-gu, Daejeon, 305-701, Korea

    Ying Zheng Liu, Woong Kang & Hyung Jin Sung

Authors
  1. Ying Zheng Liu
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  2. Woong Kang
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  3. Hyung Jin Sung
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Correspondence to Hyung Jin Sung.

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Liu, Y.Z., Kang, W. & Sung, H.J. Assessment of the organization of a turbulent separated and reattaching flow by measuring wall pressure fluctuations. Exp Fluids 38, 485–493 (2005). https://doi.org/10.1007/s00348-005-0929-0

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  • DOI: https://doi.org/10.1007/s00348-005-0929-0

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