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Surface pressure fluctuations in a separating turbulent boundary layer

Published online by Cambridge University Press:  21 April 2006

Roger L. Simpson ,
M. Ghodbane  and
B. E. Mcgrath
Roger L. Simpson
Affiliation:
Southern Methodist University, Dallas, TX 75275, USA Present address: Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA.
M. Ghodbane
Affiliation:
Southern Methodist University, Dallas, TX 75275, USA
B. E. Mcgrath
Affiliation:
Southern Methodist University, Dallas, TX 75275, USA Present address: Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA.
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Abstract

Measurements of surface pressure-fluctuation spectra and wave speeds are reported for a well-documented separating turbulent boundary layer. Two sensitive instrumentation microphones were used in a new technique to measure pressure fluctuations through pinhole apertures in the flow surface. Because a portion of the acoustic pressure fluctuations is the same across the nominally two-dimensional turbulent flow, it is possible to decompose the two microphone signals and obtain the turbulent flow contributions to the surface pressure spectra. In addition, data from several earlier attached-flow surface-pressure-fluctuation studies are re-examined and compared with the present measurements.

The r.m.s. of the surface pressure fluctuation p′ increases monotonically through the adverse-pressure-gradient attached-flow region and the detached-flow zone. Apparently p′ is proportional to the ratio α of streamwise lengthscale to lengthscales in other directions. For non-equilibrium separating turbulent boundary layers, α is as much as 2.5, causing p′ to be higher than equilibrium layers with lower values of α.

The maximum turbulent shearing stress τM appears to be the proper stress on which to scale p′; p′/τM from available data shows much less variation than when p′ is scaled on the wall shear stress. In the present measurements p′/τM increases to the detachment location and decreases downstream. This decrease is apparently due to the rapid movement of the pressure-fluctuation-producing motions away from the wall after the beginning of intermittent backflow. A correlation of the detached-flow data is given that is derived from velocity- and lengthscales of the separated flow.

Spectra Φ (ω) for ωδ*/U∞ > 0.001 are presented and correlate well when normalized on the maximum shearing stress τM. At lower frequencies, for the attached flow Φ (ω) ∼ ω−0.7 while Φ(ω) ∼ (ω)−3 at higher frequencies in the strong adverse-pressuregradient region. After the beginning of intermittent backflow, Φ(ω) varies with ω at low frequencies and ω−3 at high frequencies; farther downstream the lower-frequency range varies with ω1.4.

The celerity of the surface pressure fluctuations for the attached flow increases with frequency to a maximum; at higher frequencies it decreases and agrees with the semi-logarithmic overlap equation of Panton & Linebarger. After the beginning of the separation process, the wave speed decreases because of the oscillation of the instantaneous wave speed direction. The streamwise coherence decreases drastically after the beginning of flow reversal.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 177 , April 1987 , pp. 167 - 186
Copyright
© 1987 Cambridge University Press

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References

Bendat, J. S. & Piersol, A. G. 1971 Random Data: Analysis and Measurement Procedures. Wiley-Interscience.
Blake, W. K. 1970 J. Fluid Mech. 44, 637–660.
Bradshaw, P. 1967 J. Fluid Mech. 30, 241–258.
Brooks, T. F. & Hodgson, T. H. 1981 J. Sound Vib. 78, 69–117.
Brooks, T. F. & Schlinker, R. H. 1983 Vertica 7, 287–307.
Bull, M. K. 1967 J. Fluid Mech. 28, 719–754.
Bull, M. K. & Thomas, A. S. W. 1976 Phys. Fluids 19, 597–599.
Burton, T. E. 1973 Acoustics and Vibration Lab. MIT. Rep. 70208–9.
Chehroudi, B. & Simpson, R. L. 1985 J. Fluid Mech. 160, 77–92.
Coles, D. E. & Hirst, E. (eds) 1969 Computation of Turbulent Boundary Layers – 1968 AFOSR-IFP-Stanford Conference, Stanford University, Department of Mechanical Engineering.
Corcos, G. M. 1963 J. Acoust. Soc. Am. 35, 192–199.
East, L. F. & Sawyer, W. G. AGARD CP-271, paper 6.
Hahn, M. 1976 AIAA paper 76–335.
Kiya, A., Sasaki, K. & Arie, M. 1982 J. Fluid Mech. 120, 219–244.
Lim, K. G. 1971 Ph.d. thesis, Department of Mechanical Engineering, University of Adelaide.
Mabey, D. G. 1972 J. Aircraft 9, 642–645.
Mabey, D. G. 1982 AIAA J. 20, 1632.
Mcgrath, B. E. & Simpson, R. L. 1985 NASA CR Rep. (in press); M.S. thesis, Dept. Aero. and Ocean Engrg., Virginia Polytechnic Institute and State University.
Panton, R. L. & Linebarger, H. G. 1974 J. Fluid Mech. 65, 261–287.
Perry, A. E. & Schofield, W. H. 1973 Phys. Fluids 16, 2068–2074.
Schloemer, H. H. 1967 J. Acoust. Soc. Am. 42, 93–113.
Schubauer, G. B. & Klebanoff, P. S. 1951 NACA Rep. 1030.
Simpson, R. L. 1976 Max-Planck-Institut für Strömungsforschung Bericht 118.
Simpson, R. L. 1981 Trans. ASME I: J. Fluids Engng 103, 520–533
Simpson, R. L. 1985 AGARDograph 287, vol. 1, p. 21.
Simpson, R. L., Chew, Y.-T. & Shivaprasad, B. G. 1980 Project SQUID Rep. SMU-4-PU; NTIS AD-A095 252/3.
Simpson, R. L., Ghodbane, M. & McGrath, B. E. 1984 An experimental study of surface pressure fluctuations in a separating turbulent boundary layer. NASA CR Rep. (in press).Google Scholar
Simpson, R. L., Shivaprasad, B. G. & Chew, Y.-T. 1981 J. Fluid Mech. 113, 23–74.
Simpson, R. L., Strickland, J. H. & Barr, P. W. 1977 J. Fluid Mech. 79, 553–594.
Strickland, J. H. & Simpson, R. L. 1973 Thermal and Fluid Sciences Center Rep. WT-2, also AD-771170/8GA. Southern Methodist University.
Willmarth, W. W. 1975 Ann. Rev. Fluid Mech. 7, 13–38.
Wills, J. A. B. 1970 J. Fluid Mech. 45, 65–90.