Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-22T07:01:21.633Z Has data issue: false hasContentIssue false
  • English
  • Français

The structure of a separating turbulent boundary layer. Part 4. Effects of periodic free-stream unsteadiness

Published online by Cambridge University Press:  20 April 2006

Roger L. Simpson ,
B. G. Shivaprasad  and
Y.-T. Chew
Roger L. Simpson
Affiliation:
Department of Civil and Mechanical Engineering, Southern Methodist University, Dallas, Texas 75275
B. G. Shivaprasad
Affiliation:
Department of Civil and Mechanical Engineering, Southern Methodist University, Dallas, Texas 75275
Y.-T. Chew
Affiliation:
Department of Civil and Mechanical Engineering, Southern Methodist University, Dallas, Texas 75275 Present address: Department of Mechanical and Production Engineering, University of Singapore.
Get access Rights & Permissions [Opens in a new window]

Abstract

Unsteady separating turbulent boundary layers are of practical interest because of unsteady aerodynamic phenomena associated with blades in compressors and with helicopter rotors in translating motion during high-loading conditions. Extensive measurements of a steady free-stream, nominally two-dimensional, separating turbulent boundary layer have been reported by Simpson, Chew & Shivaprasad (1981a, b) and Shiloh, Shivaprasad & Simpson (1981). Here measurements are reported that show the effects of sinusoidal unsteadiness of the free-stream velocity on this separating turbulent boundary layer at a practical reduced frequency of 0·61. The ratio of oscillation amplitude to mean velocity is about 0·3.

Upstream of flow detachment, single- and cross-wire, hot-wire anemometer measurements were obtained. A surface hot-wire anemometer was used to measure the phase-averaged skin friction. Measurements in the detached-flow zone of phase-averaged velocities and turbulence quantities were obtained with a directionally sensitive laser anemometer. The fraction of time that the flow moves downstream was measured by the LDV and by a thermal flow-direction probe.

Upstream of any flow reversal or backflow, the flow behaves in a quasisteady manner, i.e. the phase-averaged flow is described by the steady free-stream flow structure. The semilogarithmic law-of-the-wall velocity profile applies at each phase of the cycle. The Perry & Schofield (1973) velocity-profile correlations fit the mean and ensemble-averaged velocity profiles near detachment.

After the beginning of detachment, large amplitude and phase variations develop through the flow. Unsteady effects produce hysteresis in relationships between flow parameters. As the free-stream velocity during a cycle begins to increase, the Reynolds shearing stresses increase, the detached shear layer decreases in thickness, and the fraction of time $\hat{\gamma}_{{\rm p}u}$ that the flow moves downstream increases as backflow fluid is washed downstream. As the free-stream velocity nears the maximum value in a cycle, the increasingly adverse pressure gradient causes progressively greater near-wall backflow at downstream locations, while $\hat{\gamma}_{{\rm p}u}$ remains high at the upstream part of the detached flow. After the free-stream velocity begins to decelerate, the detached shear layer grows in thickness and the location where flow reversal begins moves upstream. This cycle is repeated as the free-stream velocity again increases.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 127 , February 1983 , pp. 219 - 261
Copyright
© 1983 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Acharya, M. & Reynolds, W. C. 1975 Thermosciences Div., Dept Mech. Engng, Stanford Univ. Rep. TF-8.
Ashjaee, J. & Johnston, J. P. 1980 Trans. A.S.M.E. I: J. Fluids Engng 102, 275–282.
Bradshaw, P. 1978 AGARD LS-94, Paper 10.
Collins, M. A. & Simpson, R. L. 1978 A.I.A.A. J. 16, 291–292.
Cousteix, J., Desopper, A. & Houdeville, R. 1977 In Proc. Symp on Turbulent Shear Flow, Pa. State Univ., 18–20 April, paper 8-B.
Cousteix, J., Houdeville, R. & Raynaud, M. 1979 In Proc. 2nd Symp on Turbulent Shear Flow, Imperial College, London, 2–4 July, pp. 6.12–6.17.
Davis, R. E. 1974 J. Fluid Mech. 63, 673–693.
Eaton, J. K., Jeans, A. H., Ashjaee, J. & Johnston, J. P. 1979 Trans A.S.M.E. I: J. Fluids Engng 101, 364–366.
Hebbar, K. S. 1980 DISA Info. no. 25, pp. 15–16.
Houdeville, R., Desopper, A. & Cousteix, J. 1976 In La Recherche Aérospatiale 1976, pp. 183–191.
Kenison, R. C. 1977 AGARD CP-227, Paper 20.
Kline, S. J., Bardina, J. G. & Strawn, R. C. 1981 AIAA-81–1220.
Kline, S. J. & McCLINTOCK, F. A. 1953 Mech. Engng 75, 3–8.
Miller, J. A. 1976 Trans. A.S.M.E. I: J. Fluids Engng 98, 550–557.
Oka, S. & Kostić, Z. 1972 DISA Info. no. 13, pp. 29–33.
Patel, M. H. 1977 Proc. R. Soc. Lond A 353, 121–144.
Perry, A. E. & Schofield, W. H. 1973 Phys. Fluids 16, 2068–2074.
Phillips, O. M. 1955 Proc. Camb. Phil. Soc. 51, 220–229.
Rubesin, M. W., Okuno, A. F., Mateer, G. G. & Brosh, A. 1975 NASA Tech. Memo. X-62, 465.
Schofield, W. H. 1980 Australian Defence Sci. & Tech. Org. Aero. Res. Lab. Mech. Engng Rep. 157 (AR-002–218).
Shiloh, K., Shivaprasad, B. G. & Simpson, R. L. 1981 J. Fluid Mech. 113, 75–90.
Shivaprasad, B. G. & Simpson, R. L. 1982 Trans A.S.M.E. I: J. Fluids Engng 104, 162–166.
Simpson, R. L. 1976 A.I.A.A. J. 14, 124–126.
Simpson, R. L. 1977 AGARD CP-227, Paper 19.
Simpson, R. L. 1981 Trans. A.S.M.E. I: J. Fluids Engng 103, 520–533.
Simpson, R. L. & Barr, P. W. 1975 Rev. Sci. Instrum. 46, 835–837.
Simpson, R. L. & Chew, Y.-T. 1979 In Proc. 3rd Int. Workshop on Laser Velocimetry, pp. 179–196. Hemisphere.
Simpson, R. L., Chew, Y.-T. & Shivaprasad, B. G. 1980a Project SQUID Rep. SMU-4-PU, NTIS AD-A095 252/3.
Simpson, R. L., Chew, Y.-T. & Shivaprasad, B. G. 1980b Dept Civ./Mech. Engng Rep. WT-6, Southern Methodist Univ., NTIS AD-A090 585/1.
Simpson, R. L., Chew, Y.-T. & Shivaprasad, B. G. 1981a J. Fluid Mech. 113, 23–51.
Simpson, R. L., Chew, Y.-T. & Shivaprasad, B. G. 1981b J. Fluid Mech. 113, 53–73.
Simpson, R. L., Heizer, K. W. & Nasburg, R. E. 1979 Trans. A.S.M.E. I: J. Fluids Engng 101, 381–382.
Simpson, R. L., Sallas, J. J. & Nasburg, R. E. 1978 Trans. A.S.M.E. I: J. Fluids Engng 100, 287–290.
Simpson, R. L., Strickland, J. H. & Barr, P. W. 1977 J. Fluid Mech. 79, 553–594.
Wood, N. B. 1975 J. Fluid Mech. 67, 769–786.