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Near-wall response in turbulent shear flows subjected to imposed unsteadiness

Published online by Cambridge University Press:  26 April 2006

Reda R. Mankbadi  and
Joseph T. C. Liu
Reda R. Mankbadi
Affiliation:
NASA Lewis Research Center, Cleveland, Ohio 44135
Joseph T. C. Liu
Affiliation:
Division of Engineering, Brown University, Providence, Rhode Island 02912
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Abstract

Rapid-distortion theory is adapted to introduce a truly unsteady closure into a simple phenomenological turbulence model in order to describe the unsteady response of a turbulent wall layer exposed to a temporarily oscillating pressure gradient. The closure model is built by taking the ratio of turbulent shear stress to turbulent kinetic energy to be a function of the effective strain. The latter accounts for the history of the flow. The computed unsteady velocity fluctuations and modulated turbulent stresses compare favourably in the ‘non-quasi-steady’ frequency range, where quasi-steady assumptions would fail. This suggests that the concept of rapid distortion is especially appropriate for unsteady flows. This paper forms the basis for acoustical studies of the problem to be reported elsewhere.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 238 , May 1992 , pp. 55 - 71
Copyright
© 1992 Cambridge University Press

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References

Alper, A. & Liu, J. T. C. 1978 On the interactions between large-scale structure and fine-grained turbulence in a free shear flow. II. The development of the spatial interactions in the mean. Proc. R. Soc. Lond. A 359, 497–523.Google Scholar
Betchov, R. & Criminal, W. O. 1967 Stability of Parallel Flows. Academic.
Binder, G. & Kueny, J. L. 1981 Measurements of the periodic velocity oscillations near the wall in unsteady turbulent channel flow. In Unsteady Turbulent Shear Flows. IUTAM Symp. (ed. R. Michel, J. Cousteix & R. Houdeville), pp. 100–109. Springer.
Binder, G., Tardu, S., Blackwelder, R. F. & Kueny, J. L. 1985 Large amplitude periodic oscillations in the wall region of a turbulent channel flow. In 5th Symp. on Turbulent Shear Flows, pp. 16.1–16.8. Pennsylvania State University Press.
Bradshaw, P., Ferriss, D. H. & Atwell, N. P. 1967 Calculation of boundary layer development using the turbulent energy equation. J. Fluid Mech. 28, 593–616.Google Scholar
Carr, L. W. 1981 A review of unsteady boundary layer experiments. In Unsteady Turbulent Shear Flows, IUTAM Symp. (ed. R. Michel, J. Cousteix & R. Houdeville), pp. 3–35. Springer.
Cook, W. J., Murphy, J. D. & Owen, F. K. 1985 An experimental and computational study of turbulent boundary layers in oscillating flows. In 5th Symp. on Turbulent Shear Flows, pp. 18.3–18.18. Pennsylvania State University Press.
Cousteix, J. 1986 Three-dimensional and unsteady boundary-layer computations. Ann. Rev. Fluid Mech. 18, 173–196.Google Scholar
Cousteix, J., Houdeville, R. & Janvelle, J. 1981 Response of a turbulent boundary layer to a pulsation of the external flow with and without adverse pressure gradient. In Unsteady Turbulent Shear Flows. IUTAM Symp. (ed. R. Michel, J. Cousteix & R. Houdeville), pp. 120–144. Springer.
Derksen, R. W. & Azad, R. S. 1981 Behavior of the turbulent energy equation at a fixed boundary. AIAAA J. 19, 238–239.Google Scholar
El-Telbany, M. M. M. & Reynolds, A. J. 1981 Turbulence in plane channel flows. J. Fluid Mech. 111, 283–318.Google Scholar
Gibson, M. M. 1985 Boundary layers. In Turbulent Shear Flows 4, (ed. L. J. S. Bradbury et al.), pp. 219–222. Springer.
Hanjalic, K. & Stosic, N. 1983 Hysteresis of turbulent stresses in wall flows subjected to periodic disturbances. In Turbulent Shear Flows 4, (ed. L. J. S. Bradbury et al.), pp. 287–300. Springer.
Hunt, J. C. R. 1978 A review of the theory of rapidly distorted turbulent flows and its applications. Fluid Dyn. Trans. 9, 121–152.Google Scholar
Hunt, J. C. R. & Carruthers, D. J. 1990 Rapid distortion theory and the ‘problems’ of turbulence. J. Fluid Mech. 212, 497–532.Google Scholar
Hunt, J. C. R. & Maxey, M. R. 1978 Estimating velocities and shear stresses in turbulent flows of liquid metals driven by low frequency electromagnetic fields. In MHD-Flows and Turbulence II (ed. H. Branover), pp. 249–269. Israel University Press.
Karlsson, S. K. F. 1959 An unsteady turbulent boundary layer. J. Fluid Mech. 5, 622–636.Google Scholar
Kebede, W., Launder, B. E. & Younis, B. A. 1985 Large-amplitude periodic pipe flow: A second-moment closure study. In 5th Symp. on Turbulent Shear Flows 5, pp. 16.23–16.29. Pennsylvania State University Press.
Laufer, J. 1954 The structure of turbulence in fully developed pipe flow. NACA Rep. 1174.
Liu, J. T. C. 1988 Contributions to the understanding of large-scale coherent structures in developing free turbulent shear flows. Adv. Appl. Mech. 26, 183–309.Google Scholar
Liu, J. T. C. 1989 Coherent structures in transitional and turbulent free shear flows. Ann. Rev. Fluid Mech. 21, 285–315.Google Scholar
Mankbadi, R. R. 1992 Dynamics and control of coherent structures in turbulent jets. Appl. Mech. Rev. 45 (in press).Google Scholar
Mankbadi, R. R. & Mobark, A. 1991 Quasi-steady turbulence modeling of unsteady flows. J. Heat & Fluid Flow 12, 122–129.Google Scholar
Mao, Z-X. & Hanratty, T. J. 1986 Studies of the wall shear stress in a turbulent pulsating pipe flow. J. Fluid Mech. 170, 545–564.Google Scholar
Maxey, M. R. 1978 Aspects of unsteady turbulent shear flow. Ph.D. dissertation, University of Cambridge.
Maxey, M. R. 1982 Distortion of turbulence in flows with parallel streamlines. J. Fluid Mech. 124, 261–282.Google Scholar
Menendez, A. N. & Ramaprian, B. R. 1983 Study of unsteady turbulent boundary layers. Iowa Inst. Hydraul. Res. Rep. 270, (Avail. NTIS, AD-A138156.)Google Scholar
Mizushina, T., Maruyama, T. & Shiozaki, Y. 1973 Pulsating turbulent flow in a tube. J. Chem. Engng Japan 6, 287–294.Google Scholar
Parikh, P. G., Reynolds, W. C. & Jayaraman, R. 1982 Behavior of an unsteady turbulent boundary layer. AIAA J. 20, 769–775.Google Scholar
Patel, V. V., Rodi, W. & Scheuerer, G. 1985 Turbulence models for near-wall and low-Reynolds-number flows-A review. AIAA J. 23, 1308–1319.Google Scholar
Ramaprian, B. R. & Tu, S. W. 1983 Fully developed periodic turbulent pipe flow. Part 2. The detailed structure of the flow. J. Fluid Mech. 137, 59–81.Google Scholar
Ramaprian, B. R., Tu, S. W. & Menendez, A. N. 1983 Periodic turbulent shear flows. In Turbulent Shear Flows 4 (ed. L. J. S. Bradbury et al.), pp. 301–310. Springer.
Ronneberger, D. & Ahrens, C. D. 1977 Wall shear stress caused by small amplitude perturbations of turbulent boundary-layer flow: an experimental investigation. J. Fluid Mech. 83, 433–464.Google Scholar
Schubauer, G. B. 1954 Turbulent processes as observed in boundary layer and pipe. J. Appl. Phys. 25, 188–196.Google Scholar
Scott, M. R. & Watts, H. A. 1975 SUPORT - A computer code for two-point boundary value problems via orthonormalization. Sandia Labs., Rep. SAND-75–0198.
Shemer, L. & Kit, E. 1984 An experimental investigation of the quasi-steady turbulent pulsating flow in a pipe. Phys. Fluids 27, 72–76.Google Scholar
Shemer, L. & Wygnanski, I. 1981 Pulsating flow in a pipe. In Symp. on Turbulent Shear Flows 3, pp. 8.13–8.18. Pennsylvania State University Press.
Shemer, L., Wygnanski, I. & Kit, E. 1985 Pulsating flow in a pipe. J. Fluid Mech. 153, 313–337.Google Scholar
Tardu, S. F., Binder, G. & Blackwelder, R. F. 1992 Turbulent channel flow with large amplitude velocity oscillations. J. Fluid Mech. (submitted).
Townsend, A. A. 1970 Entrainment and the structure of turbulent flow. J. Fluid Mech. 41, 13–46.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn., pp. 80–88, 105–129. Cambridge University Press.
Townsend, A. A. 1980 The response of sheared turbulence to additional distortion. J. Fluid Mech. 98, 171–191.Google Scholar
Tu, S. W. & Ramaprian, B. R. 1983 Fully developed periodic turbulent pipe flow. Part 1. Main experimental results and comparison with predictions. J. Fluid Mech. 137, 31–58.Google Scholar