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An investigation of transition to turbulence in bounded oscillatory Stokes flows Part 1. Experiments

Published online by Cambridge University Press:  26 April 2006

R. Akhavan ,
R. D. Kamm  and
A. H. Shapiro
R. Akhavan
Affiliation:
Department of Mechanical Engineering, The University of Michigan, Ann Arbor, MI 48109-2125, USA Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
R. D. Kamm
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
A. H. Shapiro
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

Experimental results on flow-field statistics are presented for turbulent oscillatory flow in a circular pipe for the range of Reynolds numbers Reδ = U0δ/ν (U0 = amplitude of cross-sectional mean velocity, δ = (2ν/ω)½) = Stokes layer thickness) from 550 to 2000 and Stokes parameters Λ = R/δ (R = radius of the pipe) from 5 to 10. Axial and radial velocity components were measured simultaneously using a two-colour laser-Doppler anemometer, providing information on ensemble-averaged velocity profiles as well as various turbulence statistics for different phases during the cycle. In all flows studied, turbulence appeared explosively towards the end of the acceleration phase of the cycle and was sustained throughout the deceleration phase. During the turbulent portion of the cycle, production of turbulence was restricted to the wall region of the pipe and was the result of turbulent bursts. The statistics of the resulting turbulent flow showed a great deal of similarity to results for steady turbulent pipe flows; in particular the three-layer description of the flow consisting of a viscous sublayer, a logarithmic layer (with von Kármán constant = 0.4) and an outer wake could be identified at each phase if the corresponding ensemble-averaged wall-friction velocities were used for normalization. Consideration of similarity laws for these flows reveals that the existence of a logarithmic layer is a dimensional necessity whenever at least two of the scales R, u*/ω and ν/u* are widely separated; with the exact structure of the flow being dependent upon the parameters u*/Rω and u2*/ων. During the initial part of the acceleration phase, production of turbulence as well as turbulent Reynolds stresses were reduced to very low levels and the velocity profiles were in agreement with laminar theory. Nevertheless, the fluctuations retained a small but finite energy. In Part 2 of this paper, the major features observed in these experiments are used as a guideline, in conjunction with direct numerical simulations of the ‘perturbed’ Navier–Stokes equations for oscillatory flow in a channel, to identify the nature of the instability that is most likely to be responsible for transition in this class of flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 225 , April 1991 , pp. 395 - 422
Copyright
© 1991 Cambridge University Press

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References

Akhavan, R., Kamm, R. D. & Shapiro, A. H., 1991 An investigation of transition to turbulence in bounded oscillatory Stokes flows. Part 2. Numerical simulation. J. Fluid Mech. 225, 423–444.Google Scholar
Collins, J. I.: 1963 Inception of turbulence at the bed under periodic gravity waves. J. Geophys. Res. 18, 6007–6014.Google Scholar
Cowley, S. J.: 1987 High frequency Rayleigh instability of Stokes layers. In Stability of Time Dependent and Spatially Varying Flows (ed. D. L. Dwoyer & M. Y. Hussaini), pp. 261–275. Springer.
Hall, P.: 1978 The linear stability of flat Stokes layers. Proc. R. Soc. Lond. A 359, 151–166.Google Scholar
Hayashi, T. & Ohashi, M., 1981 A dynamical and visual study of the oscillatory turbulent boundary layer. In Turbulent Shear Flows 3, pp. 18–33. Springer.
Hino, M., Kashiwayanagi, M., Nakayama, A. & Hara, T., 1983 Experiments on the turbulence statistics and the structure of a reciprocating oscillatory flow. J. Fluid Mech. 131, 363–400.Google Scholar
Hino, M., Sawamoto, M. & Takasu, S., 1976 Experiments on transition to turbulence in an oscillating pipe flow. J. Fluid Mech. 75, 193–207.Google Scholar
Von Kerczek, C. & Davis, S. H. 1974 Linear stability theory of oscillatory Stokes layers. J. Fluid Mech. 62, 753–773.Google Scholar
Laufer, J.: 1954 The structure of turbulence in fully developed pipe flow. Natl Advisory Comm. Aeronaut. Tech. Rept. 1174.Google Scholar
Li, H.: 1954 Stability of oscillatory laminar flow along a wall. Beach Erosion Board, US Army Corps Engrs Tech. Memo 47.Google Scholar
Marchand, P. & Marmet, L., 1983 Binomial smoothing filter: a way to avoid some pitfalls of least-squares polynomial smoothing. Rev. Sci. Instrum. 54, 1034.Google Scholar
Merkli, P. & Thomann, H., 1975 Transition to turbulence in oscillating pipe flow. J. Fluid Mech. 68, 567–575.Google Scholar
Mizushina, T., Maruyama, T. & Hirasawa, H., 1975 Structure of the turbulence in pulsating pipe flow. J. Chem. Engng Japan 8, 210–216.Google Scholar
Mizushina, T., Maruyama, T. & Shiozaki, Y., 1973 Pulsating turbulent flow in a tube. J. Chem. Engng Japan 6, 487–494.Google Scholar
Monkewitz, P. A. & Bunster, A., 1987 The stability of the Stokes layer: visual observations and some theoretical considerations. In Stability of Time Dependent and Spatially Varying Flows (ed. D. L. Dwoyer & M. Y. Hussain), pp. 244–260. Springer.
Obremski, H. J. & Morkovin, M. V., 1969 Application of a quasi-steady stability model to a periodic boundary layer flow. AIAA J. 7, 1298–1301.Google Scholar
Ohmi, M., Iguchi, M., Kakehachi, K. & Masuda, T., 1982 Transition to turbulence and velocity distribution in an oscillating pipe flow. Bull. JSME 25, 365–371.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
Sergeev, S. I.: 1966 Fluid oscillations in pipes at moderate Reynolds numbers. Fluid Dyn. 1, 121–122.Google Scholar
Tardu, S., Binder, G. & Blackwelder, R., 1987 Response of turbulence to large amplitude oscillations in channel flow. In Advances in Turbulence (ed. G. Comte-Bellot & J. Mathieu), pp. 564–555. Springer.
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
Uchida, S.: 1956 The pulsating viscous flow superposed on the steady laminar motion of incompressible fluids in a circular pipe. Z. Angew. Math. Phys. 7, 403–422.Google Scholar
Womersley, J. R.: 1955 Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J. Physiol. 127, 553–563.Google Scholar