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The turbulent near wake of a flat plate at low Reynolds number

Published online by Cambridge University Press:  26 April 2006

A. Nakayama  and
B. Liu
A. Nakayama
Affiliation:
Flight Performance, Douglas Aircraft Company, Long Beach, CA 90846. USA
B. Liu
Affiliation:
Department of Aerospace Engineering, California State University, Long Beach, CA 90840, USA
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Abstract

Mean-velocity and turbulence measurements have been made in the turbulent near wake of a flat plate at various Reynolds numbers in order to investigate the low-Reynolds-number effects in this region. The results indicate that the low-Reynolds-number effects are significant enough to partially explain the discrepancies in the existing mean-velocity data. It has been found that, while the Reynolds-number-independent, inner-law similarity of the boundary layers continues to exist, the width of the inner wake that develops within the inner-law region scales with the outer variable. Therefore, the mean velocity near the wake centreline depends on the Reynolds number. It is conjectured that this is due to the influence of the large eddies of the outer layer on the spreading of the inner wake.

Measured turbulence quantities indicate that sudden changes occurring just downstream of the trailing edge are independent of the Reynolds number, but the subsequent development of the turbulent stress profiles depends on the Reynolds number. The Reynolds shear stress and the mean-velocity profiles within the inner wake show approximate similarity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 217 , August 1990 , pp. 93 - 114
Copyright
© 1990 Cambridge University Press

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References

Akdag, V. 1983 An experimental investigation of a wake merging into a boundary layer in constant pressure. MS thesis, Dept of Mech. Engng, California State University, Long Beach.
Akdag, V., Nakayama, A., Liu, B., Kilik, E. & Unt, H. 1984 Automated hot-wire measurements using a micro computer. Rep. ME84–5, Dept of Mech. Engng, California State University, Long Beach.
Alber, I. E. 1980 Turbulent wake of a thin flat plate. AIAA J. 18, 1044–1051.Google Scholar
Andreopoulos, J. 1978 Symmetric and asymmetric near wake of a flat plate. PhD thesis, Imperial College of Science and Technology, London.
Andreopoulos, J. & Bradshaw, P. 1980 Measurements of interacting turbulent shear layers in the near wake of a flat plate. J. Fluid Mech. 100, 639–668.Google Scholar
Andreopoulos, J., Durst, F. & Jovanovic, J. 1983 On the structure of turbulent boundary layers at different Reynolds numbers. In Fourth Symposium on Turbulent Shear Flows, University of Karlsruhe, Karlsruhe, FRG, pp. 2.1–2.7.
Badri Narayanan, M. A., Raghu, S. & Tulapurkara, E. G. 1985 The nonequilibrium region of a mixing layer. AIAA J. 23, 987–991.Google Scholar
Bogucz, E. A. 1984 Analysis of the turbulent near wake at a sharp trailing edge. PhD dissertation, Lehigh University, Bethlehem, PA.
Bogucz, E. A. & Walker, J. D. A. 1987 Analysis and prediction of the turbulent near wake at a sharp trailing edge. AIAA paper 87–0483.Google Scholar
Bradshaw, P. 1967 ‘Inactive’ motion and pressure fluctuations in turbulent boundary layers. J. Fluid Mech. 30, 241–258.Google Scholar
Bradshaw, P. 1970 Prediction of the turbulent near-wake of a symmetrical aerofoil. AIAA J. 8, 1507–1512.Google Scholar
Brederode, V. A. S. L. de & Bradshaw, P. 1974 A note on the empirical constants appearing in the logarithmic law for turbulent wall flows. I.C. Aero Rep. 4–03, Imperial College of Science and Technology. London.
Cebeci, T. 1973 Kinematic eddy viscosity at low Reynolds numbers. AIAA J. 11, 102–104.Google Scholar
Cebeci, T., Thiele, F., Williams, P. G. & Stewartson, K. 1979 On the calculation of symmetric wakes, I. Two-dimensional flows. Numer. Heat Trans. 2, 35–60.Google Scholar
Chang, K. C., Bui, M. N., Cebeci, T. & Whitelaw, J. H. 1986 The calculation of turbulent wakes. AIAA J. 24, 200–201.Google Scholar
Chevray, R. & Kovasznay, L. S. G. 1969 Turbulence measurements in the wake of a thin flat plate. AIAA J. 7, 1641–1643.Google Scholar
Coles, D. E. 1962 The turbulent boundary layer in a compressible fluid. RAND Corp. Rep. R-403-PR.Google Scholar
Erm, L. P., Smits, A. J. & Joubert, P. N. 1985 Low Reynolds number turbulent boundary layers on a smooth flat surface in a zero pressure gradient. Fifth Symposium on Turbulent Shear Flows, Cornell University, Ithaca, NY, pp. 2.13–2.18.
Haji-Haidari, A. & Smith, C. R. 1988 Development of the turbulent near wake of a tapered thick flat plate. J. Fluid Mech. 189, 135–163.Google Scholar
Jovic, S. & Ramaprian, B. P. 1986 Large-scale structure of the turbulent wake behind a flat plate. IIHR Rep. no. 298, The University of Iowa, Iowa City.
Maekawa, H. & Nozaki, T. 1986 Visualized large-scale motions in the turbulent wake behind a symmetrical airfoil. Proc. 3rd Asian Congress of Fluid Mech., 1–5 Sept. 1986, Tokyo, Japan, pp. 690–693.
Murlis, J., Tsai, H. M. & Bradshaw, P. 1982 The structure of turbulent boundary layers at low Reynolds numbers. J. Fluid Mech. 122, 13–56.Google Scholar
Nakayama, A. 1984 Measurements of attached and separated turbulent flows in the trailing-edge regions of airfoils. In Numerical and Physical Aspects of Aerodynamic Flows, II (ed. T. Cebeci), pp. 233–255. Springer.
Nakayama, A. & Liu, B. 1988 Low-Reynolds number effects in the near wake of a flat plate. California State University, Long Beach, Mech. Engng Dept Rep. CAR-88–1.
Nakayama, A. & Westphal, R. V. 1986 The effects of sensor length and spacing on x-wire measurements in a boundary layer. NASA TM88352.
Patel, V. C. & Chen, H. C. 1989 Turbulent wake of a flat plate. Submitted to AIAA J.Google Scholar
Patel, V. C., Rodi, W. & Scheuerer, G. 1985 Turbulence models for near-wall and low Reynolds number flows: A review. AIAA J. 23, 1308–1319.Google Scholar
Pot, P. J. 1979 Measurements in a 2-D wake and in a 2-D wake merging into a boundary layer. Data Report, NLR TR-7900638, The Netherlands.
Purtell, L. P., Klebanoff, P. S. & Buckley, F. T. 1981 Characteristics of turbulence in a boundary layer with zero pressure gradient. Phys. Fluids 24, 802–811.Google Scholar
Ramaprian, B. R., Patel, V. C. & Sastry, M. S. 1982 The symmetric turbulent wake of a flat plate. AIAA J. 20, 1228–1235.Google Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to R 0 = 1410. J. Fluid Mech. 187, 61–98.Google Scholar
Townsend, A. A. 1961 Equilibrium layers and wall turbulence. J. Fluid Mech. 11, 97–120.Google Scholar
White, B. R. 1981 Low-Reynolds-number turbulent boundary layers. Trans. ASME I: J. Fluids Engng 103, 624–630.Google Scholar