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An experimental investigation of the turbulent structure in a two-dimensional momentumless wake

Published online by Cambridge University Press:  26 April 2006

J. M. Cimbala  and
W. J. Park
J. M. Cimbala
Affiliation:
Department of Mechanical Engineering, The Pennsylvania State University, University Park, PA 16802, USA
W. J. Park
Affiliation:
Department of Mechanical Engineering, The Pennsylvania State University, University Park, PA 16802, USA
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Abstract

Mean velocity profiles have been measured in the wake of a two-dimensional airfoil with and without mass injection through a slit along its rear end. In particular, four cases have been documented: (a) a pure wake (no injection), (b) a weak wake (some injection), (c) a momentumless wake (injection adjusted to provide a thrust which exactly cancels the model's drag), and (d) a weak jet (more injection than necessary to cancel the drag). These mean velocity profiles clearly show the difference in momentum deficit for the four cases. When non-dimensionalized, the velocity profiles are self-similar.

Smoke-wire flow visualizations are also presented for both the near wake (0 < x/d < 30) and the far wake (45 < x/d < 75). The characteristic geometry of large-scale turbulent vortical structures is easily identifiable for the wake and jet cases, while the structures for the momentumless state are neither wake-like nor jet-like. Beyond about 45 diameters downstream, turbulent structures for the momentumless case become quite weak and can barely be observed.

For the momentumless wake at Re = 5400, the axial, lateral, and transverse turbulence intensities as well as the Reynolds stress were measured. Similarity of the axial and the transverse turbulence intensities was observed; the overall shape of those profiles is Gaussian except for the very near-wake region. The mean centreline velocity difference decays much faster (x−0.92) than the axial turbulent intensity (x−0.81). Consequently, the mean shear practically disappears far downstream; the flow becomes nearly isotropic beyond about 45 body diameters from the model. This turbulence behaviour is quite different from that of plane wakes or jets but rather closer to the case of grid turbulence.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 213 , April 1990 , pp. 479 - 509
Copyright
© 1990 Cambridge University Press

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References

Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence, pp. 132–138. Cambridge University Press.
Bearman, P. W. 1966 Investigation into the effect of base bleed on the flow behind a two-dimensional model with a blunt trailing edge. AGARD Conf. Proc. No. 4, pp. 479–507Google Scholar
Birkhoff, G. & Zarantonello, E. H. 1957 Jets, Wakes, and Cavities. Academic. 1957.
Bradbury, L. J. S. 1965 The Structure of a self-preserving turbulent plane jet. J. Fluid Mech. 23, 31–64.Google Scholar
Carmody, T. 1964 Establishment of the wake behind a disk. Trans. ASME D: J. Basic, Eng, 86, 869–880.Google Scholar
Chevray, R. & Kovasznay, L. S. J. 1969 Turbulence measurements in the wake of a thin flat plate. AIAA J. 7, 1641–1643.Google Scholar
Chieng, C. C., Jakubowski, A. K. & Schetz, J. A. 1974 Investigation of the turbulent properties of the wake behind self-propelled, axisymmetric bodies. VPI-Aero-025, Sept. 1974.Google Scholar
Cimbala, J. M. 1984 Large structure in the far wakes of two-dimensional bluff bodies. Ph.D. thesis, California Inst. of Technology.
Cimbala, J. M., Nagib, H. M. & Roshko, A. 1988 Large structure in the far wakes of two-dimensional bluff bodies. J. Fluid Mech. 190, 265–298.Google Scholar
Cimbala, J. M. & Park, W. J. 1989a Elimination of temperature stratification in a low-speed open-return wind tunnel. AIAA J. 27, 823–825.Google Scholar
Cimbala, J. M. & Park, W. J. 1989b A direct hot-wire calibration technique to account for ambient temperature drift in incompressible flow. Exp. Fluids (to appear).Google Scholar
Donaldson, C. Du P. 1972 Calculation of turbulent shear flows for atmospheric and vortex motions. AIAA J. 10, 4–12.Google Scholar
Finson, M. L. 1975 Similarity behavior of momentumless turbulent wakes. J. Fluid Mech. 71, 465–479.Google Scholar
Gilreath, H. E. & Brandt, A. 1983 Experiments on the generation of internal waves in a stratified fluid. AIAA Paper 83–1704.Google Scholar
Ginevskii, A. S., Pochkina, K. A. & Ukhanova, L. N. 1966 Propagation of turbulent jet flow with zero excess impulse. Izv. Akad. Nauk. SSSR Mekh. Zhid. i Gaza 1, 164–166 (in Fluid Dyn. 1967, pp. 106–107, Faraday Press).Google Scholar
Ginevskii, A. S., Ukhanova, L. N. & Pochkina, K. A. 1972 Turbulent co-flows with zero excess momentum. Fluid Mech. Soviet Res. 1, 81–86.Google Scholar
Gran, R. L. 1973 An experiment on the wake of a slender propeller-driven body. Rep. 20086–6006-RU-00, June 1973. TRW Systems.Google Scholar
Grant, H. L. 1958 The large eddies of turbulent motion. J. Fluid Mech. 4, 149–198.Google Scholar
Hanjalic, K. & Launder, B. E. 1972 A Reynolds stress model of turbulence and its application to thin shear flows. J. Fluid Mech. 52, 609–638.Google Scholar
Hassid, S. 1980 Similarity and decay law of momentumless wakes. Phy. Fluids 23, 404–405.Google Scholar
Higuchi, H. 1977 Experimental investigation on axisymmetric turbulent wakes with zero momentum defect, Ph.D. thesis, California Inst. of Technology.
Ko, D. R. S. 1973 A phenomenological model for the momentumless turbulent wake in a stratified medium. Rep. 20086–6007-RU-00, Apr. 1973. TRW Systems.
Korobko, V. I. & Shashmin, V. K. 1985 Dynamics and heat transfer of a turbulent and laminar momentumless wake. Heat Transfer Soviet Res. 17, 96–103.Google Scholar
Kubota, T. 1975 Turbulent wake behind a self-propelled body, Rep. GALCIT-138, California Inst. of Tech.
Lewellen, W. S., Teske, M. & Donaldson, C. du P. 1973 Application of turbulence model equations to axisymmetric wakes. AIAA Paper 73–648.Google Scholar
Lewellen, W. S., Teske, M. & Donaldson, C. du P. 1974 Turbulent wakes in a stratified fluid, Aero Res. Associates of Princeton, Rep. 226, Aug. 1974.
Loehrke, R. I. & Nagib, H. M. 1972 Experiments on management of freestream turbulence. AGARD-R-598.Google Scholar
Metcalfe, R. W. & Riley, J. J. 1981 Direct numerical simulations of turbulent shear flows In Proc. 7th Intl Conf on Numerical Methods in Fluid Dynamics, pp. 279–284.
Mobbs, F. R. 1968 Spreading and contraction at the boundaries of free turbulent flows. J. Fluid Mech. 33, 227–239.Google Scholar
Naudascher, E. 1965 Flow in the wake of self-propelled bodies and related sources of turbulence. J. Fluid Mech. 22, 625–656.Google Scholar
Orszag, S. A. & Pao, Y. H. 1973 Numerical computation of turbulent shear flows. Flow Research Rep. 19, July 1973. Flow Research Inc.Google Scholar
Park, W. J. 1989 An experimental investigation of the turbulent structure in two-dimensional momentumless wakes. Ph.D. thesis. The Pennsylvania State University.
Ridjanovic, M. 1963 Wake with zero change of momentum flux. Ph.D. thesis, State University of Iowa.
Roshko, A. 1954 On the development of turbulent wakes from vortex streets. NACA Rep. 1191.Google Scholar
Roshko, A. 1976 Structure of turbulent shear flows: a new look. AIAA J. 14, 1349–1357.Google Scholar
Rotta, J. 1951 Statistische Theorie Nichthomogener Turbulenz. Z. Phys. 129, 547.Google Scholar
Schetz, J. A. 1980 Injection and mixing in turbulent flow. Prog. Astronaut. Aeronaut. 68, 97–109.Google Scholar
Schetz, J. A. & Jakubowski, A. K. 1975 Experimental studies of the turbulent wake behind self-propelled slender bodies. AIAA J. 13, 1568–1575; also AIAA Paper 75–117, 1975.Google Scholar
Schetz, J. A. & Stanley, F. 1972 Analysis of free turbulent mixing flows without a net momentum defect. AIAA J. 10, 1524–1526.Google Scholar
Shashmin, V. K. 1983 Hydrodynamics and heat exchange in turbulent momentumless wakes. Engng Phys. 44, 438–442.Google Scholar
Swanson, R. C., Schetz, J. A. & Jakubowski, A. K. 1974 Turbulent wake behind slender bodies including self-propelled configurations. VPI-Aero-024, Sept. 1974. Virginia Polytechnic Inst. and State University.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Townsend, A. A. 1956 The Structures of Turbulent Shear Flow, 1st edn., pp. 49–56 Cambridge University Press.
Wang, H. 1965 Flow behind a point source of turbulence. Ph.D. thesis, State University of Iowa.
Williams, D. R. & Amato, C. W. 1988 Unsteady pulsing of cylinder wakes. 1st Natl Fluid Dynamics Congr., Cincinnati, Ohio, July 25–28.
Wood, C. J. 1964 The effect of base bleed on a periodic wake. J. R. Aero. Soc. Tech. Notes 68, 477–482.Google Scholar
Wood, C. J. 1967 Visualization of an incompressible wake with base bleed. J. Fluid Mech. 29, 259–272.Google Scholar