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The Effect of Extra Strain Rates of Streamline Curvature and Divergence on Mixing Layers

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Book cover Turbulent Shear Flows 7

Abstract

Measurements have been made in two axisymmetric single-stream mixing layers, each subjected simultaneously to curvature and divergence. The boundary layer was turbulent at separation. In the ‘very-strongly-strained’ layer, the curvature was entirely of the stabilizing sense. The large-scale structures were suppressed but not destroyed. Compared with what would be expected for curvature alone, the effect of divergence was to resist the suppression of the large-scale structures, and to increase the rate of recovery. In the ‘moderately-strained’ layer, destabilizing curvature followed the stabilizing curvature. The Reynolds stresses and triple-velocity products varied qualitatively as the lagged strains, though, quantitatively, destabilizing effects are unlikely to have been absent in the lagged region of stabilizing curvature. The approach of an undistorted layer to asymptotic stress levels is distinctly nonmonotonic.

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Abbreviations

U r :

Reference velocity

U max :

Maximum U at constant s

R :

Radius of curvature, negative for concave (i.e. stabilizing) curvature

s,n :

Shear layer curvilinear orthogonal axes, with n positive towards the low-velocity side

x,y,z :

Cartesian axes

X,r,Φ :

Cylindrical axes—X aligned with symmetry axis

Γ:

Angle between X and tangent to s

U,V,W :

Mean velocities in s-n-Φ directions

u,v,w :

Velocity fluctuations in s-n-Φ directions

q 2 :

= u 2 + v 2 + w 2

Λ:

Gradient thickness, Λ = U max/(∂U/∂n)n = 0

θ :

Momentum thickness

Φ,k :

Spectral density, and wavenumber:

$$ {u^2} = \int {{\Phi_{{11}}}(k)dk,\,{v^2} = } \int {{\Phi_{{22}}}(k)dk} $$

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Author notes

  1. A. E. Johnson

    Present address: BP Research, Sunbury Research Centre, Sunbury-on-Thames, Middlesex, TW16 7LN, UK

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Surrey, Guildford, Surrey, GU2 5XH, UK

    A. E. Johnson & P. E. Hancock

Authors
  1. A. E. Johnson
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  2. P. E. Hancock
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Editor information

Editors and Affiliations

  1. Lehrstuhl für Strömungsmechanik, Universität Erlangen-Nürnberg, Cauerstraße 4, 8520, Erlangen, Germany

    Franz Durst

  2. Department of Mechanical Engineering, Institute of Science and Technology, University of Manchester, Manchester, M60 1QD, UK

    Brian E. Launder

  3. Mechanical Engineering Department, Thermosciences Division, Stanford University, Stanford, CA, 94305-3030, USA

    William C. Reynolds

  4. Mechanical Engineering Department, The Pennsylvania State University, University Park, PA, 16802, USA

    Frank W. Schmidt

  5. Department of Mechanical Engineering, Imperial College of Science and Technology, Exhibition Road, London, SW7 2BX, England

    James H. Whitelaw

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© 1991 Springer-Verlag Berlin Heidelberg

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Johnson, A.E., Hancock, P.E. (1991). The Effect of Extra Strain Rates of Streamline Curvature and Divergence on Mixing Layers. In: Durst, F., Launder, B.E., Reynolds, W.C., Schmidt, F.W., Whitelaw, J.H. (eds) Turbulent Shear Flows 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76087-7_19

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  • DOI: https://doi.org/10.1007/978-3-642-76087-7_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-76089-1

  • Online ISBN: 978-3-642-76087-7

  • eBook Packages: Springer Book Archive

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