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A Comparison of Triple-Moment Temperature-Velocity Correlations in the Asymmetric Heated Jet with Alternative Closure Models

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Turbulent Shear Flows 4

Abstract

Measurements are reported of triple moments of velocity and temperature in a heated asymmetric two-dimensional turbulent jet involving velocity fluctuations in the x 1 − x 2 plane. The data thus obtained have been compared with those given by alternative algebraic models of the triple moments losing, in the model formulae, experimental values of the second-moment quantities and the dissipation rate of kinetic energy. The study supports the view that in strongly asymmetric flows the contribution of mean temperature gradients to the triple moments can be appreciable. The comparison also provides some support for the use of the generalized gradient transport hypothesis in approximating dissipation of the triple moments.

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Abbreviations

d :

width of exit slot

d ijk :

diffusion of \(\overline {{u_i}{u_j}{u_k}}\) (likewise for velocity-temperature 3rd moments; subscript identifies quantity)

k :

turbulence kinetic energy

l γu :

x 2 distance between the positions where γ u = 1/2

l yu :

u 2 distance between the positions where γ θ = 1/2

p :

fluctuating pressure

P ij :

generation rate of Reynolds stress

P ijk :

generation rate of \(\overline {{u_i}{u_j}{u_k}}\) due to Reynolds stress gradients (1) and mean strain (2)

q′:

\(\sqrt {2k}\)

T :

turbulent time scale (k/ε)

u i :

fluctuating velocity

U i :

mean velocity

U :

mean stream wise velocity (in x 1 direction)

u′, υ′, w′:

rms velocity fluctuations in x 1, x 2 and x 3 directions

x 1 :

sreamwise coordinate

x 2 :

cross stream Cartesian coordinate

x 2m :

x 2 position of velocity maximum

x 2θ :

x 2 position of temperature maximum

γ u :

intermittency of turbulent velocity signal

γ θ :

intermittency of turbulent temperature sequal

ε :

dissipation rate of turbulence energy

ε ijk :

“dissipation” rate of \(\overline {{u_i}{u_j}{u_k}}\)

η u :

(x 2 − x m ) /lγ u

η θ :

(x 2 − x 2θ ) /lγ θ

v :

kinematic viscosity

ϱ :

density of fluid

θ :

fluctuating temperature

θ′:

\(\sqrt {{{\overline \theta }^2}}\)

Θ :

mean temperature

ΔΘ :

temperature above ambient

ΔΘ m :

maximum temperature difference across jet

ϕ ijk :

non-dispersive pressure correlation in \(\overline {{u_i}{u_j}{u_k}}\)

References

  • André, J. C., de Moor, G, Lacarrère, P., Therry, G., du Vachat, R.: The Clipping Approximation and Inhomogeneous Turbulence Simulations, in Turbulent Shear Flows 1, ed. by F. Durst, B. E. Launder, F. W. Schmidt, J. H. Whitelaw ( Springer, Berlin, Heidelberg, New York 1979 ) p. 307

    Google Scholar 

  • André, J. C., Lacarrère, P., Traoré, K.: Pressure Effects on Triple Correlations in Turbulent Convective Flow, in Turbulent Shear Flows 3, ed. by L. J. S. Bradbury, F. J. Durst, B. E. Launder, F. W. Schmidt, J. H. Whitelaw ( Springer, Berlin, Heidelberg, New York 1982 ) p. 243

    Google Scholar 

  • Béguier, C., Fulachier, L., Keffer, J. F. (1976): The turbulent mixing layer with an asymmetrical distribution of temperature. J. Fluid Mech. 89, 561

    Article  Google Scholar 

  • Cormack, D. E., Leal, L. G., Seinfeld, J. H. (1978): An evaluation of mean Reynolds stress turbulence models: the triple velocity correlations. J. Fluids Eng. 100, 47

    Article  Google Scholar 

  • Daly, B. J., Harlow, F. H. (1970): Transport equations in turbulence. Phys. Fluids 13, 2634

    Article  ADS  Google Scholar 

  • Deardorff, J. W.: Three-Dimensional Numerical Modelling of the Planetary Boundary Layer, in Proc. Workshop on Micrometeorology, 271, (Am. Met. Soc. Boston, Massachusetts, 1973 )

    Google Scholar 

  • Dekeyser, I. (1982): Etude d’un jet plan dissymmetrique chauffé en régime turbulent incompressible. Thèse Docteur-es-Sciences, Université d’Aix-Marseille I I

    Google Scholar 

  • Dekeyser, I. (1983): Journal de Mécanique Théorique et Appliquée. Vol 2, N° 6, 1983, 915

    ADS  Google Scholar 

  • Gibson, M. M., Launder, B. E. (1978): Ground effects on pressure fluctuations in the atmospheric boundary layer. J. Fluid Mech. 86, 491

    Article  ADS  MATH  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

    Article  ADS  MATH  Google Scholar 

  • Keffer, J. F., Kawall, J. G., Giralt, F., Béguier, C.: Analysis of Turbulence Structure in Complex Shear Flows, in Proc. 2nd Symposium on Turbulent Shear Flows (Imperial College London 1979 ) p. 2

    Google Scholar 

  • Launder, B. E. (1975): On the effects of a gravitational field on the transport of heat and momentum. J. Fluid Mech. 67, 569

    Article  ADS  Google Scholar 

  • Launder, B. E., Reece, G. J., Rodi, W. (1975): Progress in the development of a Reynolds stress turbulent model. J. Fluid Mech. 68, 537

    Article  ADS  MATH  Google Scholar 

  • Launder, B. E.: Heat and Mass Transport, in Topics Appi. Phys., Vol. 12, 2nd ed., ed. by P. Bradshaw (Springer, Berlin, Heidelberg, New York 1978) p. 232

    Google Scholar 

  • Launder, B. E., Samaraweera, D. S. A. (1979): Application of a second-moment closure to heat and mass transport in thin shear flows. Int. J. Heat Mass Trans. 22, 1631

    Article  ADS  MATH  Google Scholar 

  • Launder, B. E. (1982): Second-moment closure: methodology and practice. EDF Summer School on Modélisation Numérique, Le Bréau, France

    Google Scholar 

  • Libby, P. A. (1975): On the prediction of intermittent turbulent flows. J. Fluid Mech. 68, 272

    Article  ADS  Google Scholar 

  • Lumley, J. L. (1978): Computational modeling of turbulent flows. AdV Appl. Mech. 18, 123

    MathSciNet  MATH  Google Scholar 

  • Lumley, J. L., Zeman, O., Siess, J. (1978): The influence of buoyancy on turbulent transport. J. Fluid Mech. 84, 581

    Article  MathSciNet  ADS  Google Scholar 

  • Owen, R. G. (1973): An analytical turbulent transport model applied to non-isothermal fully-developed duct flows. Ph.D. Thesis. Penn. State Univ.

    Google Scholar 

  • Schon, J.-P., Bailie, A. (1972): Méthode d’isolement des fluctuations turbulentes cinématiques et thermiques au moyen d’une sonde anémométrique à trois fils. C.R. Acad. Sci. Paris A274, 116

    Google Scholar 

  • Wyngaard, J. C., Coté, O. (1974): The evolution of a convective planetary boundary layer. A higher order closure model study. Boundary Layer Met. 7, 289

    Article  ADS  Google Scholar 

  • Wyngaard, J. C., Sundararajan, A.: The Temperature Skewness Budget in the Lower Atmosphere and Its Implications for Turbulence Modeling, in Turbulent Shear Flows 1, ( Springer, Berlin, Heidelberg, New York 1979 ) p. 319

    Google Scholar 

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Author information

Authors and Affiliations

  1. IMST, Marseille, France

    I. Dekeyser

  2. UMIST, Manchester, England

    B. E. Launder

Authors
  1. I. Dekeyser
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  2. B. E. Launder
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Editor information

Editors and Affiliations

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

    Leslie J. S. Bradbury

  2. Technische Fakultät, Friedrich-Alexander-Universität, Egerlandstraße 13, D-8520, Erlangen, Fed. Rep. of Germany

    Franz Durst (Lehrstuhl für Strömungsmechanik) (Lehrstuhl für Strömungsmechanik)

  3. Department of Mechanical Engineering, University of Manchester, Institute of Science and Technology, PO Box 88, M60 1QD, Manchester, England

    Brian E. Launder

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

    Frank W. Schmidt

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

    James H. Whitelaw

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© 1985 Springer-Verlag Berlin Heidelberg

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Dekeyser, I., Launder, B.E. (1985). A Comparison of Triple-Moment Temperature-Velocity Correlations in the Asymmetric Heated Jet with Alternative Closure Models. In: Bradbury, L.J.S., Durst, F., Launder, B.E., Schmidt, F.W., Whitelaw, J.H. (eds) Turbulent Shear Flows 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-69996-2_8

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  • DOI: https://doi.org/10.1007/978-3-642-69996-2_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-69998-6

  • Online ISBN: 978-3-642-69996-2

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