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Eddy-Viscosity Transport Modelling: A Historical Review

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50 Years of CFD in Engineering Sciences

Abstract

This contribution presents the authors’ view of the historical evolution of modelling turbulence by way of the simple (though, some would say, outrageously simplistic) notion that the local turbulent stress–strain connection should be the same as in a laminar Newtonian flow. The principal emphasis is on modelling at a level where two transport equations are solved for scalar properties of turbulence, the level of approximation popularized (though not invented) by D. B. Spalding at Imperial College in the early 1970s. The successes and failures of the approach are examined. The chapter concludes by showing examples of closure at eddy viscosity level of what would be regarded as steady flows though treated by way of a time-dependent solution of the transport equations. These lead, in appropriate circumstances, to time-dependent structures which contribute additional momentum and heat transport thereby enhancing agreement with experiment. 

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Notes

  1. 1.

    A practice retained by Daly and Harlow [13] but who discarded the eddy-viscosity approach in favour of solving transport equations for the Reynolds stresses.

  2. 2.

    The quantity \(\omega^{2}\) differs only by a constant from Spalding’s W.

  3. 3.

    If the form of model applicable to regions excluding the viscosity-affected sublayer is meant (i.e. ‘the high Re number k-ε model’), however, a more correct attribution would be to Hanjalić’s thesis [26].

  4. 4.

    The small secondary strains associated with the curvature exert strong amplification or damping effects on the turbulent stresses.

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Authors and Affiliations

  1. Faculty of Applied Sciences, Delft University of Technology, Delft, The Netherlands

    K. Hanjalić

  2. Department of Mechanical Aerospace & Civil Engineering, University of Manchester, Manchester, UK

    B. E. Launder

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  1. K. Hanjalić
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  1. ACRI, The CFD Innovators, Los Angeles, CA, USA

    Akshai Runchal

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Hanjalić, K., Launder, B.E. (2020). Eddy-Viscosity Transport Modelling: A Historical Review. In: Runchal, A. (eds) 50 Years of CFD in Engineering Sciences. Springer, Singapore. https://doi.org/10.1007/978-981-15-2670-1_9

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