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Phenomenological modelling : Present .... and future?

  • Session Six
  • Conference paper
  • First Online:
Whither Turbulence? Turbulence at the Crossroads

Part of the book series: Lecture Notes in Physics ((LNP,volume 357))

Abstract

The paper summarizes the present position of second-moment closure and outlines possible directions for future development. It is first argued that a simple form of second-moment treatment that has been widely used for computing industrial flows gives demonstrably superior predictive accuracy than any eddy-viscosity model. More complex schemes, now in the final phases of development, that exactly satisfy various limiting constraints, give a further marked improvement in our ability to mimic the response of turbulence to external inputs. The inclusion of such models into commercial software over the next few years is quite feasible.

The desirability of introducing a further second-rank tensor into the closure is considered; the conclusion reached is that, for most applications, the likely benefits would not justify the additional effort. The split-spectrum approach may, however, be attractive for certain flows with unusual spectral distributions of energy. The introduction of a second scale-related equation is arguably a more sensible approach since the extra computational cost is small while the added flexibility could bring significant benefits in modelling turbulence far from equilibrium.

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Abbreviations

aij:

anisotropic Reynolds stress \(\left( {\overline {u_i u_j } - \tfrac{1}{3}\delta _{ij} \overline {u_k u_k } } \right)/k\)

A:

stress invariant quantifying the proximity of the stresses to the two-component limit, \(1 - \tfrac{9}{8}\left( {A_2 - A_3 } \right)\)

A2 :

second invariant aij aji

A3 :

third invariant aij ajk aki

c's:

denote coefficients in turbulence model

Cij, Ciθ :

convective transport of \(\overline {u_i u_j } ,\overline {u_i \theta }\)

d:

small pipe diameter

dijk :

diffusion of Reynolds stress

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    Brian E. Launder

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Launder, B.E. (1990). Phenomenological modelling : Present .... and future?. In: Lumley, J.L. (eds) Whither Turbulence? Turbulence at the Crossroads. Lecture Notes in Physics, vol 357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52535-1_62

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