The standard κ-ϵ equations and other turbulence models are evaluated with respect to their applicability in swirling, recirculating flows. The turbulence models are formulated on the basis of two separate viewpoints. The first perspective assumes that an isotropic eddy viscosity and the modified Boussinesq hypothesis adequately describe the stress distributions, and that the source of predictive error is a consequence of the modeled terms in the κ-ϵ equations. Both stabilizing and destabilizing Richardson number corrections are incorporated to investigate this line of reasoning. A second viewpoint proposes that the eddy viscosity approach is inherently inadequate and that a redistribution of the stress magnitudes is necessary. Investigation of higher-order closure is pursued on the level of an algebraic stress closure. Various turbulence model predictions are compared with experimental data from a variety of isothermal, confined studies. Supportive swirl comparisons are also performed for a laminar flow case, as well as reacting flow cases. Parallel predictions or contributions from other sources are also consulted where appropriate. Predictive accuracy was found to be a partial function of inlet boundary conditions and numerical diffusion. Despite prediction sensitivity to inlet conditions and numerics, the data comparisons delineate the relative advantages and disadvantages of the various modifications. Possible research avenues in the area of computational modeling of strongly swirling, recirculating flows are reviewed and discussed.

Bubbles, Drops, and Particles

Presentation d'une methode numerique par volume fini pour la resolution des equations de Navier-Stokes bidimensionnelles, incompressibles, et stationnaires, en coordonnees generales curvilignes Application de la methode aux ecoulements turbulents sur des profils avec et sans separation au bord de sortie posterieur Comparaison des calculs avec des donnees experimentales

Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation

An explanation of the turbulent round-jet/plane-jet anomaly

Second-moment closure: present… and future?

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 that 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 modeling turbulence far from equilibrium.

Second-moment closure: Present ... and future?

Calculated flow properties are compared with measurements obtained in twodimensional isothermal wakes with and without recirculation. The equations of continuity and momentum were solved numerically together with equations which formed a turbulence model. Calculations were made using three turbulence models : the first comprised transport equations for turbulence kinetic energy and the rate of turbulence dissipation; the second and third comprised equations for the rate of turbulence dissipation and two forms of Reynolds-stress equations characterized by different redistribution terms. The results show that, for wakes without recirculation, the particular turbulence model is less important than the boundary condition assumed in the plane of the trailing edge of the body; though the Reynolds-stress models do, of course, provide a better representation of the individual normal stresses. In the case of wakes with recirculation, both the length of the recirculation region and the rate of spread of the downstream wake are underestimated. The second discrepancy is particularly evident and appears to stem from the form of the dissipation equation. A suggestion for improving the modelling of this equation is provided together with necessary justification.

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J. H. Whitelaw

Papers

The calculation of near-wake flows