Perturbed Free Shear Layers

The paper presents large-eddy simulation (LES) formalism, along with the various subgrid-scale models developed since Smagorinsky’s model. We show how Kraichnan’s spectral eddy viscosity may be implemented in physical space, yielding the structure-function model. Recent developments of this model that allow the eddy viscosity to be inhibited in transitional regions are discussed. We present a dynamic procedure, where a double filtering allows one to dynamically determine the subgrid-scale model constants. The importance of backscatter effects is discussed. Alternatives to the eddy-viscosity assumption, such as scale- similarity models, are considered. Pseudo-direct simulations in which numerical diffusion replaces subgrid transfers are mentioned. Various applications of LES to incompressible and compressible turbulent flows are given, with an emphasis on the generation of coherent vortices

New Trends in Large-Eddy Simulations of Turbulence

Turbulent flow over a backward-facing step is studied by direct numerical solution of the Navier–Stokes equations. The simulation was conducted at a Reynolds number of 5100 based on the step height h and inlet free-stream velocity, and an expansion ratio of 1.20. Temporal behaviour of spanwise-averaged pressure fluctuation contours and reattachment length show evidence of an approximate periodic behaviour of the free shear layer with a Strouhal number of 0.06. The instantaneous velocity fields indicate that the reattachment location varies in the spanwise direction, and oscillates about a mean value of 6.28h. Statistical results show excellent agreement with experimental data by Jovic & Driver (1994). Of interest are two observations not previously reported for the backward-facing step flow: (a) at the relatively low Reynolds number considered, large negative skin friction is seen in the recirculation region; the peak |Cf| is about 2.5 times the value measured in experiments at high Reynolds numbers; (b) the velocity profiles in the recovery region fall below the universal log-law. The deviation of the velocity profile from the log-law indicates that the turbulent boundary layer is not fully recovered at 20 step heights behind the separation.The budgets of all Reynolds stress components have been computed. The turbulent kinetic energy budget in the recirculation region is similar to that of a turbulent mixing layer. The turbulent transport term makes a significant contribution to the budget and the peak dissipation is about 60% of the peak production. The velocity–pressure gradient correlation and viscous diffusion are negligible in the shear layer, but both are significant in the near-wall region. This trend is seen throughout the recirculation and reattachment region. In the recovery region, the budgets show that effects of the free shear layer are still present.

Direct numerical simulation of turbulent flow over a backward-facing step

The entrainment assumption, relating the inflow velocity to the local mean velocity of a turbulent flow, has been used successfully to describe natural phenomena over a wide range of scales. Its first application was to plumes rising in stably stratified surroundings, and it has been extended to inclined plumes (gravity currents) and related problems by adding the effect of buoyancy forces, which inhibit mixing across a density interface. More recently, the influence of viscosity differences between a turbulent flow and its surroundings has been studied. This paper surveys the background theory and the laboratory experiments that have been used to understand and quantify each of these phenomena, and discusses their applications in the atmosphere, the ocean and various geological contexts.

Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows

The development of three-dimensional motions in a plane mixing layer was investigated experimentally. It is shown that superimposed on the primary, spanwise vortex structure there is a secondary, steamwise vortex structure. Three aspects of this secondary structure were studied. First, the spanwise vortex instability that generates the secondary structure was characterized by measurements of the critical Reynolds number and the spanwise wavelength at several flow conditions. While the critical Reynolds number was found to depend on the velocity ratio, density ratio and initial shear-layer-profile shape, the mean normalized wavelength is independent of these parameters. Secondly, flow visualization in water was used to obtain cross-sectional views of the secondary structure associated with the streamwise counter-rotating vortices. A model is proposed in which those vortices are part of a single vortex line winding back and forth between the high-speed side of a primary vortex and the low-speed side of the following one. Finally, the effect of the secondary structure on the spanwise concentration field was measured in a helium-nitrogen mixing layer. The spatial organization of the secondary structure produces a well-defined spanwise entrainment pattern in which fluid from each stream is preferentially entrained at different spanwise locations. These measurements show that the spanwise scale of the secondary structure increases with downstream distance.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S002211208600099X

Streamwise vortex structure in plane mixing layers

Hot-wire measurements of second- and third-order mean products of velocity fluctuations have been made in the flow behind a backward-facing step with a thin, laminar boundary layer at the top of the step. Measurements extend to a distance of about 12 step heights downstream of the step, and include parts of the recirculating-flow region: approximate limits of validity of hot-wire results are given. The Reynolds number based on step height is about 105, the mixing layer being fully turbulent (fully three-dimensional eddies) well before reattachment, and fairly close to self-preservation in contrast to the results of some previous workers. Rapid changes in turbulence quantities occur in the reattachment region: Reynolds shear stress and triple products decrease spectacularly, mainly because of the confinement of the large eddies by the solid surface. The terms in the turbulent energy and shear stress balances also change rapidly but are still far from the self-preserving boundary-layer state even at the end of the measurement region.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112081000670

Turbulence structure of a reattaching mixing layer

Flow-visualization investigations and correlation measurements show that the essentially two-dimensional structures which dominated the turbulent mixing layer of Brown & Roshko (1974) are formed only if the free-stream turbulence is low. If free-stream disturbances are significant, as is likely in most practical cases, including a mixing layer entraining ‘still air’ from the surroundings, three-dimensionality develops at an early stage in transition. Other recent experiments strongly suggest that the Brown-Roshko structure will not form if the initial mixing layer is turbulent or subject to instability modes other than spanwise vortices. Therefore the Brown-Roshko structure will be rare in practice. The alternative large structure in a mixing layer, found by several workers, is intense, but fully three-dimensional and thus less orderly than the Brown-Roshko structure.The balance of evidence suggests that if the Brown-Roshko structure does appear it will eventually relax into the alternative fully three-dimensional form: the Karman vortex street behind a bluff body provides a precedent for slow development of three-dimensionality. However the Brown-Roshko structure, if formed, may well relax so slowly as to be identifiable for the full length of a practical flow.

C. Chandrsuda

Papers

Turbulence structure of a reattaching mixing layer

Effect of free-stream turbulence on large structure in turbulent mixing layers