▪ Abstract We review the direct numerical simulation (DNS) of turbulent flows. We stress that DNS is a research tool, and not a brute-force solution to the Navier-Stokes equations for engineering problems. The wide range of scales in turbulent flows requires that care be taken in their numerical solution. We discuss related numerical issues such as boundary conditions and spatial and temporal discretization. Significant insight into turbulence physics has been gained from DNS of certain idealized flows that cannot be easily attained in the laboratory. We discuss some examples. Further, we illustrate the complementary nature of experiments and computations in turbulence research. Examples are provided where DNS data has been used to evaluate measurement accuracy. Finally, we consider how DNS has impacted turbulence modeling and provided further insight into the structure of turbulent boundary layers.

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DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research

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

Experimental data have been obtained in an incompressible turbulent flow over a rearward-facing step in a diverging channel flow. Mean velocities, Reynolds stresses, and triple products that were measured by a laser Doppler velocimeter are presented for two cases of tunnel wall divergence. Eddy viscosities, production, convection, turbulent diffusion, and dissipation (balance of kinetic energy equation) terms are extracted from the data. These data are compared with various eddy-viscosity turbulence models. Numerical calculations incorporating the k-epsilon and algebraic-stress turbulence models are compared with the data. When determining quantities of engineering interest, the modified algebraic-stress model (ASM) is a significant improvement over the unmodified ASM and the unmodified k-epsilon model; however, like the others, it dramatically overpredicts the experimentally determined dissipation rate.

Features of a reattaching turbulent shear layer in divergent channel flow

Measurements of fluctuating pressure and velocity, together with instantaneous smoke-flow visualizations, are presented in order to reveal the unsteady structure of a separated and reattaching flow. It is shown that throughout the separation bubble a low-frequency motion can be detected which appears to be similar to that found in other studies of separation. This effect is most significant close to separation, where it leads to a weak flapping of the shear layer. Lateral correlation scales of this low-frequency motion are less than the reattachment length, however; it appears that its timescale is about equal to the characteristic timescale for the shear layer and bubble to change between various shedding phases. These phases were defined by the following observations: shedding of pseudoperiodic trains of vortical structures from the reattachment zone, with a characteristic spacing between structures of typically 60% to 80% of the bubble length; a large-scale but irregular shedding of vorticity; and a relatively quiescent phase with the absence of any large-scale shedding structures and a significant ‘necking’ of the shear layer downstream of reattachment.Spanwise correlations of velocity in the shear layer show on average an almost linear growth of spanwise scale up to reattachment. It appears that the shear layer reaches a fully three-dimensional state soon after separation. The reattachment process does not itself appear to impose an immediate extra three-dimensionalizing effect upon the large-scale structures.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S002211208400149X

Unsteady measurements in a separated and reattaching flow

Experiments were performed in the highly turbulent and disturbed flow over a bluff plate with a long splitter plate in its plane of symmetry. The flow separates at the sharp bevelled edge of the bluff plate, forms a free shear layer on top of the reverse-flow region which is bounded on its other side by the splitter plate, and reattaches on the splitter plate over a narrow region curved in spanwise direction. Downstream of reattachment the shear flow adjusts slowly to the wall boundary conditions. Measurements of mean velocity, Reynolds-shear-stress and Reynolds-normal-stress distributions were carried out by hot-wire and pulsed-wire anemometry. The latter technique was used in those regions of the flow where reverse flow occurred or where the flow was highly turbulent. Spectra and integral lengthscales were measured to investigate the state and structure of the flow. The large-eddy structure in the inner region of the flow had lengthscales in the two cross-stream directions which were approximately equal, indicating a fast break-up of spanwise structures just downstream from separation. Mean and fluctuating quantities showed a self-similar behaviour in a short region upstream of reattachment and ‘profile similarity’ in the separated shear layer and along the splitter plate downstream from reattachment. Probability-density distributions of skin friction were measured and used to calculate mean and fluctuating values. No flapping of the reattaching shear layer could be observed. Pulsed-wire measurements revealed that the logarithmic law of the wall does not hold either in the reverse-flow region or in a region about half the length of the bubble downstream from reattachment.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112086002306

An experimental investigation of a turbulent shear flow with separation, reverse flow, and reattachment

The reattachment of a fully turbulent, two dimensional, separated shear layer downstream of a single-sided sudden expansion in a planar duct flow was examined experimentally. The importance of changing the structure of the separated shear layer on the reattachment process itself was examined. For all cases, the Reynolds number based on step height was greater than 20,000, the expansion ratio was 5/3, and the inlet boundary layer was less than one-half step height in thickness. A crucially important phase was the development of a pulsed wall probe for measurement of skin friction in the reattachment region, thus providing an unambiguous definition of the reattachment length. Quantitative features of reattachment - including streamwise development of the mean and fluctuating velocity field, pressure rise, and skin friction - were found to be similar for all cases studied when scaled by the reattachment length. A definition of the reattachment zone is proposed.

Experimental study of flow reattachment in a single-sided sudden expansion

Separated turbulent flows exhibit instantaneous reversals of flow direction which make measurement of the velocity field extremely difficult. A three-wire heat-tracer technique has been employed to measure streamwise velocity of a low-speed air flow very near a smooth, solid wall; the wall shear stress is calculated using a similarity hypothesis. Initial results presented show the evolution of average wall shear stress and rms fluctuation intensity of wall shear stress in a reattaching 2-D flow downstream of a backward-facing step.

R. V. Westphal

Papers

Experimental study of flow reattachment in a single-sided sudden expansion

A New Probe for Measurement of Velocity and Wall Shear Stress in Unsteady, Reversing Flow