Effect of spanwise-varying local forcing on turbulent separated flow over a backward-facing step

An experimental study was made of turbulent separated flows over a backward-facing step. A local forcing was given to the separated flow by means of a sinusoidally oscillating jet issuing from a thin slit near the separation line. To produce a spanwise-varying local forcing at the separation edge, a banded thin tape covered the slit. Effects of the spanwise-varying local forcings on the separated flow were scrutinized by altering the spatially banded blocking width (w) and the open slit distance (g). An optimal value of w/g was sought, which led to the minimum reattachment length (x _R ). The effect of spanwise-varying local forcing on x _R was found to be slight compared to the case of two-dimensional forcing (w=0). The experiment was made at Re _H =33000 and A ₀=0.018 by changing the forcing frequency (0?St _H ?1.0).     

Visualization of a locally-forced separated flow over a backward-facing step

A laboratory water channel experiment was made of the separated flow over a backward-facing step. The flow was excited by a sinusoidally oscillating jet issuing from a separation line. The slit was connected to a cavity in which water was forced through a rigid pipe by a scotch-yoke system. The Reynolds number based on the step height (H) was fixed at Re _H =1200. The forcing frequency was varied in the range 0.305?St _H ?0.955 at the forcing amplitude A ₀=0.3. Time-averaged flow measurements were made by a LDV system, especially in the recirculating region behind the backward-facing step. To characterize the large-scale vortex evolution due to the local forcing, flow visualizations were performed by a dye tracer method with fluorescent ink. The vortex amalgamation process was captured at the effective forcing frequency (St _H =0.477) for laminar separation. This vortex merging process enhances flow mixing, which leads to the shortening of the reattachment length.     

Finite element computation of a turbulent flow over a two-dimensional backward-facing step

This paper is devoted to the computation of turbulent flows by a Galerkin finite element method. Effects of turbulence on the mean field are taken into account by means of a k-? turbulence model. The wall region is treated through wall laws and, more specifically, Reichardt's law. An inlet profile for ? is proposed as a numerical treatment for physically meaningless values of k and ?. Results obtained for a recirculating flow in a two-dimensional channel with a sudden expansion in width are presented and compared with experimental values.     

Finite element computation of a turbulent flow over a two-dimensional backward-facing step

The present paper is devoted to the computation of turbulent flows by a Galerkin finite element method. Effects of turbulence on the mean field are taken into account by means of a (k-ε) turbulence model. The wall region is treated through wall laws and, more specifically, Reichardt's law. An inlet profile for ε is proposed as a numerical treatment for physically meaningless values of k and ε. Results obtained for a recirculating flow in a two-dimensional channel with a sudden expansion in width are presented and compared with experimental values.     

Three-dimensional coherent structure in a separated and reattaching flow over a backward-facing step

An experimental study was carried out to elucidate the large-scale vortical structure in a separated and reattaching flow over a backward-facing step. The Reynolds number based on the step height (H) was Re _H =33,000. The large-scale vortical structure was probed by means of three-dimensional velocity measurements performed at the recirculation zone (x/H=4.0) and the reattachment zone (x/H=7.5). A 32-channel microphone array extending in the streamwise and spanwise directions was used for sensing the wall pressure fluctuations. The relationship between the flow field and the relevant spatial mode of the pressure field was determined by examining the spatial box filtering. From the relevant spatial mode of the wall pressure fluctuations, a conditional averaging technique was employed to characterize the coherent structure. In addition, the cross-correlation between velocity and wall pressure fluctuations was calculated to identify the structure and the length scale of the large-scale vortex. The cross-correlation results revealed that the large-scale hairpin vortices have a three-dimensional structure, in agreement with previous findings. The present results clearly show the growth and downstream elongation of the hairpin vortices.List of symbols H step height, m - k turbulent kinetic energy, m²/s² - q freestream dynamic pressure, Pa - Re _H Reynolds number based on U ₀ and H,U _oH/ - U ₀ freestream velocity, m/s - U _c convection velocity, m/s - X ₀ streamwise coordinate of the measurement origin, m - x _R time mean reattachment length, m Greek symbols _p forward flow time fraction - cross-correlation coefficient - time delay, s - vorticity, m²/s     

Turbulent flow over a rough backward-facing step

This work characterizes the impacts of the realistic roughness due to deposition of foreign materials on the turbulent flows at surface transition from elevated rough-wall to smooth-wall. High resolution PIV measurements were performed in the streamwise-wall-normal (x–y) planes at two different spanwise positions in both smooth and rough backward-facing step flows. The experiment conditions were set at a Reynolds number of 3450 based on the free stream velocity U_∞ and the mean step height h, expansion ratio of 1.01, and the ratio of incoming boundary layer thickness to the step height, δ/h, of 8. The mean flow structures are observed to be modified by the roughness and they illustrate three-dimensional features in rough backward-facing step flows. The mean reattachment length X_r is significantly reduced by the roughness at one PIV measurement position while is slightly increased by the different roughness topography at the other measurement position. The mean velocity profiles at the reattachment point indicate that the studied roughness weakens the perturbation of the step to the incoming turbulent flow. Comparisons of Reynolds normal and shear stresses, productions of normal stresses, quadrant analysis of the instantaneous shear-stress contributing events, and mean spanwise vorticity reveal that the turbulence in the separated shear layer is reduced by the studied roughness. The results also indicate an earlier separation of the turbulent boundary layer over the current rough step, probably due to the adverse pressure gradient produced by the roughness topography even before the step.     

Effect of surface permeability on the structure of a separated turbulent flow and heat transfer behind a backward-facing step

The structure and heat transfer in a turbulent separated flow in a suddenly expanding channel with injection (suction) through a porous wall are numerically simulated with the use of two-dimensional averaged Navier–Stokes equations, energy equations, and v ²–f turbulence model. It is shown that enhancement of the intensity of the transverse mass flux on the wall reduces the separation region length in the case of suction and increases the separation region length in the case of injection up to complete boundary layer displacement. The maximum heat transfer coefficient as a function of permeability is accurately described by the asymptotic theory of a turbulent boundary layer.     

Control of backward-facing step flow using a flapping foil

The effect of oscillating a small foil in plunge on the reattachment of a separated shear layer in a two-dimensional backward-facing step flow has been studied using flow visualization and single component laser Doppler velocimetry (LDV) measurements. It has been shown that a jet instead of a wake is generated by the flapping action of the foil. Results indicate that this action induces strong mixing and entrainment when the foil is located within the recirculation flow region, thereby reducing the reattachment length by as much as 70%. Furthermore, it has been shown that the flapping foil is most effective in reducing the size of the separation zone when placed close to the wall and to the step. It is least effective when placed outside the separated shear layer or downstream of the reattachment zone. Received: 26 August 1999 / Accepted: 29 May 2001     

A numerical study of flow over a confined backward-facing step

Numerical solutions using the SIMPLE algorithms for laminar flow over a backward-facing step are presented. Five differencing schemes were used: hybrid; quadratic upwind (QUICK); second-order upwind (SOUD); central-differencing and a novel scheme named second-order upwind biased (SOUBD). The SOUBD scheme is shown to be part of a family of schemes which include the central-differencing, SOUD and QUICK schemes for uniform grids. The results of the backward-facing step problem are presented and are compared with other numerical solutions and experimental data to evaluate the accuracy of the differencing schemes. The accuracy of the differencing schemes was ascertained by using uniform grids of various grid densities. The QUICK, SOUBD and SOUD schemes gave very similar accurate results. The hybrid scheme suffered from excessive diffusion except for the finest grids and the central-differencing scheme only converged for the finest grids.     

Large eddy simulation of separation control over a backward-facing step flow by suction

Separation control over a backward-facing step (BFS) flow by continuous suction was numerically investigated using the turbulence model of large eddy simulation (LES). The effect of suction control on the flow fields was scrutinised by altering the suction flow coefficient, and the results indicate that suction is not only very effective in shortening the reattachment length but also very influential in reducing the tangential velocity gradient and turbulence fluctuations of the reattached flows. With increasing increments of the absolute suction flow coefficient, the effect of suction control is more significant. Furthermore, the detailed flow fields (including the time-averaged stream and velocity fields) and turbulence characteristics (including the time-averaged resolved kinetic energy and RMS velocity) for the BFS models with or without suction are presented to discuss the mechanism of suction control. Comparisons of the time-averaged statistics between the numerical simulations and corresponding experiments are conducted, and it shows that the LES based on the dynamic kinetic energy subgrid-scale model (DKEM) can acquire exact results. Therefore, feasibility of the numerical methods to simulate suction-controlled models is validated.     

Effects of a turbulent wall jet on heat transfer over a non-confined backward-facing step

Experimental and numerical analysis of a turbulent wall jet on the heat transfer downstream of a non-confined backward-facing step are presented. Several configurations are studied to analyse the influence of the upstream flow and the height of the step. An infrared camera and a hot wire were used to visualize a temperature map and measure the instantaneous velocity, respectively. The main objective was to visualize and compare both the fluid flow and the heat transfer, by studying the skin friction coefficient C_f and the Nusselt number Nu_d, respectively. The latter is obtained by the calculation of the heat transfer coefficient, evaluated by inverse method. Both experimental data and numerical approach provide good agreement regarding the flow structure and thermal data for measuring the position and the value of characteristics scales in the recirculation zone. A correlation between the maximum heat transfer Nu_max and the maximum Reynolds number Re_max is presented. Similarities and differences are highlighted in the paper compared to confined configurations.     

The entrance effect of laminar flow over a backward-facing step geometry

The study investigates the entrance effect for flow over a backward-facing step by comparing predictions that set the inlet boundary at various locations upstream of the sudden expansion. Differences are most significant in the sudden expansion region. If the geometry has an inlet channel, then shorter reattachment and separation lengths are predicted. Comparisons with experimental data indicate that better agreement is found using a long inlet channel, but only for low Reynolds numbers where the experimental error is less significant. For certain cases, predictions with a high expansion number are perturbed by the entrance effect more than low-expansion-number predictions; however, the effect is localized in the sudden expansion region. Channels with low expansion numbers always experience a greater entrance effect after some distance upstream and downstream of the sudden expansion. The boundary layer growth in the inlet channel was examined using a uniform inlet velocity profile. © 1997 John Wiley & Sons, Ltd.     

Numerical simulations of laminar flow over a 3D backward-facing step

A numerical investigation of laminar flow over a three-dimensional backward-facing step is presented with comparisons with detailed experimental data, available in the literature, serving to validate the numerical results. The continuity constraint method, implemented via a finite element weak statement, was employed to solve the unsteady three-dimensional Navier–Stokes equations for incompressible laminar isothermal flow. Two-dimensional numerical simulations of this step geometry underestimate the experimentally determined extent of the primary separation region for Reynolds numbers Re greater than 400. It has been postulated that this disagreement between physical and computational experiments is due to the onset of three-dimensional flow near Re ≈ 400. This paper presents a full three-dimensional simulation of the step geometry for 100⩽ Re⩽ 800 and correctly predicts the primary reattachment lengths, thus confirming the influence of three-dimensionality. Previous numerical studies have discussed possible instability modes which could induce a sudden onset of three-dimensional flow at certain critical Reynolds numbers. The current study explores the influence of the sidewall on the development of three-dimensional flow for Re greater than 400. Of particular interest is the characterization of three-dimensional vortices in the primary separation region immediately downstream of the step. The complex interaction of a wall jet, located at the step plane near the sidewall, with the mainstream flow reveals a mechanism for the increasing penetration (with increasing Reynolds number) of three-dimensional flow structures into a region of essentially two-dimensional flow near the midplane of the channel. The character and extent of the sidewall-induced flow are investigated for 100⩽Re⩽ 800. © 1997 John Wiley & Sons, Ltd.     

Experimental study of the separated flow structure behind a backward-facing step and a passive disturbance

The flow in a channel with a backward-facing step and a rib mounted upstream of the step and generating flow disturbances is studied experimentally by the method of particle image velocimetry. It is demonstrated that mounting of a single rib leads to deformation of the profiles of the mean streamwise velocities and turbulent fluctuations. The effect of the position and height of a single rib on the recirculation region behind the backward-facing step is analyzed. Reduction of the recirculation region size behind the step in the case of flow reattachment upstream of the step is validated.     

Flow visualization of supersonic laminar flow over a backward-facing step via NPLS

An experimental study on a supersonic laminar flow over a backward-facing step of 5 mm height was undertaken in a low-noise indraft wind tunnel. To investigate the fine structures of Ma = 3.0 and 3.8 laminar flow over a backward-facing step, nanotracer planar laser scattering was adopted for flow visualization. Flow structures, including supersonic laminar boundary layer, separation, reattachment, redeveloping turbulent boundary layer, expansion wave fan and reattachment shock, were revealed in the transient flow fields. In the Ma = 3.0 BFS (backward-facing step) flow, by measuring four typical regions, it could be found that the emergence of weak shock waves was related to the K–H (Kelvin–Helmholtz) vortex which appeared in the free shear layer and that the convergence of these waves into a reattachment shock was distinct. Based on large numbers of measurements, the structure of time-averaging flow field could be gained. Reattachment occurred at the location downstream from the step, about 7–7.5 h distance. After reattachment, the recovery boundary layer developed into turbulence quickly and its thickness increased at an angle of 4.6°. At the location of X = 14h, the redeveloping boundary layer was about ten times thicker than its original thickness, but it still had not changed into fully developed turbulence. However, in the Ma = 3.8 flow, the emergence of weak shock waves could be seen seldom, due to the decrease of expansion. The reattachment point was thought to be near X = 15h according to the averaging result. The reattachment shock was not legible, which meant the expansion and compression effects were not intensive.     

Control of the separated flow downstream of a two-dimensional fence by low-frequency forcing

Streamwise distributions of wall shear-stress, reverse-flow-factor and static pressure were measured in the turbulent separation regions upstream and downstream of a two-dimensional fence. In front of the fence, boundary layer profiles were measured with a pulsed-wire probe traversing out of the wall. The flow was then manipulated by a periodic disturbance which was located upstream of the forward separation region. Two different disturbances were tested: an oscillating spoiler and a two-dimensional oscillating jet with zero mean mass flow, driven by a loudspeaker. Both manipulators were orientated parallel to the fence. With appropriate tuning of the parameters, the reattachment length behind the fence could be reduced by 50%.     

Experimental investigation of flow over a backward-facing step in proximity to a flexible wall

Turbulent flow between a flexible wall and a solid surface containing a backward-facing step (BFS) was investigated using digital particle image velocimetry and high-speed photography. Stationary sheet of paper under tension was positioned above the solid surface in proximity to the BFS. The incoming air flow emerged from a planar nozzle that was located in the solid wall upstream of the BFS. Flows corresponding to two values of the Reynolds number (3,000 and 3,600) based on the step height and the maximum flow velocity at the step location were characterized in terms of patterns of time-averaged velocity, out-of-plane vorticity, streamline topology, and turbulence statistics. In addition, paper sheet oscillation was characterized using high-speed photography. For the control case of a solid upper wall with the geometry that represented the time-averaged paper profile, hydrodynamic frequencies were characterized using unsteady pressure measurements. Frequencies of the natural vibration modes of the paper sheet were well separated from the hydrodynamic frequencies corresponding to the oscillations of the shear layer downstream of the BFS. As the inflow velocity increased, the paper sheet was pulled closer to the solid surface, which resulted in increased confinement of the incoming jet. The flow reattachment length calculated on the basis of time-averaged flow patterns increased with the increasing Reynolds number.     

Simulation of supersonic turbulent flow in the vicinity of an inclined backward-facing step

Large eddy simulation (LES) is a viable and powerful tool to analyse unsteady three-dimensional turbulent flows. In this article, the method of LES is used to compute a plane turbulent supersonic boundary layer subjected to different pressure gradients. The pressure gradients are generated by allowing the flow to pass in the vicinity of an expansion–compression ramp (inclined backward-facing step with leeward-face angle of 25°) for an upstream Mach number of 2.9. The inflow boundary condition is the main problem for all turbulent wall-bounded flows. An approach to solve this problem is to extract instantaneous velocities, temperature and density data from an auxiliary simulation (inflow generator). To generate an appropriate realistic inflow condition to the inflow generator itself the rescaling technique for compressible flows is used. In this method, Morkovin's hypothesis, in which the total temperature fluctuations are neglected compared with the static temperature fluctuations, is applied to rescale and generate the temperature profile at inlet. This technique was successfully developed and applied by the present author for an LES of subsonic three-dimensional boundary layer of a smooth curved ramp. The present LES results are compared with the available experimental data as well as numerical data. The positive impact of the rescaling formulation of the temperature is proven by the convincing agreement of the obtained results with the experimental data compared with published numerical work and sheds light on the quality of the developed compressible inflow generator.