An experimental investigation of a large-scale structure of a two-dimensional backward-facing step by using advanced multi-point LDV

Measurements of spatio–temporal velocity fields at the separated shear layer and reattachment region of a two-dimensional backward-facing step flow are carried out simultaneously using a multi-point LDV. The objective of this paper is to clarify experimentally the structure of a large-scale structure of this flow field using a space and time correlation and conditional average. From the results of the correlation of the velocity fluctuation, the moving path of the vortex shedding from the separated shear layer to the reattachment region exhibits two patterns which it moves to near the wall region or the middle of the step height at the reattachment region. Especially, it moves to near the wall region when it grows larger in the separated shear layer. Moreover, the turbulence concerned with reattachment phenomenon transports from the reattachment region to a separated shear layer by recirculation flow. According to these transports of turbulence, a model for large-scale fluctuation is proposed as a self-excitation motion.     

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.     

Expansion ratio effects on the separated shear layer and reattachment downstream of a backward-facing step

Experiments were carried out to study the behavior of the incompressible turbulent separated shear layer and subsequent reattachment, downstream of a backward-facing step in a channel. The main objective of the study was to determine the effect of the expansion ratio on the development of the mean velocity and turbulence intensity in the shear layer and on the evolution of wall static pressure downstream of the step. The step height-to-upstream channel height ratio was varied between 0.5 and 2.13 while all inlet conditions were kept constant. Both hot-wire anemometry and frequency shifted laser Doppler anemometry were used for the velocity measurements. The Reynolds number based on free stream velocity and channel height upstream of the step was 16,600. The expansion ratio was found to have a particularly strong influence in the development of the turbulent, separated shear layer. Larger step height-to-inlet channel height ratios lead to higher turbulence intensities and faster growth of the unstable shear layer. As a result of this, shorter normalized reattachment lengths occurred with lager expansion ratios. For all the expansion ratios studied, the mean reattachment lenght was uniform along the spanwise direction except very near the side walls.     

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.     

A study of a 3-D double backward-facing step

An investigation of the flow over a three-dimensional (3-D) double backward-facing step is presented using a combination of both quantitative measurements from a particle image velocimetry (PIV) system and qualitative oil-flow visualizations. The arrangement of the PIV instrument allows for snap-shots of the (x, y) and (y, z) planes at various axial and spanwise positions. The measurements illustrate characteristics that are found in both two-dimensional (2-D) backward-facing steps and 3-D flows around wall mounted cubes. In particular, the development of a horseshoe vortex is found after each step alongside other vortical motions introduced by the geometry of the model. Large turbulence levels are found to be confined to a region in the center of the backstep; their mean square levels being much larger than what has been observed in 2-D backward-facing steps. The large turbulent fluctuations are attributed to a quasi-periodic shedding of the horseshoe vortex as it continuously draws energy from the spiral nodes of separation, which form to create the base of the horseshoe vortex. A combination of effects including the shedding of the first horseshoe vortex, the horizontal entrainment of air and the presence of two counter rotating vortices initiated at reattachment, are shown to cause the steering vector of the flow to jettison away from the surface in the first redeveloping region and along the center at z/h = 0. Oil-flow visualizations confirm these observations.

---

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.     

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.     

A DPIV study of a starting flow downstream of a backward-facing step

 In this paper an experimental investigation of a starting water flow downstream of a backward-facing step is described. The Reynolds number of the asymptotic steady flow is Re≈4300 based on the step height of s=2 cm and the free stream velocity of U=21.4 cm/s. Velocity measurements were performed with video-based DPIV (Digital Particle Image Velocimetry) at a sampling frequency of 25 Hz. The main purpose of this study is to reveal the temporal development of global structures which could not be analyzed with single-point probes. It was found that at initialization of the flow a regular vorticity street is formed, which collapses at a normalized time t ^* =U t/s≈17 due to vorticity interactions. After this the flow is dominated by complicated vorticity roll-up and shedding dynamics in the recirculation region. The starting phase is terminated for t ^* >40. Prior to the collapse of the vorticity street values of 9 times the steady state asymptotic wall normal stress and of twice the steady state negative wall shear stress were observed. The early increasing slope of the reattachment length is constant over a time of approximately t ^* =8. The collapse of the vorticity street and the vorticity interactions thereafter cause fluctuations both in the velocity in the free shear layer and in the reattachment length. The fully developed flow has a dominant frequency corresponding to a Strouhal number St=fs/U≈0.04. Received: 20 September 1996/Accepted: 1 April 1997     

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.     

Near-wall investigation of backward-facing step flows

The electrodiffusion technique has been used to investigate reattaching and recirculating flows behind a backward-facing step. The instantaneous wall shear rate vectors were determined using the current signals provided by a three-segment electrodiffusion probe. The near-wall extents of two counter-rotating recirculation zones located behind the step were determined under turbulent flow conditions in a water channel. The near-wall flow inside these recirculation zones was found to be very unsteady, with strong low-frequency fluctuations. The streamwise profiles of the wall shear stress were measured at several values of the Reynolds number and a high level of skin friction was obtained in the reverse-flow region. The strong dependence of the peak value of skin friction on the Reynolds number confirms the viscous-dominated character of the reverse flow appearing inside the recirculation zone. Received: 22 May 2000/Accepted: 28 March 2001     

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     

Particle dispersion in a single-sided backward-facing step flow

The paper describes the particle dispersion in a single-sided backward-facing step flow. Particles of well-known sizes in the diameter range from 1 to 70 μm were suspended in an air flow and the particle motion over a step was measured by mean of a laser-Doppler anemometer. Thus, the local and integral flow quantities, i.e. the mean and turbulent velocity data could be measured precisely. In the experiments, monodispersed particle size distributions were used to exclude particle size related information ambiguity, known as triggering effects or size bias. The results of this study show qualitatively and quantitatively the difference in time-averaged particle dynamics for selected particle sizes in a backward-facing step flow. The experiments show, for different sizes, the changes in the particle velocity field in comparison with the velocity field of the continuous phase deduced from the 1 μm particles, and also imply the strong influences which different particle sizes have on flow data evaluation when size effects are not taken into account with particle-related optical measuring techniques.     

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.     

An experimental study into the effects of streamwise and spanwise acceleration in a turbulent boundary layer

We compare two turbulent boundary layers produced in a low-speed water channel experiment. Both are subjected to an identical streamwise pressure gradient generated via a lateral contraction of the channel, and an additional spanwise pressure gradient is imposed on one of the layers by curving the contraction walls. Despite a relatively high streamwise acceleration, hot-film probe measurements of the mean-velocity distributions show that the Reynolds number increases whilst the coefficient of friction decreases downstream. Visualization of the viscous layers using hydrogen bubbles reveal an increase in the non-dimensional streak spacing in response to the acceleration. Changes in statistical moments of the streamwise velocity near the wall suggest an increased dominance of high-velocity fluctuations. The near-wall streaks and velocity statistics have little sensitivity to the boundary layer three-dimensionality induced by the spanwise pressure gradient, with the boundary-layer crossflow velocity reaching 11 % that of the local freestream velocity.     

An experimental study of a two-dimensional plane turbulent wall jet

 Laser-Doppler measurements were conducted in a plane turbulent wall jet at a Reynolds number based on inlet velocity, Re ₀, of 9600. The initial development as well as the fully developed flow was studied. Special attention was given to the near-wall region, including the use of small measuring volumes and the application of specific near-wall data corrections, so that wall shear stresses were determined directly from the mean velocity gradient at the wall using only data below y ⁺=4. It was possible to resolve the inner peak in the streamwise turbulence intensity as well as the inner (negative) peak in the shear stress. Limiting values of (u′)⁺ and uv ⁺ were determined. Turbulence data from the outer region of the flow were compared to earlier hot wire measurements and large differences in the normal turbulence intensity and the shear stress were found. These differences can be attributed to high turbulence intensity effects on the hot-wires. Received: 17 October 1996 / Accepted: 8 December 1997     

Is the steady viscous incompressible two-dimensional flow over a backward-facing step at Re = 800 stable?

A detailed case study is made of one particular solution of the 2D incompressible Navier–Stokes equations. Careful mesh refinement studies were made using four different methods (and computer codes): (1) a high-order finite-element method solving the unsteady equations by time-marching; (2) a high-order finite-element method solving both the steady equations and the associated linear-stability problem; (3) a second-order finite difference method solving the unsteady equations in streamfunction form by time-marching; and (4) a spectral-element method solving the unsteady equations by time-marching. The unanimous conclusion is that the correct solution for flow over the backward-facing step at Re = 800 is steady—and it is stable, to both small and large perturbations.     

Diffraction and re-initiation of detonations behind a backward-facing step

Diffraction phenomena of gaseous detonation waves behind a backward-facing step in a tube are observed by using high-speed schlieren photography and soot-track records as well as by pressure measurements on the sidewall. Mixtures are stoichiometric oxyhydrogen and those diluted by argon at sub-atmospheric pressures. Three types of phenomena are observed, that is, continuous propagation of detonation, re-initiation after a temporal extinction of detonation and complete extinction of detonation. The continuous propagation means that the diffracted wave does not affect the main propagation although reflected shock waves from the bottom surface of the tube may affect it. The re-initiation occurs at a wall surface of the tube behind a reflected shock wave after the main detonation wave has been extinguished. Positions and conditions of the re-initiation are discussed. The complete extinction is defined as disappearance of detonation cells behind the step within a certain length of the tube. Cases exist where an ignition occurs after several reflections off the bottom and top surface of the tube.     

Particle image velocimetry measurements of a backward-facing step flow

Particle image velocimetry (PIV) measurements were carried out on a backward-facing step flow at a Reynolds number of Re_h=U_Xh/9=4,660 (based on step height and freestream velocity). In-plane velocity, out-of-plane vorticity, Reynolds stress and turbulent kinetic energy production measurements in the x-y and x-z planes of the flow are presented. Proper orthogonal decomposition was performed on both the fluctuating velocity and vorticity fields of the x-y plane PIV data using the method of snapshots. Low-order representations of the instantaneous velocity fields were reconstructed using the velocity modes. These reconstructions provided insight into the contribution that the various length scales make to the spatial distribution of mean and turbulent flow quantities such as Reynolds stress and turbulent kinetic energy production. Large scales are found to contribute to the Reynolds stresses and turbulent kinetic energy production downstream of reattachment, while small scales contribute to the intense Reynolds stresses in the vicinity of reattachment.     

Experimental study on the flow field behind a backward-facing step using a detonation-driven shock tunnel

The supersonic combustion RAM jet (SCRAM jet) engine is expected to be used in next-generation space planes and hypersonic airliners. To develop the engine, stabilized combustion in a supersonic flow field must be attained even though the residence time of flow is extremely short. A mixing process for breathed air and fuel injected into the supersonic flow field is therefore one of the most important design problems. Because the flow inside the SCRAM jet engine has high enthalpy, an experimental facility is required to produce the high-enthalpy flow field. In this study, a detonation-driven shock tunnel was built to produce a high-enthalpy flow, and a model SCRAM jet engine equipped with a backward-facing step was installed in the test section of the facility to visualize flow fields using a color schlieren technique and high-speed video camera. The fuel was injected perpendicularly to a Mach 3 flow behind the backward-facing step. The height of the step, the injection distance and injection pressure were varied to investigate the effects of the step on air/fuel mixing characteristics. The results show that the recirculation region increases as the fuel injection pressure increases. For injection behind the backward-facing step, mixing efficiency is much higher than with a flat plate. Also, the injection position has a significant influence on the size of the recirculation region generated behind the backward-facing step. The schlieren photograph and pressure histories measured on the bottom wall of the SCRAM jet engine model show that the fuel was ignited behind the step.Communicated by K. Takayama PACS 47.40.Ki