Turbulent Backward-facing Step Flow Research Articles

Experimental study of self-sustained spanwise streaks and turbulent mixing in separated shear flow

The self-sustained streaks in turbulent backward-facing step flow are experimentally studied at a step height Reynolds number of 1.0 × 103. As one of the featured dynamic behaviors, evolution of the spanwise streaks plays an important role in the large-scale, aperiodic and vertical flapping motions of the separated/reattaching shear layer. By time-resolved particle image velocimetry, we measure the velocity vector fields in the streamwise-spanwise and streamwise-vertical planes downstream of a two-dimensional backward-facing step. The two cross-sectional velocity fields show that the shear layer remains two-dimensional along the span in the initial half of the shear layer, and then three-dimensional structures start to evolve in the latter half, leading to an unsteady reattaching shear layer and a shifting reattachment point on the downstream wall. By analyzing the finite-time Lyapunov exponent in the spanwise field of view, we find that low-speed fluid elements are vertically entrained upwards into the shear layer. As a result, the entrained fluid elements produce transient and localized low-speed fluid patches in the streamwise-spanwise plane, which move and decay downstream with strong straining and stretching motions along their boundaries. Furthermore, the large-scale streak-type and flap-type flows are clearly extracted and reconstructed by the energy-containing proper orthogonal decomposition modes.

Investigation of spanwise coherent structures in turbulent backward-facing step flow by time-resolved PIV

We experimentally investigate spanwise coherent structures in the turbulent shear layer downstream of a two-dimensional backward-facing step (BFS). The incoming free-stream flow separates from the backward-facing step edge and then reattaches to the downstream wall surface, resulting in a separated/reattaching shear layer and a recirculation region behind the step. This separated/reattaching shear flow is measured by time-resolved particle image velocimetry (PIV) in one streamwise-vertical plane and three parallel streamwise-spanwise planes, respectively. As a result, the multiple cross-sectional flow diagnosis reveals that the separated shear layer remains two-dimensional from the step edge to approximately the half of the reattachment length. Further downstream, the shear layer begins to flap vertically and it evolves spanwise-oriented structures with alternating high- and low-speed streaks. The near-wall vortex tube beneath the shear layer simultaneously evolves unsteady spanwise variation as well. The unsteady shear layer as well as the vortex tube causes entrainment of the high-momentum fluid from the shear layers downwards into the near-wall vortex tube, and entrainment of the low-momentum fluid upwards in the opposite way. By proper orthogonal decomposition and dynamic mode decomposition, the spanwise coherent structures are characterized as large in size as 2 step heights and they have the same order of frequencies as the vertical pumping and flapping motions, both of which contribute a major part of the turbulent kinetic energy in the shear layer. Further analysis by spatial-temporal cross-correlation function shows that the spanwise coherent structures have influence on the convection velocities of the coherent structures in the latter half of the shear layer.

Algebraic non-equilibrium wall-stress modeling for large eddy simulation based on analytical integration of the thin boundary-layer equation

An algebraic nonequilibrium wall-stress model for large eddy simulation is discussed. The ordinary differential equation (ODE) derived from the thin-layer approximated momentum equation, including the temporal, convection, and pressure gradient terms, is considered to form the wall-stress model. Based on the concept of the analytical wall function (AWF) for Reynolds-averaged turbulence models, the profile of the subgrid scale (SGS) eddy viscosity inside the wall-adjacent cells is modeled as a two-segment piecewise linear variations. This simplification makes it possible to analytically integrate the ODE near the wall to algebraically give the wall shear stress as the wall boundary condition for the momentum equation. By applying such integration to the wall-normal velocity component, the methodology to avoid the log-layer mismatch is also presented. Coupled with the standard Smagorinsky model, the proposed SGS-AWF shows good performance in turbulent channel flows at Reτ = 1000–5000 irrespective of the grid resolutions. This SGS-AWF is also confirmed to be superior to the traditional equilibrium wall-stress model in a turbulent backward-facing step flow.

Passive Flow Control for Reduced Load Dynamics Aft of a Backward-Facing Step

Passive flow control devices for a fully turbulent backward-facing step flow were investigated experimentally with particle image velocimetry and dynamic pressure transducers in the Trisonic Wind Tunnel Munich at Mach numbers of 0.80 and 2.00, as well as at Reynolds numbers of and 210,000, respectively. The results showed that these flow control devices, which are comprised of circular and square convoluted trailing edges on the backward-facing step, were a far more effective alternative to active flow control. The mean reattachment length was reduced by over 80% for the most effective configuration: so-called square lobes with a protrusion height of 0.4 step heights. This geometry also reduced the root mean square of the pressure fluctuations experienced by the reattachment surface by nearly 50% in transonic conditions. It was shown that the harmful step mode was weakened by forcing streamwise vorticity onto the flow through the presence of the lobes. The square lobes were more effective in diffusing this mode when compared to the circular lobes. Similarly, with increasing lobe sizes, the effectiveness of the flow control devices increased. Thus, a simple passive solution was determined for reducing the buffeting effects experienced by space launchers in transonic flight, for instance.

Reduced-order coherent structures in active flow separation control using a bio-inspired flapping actuator

An experimental study was conducted to investigate large-scale coherent structures induced by a bio-inspired flapping actuator in a turbulent backward-facing step flow. The flow field velocity dataset in the horizontal-vertical plane was obtained by planar particle image velocimetry. The flapping actuator was implemented over the step edge and it was driven to vertically oscillate, generating periodic small perturbations into the separated shear layer. As a result of active flow control, time-averaged reattachment length was reduced by 31% and Reynolds stresses as well as in-plane turbulent kinetic energy in the separated shear layer were considerably increased. In proper orthogonal decomposition analysis, the first two modes are found to be phase-correlated in the phase portrait of the coefficients. Therefore, reduced-order coherent structures are reconstructed by the first two modes, showing the phase evolution of the vortex shedding process. The extracted reduced-order coherent structures provide a better understanding of the underlying flow physics and are beneficial to effective flow separation control.

Validation of SIV measurements of turbulent characteristics in the separation region

Temporally and spatially resolved 2D measurements are important for the studies of complex turbulent flows. The recently developed SIV technique (Smoke Image Velocimetry), which is superior to PIV in some cases, can be used for this purpose. SIV validation results are presented for the steady turbulent backward-facing step flow measurements. Velocity profiles and Reynolds stress profiles are given for the regions of oncoming flow, reverse flow, flow reattachment and relaxation. The Reynolds number based on the step height and oncoming flow velocity at the boundary layer edge was Reh = 4834. The obtained data have been compared to LDA measurements and DNS.

Fiber suspension investigation in a backward-facing step by PIV

A dilute suspension (volume fraction 0.05%) of rod-like particles in a turbulent backward-facing step flow at Reynolds number ReH=14900, is investigated by means of Particle Image Velocimetry. Two-way interactions between fluid and dispersed phase are analyzed by exploiting the high spatial resolution of the acquisitions. Mutual interactions between phases can be investigated by considering flow turbulence modulations and phenomena related to preferential concentration and orientation of fibers. Slight turbulence enhancement is reported in the laden flow and concentration data show a moderate tendency of fibers to accumulate at the channel centreline. Orientation data display a strong preferential orientation of fibers. Local fiber orientation is correlated to the direction of maximum shear showing a high level of correlation also in the flow regions featuring strong gradients.

Conditions for validity of mean flow stability analysis

This article provides theoretical conditions for the use and meaning of a stability analysis around a mean flow. As such, it may be considered as an extension of the works by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to non-parallel flows and by Turton et al. (Phys. Rev. E, vol. 91 (4), 2015, 043009) to broadband flows. Considering a Reynolds decomposition of the flow field, the spectral (or temporal Fourier) mode of the fluctuation field is found to be equal to the action on a turbulent forcing term by the resolvent operator arising from linearisation about the mean flow. The main result of the article states that if, at a particular frequency, the dominant singular value of the resolvent is much larger than all others and if the turbulent forcing at this frequency does not display any preferential direction toward one of the suboptimal forcings, then the spectral mode is directly proportional to the dominant optimal response mode of the resolvent at this frequency. Such conditions are generally met in the case of weakly non-parallel open flows exhibiting a convectively unstable mean flow. The spatial structure of the singular mode may in these cases be approximated by a local spatial stability analysis based on parabolised stability equations (PSE). We have also shown that the frequency spectrum of the flow field at any arbitrary location of the domain may be predicted from the frequency evolution of the dominant optimal response mode and the knowledge of the frequency spectrum at one or more points. Results are illustrated in the case of a high Reynolds number turbulent backward facing step flow.

Interactions between fluid and fibers in a turbulent backward-facing step flow

In this work, a turbulent backward-facing step flow at Reynolds number ReH = 17 520, laden with rod-like particles, is investigated by means of particle image velocimetry. Particle loadings tested are within 0.02% and 0.05% volume fractions; thus, the suspensions may be considered as dilute. The high spatial resolution allows the identification of fiber orientation within the flow, so that mutual interactions between phases can be investigated by considering flow modifications and phenomena related to preferential concentration and orientation of fibers. Fibers’ concentration data show a moderate trend to accumulate at the channel centreline, whereas orientation data display a strong preferential orientation of fibers. Specifically, the local fibers’ orientation is correlated to the flow field in terms of mean flow direction and plane of maximum shear. The occurrence of a symmetrical orientation profile with respect to the channel centre-line is reported as well as the tendency to recover such profile downstream of the step.

0131 気泡トレーサーによるはく離流れのPIV計測(OS1 噴流,後流および剥離流れ現象の探求と技術革新,オーガナイズドセッション)

PIV measurement using micro bubbles (mean diameter 40-50μm) as tracers was attempted. Turbulent backward-facing step flow Was chosen for test case. Visualized flow image obtained by bubble tracers in our first trial was not sufficient for pattern matching in PIV process. Results show higher quality image is needed for complicated

DNS and LES of Passively Controlled Turbulent Backward-Facing Step Flow

A passive control approach (no external energy input) for an unsteady separated flow case was investigated numerically. A surface-mounted control fence was positioned upstream of a backward-facing step, and as an oncoming flow a thin and fully developed turbulent boundary layer with a thickness of δ/h = 0.8 was used. The objective of the passive control was to enhance the entrainment rate of the shear layer bounding the separation zone behind the step, thereby reducing the mean reattachment length,〈 X r0 〉. Direct Numerical Simulations (DNS) and Large-Eddy Simulations (LES) at Re h = 3000 (based on the step height, h, and the free stream velocity, U ∞) were carried out for the uncontrolled and the controlled flow case. The LES results were in good agreement with the DNS reference solutions. Adaptively controlled feedback simulations showed that a certain minimum distance between the step edge and the upstream position of the control fence is required to achieve a maximum reduction of the reattachment length.

Measurement of fluid turbulence along the path of a heavy particle in a backward-facing step flow

To accurately model the motion of a solid particle in a turbulent air flow, characteristics of the fluid turbulence in the particle-Lagrangian reference frame must be known. This paper describes a quasi-numerical technique that uses a laser Doppler anemometer (LDA) probe mounted on a two-dimensional traverse to track the path of an emulated particle through a turbulent backward-facing step flow. Fluid velocity measurements (from the LDA) are inputs to a control loop that accelerates the LDA probe as if it were a particle allowing for particle-Lagrangian fluid statistics to be measured. Particles with time constants from 0.1 to 10 s were run through a backward-facing step flow with Reynolds number 10,000 based on step height and inlet velocity. Digital particle image velocimetry (DPIV) was used to estimate the fluid vorticity along the particle path. The results show that the particle behavior is a strong function of particle path. Particles entering the shear layer see a larger range of turbulence and therefore are more affected by the flow than those that stay outside the shear layer.

Organized vortex motion in periodically perturbed turbulent separated flow over a backward-facing step

This study considers the relationship between the time-averaged and phase-averaged flow fields in turbulent backward-facing step flow under the influence of periodic perturbation. Attempts are made to clarify the interaction between organized vortex motion and turbulence statistics such as Reynolds stress. The velocity fields are measured using a particle imaging velocimeter (PIV) for three selected perturbation frequencies, one corresponding to the most effective frequency in terms of the reduction of reattachment length, one below it and another above it. The evolution of organized vortex motion due to the imposed perturbation is found remarkable except for the case of perturbation at the highest frequency, at which the organized motion dissipates so quickly behind the step that the flow is not altered. At the most effective perturbation frequency, the regions of large Reynolds stress appear as a result of strong stretching between successive vortices caused by the perturbation. It is concluded that the change in the mean velocity field due to the organized fluid motion alters the production rate of Reynolds stress, which is a key effect of the perturbation on turbulent separated flow.

SIMPLER-BASED PROCEDURE FOR NUMERICAL SIMULATION OF DYNAMIC VORTICAL CHARACTERISTICS OF SOME TURBULENT FLOWS

An unsteady numerical simulation based on the SIMPLER solution procedure with a strictly treated pressure solver is developed. This procedure greatly enhances accurate convergence in pressure as well as velocity in each iteration in the numerical simulation, so that it improves the prediction of the dynamic vortical characteristics of some turbulent flows in which pressure feedback constitutes the major contribution to the large-scale vortical behavior. The algorithm is used to investigate the coherent vortical structures and spectral evolution characteristics of jet flow and backward-facing step flow. The present numerical simulation can provide satisfactory predictions of vortex-shedding behaviors in jet and step flows without adding any artificial disturbance in the simulation. For cases of jet flows with and without excitation, the dynamic vortical evolution is predicted in good agreement with experimental observations and the well-known subharmonic evolution model. For turbulent backward-facing step flow with and without lateral mass bleed, satisfactory prediction of the time-averaged flow characteristics compared with experimental measurements is reached in the simulation. The complicated dynamic vortex-shedding process at the reattachment point of the backward-facing step flow is delineated based on the simulation results, and the results also provide evidence of the existence of both controversial shedding mechanism.

Measurements of heat transfer in a separated and reattaching flow with spatially varying thermal boundary conditions

Abstract The effect of highly varying thermal boundary conditions on the convective heat transfer in a backward-facing step flow was investigated in a two-dimensional (2D) boundary-layer tunnel in air. A modified form of the transient heat transfer technique was used that allowed variable surface temperature distributions to be imposed by heating the test surface with a radiative lamp prior to cooling. The experiments were restricted to axial variations in surface temperature. Surface temperatures were measured with both cement-on foil thermocouples and thermochromic liquid crystal thermography. A semianalytic superposition technique was developed that was capable of predicting the heat transfer for any arbitrary axial surface temperature distribution, given the general solution or “Green's” function. The Green's function was measured to a limited spatial resolution by solving a simultaneous set of equations using data from 30 experiments. The techniques were developed and tested in a 2-D flat-plate boundary layer with Re δ2 of 3500 at the leading edge and qualified against a well-verified boundary-layer code. The Green's function and inverse Green's function were then measured in a turbulent backward-facing step flow with Re based on step height of 26,000. In the separated flow, it was found that the effect of localized heating extended only a short distance upstream and downstream, and that the heat transfer was less sensitive to temperature boundary conditions than would be expected from attached flow behavior. This corroborates the conclusion of previous workers that the primary resistance to the heat transfer is localized near the wall. This localized behavior, and the spatial insensitivity of the Green's function, suggest that with proper scaling, the results could be extended to other separated flows.

Analysing turbulent backward-facing step flow with the lowpass-filtered Navier-Stokes equations

Analysing turbulent backward-facing step flow with the lowpass-filtered Navier-Stokes equations

Analysing turbulent backward-facing step flow with the lowpass-filtered navier-stokes equations

High Reynolds number turbulent backward-facing step flow is studied using the large-eddy simulation technique proposed by Schumann. Central differencing on an equidistant cartesian grid and explicit time integration are chosen to predict the complicated flow structure. The comparison with experimental data indicates good agreement for the statistical quantities. Part of the disagreement is certainly due to scatter in the experimental data. Nevertheless, the results of the simulation may be further improved using globally or locally refined grids. Valuable information on the instantaneous flow behaviour in the free-shear layer and the reattachment zone is obtained from the simulation.