Three-dimensional Backward-facing Step Research Articles

Experimental Study on the Snowfall Flow Control of Backward-Facing Steps Using a High-Durability Designed Plasma Electrode

Using a high-durability designed plasma electrode (PA), the plasma actuation effect on both a two-dimensional backward-facing step flow (standard model) and an arc-shaped three-dimensional backward-facing step flow (arc model) was investigated experimentally. First, we searched for plasma operation control conditions suitable for the two-dimensional backward-facing step flow by carrying out experiments using a medium-sized circulating wind tunnel. Next, using the natural-snow wind tunnel of the Hokkaido University of Science, we examined whether an AC-driven PA can control snowfall flow. It became clear for the first time that the amount of snow accumulation can be reduced by more than 20% when the PA is driven at a dimensionless frequency of fH/U = 0.32, where f is the pulsed modulation frequency, H is the step height, and U is the mainstream velocity, and the duty ratio D (the time ratio of PA_ON to the total time when controlled by the pulsed modulation frequency) is equal to 1.0%. It was also confirmed that by masking the arc-shaped electrode parallel to the mainstream and using only the part perpendicular to the mainstream of the PA electrode, the amount of accumulated snow could be reduced by up to 20%. It has become clear that high-durability designed plasma electrodes can control the snowfall flow and reduce the amount of accumulated snow.

Study on Flow Characteristics of Three-Dimensional Backward-Facing Step at High Reynolds

Fan, J.; Yan, C.; Lei, P.; Wang, C., and Liu, G., 2020. Study on flow characteristics of three-dimensional backward-facing step at high Reynolds. In: Gong, D.; Zhang, M., and Liu, R. (eds.), Advances in Coastal Research: Engineering, Industry, Economy, and Sustainable Development. Journal of Coastal Research, Special Issue No. 106, pp. 522–525. Coconut Creek (Florida), ISSN 0749-0208.Based on FLUENT, the three-dimensional Realizable k-e turbulence model is used to simulate the flow over a backward-facing step at 40 Reynolds numbers between 500 and 80,000, and the results are combined with the results of particle image velocimetry experiments to verify the reliability of the model. The three-dimensional flow characteristics of the flow over a backward-facing step at Re = 25,822 are analyzed. The results show that in the two-dimensional aspect, the numerical simulation results are in good agreement with the experimental values, the separation and reattachment zone length change curves are consistent, the flow field structure is similar, and the model reliability is high. In three dimensions, slight differences occur in the flow distribution of the sections perpendicular to Z axis, and the closer the section is to the wall, the greater the change of flow is. Along the Z axis, the velocity and turbulent energy of water flow are unevenly distributed in the spreading direction, showing strong three-dimensional flow characteristics.

Research on the Heat Transfer Characteristics of the Three-Dimensional Backward-facing Step Flow Using Liquid Crystal Sheet Based on SVR Method

Research on the Heat Transfer Characteristics of the Three-Dimensional Backward-facing Step Flow Using Liquid Crystal Sheet Based on SVR Method

LES/FMDF of premixed methane/air flow in a backward-facing step combustor

In the present study, a hybrid Eulerian-Lagrangian methodology is utilized for large eddy simulation (LES) of premixed fuel/air flow over a three-dimensional backward facing step (BFS). The fluid dynamic features are obtained by solving the Eulerian filtered compressible transport equations while the species are predicted by using the filtered mass density function method (FMDF). Some scalar fields are duplicated in FD and MC solvers to examine the numerical consistency between them. A good agreement is achieved by comparing the essential characteristics of the BFS flow (such as the mean and RMS values of the velocity and temperature fields and also the reattachment length) obtained from numerical results with the measurements. This ensures that the proposed hybrid method is reliable for studying the reacting flow in relatively complex combustion systems. Additionally, the performance of several SGS models are assessed, and the results indicate that the dynamic Smagorinsky and WALE models are superior to standard Smagorinsky and MKEV models.

Influence of flow tree-dimensionality on the heat transfer of a narrow channel backward facing step flows

This manuscript studies the forced-mixed convective flow on a three-dimensional backward facing step with low aspect ratio (AR = 4) and expansion ratio ER = 2 for Reynolds number in the laminar and beginning of transitional regime (Re 100–1200). The analysis is performed using large eddy simulations, with the main objective assessing the effect of sidewalls on heat transfer characteristics on bottom wall in narrow channels with sudden expansion. The numerical model has been validated with experimental and numerical results from the literature and qualitatively with the experimental results obtained through Moiré deflectometry. The bottom surface was kept at constant temperature greater than the flow inlet temperature, while the other walls are considered to be adiabatic. To decouple the three-dimensional flow features due to the sidewalls and the intrinsic three-dimensional instabilities of the separated flow, two different boundary conditions on lateral walls, slip and non-slip, have been used. The results obtained show that when slip sidewalls are considered, the three-dimensional intrinsic structures begging to appear for Re equal to 1200. These structures enhance the heat transfer in the bottom wall. On the contrary, with non-slip sidewalls, the strong three-dimensional structures caused by the sidewalls represented by the upper side recirculation bubble and the wall jets mask the intrinsic three-dimensional instability, decreasing the heat transfer in the lower wall downstream of the step. As a consequence, the surface averaged Nusselt for all Reynolds numbers corresponding to the beginning of the transitional flow is lower for the case of non-slip sidewalls than for the case of slip sidewalls. Thus, the study concludes that sidewalls have a negative effect on heat transfer in narrow channels for flow Reynolds numbers in the early transitional regime.

Numerical modeling of the self-oscillation onset near a three-dimensional backward-facing step in a transonic flow

The results of a numerical investigation of the nature of self-oscillation processes occurring in transonic flow past a backward-facing step and a cavity with a flow of the open type are presented. The turbulent flow past the above-mentioned bodies is modeled using the NOISEtte software package intended for solving problems of aerodynamics and aeroacoustics on unstructured grids. The modeling is performed using the eddy-resolving IDDES method that belongs to the class of hybrid RANS-LES approaches. The adequacy of the calculations is confirmed by means of comparing the results obtained with the available experimental data. The structure and the salient features of the self-oscillatory, hydrodynamic-in-nature process, which arises in flow past a cavity and a backward-facing step, are established.

Assessment of secondary bubble formation on a backward-facing step geometry

Flow visualization experiments and numerical simulations were performed on a narrow three-dimensional backward-facing step (BFS) flow with the main objective of characterizing the secondary bubble appearing at the top wall. The BFS has been widely studied because of its geometrical simplicity as well as its ability to reproduce most of the flow features appearing in many applications in which separation occurs. A BFS test rig with an expansion ratio of 2 and two aspect ratios (AR = 4 and AR = 8) was developed. Tests were performed at range of Reynolds numbers ranging from 50 to 1000; visualization experiments provided a qualitative description of secondary bubble and wall-jet flows. Large eddy simulations were carried out with two different codes for validation. Numerical solutions, once validated with experimental data from the literature, were used to acquire a deeper understanding of the experimental visualizations, to characterize the secondary bubble as a function of the flow variables (Reynolds and AR) and to analyze the effect of the secondary bubble on primary reattachment length. Finally, to decouple the sidewall effects due to the non-slip condition and the intrinsic flow three-dimensionality, numerical experiments with free-slip conditions over the sidewalls were computed. The main differences were as follows: When the non-slip condition is used, the secondary bubble appears at a Reynolds number of approximately 200, increases with the Reynolds number, and is limited to a small part of the span. This recirculation zone interacts with the wall-jets and causes the maximum and minimum lengths in the reattachment line of the primary recirculation. Under free slip conditions, the recirculation bubble appears at a higher Reynolds number and covers the entire channel span.

Parallelization of a Simple-Based Algorithm to Simulate Mixed Convective Flow Over a Backward-Facing Step

This article describes a parallel implementation of an algorithm for simulating mixed convective flow over a three-dimensional backward-facing step. A FORTRAN90 code was developed and parallelized using OpenMP directives for distributed shared memory (DSM) multiprocessors. Numerical experiments conducted on an IBM p5-575 multiprocessor show that the code achieves significant speed-up on up to 16 processors. Superlinear speed-up was also observed in some cases as a result of efficient cache utilization on the multiprocessor.

Optimal preconditioning of lattice Boltzmann methods

A preconditioning technique to accelerate the simulation of steady-state problems using the single-relaxation-time (SRT) lattice Boltzmann (LB) method was first proposed by Guo et al. [Z. Guo, T. Zhao, Y. Shi, Preconditioned lattice-Boltzmann method for steady flows, Phys. Rev. E 70 (2004) 066706-1]. The key idea in this preconditioner is to modify the equilibrium distribution function in such a way that, by means of a Chapman–Enskog expansion, a time-derivative preconditioner of the Navier–Stokes (NS) equations is obtained. In the present contribution, the optimal values for the free parameter γ of this preconditioner are searched both numerically and theoretically; the later with the aid of linear-stability analysis and with the condition number of the system of NS equations. The influence of the collision operator, single- versus multiple-relaxation-times (MRT), is also studied. Three steady-state laminar test cases are used for validation, namely: the two-dimensional lid-driven cavity, a two-dimensional microchannel and the three-dimensional backward-facing step. Finally, guidelines are suggested for an a priori definition of optimal preconditioning parameters as a function of the Reynolds and Mach numbers. The new optimally preconditioned MRT method derived is shown to improve, simultaneously, the rate of convergence, the stability and the accuracy of the lattice Boltzmann simulations, when compared to the non-preconditioned methods and to the optimally preconditioned SRT one. Additionally, direct time-derivative preconditioning of the LB equation is also studied.

Three-dimensional simulation of turbulent forced convection in a duct with backward-facing step

Results from three-dimensional (3-D) simulations of turbulent forced convection adjacent to backward-facing step in a rectangular duct using a k - ϵ - ζ - f turbulence model are reported. This turbulence model is numerically robust near the wall, and it has been shown to predict turbulent heat transfer in separated and wall-bounded flows better than commonly used two-equation turbulence models. FLUENT-CFD code is used as the platform for these simulations and User Defined Functions (UDF) are developed for incorporating this turbulence model into the code. The UDF implementation is validated by simulating several 2-D separated flow/heat transfer benchmark problems. The resulting excellent agreements between the simulated results and benchmark data for these 2-D problems justify the use of this resource for simulating 3-D convection problems. Three-dimensional backward-facing step geometry with an expansion ratio of 1.48 and with a step height of 4.8 mm is used in this study. Three aspect ratios of 3, 8 and infinity (2-D simulation) are considered for studying its effect on the flow and heat transfer, and similarly the effect of the Reynolds number was examined by varying its magnitude in the range of 20,000–50,000. Simulated results are presented for the general 3-D flow features, the reattachment lines, temperature and Nusselt number distributions that develop in this geometry.

Entropic Lattice Boltzmann Models for Hydrodynamics in Three Dimensions

Efficient, nonlinearly stable entropic lattice Boltzmann models for computational fluid dynamics are presented. A new method of fast evaluation of equilibria to machine precision is proposed. Analytical solution is found for the collision step which guarantees stability and thermodynamic consistency of the scheme. As an example, a novel 15-velocity lattice Boltzmann model is derived and validated with a simulation of a three-dimensional backward-facing step flow.

Exploration of vortex dynamics for transitional flows in a three-dimensional backward-facing step channel

The eddy structures and their mutual interactions in a three-dimensional channel with a backward-facing step for the transitional Reynolds number 900 were investigated numerically. The aim was to reveal the structural development of the entire vortical flow field, which could immensely enhance the knowledge about vortical structures occurring in the recirculation region near the step wall. Simulations were made to reproduce the experimental observations and provide clear indications about the strong interaction between the shear layer instabilities. Physical instabilities of this type were amplified by the shedding-type instabilities and induced by the interaction of coherent structures with the sidewalls of the duct. These interactions were responsible for the flapping motion of interior shear layer. Careful attempts were made to reveal the behaviour of these vortical structures by means of vortex stretching, roll-up of vortex lines and formation of vortex tubes. Also, the three-dimensional flow topology of the velocity field corresponding to stationary helical vortex (SHV) was analysed extensively. The SHV flow consisted of a pair of counter-rotating helical cells in a double helix structure wrapped around the vortex tube. The roll-up shear-layer hovering vortices were observed near the step to initiate the Kelvin–Helmholtz-like instability. The Kelvin–Helmholtz vortices were developed into lambda-shaped vortices which impinged on the step-wall and were elongated into the hairpin-like vortices.

Reverse flow regions in three-dimensional backward-facing step flow

Laser-Doppler velocity measurements adjacent to the bounding walls of three-dimensional (3-D) backward-facing step flow are performed for the purpose of mapping the boundaries of the reverse flow regions that develop in this geometry (adjacent to the sidewalls, the flat wall and the stepped wall) as a function of the Reynolds number. The backward-facing step geometry is configured by a step height ( S) of 1 cm, which is mounted in a rectangular duct having an aspect ratio (AR) of 8:1 and an expansion ratio (ER) of 2.02:1. Results are presented for a Reynolds number range between 100 and 8000, thus covering the laminar, transitional and turbulent flow regimes. The boundaries of the reverse flow regions are identified by locating the streamwise coordinates on a plane adjacent to the bounding walls where the mean streamwise velocity component is zero. The size of the reverse flow regions increases and moves further downstream in the laminar flow regime; decreases and moves upstream in the transitional flow regime; and remains almost constant or diminishes in the turbulent flow regime; as the Reynolds number increases. The spanwise distribution of the boundary line for the reverse flow region adjacent to the stepped wall develops a minimum near the sidewall in the laminar flow regime, but that minimum in the distribution disappears in the turbulent flow regime. Predictions agree well with measurements in the laminar flow regime and reasonably well in the turbulent flow regime.

Laminar Mixed Convection Adjacent to Three-Dimensional Backward-Facing Step

Simulations of three-dimensional laminar buoyancy-assisting mixed convection adjacent to a backward-facing step in a vertical rectangular duct are presented to demonstrate the influence of Grashof number on the distributions of the Nusselt number, and the reverse flow regions that develop adjacent to the duct’s walls. The Reynolds number, and duct’s geometry are kept constant: heat flux at the wall downstream from the step is kept uniform but its magnitude varied to cover a Grashof number range of 0–4000; all the other walls in the duct are kept at adiabatic condition; and the flow, upstream of the step, is treated as fully developed and isothermal. Increasing the Grashof number results in increasing the Nusselt number; the size of the secondary recirculation flow region adjacent to the stepped wall; the size of the reverse flow region adjacent to the sidewall and the flat wall; and the spanwise flow from the sidewall toward the center of the duct. On the other hand, the size of the primary recirculation flow region adjacent to the stepped wall decreases and detaches partially from the heated stepped wall as the Grashof number increases. Details are presented and discussed.

Time evolution of laminar flow over a three-dimensional backward-facing step

A numerical investigation of laminar flow over a backward-facing step is presented within the transient context. The analysis is concerned with the step geometry and flow conditions reported by Armaly et al. Results show that there is generally good agreement between the three-dimensional results and the experimental data for Re<400, and excellent agreement with the two-dimensional results. Insight is also provided into the rich character of the end-wall-induced three-dimensional vortices in the channel downstream of the step. To this end, the topological theory is adopted to draw the particle oil streaklines on the roof, floor, step plane and the end-wall, from which lines of separation and reattachment are theoretically determined. Together with the Lagrangian particle track plot in the flow interior, light is shed on the formation of a secondary flow pattern, and thus the development of longitudinal vortices. The present transient analysis increases the understanding of the complex interaction of the end-wall-induced vortices and the mainstream flow. This helps to reveal the mechanism responsible for the increasing penetration of the three-dimensional flow structure into a region near the mid-plane of the channel, at which the flow is essentially two-dimensional. Copyright © 1999 John Wiley & Sons, Ltd.

Analysis of 3D backward-facing step incompressible flows via a local average-based numerical procedure

SUMMARY The study of the flow over a three-dimensional backward-facing step still provides interesting research when a new numerical method is developed and an investigation of the flow topology is performed. From a numerical point of view, accurate solutions are required, preferably with little computational effort, and the numerical results must lead to the understanding of the main features of the flow. The guidelines of an integrated framework are presented in this paper, starting with the description of the numerical methods for solving three-dimensional incompressible flows, based on a local-average procedure, up to the investigation of the flow structure by means of vortex lines reconstruction and vortices identification. Several results are reported concerning an analytical benchmark, simulation of flows in laminar and incipient transitional regimes and detection of vortical structures. Preliminary results for highly unsteady flows are also presented. © 1998 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.

LEAST-SQUARES FINITE ELEMENT SOLUTIONS FOR THREE-DIMENSIONAL BACKWARD-FACING STEP FLOW

SUMMARY Comprehensive numerical solutions of the steady state incompressible viscous flow over a three-dimensional backward-facing step up to Re = 800 are presented∗. The results are obtained by the least-squares finite clement method (LSFEM) which is based on the velocity-pressurc-vorticity formulation. The computed model is of the same size as that of Armaly's experiment. Three-dimensional phenomena are observed even at low Reynolds number. The calculated values of the prima ry reattachment length are in good agreement with experimental results.

A numerical study of three-dimensional backward-facing step flow

The laminar and turbulent flow over a backward-facing step placed in a square duct was investigated numerically. The aspect ratio of the step (step width/step height) was 3 and the area expansion ratio was 2∶3. Three-dimensional effects were significant due to the small aspect ratio. To simulate turbulent flows, both a standardk-ɛ model and a non-lineark-ɛ model were employed and the results were compared. The non-linear model was found to yield better results. From the numerical results, the existence of the corner vortex and the flow field associated with it were clarified. The reattachment length of the three-dimensional flow was found to be considerably shorter than the corresponding two-dimensional flow. The evolution of longitudinal vortices was visualized. Surface flow patterns which clearly demonstrate three-dimensional aspects of the flow were presented. Based on various data available, topological flow pattern was also sketched. To support the findings explored in the present work, expeirmental data were compared with the numerical data where applicable.

MULTIGRID ACCELERATION OF THREE-DIMENSIONAL, TURBULENT. VARIABLE-DENSITY FLOWS

Muhigrid acceleration is applied to a finite-volume method for the calculation of three-dimensional, variable-density turbulent flow. Turbulence is modeled by the k-∈ model with the transport equations incorporated into the multigrid procedure. Density variations are fully accounted for. A full approximation multigrid method is developed using mass-conserving restriction and prolongation operators. A significant reduction in overall computing time is shown for both constant-density and variable-density flow over a three-dimensional backward-facing step. It is concluded that the method is suitable for application to complex three-dimensional flows of practical engineering interest.