Recirculation Length Research Articles

Gap ratio effects on the coherent structures surrounding a near-wall square cylinder

Turbulent flow around a square cylinder offset at different heights from an upstream rough wall are investigated using time-resolved particle image velocimetry. The Reynolds number based on the freestream velocity and cylinder height was 12750 and the incoming turbulent boundary layer thickness was 7.2 times the cylinder height. The examined gaps beneath the cylinder were 0.0, 0.3, 0.5, 1.0, 2.0, 4.0, and 8.0 times the cylinder height. The results show that the mean recirculation length remains relatively constant for cases with a gap size greater than or equal to 1.0 times the cylinder height. Flow acceleration through the gap under the cylinder is strongest with a gap size of 2.0 times cylinder height. Downstream of the cylinder, the vertical velocity fluctuations contribute strongly to the production of turbulent kinetic energy by interacting with mean wall-normal velocity gradient in the vertical direction. The dominant frequency embedded in the incoming turbulent boundary layer persists in the wake of the cylinder when the gap size is less than 1.0 cylinder height. Kelvin-Helmholtz vortices originating from the top leading edge of cylinder occur at Strouhal numbers of 2.77-3.11 for the cases with gap ratio ranging from 0.3-8.0 cylinder heights, while spectral migration towards lower frequencies is observed for cases with gap sizes equal to 0.3 and 0.5 cylinder heights. The spatial trajectory of top Kelvin-Helmholtz vortices extends further away from the cylinder as the gap size increases. Spectral proper orthogonal decomposition analysis shows that the von Kármán vortex shedding structures possess the highest spectral energy for all offset cases despite regular vortex shedding being disrupted when the gap size is 0.3 times the cylinder height.

Three-dimensional numerical investigation on flow behaviors around a diversion dike

Three-dimensional numerical simulations of a flow past a non-submerged diversion dike are performed for various blockage ratios (1/6 ≤ β ≤ 1/3) and Froude numbers (0.152 ≤ Fr ≤ 0.253). The instantaneous and time-averaged flow characteristics, the evolution process of mixing layers, and the bed shear stress of the dike are analyzed. The blockage ratio β plays an important role in the momentum redistribution and turbulent kinetic energy of the diversion dike. As the blockage ratio increases, the flow velocity gradient and the vortex shedding frequency in the mixing layer significantly increase. The Froude number Fr has little effect on the flow field. A large recirculation zone is observed in the wake of the dike, and the recirculation length is more depended on the length of the dike rather than the Froude number. The bed shear stress around the dike increases significantly with the increase in the blockage ratio.

Cooling of Heated Blocks with Triangular Guide Protrusions Simulating Printed Circuit Boards

There is no study that investigates triangular guide protrusions including their systematical geometrical changes together with the effects of channel height in the open literature in the context of the authors’ knowledge. Moreover, the number of laminar studies is less than turbulent studies, whereas low velocity or natural convection cases are still important, especially for small devices in small PCB passages. The objective of this study is to investigate numerically the effects of triangular guide protrusions for the enhancement of heat transfer from the blocks’ simulated electronic components in laminar flow conditions. Two-dimensional, incompressible, steady, and laminar flow analysis was performed to predict fluid flow and heat transfer characteristics for three heated blocks in a PCB (printed circuit board) passage with triangular guide protrusions mounted on the upper wall. The Galerkin finite element method of weighted residuals was used to discretize conservation equations. The effects of the channel expansion ratio and inlet velocity were investigated for five geometrical cases. If the size of the protrusions is increased, the existence of protrusions starts to affect the flow patterns on the lower wall. The size of the last protrusion controls the flow structure downstream of the last block. On the upper wall, after the last protrusion, a recirculation is formed and the length of the recirculation increases with an increasing Re number. Moreover, the reattachment length of recirculation after the last block increases with an increasing Reynolds number for a fixed expansion ratio. Expansion ratio and inflow conditions caused by blocks and protrusions have a great influence on the formation of secondary recirculation in addition to the Reynolds number. Heat transfer increases with increasing sizes of upper triangular protrusions. Maximum overall heat transfer enhancement is provided as 47.7% with the geometry of the maximum sized protrusions for the channel height of 3 h. In the case of 4 h, the maximum overall heat transfer enhancement is 24.21%. These enhancements in heat transfer that can be encountered in PCB cooling applications may help the PCB cooling designers.

Numerical Investigation of Flow Past Bio-Inspired Wavy Leading-Edge Cylinders

A numerical investigation is proposed to explore the flow past a novel wavy circular cylinder as a passive flow control, whose shape is determined by a sinusoidal function applied to its leading edge line, similar to studies with wavy leading-edge airfoils. The latter are motivated by the wavy-shaped tubercles found in the flippers of humpback whales, which are believed to improve their maneuverability. Our attempt is, therefore, to assess the effects of leading-edge waviness now on a simpler and canonical geometry: circular cylinders. The present work relies on iLES simulations conducted with Nektar++ at a Reynolds number of 3900. Besides the straight cylinder, two wavy geometries are assessed, which are determined by a single wavelength of 37.5% for two amplitudes, 3% and 11%, based on the mean diameter of the wavy cylinder. Our results showed that, contrary to what is usually the case with traditional wavy cylinders at similar Reynolds numbers, waviness caused a reduction in the near-wake recirculation length and an increase in the mean near-wake turbulent kinetic energy compared to the straight cylinder. This was followed by a reduction in base pressure (up to about 36%) leading to a rise in lift oscillations and also to a significant increase in the mean drag coefficient of up to about 28%. An attempt to detail the flow phenomena is provided, evidencing the emergence of counter-rotating pairs of streamwise vortices between peaks. It is argued that the differences observed in recirculation length, turbulent kinetic energy, and force coefficients start even prior to the formation of these coherent structures and end up with interactions with the near wake.

Drag mitigation by steady blowing and Coanda effect on a square back Ahmed body

The impact of converging steady blowing on the global drag past a square back Ahmed bluff body is investigated experimentally. The dynamics of the recirculation bubble are studied for a width to height aspect ratio, w/h of 1.346, with a ground clearance of g/w=0.154, and for a nominal Reynolds number of Reh=2.86×105. When unforced, the bistable wake alternates between a left and right skewed states. Adaptable Coanda devices are used in combination with side air-knife blowers to deflect steady blowing jets into a converging (boat-tail) configuration. Two jet injection angles are investigated: 45° and 90°. Planar PIV and time-history force and pressure measurements indicate that inwards steady blowing reshapes the recirculation bubbles and induces significant variations of the pressure drag. On one hand, bilateral steady blowing leads to the interruption of bistability associated with a removal of the vertical pressure gradient for velocity ratios VR≈0.35−0.4. This has a favourable impact on the total drag with a reduction up to 3%. On the other hand, the boat-tailing effect shortens the recirculation length which tends to increase drag. This counter-productive effect limits and then outweighs drag reduction for higher velocity ratios. Another symmetry breaking is brought to light for intense highly deflected forcing.

LES and PIV Investigation of the Flow Past a Cactus-Shaped Cylinder with Four Ribs

The flow past a cactus-shaped cylinder with four ribs is investigated numerically using large eddy simulations (LES) at Reynolds number of 20,000 and experimentally using particle image velocimetry (PIV) at Reynolds number of 50,000. In both approaches, the full range of angle of attack is covered. LES results show a good qualitative and quantitative match of the aerodynamic properties to previous experimental data, although the value of the critical angle of attack is slightly lower. The results confirm that there is no Reynolds number dependency within the investigated range allowing a comparison of the flow fields from the present LES and PIV. Significant variations of the flow patterns with the angle of attack are found and quantified using the recirculation length and wake width. Overall, the observed angle of attack dependence resembles the behaviour of the square cylinder. However, the studied cylinder has a narrower wake at all angular orientations. Proper orthogonal decomposition is used to identify large coherent structures in the flow. At all angles of attack the first two modes remain dominant making it possible to reconstruct the periodic vortex shedding process using a low-order model.

Numerical prediction of flow recirculation length zone in an artery with multiple stenoses at low and high Reynolds number

Numerical prediction of flow recirculation length zone in an artery with multiple stenoses at low and high Reynolds number

Effect of aspect ratio on entrance length in rectangular minichannels with plenum

In the case of a long, straight rectangular channel, hydrodynamic development of flows is influenced by the growth of the boundary layer along the walls of the channel. Though such a geometry is well-studied in the literature, in reality, the flow often happens in channels with plenums on each end and is not studied extensively. This work addresses this gap. There is a sudden contraction from the plenum to the channel which causes the flow to separate at the entrance of the channel. Hence, the flow development is influenced not only by the boundary layer growth but also by recirculation and the presence of a continuous wall along one direction in the case of planar geometries. This causes the centerline velocity in the entrance region to overshoot the value at the fully developed region, which makes the conventional usage of 99% of the fully developed value difficult. Hence, an alternate method of defining entrance length, based on the slowest development across the channel cross section, is proposed. Based on this approach, the entrance length value shows a non-monotonic variation with the aspect ratio (AR)—its value reduces between 0.6 and 1.66; beyond 1.66, it increases up to 20 before becoming flat. The entrance length also shows a weak dependence on the Reynolds number for AR between 2 and 20. A new set of correlations of entrance and recirculation lengths are proposed.

Enhancement of thermo-fluid performance of square cylinder by dual splitter plates

In various applications of flow over a cylinder, the convective heat transfer is required to be enhanced for better operation by maintaining the operating temperature. In this paper, the influence of splitter plates on the fluid forces and heat transfer around a square cylinder is discussed thoroughly. The placement of the splitter plates is novel in its kind as these are placed at the top and bottom surfaces of a square cylinder instead of the conventional position i.e. downstream or upstream of the cylinder. Effect of this novel position of the splitter plates on the heat transfer along with the wake topology for a range of Reynolds number (Re) (60 ≤ Re ≤ 150) is not available in the previous study and accordingly, a rigorous investigation of the flow physics is presented here. Two splitter plates are utilized of the same geometry with varying lengths, locations, and orientations. It is found that the primary recirculation length decreases with increasing Re by introducing the splitter plates compared to a bare cylinder and the corresponding primary separation angle, ψS1 is significantly affected by the geometry of the splitter plates. The splitter plates have a mixed effect on the fluid forces and heat transfer rate for all the considered Re. A maximum percentage of reduction on the mean drag coefficient and R.M.S (root mean squared) lift coefficient is found as 9% and 20%, respectively. Whereas, a maximum percentage enhancement of 40.7% is obtained on the heat transfer rate by introducing the splitter plates. However, the splitter plate geometry and its location can be decided according to the requirement of the heat transfer rate based on the application and the corresponding demand on the fluid forces.

A large eddy simulation of flow over a circular cylinder with circumferential triangular riblets: Effects of spanwise coverage ratio

Flow over circular cylinders covered with circumferential riblets of triangular shape with spanwise coverage ratios from 0 (bare cylinder) to 1 (fully covered) is investigated by large eddy simulation at three subcritical Reynolds numbers (2000, 3000 and 3900 respectively). The bare cylinder is considered as a reference case and for validation purpose. Detailed flow structures and boundary layer characteristics are described. For the fully covered cylinder, it is found that flows on the two sides of each riblet interact, forming a structure with stronger turbulent fluctuations and leading to a significantly shorter recirculation length compared to the other cases. The turbulent fluctuations are attenuated to various degrees for the partly covered cylinders. Two semicircular-shaped flow zones with distinct spanwise flows are observed around the riblets adjacent to the bare sections. Among the three partly covered cases under consideration (with spanwise coverage ratios of 0.25, 0.5 and 0.75 respectively), the half-covered cylinder has the largest semicircular-shaped flow zones, associated with the lowest turbulence in the flow field. A zigzag flow separation line is observed on all sections covered with riblets. The variations of the flow behaviours result in different characteristics of the hydrodynamic forces acting on the various cylinders. It is revealed that the lift fluctuation is the lowest for the half-covered cylinder and the highest for the fully covered cylinder. An examination of the sectional hydrodynamic forces further reveals that the sectional drag is higher at the riblet tip than that in the valley.

Effect of wall slip on laminar flow past a circular cylinder

A numerical study of two-dimensional flow past a confined circular cylinder with slip wall is performed. A dimensionless number, Knudsen number ($Kn$) is used to describe the slip length of cylinder wall. The Reynolds number ($Re$) and Knudsen number ($Kn$) ranges considered are $Re = [1, 180]$ and $Kn = [0, \infty)$, respectively. Time-averaged flow separation angle ($\bar{\theta_s}$), dimensionless recirculation length ($\bar{L_s}$) and the tangential velocity ($\bar{u_{\tau}}$) distributed on the cylinder's wall, drag coefficient ($\bar{C_d}$) and drag reduction ($DR$) are investigated. The time-averaged tangential velocity distribution on the cylinder's wall fit well with the formula $\bar{u_{\tau}} = [\frac{\alpha}{1+{\beta}e^{-{\gamma}({\pi}-{\theta})}}+{\delta}]sin(\theta) $, where the coefficients ($\alpha$, $\beta$, $\gamma$, $\delta$) are related with $Re$ and $Kn$. Several scaling-laws are found, $log(\bar{u_{{\tau}max}})\sim{log(Re)}$ and $\bar{u_{{\tau}max}}\sim{Kn}$ for low $Kn$, ($\bar{u_{{\tau}max}}$ is the maximum tangential velocity on the cylinder's wall), $log(DR)\sim{log(Re)}$ ($Re\leq45$ and $Kn\leq0.1$), $log(DR)\sim{log(Kn)}$ ($Kn\leq0.05$). At low $Re$, $DR_v$ (the friction drag reduction) is the main source of $DR$. However, $DR_p$ (the differential pressure drag reduction) contributes the most to $DR$ at high $Re$ ($Re>\sim60$) and $Kn$ over a critical number. $DR_v$ is found almost independent to $Re$.

Effect of transverse magnetic field on wake dynamics and heat transfer through a porous circular cylinder

AbstractA two‐dimensional numerical simulation using the commercial computational fluid dynamics package ANSYS Fluent 15.0 is performed to investigate the effect of a transverse magnetic field on the wake dynamics around a heated porous circular cylinder. The study is conducted considering a Newtonian, incompressible, and electrically conductive fluid with constant properties for the low Reynolds number laminar regime. In the range of Reynolds number (Re = 10–40), recirculating vortices are observed to penetrate (or detach) into (from) the porous cylinder surface depending on the Darcy number, Da (10−6 to 10−2). The effect of the magnetic field parameter (Hartmann number) Ha (0–10) on the detachment and penetration characteristics of a porous cylinder is reported for the first time. A steady separated flow behind the cylinder turns into an attached flow at a critical magnetic field strength. Accordingly, the critical Hartmann number (Hacr) is estimated for the complete suppression of the flow separation behind the porous cylinder. Hacr is found to decrease with an increase in Da and a decrease in Re. The wake behind the cylinder is also found to be detached from the cylinder surface at a particular value of the magnetic field strength termed as the detachment Hartmann number (Had). Had also decreased with an increase in Da and decrease of Re. In addition, the effect of Ha on the separation angle, recirculation length, detachment length, and drag coefficient is also discussed. Furthermore, the effect of the magnetic field on the forced convective heat transfer characteristics is also studied considering various fluids (Prandtl number, Pr = 0.02, 0.71, and 7) past the circular permeable cylinder. At a particular Pr, the heat transfer rate is almost invariant for low permeability, whereas it increases significantly at higher permeability with an applied magnetic field. The rate of heat transfer increases with the Prandtl number for all Hartmann and Darcy numbers. Finally, a correlation is developed to predict the average heat transfer as a function of Re, Pr, Da, and Ha.

Interaction between a stationary sphere and turbulent flow in a boundary layer

We investigate the interaction of a stationary sphere with turbulent flows in a spatially developing boundary layer over a flat plate by means of fully resolved direct numerical simulations. The diameter of the sphere D is much larger than the Kolmogorov length scale. The sphere Reynolds number ReD is changed by varying the sphere diameter, while the gap ratio is held constant with G/D=0.1, where G is the distance between the bottom of the sphere and the flat plate. The simulation results indicate that there exist complex interactions between the small-scale vortex in the wake of the sphere and the large-scale coherent structures inside the turbulent boundary layer. The jet-like flow through the gap is deflected away from the wall, and the level of deflection increases with ReD. As a result, asymmetrical flow structures are observed in the recirculation zone. In addition, the mean recirculation length is found to decrease with the increase in ReD. Concerning the turbulence modulation, statistics show that the skin-friction drag and boundary layer thickness are decreased in the recirculation region with respect to the undisturbed flow, whereas the displacement thickness is increased due to the presence of reverse flow. These effects become more pronounced as ReD increases. The budget of the turbulent kinetic energy in the sphere wake is also examined. It is revealed that the turbulent production and viscous dissipation rate are significantly enhanced under the effect of the sphere with size of the same order of magnitude as the local boundary layer thickness.

Effects of flow fluctuations and buoyancy on heat transfer from a sphere in non-Newtonian nano fluids: Potential for intensification

This work numerically explores the combined effects of buoyancy-induced flow and pulsating velocity for nanofluids (power-law type fluids) over a sphere to ascertain the potential of this approach for process intensification. The pertinent field equations are solved numerically for a range of dimensionless variables as, Richardson number (0 ≤ Ri ≤ 5), amplitude of fluctuations (0 ≤ A ≤ 0.8), frequency of pulsation (π/4 ≤ ω* ≤ π), Reynolds number (5 ≤ Re ≤ 100), power-law index (0.3 ≤ n ≤ 1.5) and Prandtl number (1 ≤ Pr ≤ 100). The aiding-buoyancy flow suppresses the transient effects of the flow pulsations. The recirculation length (wake) is considerably shortened as the buoyancy-driven flow strengthens. Even a weak buoyancy-induced flow (for instance, Ri = 1) is sufficient to mar the influence of pulsatile velocity. The Richardson and Prandtl numbers do not influence the phase difference in the growth of the momentum boundary layer. Overall, the improvement in the Nusselt number is significantly lowered by the aiding-buoyancy mixed convection than that in the forced convection regime. While this may seem like a detrimental effect on the overall heat transfer, this offers a potential tool for modulating the rate of heat transfer for the processing of temperature-sensitive materials wherein the main consideration is to limit the maximum temperature in the system. The present results can be used to devise an operating envelope of conditions depending upon the envisaged application. Finally, the mean Nusselt number is correlated by using the modified velocity and viscosity scales accounting for the contribution of the mean flow and the buoyancy-induced flow.

Effect of the Inner Diameter and Reynolds Number on the Recirculation Zone in Annular Jet Flow

In this paper, we focus on the effect of the inner diameter and Reynolds number on the recirculation zone in an annular jet flow with numerical simulation by resolving the Reynolds-averaged Navier-Stokes equations with the first closed model of turbulence k-epsilon. The annular jet plays an essential role in stabilizing the flame in the burner which is used in many industrial applications. The annular jet is characterized by the inner and outer diameter. In this study, three different inner diameters are adopted with constant width of the annular jet. We adopted also three different values of the Reynolds number show the effect of the Reynolds number on the recirculation zone. The simulation is realized by a CFD code which uses the finite element method. The results obtained from this study are in good agreement with the experimental data. Two recirculation zones are shown; a large recirculation zone at the outlet of the flow and a small recirculation zone just near the injection generated by the annular flow and the inner diameter <i>Di</i>; it is observed that the size of the recirculation zone increases when the inner diameter increases and the length of the recirculation zone depends only on the inner diameter. This recirculation zone is also affected by the Reynolds number with a very low variation of the recirculation length.

Low-frequency resolvent analysis of the laminar oblique shock wave/boundary layer interaction

Resolvent analysis is used to study the low-frequency behaviour of the laminar oblique shock wave/boundary layer interaction (SWBLI). It is shown that the computed optimal gain, which can be seen as a transfer function of the system, follows a first-order low-pass filter equation, recovering the results of Touber & Sandham (J. Fluid Mech., vol. 671, 2011, pp. 417–465). This behaviour is understood as proceeding from the excitation of a single stable, steady global mode whose damping rate sets the time scale of the filter. Different Mach and Reynolds numbers are studied, covering different recirculation lengths $L$ . This damping rate is found to scale as $1/L$ , leading to a constant Strouhal number $St_{L}$ as observed in the literature. It is associated with a breathing motion of the recirculation bubble. This analysis furthermore supports the idea that the low-frequency dynamics of the SWBLI is a forced dynamics, in which background perturbations continuously excite the flow. The investigation is then carried out for three-dimensional perturbations for which two regimes are identified. At low wavenumbers of the order of $L$ , a modal mechanism similar to that of two-dimensional perturbations is found and exhibits larger values of the optimal gain. At larger wavenumbers, of the order of the boundary layer thickness, the growth of streaks, which results from a non-modal mechanism, is detected. No interaction with the recirculation region is observed. Based on these results, the potential prevalence of three-dimensional effects in the low-frequency dynamics of the SWBLI is discussed.

LES predictions of confinement effect on swirling flow generated by single helical axial swirler

PurposeFor higher swirling flows (swirl > 0.5), flow confinement significantly impacts fluid flow, flame stability, flame length and heat transfer, especially when the confinement ratio is less than 9. Past numerical studies on helical axial swirler type systems are limited to non-reacting or reacting flows type Reynolds averaged Navier Stokes closure models, mostly are non-parametric studies. Effects of parametric studies like swirl angle and confinement on the unsteady flow field, either numerical or experimental, are very minimal. The purpose of this paper is to document modeling practices for a large eddy simulation (LES) type grid, predict the confinement effects of a single swirler lean direct injection (LDI) system and validate with literature data.Design/methodology/approachThe first part of the paper discusses the approach followed for numerical modelling of LES with the minimum number of cells required across critical sections to capture the spectrum of turbulent energy with good accuracy. The numerical model includes all flow developing sections of the LDI swirler, right from the axial setting chamber to the exit of the flame tube, and its length is effectively modelled to match the experimental data. The computational model predicts unsteady features like vortex breakdown bubble, represented by a strong recirculation zone anchored downstream of the fuel nozzle. It is interesting to note that the LES is effective in predicting the secondary recirculation zones in the divergent section as well as at the corners of the tube wall.FindingsThe predictions of a single helical axial swirler with a vane tip angle of 60°, with a duct size of 2 × 2 square inches, are compared with the experimental data at several axial locations as well as with centerline data. Both mean and unsteady turbulent quantities obtained through the numerical simulations are validated with the experimental data (Cai et al., 2005). The methodology is extended to the confinements effect on mean flow characteristics. The time scale and length scale are useful parameters to get the desired results. The results show that with an increase in the confinement ratio, the recirculation length increases proportionally. A sample of three cases has been documented in this paper.Originality/valueThe novelty of the paper is the modelling practices (grid/unsteady models) for a parametric study of LDI are established, and the mean confinement effects are validated with experimental data. The spectrum of turbulent energies is well captured by LES, and trends are aligned with experimental data. The methodology can be extended to reacting flows also to study the effect of swirl angle, fuel injection on aerodynamics, droplet characteristics and emissions.

Numerical investigation of the effect of spanwise length and mesh density on flow around cylinder at Re = 3900 using LES model.

Flow around circular cylinder has been extensively studied by researchers for several decades due to its wide range of engineering applications such as in heat exchangers, marine cables, high rise building, chimneys, and offshore structures. The lack of clear understanding of the unsteady flow dynamics in the wake of circular cylinder and high computational cost are still an area of high interest amongst the researchers. The aim of the current study is to investigate the effect of variation in spanwise length and grid resolution in the spanwise direction on the recirculation length, separation angle of wake flow by performing large eddy simulations (LES). This study is an extension to previous work by Khan, NB et al, 2019 in which the spanwise length is restricted to 4D only. In current study, the spanwise length is changed from 0.5D to 8D where D is diameter of cylinder and mesh resolution in the spanwise direction is changed from 1 to 80 elements in the present study. The recirculation length, separation angle and wake characteristics are analyzed in detail. It is concluded that after getting optimize spanwise length, mesh resolution in the spanwise direction is the only parameter contributing toward better result.

Magnetic Field Effects on Backward-Facing Step Flow of Ferrofluids

Abstract Backward-facing step (BFS) flow is a benchmark case study in fluid mechanics. Its control by means of electromagnetic actuation has attracted great interest in recent years. This paper focuses on the effects of a uniform stationary magnetic field on the laminar ferrofluid BFS flows for the Reynolds number range 0.1≤Re≤400 and different expansion ratios. The coupled ferrohydrodynamic equations, including the microscopically derived magnetization equation, for a two-dimensional domain are solved numerically by an openfoam solver after validation and a test of accuracy. The application of a magnetic field causes the corner vortices in the concave corner behind the step to be retracted compared with their positions in the absence of a magnetic field. The maximum percentage of the normalized decrease in length of these eddies reaches 41.23% in our simulations. For small Reynolds numbers (<10), the flow separation points on the convex corner are lowered in the presence of a magnetic field. Furthermore, the dimensionless total pressure drop between the channel inlet and outlet decreases almost linearly with Reynolds number Re, but the drop is greater when a magnetic field is applied. On the whole, the normalized recirculation length of the corner vortex increases nonlinearly with increasing magnetic Reynolds number Rem and Brownian Péclet number Pe, but it tends to constant values in the limits Rem≪1 and Rem≫1.

Computational Analysis of Active and Passive Flow Control for Backward Facing Step

The internal steady and unsteady flows with a frequency and amplitude are examined through a backward facing step (expansion ratio 2), for low Reynolds numbers (Re=400, Re=800), using the immersed boundary method. A lower part of the backward facing step is oscillating with the same frequency as the unsteady flow. The effect of the frequency, the amplitude, and the length of this oscillation is investigated. By suitable active control regulation, the recirculation lengths are reduced, and, for a percentage of the time period, no upper wall, negative velocity, region occurs. Moreover, substituting the prescriptively moving surface by a pressure responsive homogeneous membrane, the fluid–structure interaction is examined. We show that, by selecting proper values for the membrane parameters, such as membrane tension and applied external pressure, the upper wall flow separation bubble vanishes, while the lower one diminishes significantly in both the steady and the unsteady cases. Furthermore, for the time varying case, the length fluctuation of the lower wall reversed flow region is fairly contracted. The findings of the study have applications at the control of confined and external flows where separation occurs.