Flow Past Square Research Articles

A formulation for fluid–structure interaction problems with immersed flexible solids: Application to splitters subjected to flow past cylinders with different cross-sections

In the finite element method framework, a fluid–structure formulation is developed by coupling an Eulerian fixed-mesh fluid approach with a Lagrangian deforming-mesh description for a flexible solid. The coupled formulation is solved using a staggered scheme during time. For the fluid solution stage, the solid walls are considered as a time-variable internal boundary. The velocity and pressure fields are obtained by solving the weak form of the fluid dynamic equations in which the solid velocity is imposed on the internal boundary via a penalization term. For the solid solution stage, the displacement field is obtained by solving the discrete solid dynamic equations which consider traction forces computed by integrating pressures and viscous stresses on the nodes belonging to the solid walls. This novel technique is firstly applied to analyze a flexible splitter under the shedding of a flow past square cylinder due to this problem is considered as a benchmark in the literature. The present solutions agree with those computed using body-fitted techniques, thus validating the proposal. Secondly, flexible splitter motions under the shedding of flow past cylinders with different cross-sections and splitter lengths are comprehensively studied. Overall, the computed results confirmed that the hydrodynamic coefficients on the cylinders were reduced because of the presence of the splitter.

Influence of the slip boundary on square cylinders with lattice Boltzmann method

In this investigation, two-dimensional flow past square cylinders with slip boundary have been studied with the lattice Boltzmann method. Three modes, which are a single cylinder, an oblique cylinder, and side-by-side cylinders, are investigated with Reynolds numbers from 25 to 200 while relative slip length ranges from 0 to 0.1. It can be concluded that both the flow state and the slip boundary have a great effect on the drag reduction rate. For a single square cylinder, drag forces decrease with larger slip length while the Strouhal number is almost constant. For an oblique cylinder, the slip length also has effects on the stability of the flow except the drag and lift forces. Vortex separation delays with a slip wall of oblique cylinder. For side-by-side cylinders, the jet between two cylinders is not conducive to the drag reduction rate of the slip boundary. Moreover, the application of slip boundary may also lead to additional drag force as vortex separation intensifies, which is extremely different from simple channel flows. Studies have shown that the slip boundary does not always reduce the drag in some complex flow fields. It can be concluded that the drag reduction effect of slip boundaries is more effective in uniform flow.

Low Reynolds Number Flow Past Square Cylinder in the Vicinity of a Plane Wall

The characteristics of flow over a square cylinder in the vicinity of a plane stationary wall have been numerically investigated. 2D time-dependent incompressible flow at low-Reynolds numbers of 100 and 200 has been calculated using the finite volume method. CFRUNS scheme is used for pressure-velocity coupling in numerical calculation. The authors have tried to make an attempt to analyze the features of the complex flow field through flow streamlines and the vorticity contours. The impact of the gap between the cylinder and the plane wall upon flow pattern behavior is also studied. An intense interaction between vorticity in the boundary layer generated over the plane wall and the vorticity associated with the shear layer emanating from the separation points on the cylinder surface has been observed producing a very complex flow field in the cylinder wake and the gap between the cylinder and the wall.

Variational multiscale stabilized finite element analysis of non-Newtonian Casson fluid flow model fully coupled with Transport equation with variable diffusion coefficients

This paper presents a new subgrid multiscale stabilized formulation for non-Newtonian Casson fluid flow model tightly coupled with variable diffusion coefficients Advection–Diffusion–Reaction equation (VADR). Both the subscales are chosen to be time dependent and the stabilized formulation has been reached through the complete elimination of the unresolvable scales in terms of the coarse scale solution. Hence the resultant formulation emerges as a set of equations involving only the coarse scale solution instead of multiple scales and makes the formulation simpler to handle. In this study the shear-rate dependent Casson viscosity coefficient is assumed to be a function of the solute mass concentration, resulting in a two way coupling. This paper investigates the stability and the convergence properties of the stabilized finite element solution, without imposing any additional regularity condition other than the admissible space requirement on it. The proposed expressions of the stabilization parameters play a significant role in obtaining optimal order of convergences. During various theoretical derivations the estimations of the non-linear apparent viscosity coefficient have been carefully carried out assuming sufficiently regular exact solution. The performance of the scheme has been numerically validated with lid driven cavity problem. The theoretically established rate of convergence results are appropriately verified through numerical studies. In addition the transient Casson fluid flow behavior in a flow past square cylinder has been analyzed thoroughly.

Lattice Boltzmann study of low-Reynolds-number flow past square cylinders with varying slip distributions

Slip distributions have been proved to have significant influence on the flow-past-cylinder problems. However, rare studies focus on the square cylinders. To obtain better understanding of the effect of slip distributions on the flow-past-square-cylinder problems that widely appear in the engineering fields, the flows past a single square cylinder, and two tandem square cylinders under different slip distributions and gap ratios are numerically investigated using the lattice Boltzmann method at low-Reynolds-numbers (25∼200, mainly at 100). The flow structures and drag properties (including the friction drag and the pressure drag) are analyzed. Various slip distributions are found to have minor impacts on the drag reduction of a single cylinder (3.5% in maximum) but larger impacts on that of the tandem cylinders, especially the downstream cylinder (100% in maximum). In addition, flank side slip is found to have important contributions to the drag reduction.

Onsager-regularized lattice Boltzmann method: A nonequilibrium thermodynamics-based regularized lattice Boltzmann method.

The regularized class of lattice Boltzmann methods (LBMs) leverage the potency of the standard lattice-Bhatnagar-Gross-Krook method by filtering out spurious nonhydrodynamic moments from the moment space; this is achieved through evaluating regularized populations via a multiscale or a Hermite polynomial expansion approach. In this paper, we propose an alternative approach for evaluating the lattice populations. This approach is based on a kinetic theory that is consistent with nonequilibrium thermodynamics and obeys the Onsager-reciprocity principle. The proposed method is verified and validated for a number of canonical problems such as the athermal shock tube, the double periodic shear layer, the lid driven cavity, flow past square cylinder, and Poiseuille flow at nonvanishing Knudsen numbers. Additionally, the proposed method is compared to existing regularized LBM schemes and is shown to yield significant improvement in the stability and accuracy of the simulations.

Visualization of flow past square cylinders with corner modification

This article presents the results for flow past a square cylinder and two square cylinders of the same and different sizes with corner modifications by varying the spacing ratio. Here, experimental work is conducted in a recirculatory channel filled with water. A set of aluminum discs made to rotate to create the flow in the test section. The motor is used to vary the speed of the water. Fine aluminum powder is used as a tracer medium. It is observed that vortex shedding frequency decreases by placing the second cylinder in the downstream of the first cylinder. For similar size cylinders, the width of the eddy in the middle of the cylinders increases with an increase in spacing ratio. With the increase of spacing ratio to 6, the flow past each cylinder behaves like a single square cylinder. If the upstream square cylinder size is smaller than the downstream square cylinder, the eddy size is reduced in between the cylinder compared to the downstream of the second cylinder. If the upstream square cylinder size is bigger than the downstream square cylinder, the eddy size is larger in between the cylinder compared to the downstream of the second cylinder.

Multi-Objective Drag and Sound Optimization of Square Cylinder Retrofitted with Splitter Plate

The application of a splitter plate on square cylinders to reduce drag in cross-flow is an active research area. However, the associated aeroacoustic sound in the surrounding fluid also undergoes reduction, an aspect which has received less attention. This paper presents a numerical methodology for coupled aerodynamic and aeroacoustic calculations for flow past square cylinders with various splitter plate lengths. Computations are performed at a Re of 22000 using URANS technique and FW-H analogy. Observing that drag reduction and sound reduction occur at different splitter plate lengths, a two-objective optimization problem is posed to minimize the drag and OASPL simultaneously

Features of flow past square cylinder with a perforated plate

A numerical investigation was performed on the reduction of the fluid forces acting on the square cylinder in the laminar flow regime with a perforated plate. The effects of geometric parameters such as the distance between the square cylinder and the perforated plate on the wake of the square cylinder were discussed. Furthermore, the flow characteristics such as the drag coefficient, lift coefficient, Strouhal number and flow pattern were obtained. It can be concluded that the drag force of the square cylinder reduces to some extent due to the addition of the perforated plate. The flow structure varies when the perforated plate is located behind the square cylinder. Moreover, the recirculation zone augments with the increase of L/D, and the vortex trace on the upper and lower surface of the square cylinder moves gradually backwards until a stable recirculation zone formed between the square cylinder and the perforated plate.

Variation of wake patterns and force coefficients of the flow past square bodies aligned inline

In this numerical study, the variation of wake patterns and force coefficients of the flow past four square bodies aligned inline are investigated. A two-dimensional numerical code is developed using the Lattice Boltzmann method (LBM) for this study. The code is first validated for the flow past a single and two tandem square cylinders. The results are compared to those available in literature and found to be in good agreement. After validation the calculations are further performed to investigate the effect of gap spacing (g) for the flow past four inline square cylinders at two different Reynolds numbers (Re) 100 and 200. The gap spacing is chosen in the range 0.25 ≤ g ≤ 7. Six different flow patterns: Single slender body, alternate reattachment, quasi steady reattachment, intermittent shedding, chaotic flow and periodic flow are found in this study with successive increment in spacing. It is found that some flow patterns existing at Re = 100 do not exist at Re = 200. The generated vortices at Re = 200 are much stronger as compared to those at Re = 100. The spacing value g = 3 is found to be critical at Re = 100 while at Re = 200 the spacing value g = 2 is critical due to abrupt changes in flow characteristics. At some spacing values the downstream cylinders have higher values of average drag coefficients as compared to upstream ones. In general the upstream cylinder (c1) have higher drag forces at Re = 200 than at Re = 100. The root mean square values of lift coefficient are found to be greater than the corresponding root mean square values of drag coefficient.

Numerical Study of Shear Flow Past a Square Cylinder at Reynolds Numbers 100, 200

A numerical study of two-dimensional incompressible shear flow past a square cylinder is presented in this paper. Numerical simulations are performed using the recently developed higher order compact (HOC) scheme for K = 0.0, 0.1 for Re = 100, 200, where Re is the Reynolds number and K is the shear rate based on cylinder side. We investigate the effect of shear rate on the vortex shedding phenomenon in terms of stream function and vorticity contours, lift and drag coefficients employed on the cylinder and corresponding power spectra. The results presented here show that the vortex shedding phenomenon strongly depends on the Reynolds number as well as on the shear rate. In general, average drag coefficient decreases with increase in the shear rate for fixed Re and for K = 0.0 − 0.1, this change is negligible. In contrary to shear flow around circular cylinder, Strouhal number for flow past square cylinder decreases with increase in K.

Effect of arrangement of inline splitter plate on flow past square cylinder

Two-dimensional numerical study has been carried out to investigate the effect of the presence of a single splitter plate in upstream location, and presence of two splitter plates, in upstream as well as downstream locations, for low Reynolds number incompressible flow past a square cylinder. Using finite difference discretisation and MAC algorithm, an indigenously developed computational code has been used for solution of the governing flow equations. The length of the plate and its position do play good role in controlling the flow past the cylinder. The difficulty lies in identifying an optimum configuration of these parameters. The length of the attached splitter plate as well as separation of the detached splitter plate of fixed length are varied for both the upstream and downstream configurations up to maximum Reynolds number of 200. To begin with, the effect of upstream splitter plate alone in attached as well as detached configuration is studied with an aim to identify the optimum configuration associated with reduced drag as well as delayed onset of vortex shedding. Then, for the optimum configuration of the upstream plate, the effect of downstream plate on flow characteristics and critical Reynolds number for onset of vortex shedding has been studied.

Effect of blockage ratio on wake transition for flow past square cylinder

Two-dimensional numerical investigations are carried out to study the behavior of wake transition for flow past square cylinder confined between two parallel walls. It is known from past literature that nature of wall confinement affects the behavior of vortex shedding behind the obstacle. The present work reports dependence of the critical Reynolds number ( Re cr ) for onset of planar vortex shedding on blockage ratio. The effect of wall confinement on characteristic features of the wake, such as wake bubble size and shear layer behavior has been studied. The characteristic relationship between Strouhal number and flow Reynolds number has been presented for different values of blockage ratios. The temporal characteristics of the wake are presented.

Numerical calculation of separated flow past square and rectangular cylinders using panel technique

AbstractIn the present investigation, a potential flow model based on panel method has been developed for calculation of two dimensional separated flows past square and rectangular cylinders. Free vortex lines are assumed to emanate from the points of separation that converge downstream of the body. The converged wake shape is iteratively obtained by integrating the velocity vectors at the collocation points. For solving separated flow past square and rectangular cylinders, four different versions of the solver have been developed for a wide range of incidence, namely, for zero, low, moderate and high angles of incidence. For validation of computed results, experimental investigations have been carried out in a low speed wind tunnel to obtain the surface pressure distribution on square cylinder and rectangular cylinder over a range of angles of incidence. Comparison is reasonably good.

Numerical solutions of a viscous uniform approach flow past square and diamond cylinders

Numerical results are presented for a uniform approach flow past square and diamond cylinders, with and without rounded corners, at Reynolds numbers of 250 and 1000. This unsteady viscous flow problem is formulated by the 2-D Navier–Stokes equations in vorticity and stream-function form on body-fitted coordinates and solved by a finite-difference method. Second-order Adams-Bashforth and central-difference schemes are used to discretize the vorticity transport equation while a third-order upwinding scheme is incorporated to represent the nonlinear convective terms. A grid generation technique is applied to provide an efficient mesh system for the flow. The elliptic partial differential equation for stream-function and vorticity in the transformed plane is solved by the multigrid iteration method. The Strouhal number and the average in-line force coefficients agree very well with the experimental and previous numerical values. The vortex structures and the evolution of vortex shedding are illustrated by vorticity contours. Rounding the corners of the square and diamond cylinders produced a noticeable decrease on the calculated drag and lift coefficients.

Laminar flow and heat transfer in confined channel flow past square bars arranged side by side

A numerical investigation was conducted to analyze the unsteady laminar flow field and heat transfer characteristics in a plane channel with two square bars mounted side by side to the approaching flow. A finite volume technique is applied with a fine grid and time resolution. The transverse separation distance between the bars (G/d) is varied from 0 to 5, whereas the bar height to channel height is d/H=1/8, and the channel length is L=5H. Different flow regimes develop in the channel due the interaction between the two mounted square bars, steady flow, flow with vortex shedding synchronization either in phase or in anti-phase, or biased flow with low frequency modulation of vortex shedding are found. Results show that the pressure drop increase and heat transfer enhancement are strongly dependent of the transverse separation distance of the bars and the channel Reynolds number.

A numerical simulation of the convective heat transfer in confined channel flow past square cylinders: comparison of inline and offset tandem pairs

A numerical investigation was conducted to analyze the unsteady flow-field and heat-transfer characteristics for a tandem pair of square cylinders in a laminar channel flow. The drag, lift, and heat transfer coefficients from the downstream heated cylinder due to inline and offset eddy-promoting cylinders were studied. The results show that the drag coefficient and cylinder Nusselt number decrease as the heated cylinder approaches the wall. The highest Strouhal number value is observed in the channel-centered, inline-eddy configuration. Complex periodic vortex shedding develops when the eddy promoter is offset from the primary cylinder.

Large-Eddy Simulations of the Flow past Bluff Bodies: State-of-the Art.

The flow past bluff bodies, which occurs in many engineering situations, is very complex, involving often unsteady behaviour and dominant large-scale structures, and it is therefore not very amenable to simulation by statistical turbulence models. The large-eddy simulation technique is more suitable for these flows, and recent work in the area of large-eddy simulations of bluff body flows is summarised, with emphasis on work by the author's research group as well as on experiences gained from two LES workshops. Results are presented and compared for the vortex-shedding flow past square and circular cylinders and for the flow around a surface-mounted cube. The performance, the cost and the potential of the LES method for simulating bluff body flows, also vis-a-vis statistical turbulence models, is assessed.

Application of higher order finite element methods to viscoelastic flow in porous media

A higher order Galerkin finite element scheme for simulation of two‐dimensional viscoelastic fluid flows has been developed. The numerical scheme used in this study gives rise to a stable discretization of the continuum problem as well as providing an exponential convergence rate toward the exact solution. Hence, with this method, spurious oscillatory modes are effectively eliminated by increasing the order of the interpolant within each subdomain. In our calculations, an upper limit for the Weissenberg number due to numerical instability was not encountered. However, the memory requirements of the discretization grow quadratically with the polynomial order. Consequently, the maximum attainable We is determined by the availability of computational resources. The algorithm was tested for flow of upper convected Maxwell and Oldroyd‐B fluids in the undulating tube problem and it was subsequently applied to viscoelastic flow past square cylindrical arrangements. The results obtained show no increase in the flow resistance with increasing elasticity. These findings are in contrast to the experimental data reported in the literature. However, recent experimental investigations have indicated that this dramatic increase in flow resistance is due to a purely elastic instability. Hence, numerical simulation based on two‐dimensional steady flow of viscoelastic fluids cannot be expected to capture this phenomenon.

Flow past square cylinder of finite length placed on ground plane.

This paper describes an experimental study of the flow past a square cylinder of finite length placed on a ground plane. The experiment was carried out in an N.P.L. blowdown-type wind tunnel having a working section of 500 mm×500 mm×2000 mm in size at the Reynolds number 2.5×104. The surface pressure distributions on the square cylinder were measured and the drag coefficient was determined from them. The vortices of two kinds generated in the flow field around a square cylinder have also been observed. As a result, it was found that the flow pattern changes rapidly at height-width ratio H/D=7, changing the shedding vortices from arch type to Karman type.