Past Circular Cylinders Research Articles

Transient growth analysis of the flow past a circular cylinder

We apply direct transient growth analysis in complex geometries to investigate its role in the primary and secondary bifurcation/transition process of the flow past a circular cylinder. The methodology is based on the singular value decomposition of the Navier–Stokes evolution operator linearized about a two-dimensional steady or periodic state which leads to the optimal growth modes. Linearly stable and unstable steady flow at Re=45 and 50 is considered first, where the analysis demonstrates that strong two-dimensional transient growth is observed with energy amplifications of order of 103 at U∞τ/D≈30. Transient growth at Re=50 promotes the linear instability which ultimately saturates into the well known von-Kármán street. Subsequently we consider the transient growth upon the time-periodic base state corresponding to the von-Kármán street at Re=200 and 300. Depending upon the spanwise wavenumber the flow at these Reynolds numbers are linearly unstable due to the so-called mode A and B instabilities. Once again energy amplifications of order of 103 are observed over a time interval of τ/T=2, where T is the time period of the base flow shedding. In all cases the maximum energy of the optimal initial conditions are located within a diameter of the cylinder in contrast to the spatial distribution of the unstable eigenmodes which extend far into the downstream wake. It is therefore reasonable to consider the analysis as presenting an accelerator to the existing modal mechanism. The rapid amplification of the optimal growth modes highlights their importance in the transition process for flow past circular cylinder, particularly when comparing with experimental results where these types of convective instability mechanisms are likely to be activated. The spatial localization, close to the cylinder, of the optimal initial condition may be significant when considering strategies to promote or control shedding.

Simulation of viscoplastic flow past cylinders in tubes

Drag flow past circular cylinders concentrically placed in a tube filled with viscoplastic fluids, obeying the Herschel–Bulkley model, is analyzed via numerical simulations with the finite element method. The purpose it to find limiting drag values for cessation of motion of the object in steady flow. Different aspect ratios have been studied ranging from a disk to a long cylinder. For the simulations, the viscoplastic model is used with an appropriate modification proposed by Papanastasiou, which applies everywhere in the flow field in both yielded and practically unyielded regions. The extent and shape of yielded/unyielded regions are determined along with the drag coefficient for a wide range of Bingham numbers. The simulation results are compared with previous experimental values [L. Jossic, A. Magnin, AIChE J. 47 (2001) 2666–2672] for cessation of flow. They show that the values of the drag coefficient are lowest for the disk and highest for the long cylinder. Discrepancies are found and discussed between the simulations and the experiments, with the simulations providing lower values in the limit of very high Bingham numbers.

Spatially distributed control for optimal drag reduction of the flow past a circular cylinder

We report high drag reduction in direct numerical simulations of controlled flows past circular cylinders at Reynolds numbers of 300 and 1000. The flow is controlled by the azimuthal component of the tangential velocity of the cylinder surface. Starting from a spanwise-uniform velocity profile that leads to high drag reduction, the optimization procedure identifies, for the same energy input, spanwise-varying velocity profiles that lead to higher drag reduction. The three-dimensional variations of the velocity field, corresponding to modes A and B of three-dimensional wake instabilities, are largely responsible for this drag reduction. The spanwise wall velocity variations introduce streamwise vortex braids in the wake that are responsible for reducing the drag induced by the primary spanwise vortices shed by the cylinder. The results demonstrate that extending two-dimensional controllers to three-dimensional flows is not optimal as three-dimensional control strategies can lead efficiently to higher drag reduction.

A finite element study of the onset of vortex shedding in a flow past two-dimensional circular cylinder

The objective of this investigation is to study the onset of vortex shedding. The simulation of the flow throws deep insight into the wake-zone dynamics. The diagnostic tools such as Fast Fourier Transform and phase portrait are used to understand the wake dynamics better. Furthermore, a stability analysis is accomplished by involving the complex Stuart-Landau model. The critical value of the Reynolds number is estimated from the Landau constants that correspond to the non-linearity. Three different blockages were considered in this study and are found that the critical values of the Reynolds number and the Strouhal number are sensitive to the blockage ratio. The Landau model was suggested for the local wake variable rather than a global variable. The bifurcation diagram, culminated from the simulation results, clearly reveals the occurrence of super critical Hopf bifurcation.

Simulation of incompressible flows around moving bodies using meshless finite differencing

A scheme using the mesh-free generalized finite differencing (GFD) on flows past moving solid bodies is proposed. The aim is to devise a method which can be applied to simulate flows past immersed moving bodies with reduced computational effort by eliminating the need to perform remeshing for every time step and the intense interpolation procedures. The generalized finite difference method (GFD) with weighted least squares approximation was used to solve the incompressible Navier Stokes equations under the arbitrary Lagrangian-Eulerian (ALE) formulation, on a stationary background set of Cartesian nodes and a cloud of nodes following each moving solid boundary to simulate flows near the solid-fluid interface. A combination of standard central-spaced finite differencing and GFD is applied to the background region and cloud region respectively as spatial discretization. The second-ordered Crank Nicolson time discretization is applied in the projection method, which computes an intermediate set of velocities and uses the pressure Poisson equation to obtain the divergence-free velocity field. Test cases were performed for workability and accuracy of the method, and satisfactory results were obtained for the driven cavity, the decaying vortex, the flow past circular cylinder and a flapping elliptic body in a square enclosed space.

A sharp interface immersed boundary method for compressible viscous flows

An immersed boundary method for computing viscous, subsonic compressible flows with complex shaped stationary immersed boundaries is presented. The method employs a ghost-cell technique for imposing the boundary conditions on the immersed boundaries. The current approach leads to a sharp representation of the immersed boundaries, a property that is especially useful for flow simulations at high Reynolds numbers. Another unique feature of the method is that it can be applied on Cartesian as well as generalized body non-conformal curvilinear meshes. A mixed second-order central difference-QUICK scheme is used which allows a high degree of control over the numerical damping. A bilinear interpolation scheme used in conjunction with the ghost-cell approach results in second-order global as well as local spatial accuracy. The solver is parallelized for distributed memory platforms using domain decomposition and message passing interface (MPI) and salient features of the parallel algorithm are presented. The accuracy, fidelity and efficiency of the solver are examined by simulating flow past circular cylinders and airfoils and comparing against experimental data and other established results. Finally, we present results from a simulation of wing-tip flow at a relatively high Reynolds number in order to demonstrate the ability of the solver to model complex, non-canonical three-dimensional flows.

Numerical calculation of separated flow past a circular cylinder using panel technique

In the present investigation, a potential flow model based on panel technique, has been developed for calculation of bubble type separated flow past smooth and rough circular cylinder. 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 on the wake panels. Effect of vorticity dispersion in the wake, which plays the dominant role in the flow separation phenomena, is incorporated in the flow model. It has been observed that separated flow past circular cylinder for different Reynolds number and surface roughness can be calculated with reasonable accuracy with appropriate values of vorticity dispersion factor ( λ).

Optimal rotary control of the cylinder wake using proper orthogonal decomposition reduced-order model

In this paper we investigate the optimal control approach for the active control and drag optimization of incompressible viscous flow past circular cylinders. The control function is the time angular velocity of the rotating cylinder. The wake flow is solved in the laminar regime (Re=200) with a finite-element method. Due to the CPU and memory costs related to the optimal control theory, a proper orthogonal decomposition (POD) reduced-order model (ROM) is used as the state equation. The key enablers to an accurate and robust POD ROM are the introduction of a time-dependent eddy-viscosity estimated for each POD mode as the solution of an auxiliary optimization problem and the use of a snapshot ensemble for POD based on chirp-forced transients. Since the POD basis represents only velocities, we minimize a drag-related cost functional characteristic of the wake unsteadiness. The optimization problem is solved using Lagrange multipliers to enforce the constraints. 25% of relative drag reduction is found when the Navier-Stokes equations are controlled using a harmonic control function deduced from the optimal solution determined with the POD ROM. Earlier numerical studies concerning mean drag reduction are confirmed: it is shown, in particular, that without a sufficient penalization of the control input, our approach is energetically inefficient. The main result is that cost-reduction factors of 100 and 760 are obtained for the CPU time and the memory, respectively. Finally, limits of the performance of our approach are discussed.

Experiments on the flow past long circular cylinders in a shear flow

This paper describes an experimental investigation of the flow past circular cylinders, with the mean flow perpendicular to the cylinder axis, at conditions that yield a strong three-dimensional behaviour. The experiments were carried out in the subcritical regime. Long cylinders with end plates were subjected to shear flow with a linear velocity profile in the spanwise direction generated by means of a curved gauze. It was concluded that spanwise cellular structures of vortex shedding emerged in the wake, more clearly for some boundary conditions than others. These structures are characterised by a portion of spanwise length, a cell, having constant shedding frequency over a time average, which implies that there were no vortex dislocations inside that cell during that time. These features were studied using flow visualisation and hot-film anemometry. Spectra of the local shedding frequency are shown, revealing the effect of the shear parameter β (=0.02 and 0.04) and aspect ratio L/D (=20.6 and 8) on the stability and geometry of the cells at several Reynolds numbers in the range of 3.13×103≤Rem≤1.25×104.

Visco-elastic flow past circular cylinders mounted in a channel: experimental measurements of velocity and drag

Experimental results are described of a flow in a rectangular channel with a width of 20 mm and a height of 0.16 m. In the symmetry plane of this channel we can mount one or two cylinders each with a diameter of 10 mm. In the case of the two cylinders they are displaced with respect to each other in the streamwise direction. In this set-up, the velocity field is measured by means of Laser Doppler Velocimetry (LDV) under various flow conditions and along various traverses. First, a reference experiment is carried out with a Newtonian fluid. For this Newtonian case we have also carried out a numerical computation which can be used to test the accuracy of our measuring system. The computational results agree excellently with the experimental data. The computations also show that the flow in the channel cannot be considered as 2D. After this a series of experiments are discussed which have been carried out with visco-elastic polymer fluids. Material parameters of the fluids, such as the shear viscosity and the first normal stress difference, are obtained with help of rheometric measurements. For the visco-elastic polymer fluids our observations indicate differences with the Newtonian case, especially, in the wake of the cylinders when the velocity is increased. Eventually, at some critical velocity elastic instabilities occur. Finally, we note that, while in a Newtonian fluid the drag varies linearly with the flow rate, this is no longer the case in a visco-elastic fluid, where we find that the drag increases with the square of the flow rate.

Numerical simulation of high‐Reynolds number flow around circular cylinders by a three‐step FEM–BEM model

AbstractAn innovative computational model, developed to simulate high‐Reynolds number flow past circular cylinders in two‐dimensional incompressible viscous flows in external flow fields is described in this paper. The model, based on transient Navier–Stokes equations, can solve the infinite boundary value problems by extracting the boundary effects on a specified finite computational domain, using the projection method. The pressure is assumed to be zero at infinite boundary and the external flow field is simulated using a direct boundary element method (BEM) by solving a pressure Poisson equation. A three‐step finite element method (FEM) is used to solve the momentum equations of the flow. The present model is applied to simulate high‐Reynolds number flow past a single circular cylinder and flow past two cylinders in which one acts as a control cylinder. The simulation results are compared with experimental data and other numerical models and are found to be feasible and satisfactory. Copyright © 2001 John Wiley & Sons, Ltd.

Simulation of laminar vortex shedding flow past cylinders using a coupled BEM and FEM model

This paper describes a novel computational model developed to simulate laminar vortex-shedding flows past circular cylinders in 2D incompressible viscous flows in external flow fields. The model based on unsteady 2D Navier–Stokes equations in primitive variables is able to solve the infinite boundary value problems by extracting the boundary effects on a specified finite computational domain, using the projection method. The external flow field is simulated using the boundary element method (BEM) by solving a pressure Poisson equation that assumes the pressure as zero at the infinite boundary. The momentum equation of the flow motion is solved using the three-step finite element method (FEM). The present model is applied to simulate vortex-shedding flow past a single circular cylinder and flow past two cylinders in which one act as a control cylinder, for low Reynolds number flows. For both the cases, the time development of the flow towards periodic vortex shedding, are illustrated by streamline pictures. The simulation results are compared with experimental data and other numerical models and found to be very reasonable and satisfactory.

4. 3D flows past circular cylinder of low aspect ratio

4. 3D flows past circular cylinder of low aspect ratio

Computation of three-dimensional flows past circular cylinder of low aspect ratio

Results are presented for finite element simulation of three-dimensional unsteady flows past cylinders of low aspect ratio. The end-conditions are specified to model the effect of a wall that may correspond to the flow in a wind tunnel, water channel or a tow-tank experiment with a cylinder having large end-plates. Results are computed for Reynolds number 100, 300, and 1000 for a cylinder of aspect ratio 16. The computations confirm that it is the end conditions for the finite cylinder that determine the mode of vortex shedding (parallel or oblique). Preliminary results for Re=106 flow past a cylinder of aspect ratio 8 are also presented. The Re=100 and 1000 flows exhibit oblique mode of vortex shedding. The flow for Re=100 is very organized, devoid of any vortex dislocations and is associated with only one cell along the cylinder span. The flow at Re=1000 is interspersed with vortex dislocations and the vortex shedding angle varies, both, temporally and spatially. The presence of vortex dislocations is responsible for the breakdown of spanwise coherence of vortex structures. Mode B pattern of vortex shedding is observed. Flow at Re=300 results in flow patterns that correspond to the wake transition regime. Mode A and Mode B patterns of vortex shedding in addition to vortex dislocations are observed at different time instants. The present results indicate that the wake transition regime, that is known to occur in the Re range 190–250 for large aspect-ratio cylinders, is either extended and/or delayed for a cylinder of small aspect ratio with “no-slip” walls.

A challenging test case for large eddy simulation: high Reynolds number circular cylinder flow

A thorough numerical investigation of high Reynolds number (Re=140,000) circular cylinder flow was performed based on large eddy simulation (LES). The objective was to evaluate the applicability of LES for practically relevant high-Re flows and to investigate the influence of subgrid scale modeling and grid resolution on the quality of the predicted results. Because the turbulent von Kármán vortex street past circular cylinders involves most of the characteristic features of technical applications, it is an ideal test case for this purpose. Based on a parallelized finite-volume Navier–Stokes solver, computations were carried out on a series of grids applying both the Smagorinsky and the dynamic subgrid scale model. The simulations yielded information on the time-averaged flow field, the resolved Reynolds stresses and integral parameters such as drag coefficient, recirculation length and Strouhal number. The results were analyzed in detail and compared with experimental data. In general, the LES results agreed fairly well with the experimental data, especially in the near wake. Owing to the coarse resolution in the far wake, larger deviations were observed here. As expected, the importance of the subgrid scale model significantly increased for the high-Re case in comparison with a low-Re case predicted earlier. A critical issue for LES is grid refinement which did not automatically lead to an improved agreement between the predicted results and the experimental measurements. Possible explanations are offered in the paper.

A Critical Evaluation of the Classical k-ε Model and Wall-Laws for Unsteady Flows Over Bluflf Bodies

The classical k-ε model and a new implementation of wall-laws have been evaluated for unsteady turbulent flows past square and circular cylinders. We show that good numerics can lead to a serious improvement of the results. In the case of the flow past a square cylinder (Lyn's test case), results agree surprisingly well with the experimental data. In the analysis of the vortex shedding flow past a circular cylinder also the agreement is quite good for the sub-critical regime but not entirely satisfactory after the critical Reynolds number (i.e., the drag crisis phenomenon).

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.

Effect of three-dimensionality on the lift and drag of nominally two-dimensional cylinders

It has been known for some time that two-dimensional numerical simulations of flow over nominally two-dimensional bluff bodies at Reynolds numbers for which the flow is intrinsically three dimensional, lead to inaccurate prediction of the lift and drag forces. In particular, for flow past a normal flat plate (International Symposium on Nonsteady Fluid Dynamics, edited by J. A. Miller and D. P. Telionis, 1990, pp. 455–464) and circular cylinders [J. Wind Eng. Indus. Aerodyn. 35, 275 (1990)], it has been noted that the drag coefficient computed from two-dimensional simulations is significantly higher than what is obtained from experiments. Furthermore, it has been found that three-dimensional simulations of flows lead to accurate prediction of drag [J. Wind Eng. Indus. Aerodyn. 35, 275 (1990)]. The underlying cause for this discrepancy is that the surface pressure distribution obtained from two-dimensional simulations does not match up with that obtained from experiments and three-dimensional simulations and a number of reasons have been put forward to explain this discrepancy. However, the details of the physical mechanisms that ultimately lead to the inaccurate prediction of surface pressure and consequently the lift and drag, are still not clear. In the present study, results of two-dimensional and three-dimensional simulations of flow past elliptic and circular cylinders have been systematically compared in an effort to pinpoint the exact cause for the inaccurate prediction of the lift and drag by two-dimensional simulations. The overprediction of mean drag force in two-dimensional simulations is directly traced to higher Reynolds stresses in the wake. It is also found that the discrepancy in the drag between two-dimensional and three-dimensional simulations is more pronounced for bluffer cylinders. Finally, the current study also provides a detailed view of how the fluctuation, which are associated with the Kármán vortex shedding in the wake, affect the mean pressure distribution and the aerodynamic forces on the body.

Second-Order Accurate No-Slip Conditions for Solving Problems of Incompressible Viscous Flows

Boundary condition of the third kind (also known as Robbins condition) has been used to devise an extremely simple method of satisfying the no-slip boundary condition to second-order accuracy for solving problems of incompressible viscous flows using the vorticity-stream function form of the complete unsteady Navier-Stokes equations. It has been applied to the much-tested problem of flow past circular cylinders. Excellent agreement has been obtained with previous theoretical and experimental results despite the use of simple finite-difference techniques. The results obtained using the proposed approach have been compared with those obtained by straightforward use of the Dirichlet condition and it is easy to see that for unsteady problems the proposed technique is much superior to the conventional one. Finally, a study has been carried out to check the dependence of the present scheme on spatial discretization and the position of the outer boundary. It has been concluded that despite the "local" nature of the improvement, the proposed technique is encouragingly fast, stable, and accurate because it allows satisfaction of no-slip to a higher order of accuracy.

Experiments on flow past rough circular cylinders at large Reynolds numbers

Data have been obtained in the 12-foot pressurized wind tunnel at NASA Ames Research Center on flow past smooth and rough circular cylinders at high Reynolds numbers. Steady and unsteady surface pressures were measured around and along the cylinders. Analysis of the results provides lift and drag coefficients and Strouhal numbers for cylinders of several roughness at Reynolds numbers up to 8 × 106.