Suppression of vortex-induced vibration of a circular cylinder at subcritical Reynolds numbers using shape optimization

Structural and Multidisciplinary Optimization - In this paper, shape optimization is employed to improve the stability of the flow past an elastically mounted circular cylinder at subcritical...     

Large eddy simulation of turbulent flow past a square cylinder confined in a channel

Turbulent flow past a square cylinder confined in a channel is numerically investigated by large eddy simulation (LES). The main objectives of this study are to extensively verify the experimental results of Nakagawa et al. [Exp. Fluids 27(3) (1999) 284] by LES and to identify the features of flows past a square cylinder confined in a channel in comparison with the conventional one in an infinite domain. The LES results obtained are in excellent agreement with the experiment both qualitatively and quantitatively. The well-known Kármán vortex shedding is observed. However, the vortices shed from the cylinder are significantly affected by the presence of the plates; mean drag and fluctuation of lift force increase significantly. Furthermore, periodic and alternating vortex-rollups are observed in the vicinity of the plates. The rolled-up vortex is convected downstream together with the corresponding Kármán vortex; they form a counter-rotating vortex pair. It is also revealed that the cylinder greatly enhances mixing process of the flow.     

Variational multiscale large-eddy simulations of the flow past a circular cylinder: Reynolds number effects

Variational multiscale large-eddy simulations (VMS–LES) of the flow around a circular cylinder are carried out at different Reynolds numbers in the subcritical regime, viz. Re = 3900, 10,000 and 20,000, based on the cylinder diameter. A mixed finite-element/finite-volume discretization on unstructured grids is used. The separation between the largest and the smallest resolved scales is obtained through a variational projection operator and finite-volume cell agglomeration. The WALE subgrid scale model is used to account for the effects of the unresolved scales; in the VMS approach, it is only added to the smallest resolved ones. The capability of this methodology to accurately predict the aerodynamic forces acting on the cylinder and in capturing the flow features are evaluated for the different Reynolds numbers considered. The sensitivity of the results to different simulation parameters, viz. agglomeration level and numerical viscosity, is also investigated at Re = 20,000.     

Steady and unsteady flow past a rotating circular cylinder at low Reynolds numbers

Results of calculations of the steady and unsteady flows past a circular cylinder which is rotating with constant angular velocity and translating with constant linear velocity are presented. The motion is assumed to be two-dimensional and to be governed by the Navier-Stokes equations for incompressible fluids. For the unsteady flow, the cylinder is started impulsively from rest and it is found that for low Reynolds numbers the flow approaches a steady state after a large enough time. Detailed results are given for the development of the flow with time for Reynolds numbers 5 and 20 based on the diameter of the cylinder. For comparison purposes the corresponding steady flow problem has been solved. The calculated values of the steady-state lift, drag and moment coefficients from the two methods are found to be in good agreement. Notable, however, are the discrepancies between these results and other recent numerical solutions to the steady-state Navier-Stokes equations. Some unsteady results are also given for the higher Reynolds numbers of 60, 100 and 200. In these cases the flow does not tend to be a steady state but develops a periodic pattern of vortex shedding.     

Numerical simulation of flow over three circular cylinders in equilateral arrangements at low Reynolds number by a second-order characteristic-based split finite element method

In this paper, two versions of a second-order characteristic-based split scheme are developed in the framework of incremental projection method for the solution of incompressible flow problem. After the demonstration of the good accuracy and effectiveness of the developed schemes, a flow over three equal circular cylinders arranged in equilateral-triangle arrangement is numerically investigated on unstructured mesh systems. The examined Reynolds number is 100 and the flow is supposed to be laminar. Computations by the developed algorithm are then performed for six gap spacings, s, ranging from 0.5 to 4.0, and for three incidence angles, α = 0°, 30° and 60°. Numerical results show that, at sufficiently small and large s, the range of which is different for different α, the flow interference is dominated by proximity and wake effect, respectively. And in the intermediate range of the spacing, the flow pattern is influenced by both of them. The mean force results are compared with the existing experimental measurements and that shows a similar trend in the variation of mean force with the spacing for different Reynolds number. It is also observed that the interference effect transitions plays an important role in the variation of the fluctuating forces and Strouhal number.     

Large eddy simulation of complex flow fields

The large eddy simulation (LES) technique can provide detailed information about time-dependent and three-dimensional turbulent flow fields at high Reynolds number. The application of LES to practical problems and in the basic study of turbulence require investigation. More studies are needed on the boundary conditions and on the subgrid-scale (SGS) model in order to make LES practical. In this paper, the laws of the wall (two-layer model or Spalding's law) are applied as a special approach to the solid boundary in LES. This wall boundary condition is adapted to plane channel flow and the suitability of this method is tested. Further, improvements of the SGS model in which the Smagorinsky model coefficient C_S is not constant are attempted. Recently, Yoshizawa [Phys. Fluids A1(7), 1293 (1989)] derived the form of the variable C_S from a statistical analysis. Here, we optimize this new model in both the decay of isotropic turbulence and plane channel flow simultaneously.     

An investigation of pulsating turbulent open channel flow by large eddy simulation

Pulsating turbulent open channel flow is investigated by use of large eddy simulation (LES) technique coupled with a dynamic subgrid-scale (SGS) model for turbulent SGS stress. The three-dimensional filtered Navier-Stokes equation is numerically solved by a fractional-step method. The objective of this study is to deal with the behaviors of pulsating turbulent open channel flow, in particular turbulence characteristics in the free surface-influenced layer, and to examine the reliability of the LES approach for predicting the pulsating turbulent flow with a free surface. In this study, the frequency of driving pressure gradient ranges low, medium and high value. The mean and phase-averaged statistical turbulence quantities, the resolved turbulent kinetic energy and Reynolds stresses budgets, and the flow structures are obtained and analyzed. With the increase of the driving frequency, the depth of the surface-influenced layer increases and the turbulent Stokes length near the bottom wall decreases. Different turbulence characteristics between the accelerating and decelerating phases are interpreted comprehensively. Turbulence intensities reveal that turbulent flow has a strong anisotropy in the free surface-influenced layer, in particular in the decelerating phases during the pulsating cycle. The budget terms of the resolved turbulent kinetic energy, the vertical and spanwise Reynolds stresses in the free surface region are analyzed. The flow structures clearly exhibit that bursting processes near the bottom wall are ejected toward the surface and the most surface renewal events are closely correlated with the bursting processes. These processes are strengthened during the decelerating period since strong turbulence intensities are generated.     

Recent developments in transonic Euler flow over a circular cylinder

Numerical solutions to the Euler equations for transonic flow over a circular cylinder indicate that the inviscid flow separates ahead of the rear stagnation point. Our understanding of this phenomenon and various solutions presented at a workshop on this subject are discussed.     

Numerical simulation of an oscillating cylinder in a cross-flow at low Reynolds number: Forced and free oscillations

A numerical simulation of the flow past a circular cylinder which is able to oscillate transversely to the incident stream is presented in this paper for a fixed Reynolds number equal to 100. The 2D Navier-Stokes equations are solved by a finite volume method with an industrial CFD code in which a coupling procedure has been implemented in order to obtain the cylinder displacement. A preliminary work is first conducted for a fixed cylinder to check the wake characteristics for Reynolds numbers smaller than 150 in the laminar regime. The Strouhal frequency f_S and the aerodynamic coefficients are thus controlled among other parameters. Simulations are then performed with forced oscillations characterized by the frequency ratio F = f₀/f_S, where f₀ is the forced oscillation frequency, and by the adimensional amplitude A. The wake characteristics are analyzed using the time series of the fluctuating aerodynamic coefficients and their power spectral densities (PSD). The frequency content is then linked to the shape of the phase portraits and to the vortex shedding mode. By choosing interesting couples (A, F), different vortex shedding modes have been observed, which are similar to those of the Williamson-Roshko map. A second batch of simulations involving free vibrations (so-called vortex-induced vibrations or VIV) is finally carried out. Oscillations of the cylinder are now directly induced by the vortex shedding process in the wake and therefore, the time integration of the motion is realized by an explicit staggered algorithm which provides the cylinder displacement according to the aerodynamic charges exerted on the cylinder wall. Amplitude and frequency response of the cylinder are thus investigated over a wide range of reduced velocities to observe the different phenomena at stake. In particular, the vortex shedding modes have also been related to the frequency response observed and our results at Re = 100 show a very good agreement with other studies using different numerical approaches.     

Flow over a bluff body from moderate to high Reynolds numbers using large eddy simulation

Large eddy simulation (LES) is performed to study the uniform approach flow over a square-section cylinder with different Reynolds numbers, ranging from 10³ to 5 × 10⁶. Two different sub-grid scale models, the Smagorinsky and a dynamic one-equation model, are employed. An incompressible finite-volume code, based on a non-staggered grid arrangement and an implicit fractional step method with second-order accuracy in space and time, is used.

The structure of the flow is studied with the instantaneous and the mean quantities such as pressure, turbulent stresses, turbulent kinetic energy, vorticity, the second invariant of velocity gradient and streamlines. The Strouhal number, the mean and RMS values of the lift and drag are computed for various Reynolds numbers, which show a good agreement with the available experimental results. It is found that the effect of Reynolds number on the global quantities, the mean and the large scale instantaneous flow-structures is not much at the higher Reynolds numbers, i.e. Re > 2 × 10⁴. In this range of Reynolds numbers, the small scales of the instantaneous structures are more complex and chaotic as they compare with the larger ones.     

Large eddy simulation of turbulent open duct flow using a lattice Boltzmann approach

Large eddy simulations of turbulent open duct flow are performed using the lattice Boltzmann method (LBM) in conjunction with the Smagorinsky sub-grid scale (SGS) model. A smaller value of the Smagorinsky constant than the usually used one in plain channel flow simulations is used. Results for the mean flow and turbulent fluctuations are compared to experimental data obtained in an open duct of similar dimensions. It is found that the LBM simulation results are in good qualitative agreement with the experiments.     

End-wall effects on vortex shedding in planar shear flow over a circular cylinder

A prevailing controversy regarding the suppression of periodic vortex shedding from a circular cylinder embedded in a planar shear flow has been addressed. Three-dimensional computer simulations utilizing the advanced MGLET software [11] demonstrated the importance of the end-wall conditions. Earlier results from two-dimensional simulations at Re = 100 were reproduced only with free-slip conditions. With no-slip conditions imposed at one or both end-walls, the vortex shedding was suppressed near the no-slip boundary and the shedding pattern was substantially affected even at mid-span. The Strouhal number decreased when the shear-rate parameter was increased from 0.1 to 0.2, irrespective of the choice of boundary conditions.     

Computation of a high Reynolds number jet and its radiated noise using large eddy simulation based on explicit filtering

An isothermal circular jet with a Mach number of M = 0.9 and a Reynolds number of Re_D = 4 × 10⁵ is computed by compressible large eddy simulation (LES). The LES is carried out using an explicit filtering to damp the scales discretized by less than four grid points without affecting the resolved large scales. The jet features are thus found not to appreciably depend on the filtering procedure. The flow development is also shown from simulations on different grids to be independent of the location of the grid boundaries. The flow and the sound field obtained directly by LES are compared to measurements of the literature. The acoustic radiation especially displays spectra and azimuthal correlation functions which behave according to the observation angle as expected for a high Reynolds number. Furthermore the two components of jet noise usually associated to large structures and to fine-scale turbulence, respectively, are apparently found.     

Simulation of three-dimensional nonideal MHD flow at high magnetic Reynolds number

A conservative TVD scheme is adopted to solve the equations governing the three-dimensional flow of a nonideal compressible conducting fluid in a magnetic field.The eight-wave equations for magnetohydrodynamics(MHD) are proved to be a non-strict hyperbolic system,therefore it is difficult to develop its eigenstructure.Powell developed a new set of equations which cannot be numerically simulated by conservative TVD scheme directly due to its non-conservative form.A conservative TVD scheme augmented with a ne...     

Large eddy simulation of two-dimensional isotropic turbulence

Large eddy simulation (LES) of forced, homogeneous, isotropic two-dimensional (2D) turbulence in the energy transfer subrange is the subject of this paper. A difficulty specific to this LES and its subgrid scale (SGS) representation is in that the energy source resides in high wave number modes excluded in simulations. Therefore, the SGS scheme in this case should assume the function of the energy source. In addition, the controversial requirements to ensure direct enstrophy transfer and inverse energy transfer make the conventional scheme of positive and dissipative eddy viscosity inapplicable to 2D turbulence. It is shown that these requirements can be reconciled by utilizing a two-parametric viscosity introduced by Kraichnan (1976) that accounts for the energy and enstrophy exchange between the resolved and subgrid scale modes in a way consistent with the dynamics of 2D turbulence; it is negative on large scales, positive on small scales and complies with the basic conservation laws for energy and enstrophy. Different implementations of the two-parametric viscosity for LES of 2D turbulence were considered. It was found that if kept constant, this viscosity results in unstable numerical scheme. Therefore, another scheme was advanced in which the two-parametric viscosity depends on the flow field. In addition, to extend simulations beyond the limits imposed by the finiteness of computational domain, a large scale drag was introduced. The resulting LES exhibited remarkable and fast convergence to the solution obtained in the preceding direct numerical simulations (DNS) by Chekhlovet al. (1994) while the flow parameters were in good agreement with their DNS counterparts. Also, good agreement with the Kolmogorov theory was found. This LES could be continued virtually indefinitely. Then, a simplified SGS representation was designed, referred to as the stabilized negative viscosity (SNV) representation, which was based on two algebraic terms only, negative Laplacian and positive biharmonic ones. It was found that the SNV scheme performed in a fashion very similar to the full equation and it was argued that this scheme and its derivatives should be applied for SGS representation in LES of quasi-2D flows.     

Lattice Boltzmann large eddy simulation of subcritical flows around a sphere on non-uniform grids

In this work, the suitability of the lattice Boltzmann method is evaluated for the simulation of subcritical turbulent flows around a sphere. Special measures are taken to reduce the computational cost without sacrificing the accuracy of the method. A large eddy simulation turbulence model is employed to allow efficient simulation of resolved flow structures on non-uniform computational meshes. In the vicinity of solid walls, where the flow is governed by the presence of a thin boundary layer, local grid-refinement is employed in order to capture the fine structures of the flow. In the test case considered, reference values for the drag force in the Reynolds number range from 2000 to 10 000 and for the surface pressure distribution and the angle of separation at a Reynolds number of 10 000 could be quantitatively reproduced. A parallel efficiency of 80% was obtained on an Opteron cluster.     

Steady flow around and through a permeable circular cylinder

The steady flow around and through a porous circular cylinder was studied numerically. The effects of the two important parameters, the Reynolds and Darcy numbers, on the flow were investigated in details. The recirculating wake existing downstream of the cylinder is found to either penetrate into or be completely detached from the cylinder. It is also found that, contrary to that of the solid cylinder, the recirculating wake develops downstream of or within the porous cylinder, but not from the surface of it. These new findings provide additional evidence to Leal’s conclusion (Leal LG. Vorticity transport and wake structure for bluff bodies at finite Reynolds number. Phys Fluids A 1989;1:124) that the appearance of recirculating wakes at finite Reynolds number is due to vorticity accumulation, but not a result of the same physical phenomena associated with separation in boundary layers in adverse pressure gradients. Also presented in the current study are the variation of the critical Reynolds number for the onset of a recirculating wake as a function of Darcy number and the variation of a newly defined parameter, the penetration depth, as a function of the Reynolds number and Darcy number.     

Spectral simulations of an unsteady compressible flow past a circular cylinder

An unsteady compressible viscous wake flow past a circular cylinder has been successfully simulated using spectral methods. A new approach in using the Chebyshev collocation method for a periodic problem is introduced. We have further proved that the eigenvalues associated with the differentiation matrix are purely imaginary, reflecting the periodicity of the problem. It has been shown that the solution of a model problem has exponential growth in time if an ‘improper’ boundary conditions procedure is used. A characteristic boundary conditions, which is based on the characteristics of the Euler equations of gas dynamics, has been derived for the spectral code. The primary vortex shedding frequency computed agrees well with the results in the literature for Mach = 0.4, Re = 80. No secondary frequency is observed in the power spectrum analysis of the pressure data.     

MHD flow past a circular cylinder using the immersed boundary method

The immersed boundary method (IB hereafter) is an efficient numerical methodology for treating purely hydrodynamic flows in geometrically complicated flow-domains. Recently Grigoriadis et als. [1] proposed an extension of the IB method that accounts for electromagnetic effects near non-conducting boundaries in magnetohydrodynamic (MHD) flows. The proposed extension (hereafter called MIB method) integrates naturally within the original IB concept and is suitable for magnetohydrodynamic (MHD) simulations of liquid metal flows. It is based on the proper definition of an externally applied current density field in order to satisfy the Maxwell equations in the presence of arbitrarily-shaped, non-conducting immersed boundaries. The efficiency of the proposed method is achieved by fast direct solutions of the two poisson equations for the hydrodynamic pressure and the electrostatic potential.The purpose of the present study is to establish the performance of the new MIB method in challenging configurations for which sufficient details are available in the literature. For this purpose, we have considered the classical MHD problem of a conducting fluid that is exposed to an external magnetic field while flowing across a circular cylinder with electrically insulated boundaries. Two- and three-dimensional, steady and unsteady, flow regimes were examined for Reynolds numbers Re_d ranging up to 200 based on the cylinder’s diameter. The intensity of the external magnetic field, as characterized by the magnetic interaction parameter N, varied from N=0 for the purely hydrodynamic cases up to N=5 for the MHD cases. For each simulation, a sufficiently fine Cartesian computational mesh was selected to ensure adequate resolution of the thin boundary layers developing due to the magnetic field, the so called Hartmann and sidewall layers. Results for a wide range of flow and magnetic field strength parameters show that the MIB method is capable of accurately reproducing integral parameters, such as the lift and drag coefficients, as well as the geometrical details of the recirculation zones. The results of the present study suggest that the proposed MIB methodology provides a powerful numerical tool for accurate MHD simulations, and that it can extend the applicability of existing Cartesian flow solvers as well as the range of computable MHD flows. Moreover, the new MIB method has been used to carrry out a series of accurate simulations allowing the determination of asymptotic laws for the lift and drag coefficients and the extent of the recirculation length as a function of the amplitude of the magnetic field. These results are reported herein.     

Numerical solutions of 2-D steady incompressible flow over a backward-facing step, Part I: High Reynolds number solutions

Numerical solutions of 2-D laminar flow over a backward-facing step at high Reynolds numbers are presented. The governing 2-D steady incompressible Navier-Stokes equations are solved with a very efficient finite difference numerical method which proved to be highly stable even at very high Reynolds numbers. Present solutions of the laminar flow over a backward-facing step are compared with experimental and numerical results found in the literature.