Numerical simulation of the flow around rows of cylinders

Two-dimensional, laminar, unsteady, water flow around cylinder arrays of unequal sizes was simulated using FLUENT™ at Reynolds numbers below 150 (based on the free-stream velocity and first row cylinder diameter). The flow pattern through two rows of inline cylinders showed incomplete vortex shedding behind the first row at a separation distance less than 2d. Karman vortices were not formed and a near-stagnant separated flow region appeared between the aligned cylinders. Cylinders in staggered arrangements shed Karman vortices regardless of the separation between the two rows. This research has shed light on the detailed flow through paper machine forming fabrics.     

Effect of tube spacing on the vortex shedding characteristics of laminar flow past an inline tube array: A numerical study

The effect of tube spacing on the vortex shedding characteristics and fluctuating forces in an inline cylinder array is studied numerically. The examined Reynolds number is 100 and the flow is laminar. The numerical methodology and the code employed to solve the Navier-Stokes and continuity equations in an unstructured finite volume grid are validated for the case of flow past two tandem cylinders at four spacings. Computations are then performed for a six-row inline tube bank for eight pitch-to-diameter ratios, s, ranging from 2.1 to 4. At the smallest spacing examined (s = 2.1) there are five stagnant and symmetric recirculation zones and weak vortex shedding activity occurs only behind the last cylinder. As s increases, the symmetry of the recirculation zones breaks leading to vortex shedding and this process progressively moves upstream, so that for s = 4 there is clear shedding from every row. For any given spacing, the shedding frequency behind each cylinder is the same. A critical spacing range between 3.0 and 3.6 is identified at which the mean drag as well as the rms lift and drag coefficients for the last three cylinders attain maximum values. Further increase to s = 4 leads to significant decrease in the force statistics and increase in the Strouhal number. It was found that at the critical spacing there is 180° phase difference in the shedding cycle between successive cylinders and the vortices travel a distance twice the tube spacing within one period of shedding.     

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.     

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.     

Numerical modeling of interaction of a current with a circular cylinder near a rigid bed

The numerical modeling of 2D turbulent flow around a smooth horizontal circular cylinder near a rigid bed with gap ratio G/D = 0.3 at Reynolds number Re_D = 9500 is investigated. Ansys^® 10.0-FLOTRAN program package is used to solve the governing equations by FEM, and the performance of the standard k ? ε, standard k ? ω, and SST turbulence models are examined. A sensitivity study for the three turbulence models is carried out on three computational meshes with different densities near the cylinder surface. The computational velocity fields and the Strouhal numbers from the present simulations are compared with those obtained from the PIV measurement. It is found that the time-averaged velocity field of the flow in the proximity of the cylinder is closely affected by the mesh resolution near the cylinder surface, and the mesh refinement in radial direction improves the results of present simulations. The shedding of vortices in the cylinder wake is not predicted by k ? ε model on all the three meshes. The results for the time-averaged velocity field show that the numerical modeling using either of k ? ω and SST turbulence models on the finest mesh used on the cylinder surface is reasonably successful.     

A numerical investigation of fluid flow over a rotating cylinder with cross flow oscillation

This paper studies a two-dimensional incompressible viscous flow past a rotating cylinder with cross flow oscillation using a finite element method based on the characteristic based split (CBS) algorithm to solve governing equations including full Navier–Stokes and continuity equations. Dynamic unstructured triangular grid is used employing lineal and torsional spring analogy which is coupled with the solver by an Arbitrary Lagrangian–Eulerian (ALE) formulation. After verifying the accuracy of the numerical code, simulations are conducted for the flow past a rotating cylinder with cross flow oscillation at moderate Reynolds numbers of 50, 100, and 200 considering different non-dimensional rotational speeds based on the free-stream velocity in the range 0–2.5, and various oscillating amplitudes and frequencies. Effects of the oscillation and rotation of the cylinder on the vortex shedding both in lock-on and non-lock-on regions, the mean drag and lift coefficients, and the Strouhal number are investigated in detail. It is found that similar to the fixed cylinder beyond a critical non-dimensional rotational speed the vortex shedding is highly suppressed. In addition, by increasing the rotational speed of the cylinder, the lift coefficient increases while decreasing the drag coefficient. However, in the vortex lock-on region both the lift and the drag coefficients increase significantly.     

柴油机可调涡流比燃烧过程三维仿真

在柴油机进气歧管前安装蝶形涡流调节阀,通过调整直气道侧的有效流通面积改变缸内涡流强度。在稳流吹风试验平台,研究涡流调节阀角度对进气道流量因数和涡流比的影响,并结合粒子图像测速（particle image velocimetry,PIV）分析缸内涡流的形成过程。采用计算流体力学（computational fluid dynamics,CFD）评估涡流调节阀角度对缸内混合气体形成过程的影响,计算结果可复现三维 PIV测量的缸内流场结构和相似的涡心位置。随着进气门关闭,涡流比从0.57提高到2.05,油气在周向的相互作用增强,从而加速预混燃烧阶段的放热速度,促使燃烧重心提前、燃烧持续期缩短。在相同进气流量条件下,强涡流运动也促使累积放热量增加。     

On the use of several compact methods for the study of unsteady incompressible viscous flow round a circular cylinder

Fourth order accurate methods of mehrstellen type are compared to second order accurate methods for the solution of the unsteady incompressible Navier-Stokes equations in their vorticity stream function formulation. These methods are applied to the study of separated flow around a circular cylinder at several Reynolds numbers. The impulsively started cylinder at Re = 200 and 550, is considered without symmetry restrictions. The features illustrated include the bulge phenomenon at Re = 200, the occurrence of secondary vortices depending on the schemes used at Re = 550, and of twin secondary vortices at Re = 3000. The Karman vortex street is investigated at Re = 200 with a uniform flow in the far field and with superimposed motions of the cylinder. In this last case, a frequency analysis has allowed a critical examination of results pertaining to locked-in situations with respect to confinement effects.     

A numerical analysis of two-dimensional flow past a rectangular prism by a discrete vortex model

A discrete vortex model is developed to analyse the two-dimensional fully separated unsteady flow past a rectangular prism. The effects of viscous diffusion of vortices and the loss in vorticity after the stationary prism with a thickness ratio ranging from 0.5 to 2.0. The formation of Karman vortices, the vortex shedding frequency, and the fluid forces acting on the body are favourably compared with the experimental results by various research workers. The method of analysis is also shown to be applicable to the flow past a prism that is in forced vibration.     

Implementation of a transient adaptive sub-cell module for the parallel-DSMC code using unstructured grids

A method of transient adaptive sub-cells (TAS) suitable for unstructured grids that is modified from the existing one for the structured grids of DSMC is introduced. The TAS algorithm is implemented within the framework of a parallelized DSMC code (PDSC). Benchmarking tests are conducted for steady driven cavity flow, steady hypersonic flow over a two-dimensional cylinder, steady hypersonic flow over a cylinder/flare and the unsteady vortex shedding behind a two-dimensional cylinder. The use of TAS enables a reduction in the computational expense of the simulation since larger sampling cells and less simulation particles can be employed. Furthermore, the collision quality of the simulation is maintained or improved and the preservation of property gradients and vorticity at the scale of the sub-cells enables correct unsteady vortex shedding frequencies to be predicted. The use of TAS in a parallel-DSMC code allows simulations of unsteady processes at a level to be carried out efficiently, accurately and with acceptable computational time.     

High-order finite-difference implementation of the immersed-boundary technique for incompressible flows

A high-resolution, two-dimensional (2-D), vortex particle method is implemented, and simulations of flows around various bluff bodies are presented, with a detailed analysis of the flow around rectangular cylinders. Long-time simulations of flows around square and rectangular cylinders at low to moderate Reynolds numbers are then performed, and the resulting Strouhal–Reynolds number relationships are compared with experimental and numerical data in the literature. The well-known stepwise variation of the chord-based Strouhal number with chord-to-thickness ratio for rectangular cylinders is replicated, and the flow field is explored and compared with experimental observations. Further analyses with identified vortices provide new insights into the shedding process that leads to the stepwise variation of chord-based Strouhal numbers and the frequency jumps.     

Optimal control of cylinder wakes via suction and blowing

A general method based on adjoint formulation is discussed for the optimal control of distributed parameter systems (including boundary parameter) which is especially suitable for large dimensional control problems. Strategies for efficient and robust implementation of the method are described. The method is applied to the problem of controlling vortex shedding behind a cylinder (through suction/blowing on the cylinder surface) governed by the unsteady two-dimensional incompressible Navier-Stokes equations space discretized by finite-volume approximation with time-dependent boundary conditions. Three types of objective functions are considered, with regularization to circumvent ill-posedness. These objective functions involve integration over a space-time domain. The minimization of the cost function uses a quasi-Newton DFP method.A complete control of vortex shedding is demonstrated for Reynolds numbers up to 110. The optimal values of the suction/blowing parameters are found to be insensitive to initial conditions of the model when the time window of control is larger than the vortex shedding period, the inverse of the Strouhal frequency. Although this condition is necessary for robust control, it is observed that a shorter window of control may suffice to suppress vortex shedding.     

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.     

On the use of incomplete sensitivities for feedback control of laminar vortex shedding

A feedback control method based on incomplete sensitivities and gradient evaluation by complex variable method is proposed and applied to the problem of the control of the laminar vortex shedding past a circular cylinder. This procedure results in a low-cost control algorithm, which does not require to compute the gradient of the Navier–Stokes solution with respect to the controllers. For the sake of usability for practical applications, realistic sensors and actuators are used. Validation simulations aiming at controlling the drag of the cylinder are presented and compared with previous published results, proving the efficiency of the proposed method. Application to the control of the cylinder lift is also shown.     

Incompressible moving boundary flows with the finite volume particle method

Mesh-free methods offer the potential for greatly simplified modeling of flow with moving walls and phase interfaces. The finite volume particle method (FVPM) is a mesh-free technique based on interparticle fluxes which are exactly analogous to intercell fluxes in the mesh-based finite volume method. Consequently, the method inherits many of the desirable properties of the classical finite volume method, including implicit conservation and a natural introduction of boundary conditions via appropriate flux terms. In this paper, we describe the extension of FVPM to incompressible viscous flow with moving boundaries. An arbitrary Lagrangian–Eulerian approach is used, in conjunction with the mesh-free discretisation, to facilitate a straightforward treatment of moving bodies. Non-uniform particle distribution is used to concentrate computational effort in regions of high gradients. The underlying method for viscous incompressible flow is validated for a lid-driven cavity problem at Reynolds numbers of 100 and 1000. To validate the simulation of moving boundaries, flow around a translating cylinder at Reynolds numbers of 20, 40 and 100 is modeled. Results for pressure distribution, surface forces and vortex shedding frequency are in good agreement with reference data from the literature and with FVPM results for an equivalent flow around a stationary cylinder. These results establish the capability of FVPM to simulate large wall motions accurately in an entirely mesh-free framework.     

均匀流场中四边形锥柱的压力试验研究

通过水池试验研究了在雷诺数Re为3.19×104~1.15×106,攻角为0°~180°,以15°为间隔,表面倾斜且前后不对称的四边形锥柱状结构在均匀流场中所受的压力载荷。分析了模型所受的周向压力和斯特劳哈尔数Sr随Re和攻角的变化趋势。结果表明:与圆柱绕流相比,倾斜壁面和攻角使压力在背压区和边界层分离点发生变化,同时,Sr也由0.2降到0.13。     

Source Seeking for Two Nonholonomic Models of Fish Locomotion

In this paper, we present a method of locomotion control for underwater vehicles that are propelled by a periodic deformation of the vehicle body, which is similar to the way a fish moves. We have developed control laws employing ldquoextremum seekingrdquo for two different ldquofishrdquo models. The first model consists of three rigid body links and relies on a 2-degree-of-freedom (DOF) movement that propels the fish without relying on vortices. The second fish model uses a Joukowski airfoil that has only 1 DOF in its movement and, thus, relies on vortex shedding for propulsion. We achieve model-free and position-free ldquosource seeking,rdquo and, if position is available, navigation along a predetermined path.     

Microfluidic two-phase interactions under variable liquid to cross-flow gas momentum flux ratios

Volume of fluid (VOF) and large eddy simulations (LES) are coupled to investigate the microfluidic two-phase interactions during the liquid emergence into the cross-flow gas in a super-hydrophobic micro-channel. Spatio-temporal evolution of the gas/liquid interface is presented for nine different cases of the liquid to gas momentum flux ratios, gas/liquid Reynolds numbers and gas/liquid Weber numbers. With increased momentum of the gas flow, the liquid topology is found deflected towards the downstream. Under variable gas resistance effects, the liquid flow emerging through the square pore may or may not develop a circular cross-section governed by the axis-switching phenomenon. At strong gas inertia, vortex shedding in the downstream of the liquid generates vorticular ligaments in the wake region. Shearing effects on the liquid surface are increased at higher liquid injection velocities and/or gas densities. Depending on the competing effects of the viscous diffusion versus gas/liquid inertia, different combinations of the interactions among the three building blocks of the fluid flow problems (boundary layer, shear layer and wake) are described in microfluidics scales. The complexity of the liquid topology is found correlated with the occurrence of the phenomena such as the Kelvin–Helmholtz (KH) instability, the horseshoe vortex system, stationary/shedding vortices in the wake of the liquid topology as well as their interaction with the micro-channel wall boundary layers.     

Electrodynamics of type-II superconductor with periodic pinning array

Static and dynamic distribution of the superconducting condensate order parameters and current density is studied by numerical simulation of the 2D time-dependent Ginzburg–Landau equations. The vortex flux lattice in layered type-II superconductors under magnetic field above the lower critical field is described by the order parameters. Moreover, the pinning effect has been considered in this work. The Abrikosov lattice which is hexagonal in the static case is deformed due to the size of pinning centers. The dynamical order parameters distribution shows that the vortex transport (flux flow) is conducted via diffusive motion of the so-called interstitial vortices. The trajectories for interstitial vortices with different sizes of pinning centers are shown.     

Discrete-vortex simulation of flow over inclined and normal plates

The wake flow behind a normal or an inclined plate is predicted by a discrete-vortex method. The vortex shedding phenomenon at the leading and the trailing edges is simulated by a vorticity creation technique according to the Kutta condition. This approach required that the strengths and locations of discrete vortices just shed from the edges be determined such that their presence in the flow field will offset the potential flow singularities at the edges of the plate.

For gross features in the flow, the current model closely reproduced the measured values of previous experiments. As to the microscopic features in the wake flow, the predictions by the current model compare favorably with the experiments and with the previous solutions also by discrete-vortex simulation. For similar or better solutions, this approach requires about half of the computing time reported by other discrete-vortex approaches.