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.     

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.     

Two-dimensional side-by-side circular cylinders at moderate Reynolds numbers

In a companion article [1], we described computer simulations of the flow around 2 two-dimensional, tandem circular cylinders in a flow for 1?Re?20. In this article we adopt a similar approach to characterize the flow around side-by-side cylinders with surface-to-surface separation/diameter in the range 0.1 < s/D < 30. The results revealed some distinct and interesting features of the flow, which are completely different than those observed at higher Reynolds numbers.At low Reynolds numbers, 1?Re?5, for all gap spacings, the flow contains no regions of flow separation. At higher Re, four distinct flow behaviors were observed. For very small gap spacings, e.g. 0.1 < s/D < 0.6 at Re = 20, two elongated “detached vortices” form downstream of the cylinders. The drag coefficient increases sharply with the gap spacing. For gap spacings 0.6 < s/D < 0.7 at Re = 20, no vortices form anywhere in the flow. For gap spacings around s/D ≈ 1 separation regions form only on the inside portions of the cylinders. For larger gap spacings s/D > 1 the flow reverts to something similar to that around an isolated cylinder in the flow, i.e. two attached vortices on the rear side of each cylinder. In general, the drag coefficient increases as the gap spacing increases. At higher Reynolds number it is known that the cylinder lift coefficients decrease monotonically with gap spacing. In contrast, at these lower Reynolds number the lift coefficient curves rise to a maximum for 0.3 < s/D < 3 and then decrease monotonically for larger s/D.     

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.     

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.     

Lattice Boltzmann simulations to determine drag, lift and torque acting on non-spherical particles

The drag, lift and moment coefficients of differently shaped single particles have been determined as a function of the angle of incidence at particle Reynolds numbers between Re = 0.3 and 240 under different conditions. For this purpose simulations of the flow around these particles have been performed using the three-dimensional Lattice Boltzmann method. In the first case studied a particle is fixed in a uniform flow, in the second case the particle is rotating in a uniform flow to determine, among others, the Magnus lift force and in the third case the particle is fixed in a linear shear flow. In the first case six particle shapes are considered, i.e. a sphere, a spheroid, a cube, a cuboid and two cylinders with an axis ratio of 1 and 1.5, respectively. In the second and third case the sphere and the spheroid are considered. At the higher Re considered, the drag depends strongly on particle shape, the angle of incidence and particle rotation. The lift and the torque of both the sphere and the spheroid are strongly affected by particle rotation and fluid shear. For approximately Re ? 1, the shear induced lift for unbounded flow could not be simulated as the top and bottom wall have a significant influence in the current flow configuration. The shear induced lift of the sphere changes direction at approximately Re = 50 and the mean (over the orientation) shear induced lift of the spheroid changes direction at approximately Re = 90.     

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.     

Surface effects on transient three-dimensional flows around rotating spheres at moderate Reynolds numbers

Transient wake flow patterns and dynamic forces acting on a rotating spherical particle with non-uniform surface blowing are studied numerically for Reynolds numbers up to 300 and dimensionless angular velocities up to Ω=1. This range of Reynolds numbers includes the three distinct wake regimes i.e., the steady axisymmetric, the steady non-symmetrical and the unsteady with vortex shedding. The Navier–Stokes equations for an incompressible viscous flow are solved by a finite volume method in a three-dimensional, time accurate manner. An interesting feature associated with particle rotation and surface blowing is that they can affect the near wake structure in such a way that unsteady three-dimensional wake flow with vortex shedding develops at lower Reynolds numbers as compared to flow over a solid sphere in the absence of these effects and thus, vortex shedding occurs even at Re=200. Global properties, such as the lift and drag coefficients, and the Strouhal number are also significantly affected. It is shown that the present data for the average lift and drag coefficients correlate well with:

C_L/(1+Ω)^3.6=0.11

C_D(1+20V_S)^0.2/(1+Ω)^Re/1000=24(1+Re^2/3/6)/Re

where V_S is the average surface blowing velocity normalized by the free stream velocity.     

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.     

Particle mixing and reactive front motion in unsteady open shallow flow - Modelled using singular value decomposition

Passive and active tracers are used to examine particle mixing and reactive front dynamics in an open shallow flow of water past a circular cylinder. A quadtree grid based Godunov-type shallow water equation solver predicts the unsteady flow hydrodynamics of the wake behind the cylinder. The resulting periodic flow field consisting of a von Kármán vortex street is decomposed and stored over one oscillatory period using Singular Value Decomposition (SVD). Particles are advected according to the reconstructed flow field from the SVD modes, with continuous spatial velocity information obtained via bilinear interpolation. Passive particle dynamics driven by different SVD flow modes is investigated, and it is found that the flow field recovered from the mean flow and the first pair of time varying modes is adequate to represent the complicated dynamical properties induced by the original flow field. Active autocatalytic reaction, A + B → 2B, is incorporated into the particle advection model, assuming surface reaction. Active particles are found to trace out an expanded version of the unstable manifold of the chaotic saddle in the wake, in qualitative agreement with published analytical results. The numerical model is applicable to mixing and transport processes in more complicated shallow environmental flows.     

Wall modeling for LES of high Reynolds number channel flows: What turbulence information is retained?

A novel near-wall eddy-viscosity formulation for Large-eddy simulation (LES) has been used to compute high Reynolds number channel flows up to Re_τ = 1,000,000. These computations allow an insight into what turbulence information is retained when LES with a wall model is applied to such high Reynolds numbers. Detailed results are presented for the mean and rms velocities, as well as energy spectra. It is observed that, when an appropriate scaling is used, the rms velocities, energy spectra and the production of turbulence kinetic energy are weakly Reynolds number dependent at these high Reynolds numbers.     

A Parallel Overset Grid High-Order Flow Solver for Large Eddy Simulation

This work describes the development and validation of a parallel high-order compact finite difference Navier–Stokes solver for application to large-eddy simulation (LES) and direct numerical simulation. The implicit solver can employ up to sixth-order spatial formulations and tenth-order filtering. The parallelization of the solver is founded on the overset grid technique. LES were then performed for turbulent channel flow with Reynolds numbers ranging from Re _τ=180 to 590, and flow past a circular cylinder with a transitional wake at Re _D =3900. The channel flow solutions were obtained using both an implicit LES (ILES) approach and a dynamic sub-grid scale model. The ILES method obtained virtually identical solutions at half the computational cost. The original vector and new parallel solvers produce indistinguishable mean flow solutions for the circular cylinder. Repeating the cylinder simulation on a much finer mesh resulted in significantly better agreement with experimental data in the near wake than the coarse grid solution and other previous numerical studies.     

Control of flow using genetic algorithm for a circular cylinder executing rotary oscillation

We propose here a new approach to optimally control incompressible viscous flow past a circular cylinder for drag minimization by rotary oscillation. The flow at Re = 15000 is simulated by solving 2D Navier-Stokes equations in stream function-vorticity formulation. High accuracy compact scheme for space discretization and four stage Runge-Kutta scheme for time integration makes such simulation possible. While numerical solution for this flow field has been reported using a fast viscous-vortex method, to our knowledge, this has not been done at such a high Reynolds number by computing the Navier-Stokes equation before. The importance of scale resolution, aliasing problem and preservation of physical dispersion relation for such vortical flows of the used high accuracy schemes [Sengupta TK. Fundamentals of computational fluid dynamics. Hyderabad, India: University Press; 2004] is highlighted.For the dynamic problem, a novel genetic algorithm (GA) based optimization technique has been adopted, where solutions of Navier-Stokes equations are obtained using small time-horizons at every step of the optimization process, called a GA generation. Then the objective functions is evaluated that is followed by GA determined improvement of the decision variables. This procedure of time advancement can also be adopted to control such flows experimentally, as one obtains time-accurate solution of the Navier-Stokes equation subject to discrete changes of decision variables. The objective function - the time-averaged drag - is optimized using a real-coded genetic algorithm [Deb K. Multi-objective optimization using evolutionary algorithms. Chichester, UK: Wiley; 2001] for the two decision variables, the maximum rotation rate and the forcing frequency of the rotary oscillation. Various approaches to optimal decision variables have been explored for the purpose of drag reduction and the collection of results are self-consistent and furthermore match well with the experimental values reported in [Tokumaru PT, Dimotakis PE. Rotary oscillation control of a cylinder wake. J Fluid Mech 1991;224:77].     

A numerical study of flow past a cylinder with cross flow and inline oscillation

Two-dimensional fluid flow around an oscillating circular cylinder is studied numerically at different values of oscillation frequency and amplitude. A novel finite element method which uses discretization along the characteristic line is used for simulation. The solver is coupled to a mesh movement scheme using the Arbitrary Lagrangian-Eulerian (ALE) formulation to account for body motion in the flow field. Two cases of cylinder motion have been studied, cross flow and inline oscillation. In both cases, occurrence of lock on is investigated and the bounds of the lock on region are determined. A comparison of the numerical results with the experimental data indicates that 2D simulation is valid up to Re = 300. Beyond that, 3D effects appear. By using flow visualization, effect of a cylinder oscillation on the flow field and wake pattern has been studied. Also, variation of the mean drag coefficient against the oscillation parameters is discussed. The numerical results are in good agreement with the experimental data available in the literature.     

Time-dependent solutions of the viscous incompressible flow past a circular cylinder by the method of series truncation

Semi-analytic solutions of the Navier-Stokes equations are calculated for two-dimensional, symmetrical, viscous incompressible flow past a circular cylinder. The stream and vorticity functions are expanded in the finite Fourier series and then substituted in the Navier-Stokes equations. This led to a system of coupled parabolic partial differential equations which are solved numerically. More terms of the series are required as Reynolds number increases and the present calculations were terminated at Reynolds number 600 with 60 terms of Fourier series. The results are compared with similar calculations and experimental data for Reynolds numbers 60, 100, 200, 500, 550 and 600. At the termination of the calculations for Reynolds numbers 60 and 100, the separation angle, the wake length, the drag coefficient, and the vorticity distributions around the surface were very close to their steady-state values. A secondary vortex appeared on the surface of the cylinder in the case of Reynolds numbers 500, 550 and 600. The wake length, the drag coefficient and the separation angle differ slightly at a given instant in the case of Reynolds numbers 500, 550 and 600.     

Computations of optimal cylinder flow control in weakly conductive fluids

A nonlinear adjoint-based optimal control approach of cylinder wake by electromagnetic force has been investigated numerically in the paper. A cost functional representing the balance of the regulated quantities with different weights and interaction parameter N (Lorentz force) has been constituted, where the regulated quantities related with flow and force are taken as targets of regulation and the Lorentz force, (as interaction parameter N), is taken as a control input. Based on the cost functional and Navier-Stokes equations, the corresponding adjoint equations have been derived and the sensitivity of the cost functional is found to be a simple function of the adjoint stream function in the adjoint field. For the different regulations, the forms of optimal control rules are similar while the adjoint equations are different. The receding-horizon predictive control setting is employed to discuss the optimal control problems. Under the action of optimal N(t), the flow separation is suppressed fully, so that the oscillations of drag and lift are suppressed and the total drag coefficient decreases dramatically. For the different regulations, the control effects have some differences due to the different values of optimal inputs corresponding to the different adjoint flow fields.     

Large-eddy simulations of film cooling flows

Large-eddy simulations (LES) of a jet in a cross-flow (JICF) problem are carried out to investigate the turbulent flow structure and the vortex dynamics in gas turbine blade film cooling. A turbulent flat plate boundary layer at a Reynolds number of Re_∞ = 400,000 interacts with a jet issued from a pipe. To study the effect of the jet inclination angle α on the flow field, two angles are chosen, the perpendicular injection at 90° and the streamwise inclined injection at 30°. For the normal injection case a small blowing ratio of the jet velocity to the cross-stream velocity R = 0.1 is examined. For the streamwise inclined injection case two blowing ratios R = 0.1 and R = 0.48 are investigated to check the impact of the jet velocity on the cooling performance. The time-dependent turbulent inflow information for the cross-flow is provided by a simultaneously performed LES of a spatially developing turbulent boundary layer. Whereas in the perpendicular injection case a rather large separation region is found at the leading edge of the jet hole, in the streamwise inclined injection cases no separation is observed. Compared with the normal injection case at the same blowing ratio, the streamwise inclination weakens the jet-cross-flow interaction significantly. Thus, the first appearance of the counter-rotating vortex pair (CVP) is shifted downstream and its strength is reduced. The increase of the blowing ratio leads to a stronger penetration of the jet into the cross-flow, resulting in a more upstream located and more pronounced CVP. Downstream of the jet exit the streamwise vortices are so large that besides the jet fluid also the cross-stream is partially entrained into this zone, which yields the worst cooling performance.     

Flow around the impulsively started elliptic cylinder at various angles of attack

The flow around an impulsively started elliptic cylinder at 0, 30, 45 and 90° incidence is investigated. The fluid is viscous, incompressible and its flow is governed by the Navier-Stokes equations. Semi-analytical solutions are calculated by solving numerically the system of coupled partial differential equations which are obtained by substituting the expanded finite Fourier Series of the stream and vorticity functions in the Navier-Stokes equations. The symmetrical solutions are presented for Reynolds number 200 and eccentricity 0.809 and 0.943 in terms of patterns of streamlines, lines of constant vorticity, pressure and vorticity distributions around the surface, drag coefficient and wake length at 0 and 90° and compared with the experimental results. A comparison of the calculations has been made for Reynolds number 100 and eccentricity 0.648 with different number of terms at 90°. A Kármán vortex street develops for Reynolds numbers 200 and 60 at 30 and 45° incidence and the solutions are presented in terms of various characteristics including Strouhal number. The vanishing of wall-shear does not denote separation in any meaningful sense in various cases.     

圆柱绕流的二维数值模拟和尾迹分析

为指导机械设计中参数和布局的选择,研究固定在水流中的圆柱结构件的受力情况和流场分布．利用FLUENT中的三种湍流模型对雷诺数为3900的圆柱绕流进行二维数值模拟并进行对比,得到升力因数、阻力因数、分离角、斯特劳哈尔数和涡街尺寸等参数的模拟结果,与参考文献中的实验结果对比验证二维模拟的预测精度．RKE（Realizable k-ε）和雷诺应力模型（Reynolds Stress Model,RSM）均能在此雷诺数下得出接近实验结果的流场,RSM模型使用POWER LAW离散格式的结果优于QUICK格式．与三维模拟的对比表明二维模拟适合在设计初期的快速估算,能够快速得到合适精度的模拟结果．     

Flow characteristics of two rotating side-by-side circular cylinder

This paper presents a numerical investigation of the characteristics of the two-dimensional laminar flow around two rotating circular cylinders in side-by-side arrangements. In order to consider the combined effects of the rotation and the spacing between two cylinders on the flow, numerical simulations are performed at a various range of absolute rotational speeds (|α|?2) for four different gap spacings of 3, 1.5, 0.7 and 0.2 at Reynolds number of 100 showing the typical two-dimensional vortex shedding. As |α| increases, the flow changes its condition from periodic to steady after a critical rotational speed, which depends on the gap spacing. In the cases of gap spacings of 3 and 0.2, the wake keeps the same pattern, until flow reaches the steady state. However, for the gap spacings of 1.5 and 0.7, the wake patterns change in the unsteady regimes. For the cases in which the flow is unsteady, the Strouhal number strongly depends on the gap. For a fixed gap spacing, the variation of the Strouhal number is significant when the wake pattern is changed according to the rotational speed. Regardless of the gap spacing, as |α| increases, the lift increases and the drag decreases. Quantitative information about the flow variables such as the pressure coefficient and wall vorticity distributions on the cylinders is highlighted.