Orbital flow past a cylinder: A numerical approach

Orbital flow past a cylinder is relevant to offshore structures. The numerical scheme presented here is based on a finite-difference solution of the Navier–Stokes equations. Alternating-directional-implicit (ADI) and successive-over-relaxation (SOR) techniques are used to solve the vorticity-transport and stream-function equations. Theoretical simulations to low Reynolds number flows (up to 1000) are discussed for cases involving uniform flow past stationary and rotating cylinders and orbital flow past a cylinder. The separation points for cylinders that are rotating or immersed in an orbital flow are deduced from velocity profiles through the boundary layer using a hybrid mesh scheme. During the initial development of orbital flow surface vorticity on the impulsively started cylinder dominates the flow. A vortex then detaches from behind the cylinder and establishes the flow pattern of the orbit. After some time a collection of vortices circles the orbit and distorts its shape a great deal. These vortices gradually spiral outward as others detach from the cylinder and join the orbital path.     

An experimental study of the dynamic characteristics in boundary layer in the flow past a two-dimensional circular cylinder at subcritical reynolds numbers

An experimental study of the dynamic characteristics of flow past a two-dimensional circular cylinder is described. The fluctuationsoof wall shear stress, surface-pressure and velocity of the flow are measured with hot-film, hot-wire and pressure transducer. The frequency feature of fluctuations of wall shear stress is given. The cross-correlation functions of these fluctuations at any two points are calculated. The experimental results reveal that there is an overall syncronous fluctuation, at the shedding frequency, in boundary layer in the flow past a two-dimensional circular cylinder at subcritical Reynolds number.     

High-order ghost-point immersed boundary method for viscous compressible flows based on summation-by-parts operators

A high-order immersed boundary method is devised for the compressible Navier-Stokes equations by employing high-order summation-by-parts difference operators. The immersed boundaries are treated as sharp interfaces by enforcing the solid wall boundary conditions via flow variables at ghost points. Two different interpolation schemes are tested to compute values at the ghost points and a hybrid treatment is used. The first method provides the bilinearly interpolated flow variables at the image points of the corresponding ghost points and the second method applies the boundary condition at the immersed boundary by using the weighted least squares method with high-order polynomials. The approach is verified and validated for compressible flow past a circular cylinder at moderate Reynolds numbers. The tonal sound generated by vortex shedding from a circular cylinder is also investigated. In order to demonstrate the capability of the solver to handle complex geometries in practical cases, flow in a cross-section of a human upper airway is simulated.     

NUMERICAL SIMULATION OF FLOW INDUCED BY A CYLINDER ORBITING IN A LARGE VESSEL

The flow field induced by a circular cylinder orbiting in a large vessel filled with fluid is investigated numerically. A finite-volume method is applied to the two-dimensional incompressible Navier–Stokes equations to compute the unsteady laminar flow fields. Moving reference systems are employed to allow an easy imposition of boundary conditions and to avoid grid deformation. Aspects of numerical accuracy related to the number of grid points and time steps employed are discussed. The flow is governed by two dimensionless parameters: a Reynolds number and a Keulegan–Carpenter number. These are varied systematically in order to find their influence on the flow pattern. In particular, the temporal development of the vorticity field and the lift on the cylinder are examined.     

Flow regimes and frequency selection of a cylinder oscillating in an upstream cylinder wake

This paper describes flow around a pair of cylinders in tandem arrangement with a downstream cylinder being fixed or forced to oscillate transversely. A sinusoidal parietal velocity is applied to simulate cylinder oscillation. Time-dependent Navier-Stokes equations are solved using finite element method. It is shown that there exist two distinct flow regimes: ‘vortex suppression regime’ and ‘vortex formation regime’. Averaged vortex lengths between the two cylinders, pressure variations at back and front stagnant points as well as circumferential pressure profiles of the downstream cylinder are found completely different in the two regimes and, thus, can be used to identify the flow regimes. It is shown that frequency selection in the wake of the oscillating cylinder is a result of non-linear interaction among vortex wakes upstream and downstream of the second cylinder and its forced oscillation. Increasing cylinder spacing results in a stronger oscillatory incident flow upstream of the second cylinder and, thus, a smaller synchronization zone.     

A mesh-free radial basis function–based semi-Lagrangian lattice Boltzmann method for incompressible flows

In this paper, a local radial basis function–based semi-Lagrangian lattice Boltzmann method (RBF-SL-LBM) is proposed. This is a mesh-free method that can be used for the simulation of incompressible flows. In this method, the collision step is performed locally, which is the same as in the standard LBM. In the meanwhile, the steaming step is solved in a semi-Lagrangian framework. The distribution functions at the departure points, which may be not the grid points in general, are computed by the local radial basis function interpolation. Several numerical tests are conducted to validate the present method, including the lid-driven cavity flow, the steady and unsteady flow past a circular cylinder, and the flow past an NACA0012 airfoil. The present results are in good agreement with those published in the previous literature, which demonstrates the capability of RBF-SL-LBM for the simulation of incompressible flows.     

Combined action of transverse oscillations and uniform cross-flow on vortex formation and pattern of a circular cylinder

This paper attempts to study the roles of lateral cylinder oscillations and a uniform cross-flow in the vortex formation and wake modes of an oscillating circular cylinder. A circular cylinder is given lateral oscillations of varying amplitudes (between 0.28 and 1.42 cylinder-diameters) in a slow uniform flow stream (Reynolds number=284) to produce the 2S, 2P and P+S wake modes. Detailed flow information is obtained with time-resolved particle-image velocimetry and the phase-locked averaging techniques. In the 2S and 2P mode, the flow speeds relative to the cylinder movement are less than the uniform flow velocity and it is found that initial formation of a vortex is caused by shear-layer separation of the uniform flow on the cylinder. Subsequent development of the shear-layer vortices is affected by the lateral cylinder movement. At small cylinder oscillation amplitudes, vortices are shed in synchronization with the cylinder movement, resulting in the 2S mode. The 2P mode occurs at larger cylinder oscillation amplitudes at which each shear-layer vortex is found to undergo intense stretching and eventual bifurcation into two separate vortices. The P+S mode occurs when the cylinder moving speeds are, for most of the time, higher than the speed of the uniform flow. These situations are found at fast and large-amplitude cylinder oscillations in which the flow relative to the cylinder movement takes over the uniform flow in governing the initial vortex formation. The formation stages of vortices from the cylinder are found to bear close resemblance to those of a vortex street pattern of a cylinder oscillating in an otherwise quiescent fluid at Keulegan–Carpenter numbers around 16. Vortices in the inclined vortex street pattern so formed are then convected downstream by the uniform flow as the vortex pairs in the 2P mode.     

A local domain‐free discretization method for simulation of incompressible flows over moving bodies

This paper presents a local domain‐free discretization (DFD) method for the simulation of unsteady flows over moving bodies governed by the incompressible Navier–Stokes equations. The discretization strategy of DFD is that the discrete form of partial differential equations at an interior point may involve some points outside the solution domain. All the mesh points are classified as interior points, exterior dependent points and exterior independent points. The functional values at the exterior dependent points are updated at each time step by the approximate form of solution near the boundary. When the body is moving, only the status of points is changed and the mesh can stay fixed. The issue of ‘freshly cleared nodes/cells’ encountered in usual sharp interface methods does not pose any particular difficulty in the presented method. The Galerkin finite‐element approximation is used for spatial discretization, and the discrete equations are integrated in time via a dual‐time‐stepping scheme based on artificial compressibility. In order to validate the present method for moving‐boundary flow problems, two groups of flow phenomena have been simulated: (1) flows over a fixed circular cylinder, a harmonic in‐line oscillating cylinder in fluid at rest and a transversely oscillating cylinder in uniform flow; (2) flows over a pure pitching airfoil, a heaving–pitching airfoil and a deforming airfoil. The predictions show good agreement with the published numerical results or experimental data. Copyright © 2010 John Wiley & Sons, Ltd.     

Optical visualization of accelerated and decelerated flow over a circular cylinder

Prandtl and Tietjens [1] obtained the spectra of flow over a circular cylinder. Later, other authors returned to this question (see, in particular, [2, 3]). The investigations showed that the time-dependent picture of the separation flow over the cylinder can be divided into two main phases: an initial phase of symmetric flow and a phase of steady, periodic, and asymmetric flow. In the symmetric flow over the cylinder [1] one observes in the neighborhood of the separation points delta-shaped regions, whose structure it would be interesting to elucidate. In the present paper, we present the results of an investigation by a method of optical visualization of some features of the flow over a circular cylinder in regimes when the flow is accelerated and decelerated.Translated from Izvestiya Akademii Nauk SSSE, Mekhanika Zhidkosti i Gaza, No. 2, pp. 136–142, March—April, 1981.     

A continuous shape sensitivity equation method for unsteady laminar flows

This paper presents the application of a general shape sensitivity equation method (SEM) to unsteady laminar flows. The formulation accounts for complex parameter dependence and is suitable for a wide range of problems. The flow and sensitivity equations are solved on 3D meshes using a Streamline-Upwind Petrov Galerkin (SUPG) finite element method. In the case of shape parameters, boundary conditions for sensitivities depend on the flow gradient at the boundary. Therefore, an accurate recovery of solution gradients is crucial to the success of shape sensitivity computations. In this work, solution gradients at boundary points are extracted using the Finite Node Displacement (FiND) method on which the finite element discretization is enriched locally via the insertion of nodes close to the boundary points. The normal derivative of the solution is then determined using finite differences. This approach to evaluate shape sensitivity boundary conditions is embedded in the continuous SEM. The methodology is applied to the flow past a cylinder in ground proximity. First, the proposed method is verified on a steady state problem. The computed sensitivity is compared to the actual change in the solution when a small perturbation is imposed to the shape parameter. Then, the study investigates the ability of the SEM to anticipate the unsteady flow response to changes in the ground to cylinder gap. A reduction of the gap causes damping of the vortex shedding while an increase amplifies the unsteadiness.     

薄矩形柱绕流旋涡脱落的抑制

用窄条形控制件对截面宽度为B、厚度为H的矩形柱体绕流的旋涡脱落进行抑制.实验在风洞中进行, 实验范围为B/H=2.0~5.0,Re=V_∞H/\nu=3.75× 103~1.05×104. 矩形柱的宽边B与来流平行, 窄条与柱体等长, 且两者轴线相互平行放置. 窄条宽度为b/H=0.5, 窄条厚度远小于其宽度; 窄条位置可变, 但窄条表面保持与来流垂直. 尾流脉动速度测量和流动显示结果表明: 当窄条位于一个有效区内时, 矩形柱体两侧的旋涡脱落被抑制; 而当窄条位于一个单侧有效区内时, 矩形体一侧的旋涡脱落被抑制, 在另一侧旋涡脱落却仍存在. 有效区范围从矩形体的上游某点一直延续到矩形体的下游某点. 单侧有效区将整个有效区围在其中. 有效区和单侧有效区范围随着B/H的增大而增大, 但随着Re的增大而减小.      

Computation of high Reynolds number flow around a circular cylinder with surface roughness

Incompressible high-Reynolds-number flows around a circular cylinder are analyzed by direct integration of the Navier-Stokes equations using finite-difference method. A generalized coordinate system is used so that a sufficient number of grid points are distributed in the boundary layer and the wake. A numerical scheme which suppresses non-linear instability for calculations of high-Reynolds-number flows is developed. The computation of an impulsively started flow at Re = 1200 is compared with corresponding experimental observations, and excellent agreements are obtained.A series of computations are carried out on the flow around a circular cylinder with surface roughness. The height of the roughness in these computations is 0.5% of the diameter. The range of Reynolds numbers is from 10³ to 10⁵; no turbulence model is employed. Sharp reduction of drag coefficient is observed near Re = 2 × 10⁴, which indicates that the critical Reynolds number is captured in the present computation.     

Reconstructing the vortex-induced-vibration response of flexible cylinders using limited localized measurement points

A series of experiments was conducted in a re-circulating water tunnel with a uniform flow profile, in which a flexible tension-dominated cylinder was held fixed at both ends and placed perpendicular to the incoming flow direction. The circular cylinder had an aspect ratio of L/D=67 and a low mass ratio of m*=0.43. Dynamic response of the system was studied in the reduced velocity range of U*=2.9–14.5 and Reynolds numbers of Re=315–1580. The oscillations of the cylinder in the inline (IL) and crossflow (CF) directions were captured using two synchronized high speed cameras. Continuous response of the cylinder was reconstructed from limited number of measurement points based on modal expansion theorem modified using Modal Assurance Criterion (MAC). The MAC enhanced the response reconstruction by adjusting the contributions from each structural mode. A distinct advantage of implementing the MAC in this method compared with the previously used methods was reconstructing the VIV response accurately when the experimental measurement points were clustered in a small region along the length of the cylinder. Mono- and multi-frequency excitation responses as well as transition from a low mode number to a higher one were observed. Flow forces acting on the cylinder were calculated and a consistent relation between the regions where the cylinder was being excited by the flow and the counterclockwise figure-eight trajectories of oscillations was observed.     

Flow above the free end of a surface-mounted finite-height circular cylinder: A review

The wake of a surface-mounted finite-height circular cylinder and the associated vortex patterns are strongly dependent on the cylinder aspect ratio and the thickness of the boundary layer on the ground plane relative to the dimensions of the cylinder. Above a critical aspect ratio, the mean wake is characterized by streamwise tip vortex structures and Kármán vortex shedding from the sides of the cylinder. Below a critical aspect ratio, a unique mean wake structure is observed. Recent experimental studies in the literature that used phase-averaged techniques, as well as recent numerical simulations, have led to an improved physical understanding of the near-wake vortex flow patterns. However, the flow above the free end of the finite circular cylinder, and its relationship to the near wake, has not been systematically studied. The effects of aspect ratio and boundary layer thickness on the free-end flow field are also not completely understood, nor has the influence of Reynolds number on the free-end flow field been fully explored. Common features associated with the free end include separation from the leading edge, a mean recirculation zone containing a prominent cross-stream arch (or mushroom) vortex, and reattachment onto the free-surface. Other flow features that remain to be clarified include a separation bubble near the leading edge, one or two cross-stream vortices within this separation bubble, the origins of the streamwise tip or trailing vortices, and various critical points in the near-surface flow topology. This paper reviews the current understanding of the flow above the free end of a surface-mounted finite-height circular cylinder, with a focus on models of the flow field, surface oil flow visualization studies, pressure and heat flux distributions on the free-end surface, measurements of the local velocity field, and numerical simulations, found in the literature.     

流体边界层上电磁力的控制效应研究

利用作用于流体边界层上的电磁体积力改变流体边界层的结构，研究电磁力对流场的控制 作用效果. 电极与磁极交替分布的电磁场激活板包覆在圆柱体表面置于流动的电解质溶液 中，产生的电磁力沿圆柱体表面分布，可以改变流体边界层的结构，从而实现对流场的控制. 用电磁屏蔽和时域控制的方法调整电磁力的时空分布参数，圆柱绕流分离点可以在前驻点和 后驻点之间变动，产生不同的控制效果. 流体边界层上的电磁力能连续控制圆柱绕流、尾流 涡街的形态. 正向电磁力具有较好的消涡、减震和减阻控制效应. 反向电磁力具有明显的增 涡控制效应，具有较强的制动控制效应，此时圆柱体表面涡量分布的对称性和稳定性被破坏.     

Measurements of velocity fields in finite cylinder arrays with and without tip clearance

The velocity field in a finite cylinder array was investigated experimentally in a water towing tank and an acoustic Doppler velocimeter (ADV). The experimental system consisted of a staggered cylinder array having 14 rows to permit streamwise evolution of the flow. The boundaries were manipulated to create several global flow configurations. Three basic configurations were studied: a globally unidirectional flow, a flow with partial lateral blockage at the inlet and outlet planes, and a flow with the top boundary separated from the cylinders creating a tip clearance. The three components of the velocity vector were measured at various points within the model. Time-averaged results are presented for the different flow configurations. The results provide insight into the development of the flow field in cases of a finite array with complex geometry and boundary effects.     

Characterization of long time fluctuations of forces exerted on an oscillating circular cylinder at KC=10

Flow dynamics, in-line and transverse forces exerted on an oscillating circular cylinder in a fluid initially at rest are studied by numerical resolution of the two-dimensional Navier-Stokes equations. The Keulegan-Carpenter number is held constant at KC=10 and Re is increased from 40 to 500. For the different flow regimes, links between flow spatio-temporal symmetries and force histories are established. Besides simulations of long duration show that in two ranges of Re, forces exhibit low frequency fluctuations compared to the cylinder oscillation frequency. Such observations have been only mentioned in the literature and are more deeply examined here. In both ranges, force fluctuations correspond to oscillations of the front and rear stagnation points on the cylinder surface. However, they occur in flow regimes whose basic patterns (V-shaped mode or diagonal mode) have different symmetry features, inducing two distinct behaviors. For 80≤Re≤100, fluctuations are related to a spectral broadening of the harmonics and to a permutation between three vortex patterns (V-shaped, transverse and oblique modes). In the second range 150≤Re≤280, amplitude fluctuations are correlated to the appearance of low frequency peaks interacting with harmonics of the cylinder frequency. Fluctuations are then a combination of a wavy fluctuation and an amplitude modulation. The carrier frequency corresponding to the wavy fluctuation depends on Re and is related to a fluid characteristic time; the modulation frequency is independent of Re and equal to 1/4 of the cylinder oscillation frequency.     

Instability of an Oscillating Cylinder in a Circulation Flow of Ideal Fluid

The problem of the stability of a circular cylinder in a circulation flow is considered under the condition that the cylinder can perform both free (free cylinder) and forced oscillations (cylinder on a spring). It is shown that this simple system can be unstable in the presence of flow vorticity. Particular cases of vorticity distributions which make it possible to obtain an analytic solution are considered. The case of weak monotonically decreasing vorticity of an arbitrary form is analyzed for an arbitrary relation between the densities of the cylinder and the fluid. It turns out that the instability can develop only for a cylinder whose density is greater than that of the fluid. An approximate method of solving this problem based on consideration of the energy balance in the system is constructed. This makes it possible to obtain an expression for the growth rates and explain the physical mechanism realizing the instability, which is associated with the possibility of energy transfer from perturbations in the critical layer to the cylinder oscillations.     

On the use of adaptive hierarchical meshes for numerical simulation of separated flows

This paper describes the use of adaptive hierarchical grids to predict incompressible separated flow at low Reynolds number. The grids consist of a quadtree system of hierarchical Cartesian meshes which are generated by recursive subdivision about seeding points. The governing equations are discretized in collocated primitive variable form using finite volumes and solved using a pressure correction scheme. The mesh is locally adapted at each time step, with panel division or removal dependent on the vorticity magnitude. The resulting grids have fine local resolution and are economical in array size. Results are presented for unidirectional, impulsively started flow past a circular and a square cylinder at various Reynolds numbers up to 5000 and 250 respectively. It is clear that hierarchical meshes may offer gains in efficiency when applied to complex flow domains or strongly sheared flows. However, as expected, the stepped approximation to curved boundaries resulting from the Cartesian quadtree representation adversely affects the accuracy of the results for flow past a circular cylinder. © 1998 John Wiley & Sons, Ltd.