NUMERICAL PREDICTION OF FORCE ON RECTANGULAR CYLINDERS IN OSCILLATING VISCOUS FLOW

Numerical results are presented for an oscillating viscous flow past a square cylinder with square and rounded corners and a diamond cylinder with square corners at Keulegan–Carpenter numbers up to 5. This unsteady flow problem is formulated by the two-dimensional Navier–Stokes equations in vorticity and stream-function form on body-fitted coordinates and solved by a finite-difference method. Second-order Adams-Bashforth and central-difference schemes are used to discretize the vorticity transport equation while a third-order upwinding scheme is incorporated to represent the nonlinear convective terms. Since the vorticity distribution has a mathematical singularity at a sharp corner and since the force coefficients are found in experiments to be sensitive to the corner radius of rectangular cylinders, a grid-generation technique is applied to provide an efficient mesh system for this complex flow. Local grid concentration near the sharp corners, instead of any artificial treatment of the sharp corners being introduced, is used in order to obtain high numerical resolution. The elliptic partial differential equation for stream function and vorticity in the transformed plane is solved by a multigrid iteration method. For an oscillating flow past a rectangular cylinder, vortex detachment occurs at irregular high frequency modes at KC numbers larger than 3 for a square cylinder, larger than 1 for a diamond cylinder and larger than 3 for a square cylinder with rounded corners. The calculated drag and inertia coefficients are in very good agreement with the experimental data. The calculated vortex patterns are used to explain some of the force coefficient behavior.     

Application of Differing Forcing Function Models on Simulated Flow Past an Oscillating Cylinder in a Uniform Low Reynolds Number Flow

A Computational Fluid Dynamics (CFD) model is presented for the uniform viscous two dimensional flow past an oscillating cylinder at low Reynolds number. Numerical simulations are made to study the effect of differing forced induced oscillation mechanisms with a large range of cylinder forcing frequencies. In the first case sinusoidal velocity slip boundary conditions are adopted for the cylinder surface to simulate cylinder oscillation. The implication suggests that no modification or additional term need to be added to the Navier-Stokes equations. In the second case this time extra body force terms which are assumed to account for velocity effects due to cylinder movement are included in the Navier-Stokes equations with the imposition of same boundary conditions. Drag and lift coefficients are extracted from present numerical results and other detailed computations of these coefficients are made at a Reynolds number of 80 and an amplitude-to diameter ratio 0.14. The results are found to be in agreement with each other at low force driving frequencies below and near lock-in. However, differences are found at higher frequencies above lock-in. Agreement are also found with experimental results at some frequency ranges.     

Heat transfer on a cylinder in accelerated slip flow

The axisymmetric laminar boundary layer flow along the entire length of a semi-infinite stationary cylinder under an accelerated free-stream is investigated. Considering flow at reduced dimensions, the boundary layer equations are developed with the conventional no-slip boundary condition for tangential velocity and temperature replaced by a linear slip-jump boundary condition. Asymptotic series solutions are obtained for the heat transfer coefficient in terms of the Nusselt number. These solutions correspond to prescribed values of the momentum and temperature slip coefficients and the index of acceleration. Heat transfer at both small and large axial distances is determined in the form of series solutions; whereas at intermediate distances, exact and interpolated numerical solutions are obtained. Using these results, the heat transfer along the entire cylinder wall is evaluated in terms of the parameters of acceleration and slip.     

Deformation of a fluid-filled compliant cylinder in a uniform flow

We investigated surface compliance effects of a fluid-filled object in flow on its shape and internal flow through numerical simulation. A two-dimensional compliant cylinder containing fluid in a flow is a simple model of a cell, e.g. an erythrocyte, leukocyte or platelet. The thin membrane of the cylinder consisted of a network of mass-spring-damper (MSD) systems, representing its mechanical characteristics. We assumed that the stiffness and damping coefficients were those of latex gum. The two-dimensional flow inside and outside the membrane was obtained by solving the two-dimensional Navier–Stokes equations by using the finite element scheme at Re=400, based on the external flow velocity and diameter of an initial circular cylinder. The deformation of the membrane was calculated by solving the equation of motion for an MSD system by using the fourth-order Runge-Kutta method. The compliant cylinder deformed more if its stiffness was smaller than that of latex gum. The initial circular section of the cylinder became oval, with a flat front and a convex rear. The aspect ratio of the lateral to streamwise axis length of the oval became larger than unity, and increased with decreasing stiffness. The drag coefficient of the oval cylinder became larger than that of the circular cylinder, and increased with decreasing stiffness. The partial vibration at the rear, caused by shedding vortices, induced oscillating internal flows between two antinodes of the vibrating membrane. Since the object with smaller stiffness had higher ductility, velocity fluctuations of the external flow influenced the internal flow of the compliant object through deformation of the membrane.     

Suppression of vortex-induced vibration of a circular cylinder using suction-based flow control

In the present study, a flow control method is employed to mitigate vortex-induced vibration (VIV) of a circular cylinder by using a suction flow method. The VIV of a circular cylinder was first reproduced in a wind tunnel by using a spring–mass system. The time evolution of the cylinder oscillation and the time histograms of the surface pressures of 119 taps in four sections of the circular cylinder model were measured during the wind tunnel experiments. Four steady suction flow rates were used to investigate the effectiveness of the suction control method to suppress VIV of the circular cylinder. The vibration responses, the mean and fluctuating pressure coefficients, and the resultant aerodynamic force coefficients of the circular cylinder under the suction flow control are analyzed. The measurement results indicate clearly that the steady suction flow control method exhibits excellent control effectiveness and can distinctly suppress the VIV by dramatically reducing the amplitudes of cylinder vibrations, fluctuating pressure coefficients and lift coefficients of the circular cylinder model. By comparing the test cases with different suction flow rates, it is found that there exists an optimal suction flow rate for the maximum VIV control. The cases with higher suction flow rates do not necessarily behave better than those with lower suction flow rates. With the experimental setting used in the present study, the suction flow control method is found to behave better for VIV suppression when the ratio of the suction flow velocity to the oncoming flow velocity is less than one.     

Numerical investigation of flow and combined natural-forced convection from an isothermal square cylinder in cross flow

Unsteady flow and heat transfer from a horizontal isothermal square cylinder is studied numerically using a three-dimensional computational model to investigate the influence of buoyancy on the forced flow and heat transfer characteristics. The numerical model is based on a horizontal square cylinder subjected to laminar fluid flow in an unconfined channel. The governing equations in 3D form are solved using a fractional step method based on the finite difference discretization in addition to a Crank–Nicholson scheme employed to the convective and the viscous terms. Two working fluids–air (Pr = 0.7) and water (Pr = 7)–are considered, and the flow and heat transfer simulations were carried out for the Reynolds and Richardson numbers in the intervals 55 ≤ Re ≤ 250 and 0 ≤ Ri ≤ 2, respectively. The flow characteristics such as time-averaged drag/lift, rms drag/rms lift coefficients as well as Strouhal number were computed. The heat transfer from the cylinder is assessed by mean Nusselt number (and rms Nusselt number) over the total heated cylinder walls. As the buoyancy increases, the mass and the velocity of the fluid flowing underneath the cylinder increases. The fluid is injected into the near wake region with an upward motion which significantly alters the flow field in the downstream as well as upstream regions. The effects of Reynolds, Richardson and Prandtl numbers on the flow field and temperature distributions are discussed in detail. It is shown that the flow and heat transfer characteristics are influenced more for air than water. To fill the void in the literature, useful empirical correlations of practical importance are derived for pure forced and pure natural as well as mixed convection. The mixed convection correlations, in terms of the ratio of pure forced convection, are also developed, and their implications are discussed.     

Large eddy simulation of flow around a rectangular cylinder

A large eddy simulation (LES) of turbulent flow around a stationary rectangular cylinder at high Reynolds number of 2.2×10⁴ is conducted as the first step to prove the applicability of LES to practical engineering problems. Time-averaged and phase-averaged velocities and turbulent stresses are obtained and they are compared with the experimental data. To investigate mesh dependence on computational results of the LES, two kinds of grid resolution are used. In addition, the effect of a second-order upwind scheme QUICK for convection terms is also investigated due to its dependence on grid resolution. The drag coefficients, the base pressure coefficients and Strouhal numbers are in fairly good agreement with the experimental results, while the computational results show that the artificial dissipative and dispersive effect of QUICK is large in the vicinity of the cylinder in our computation. Thus, it is necessary to use higher-order upwind schemes to reduce the numerical errors, since it is effective in applying LES to practical engineering problems with complicated geometry.     

Hydrodynamics of a flexible cylinder under modulated vortex-induced vibrations

Both amplitude modulation and frequency modulation of Vortex-induced Vibration (VIV) are observed in a recent model test of a flexible cylinder under oscillatory flow, but its hydrodynamics has not yet been broached in detail. This paper employs the Forgetting Factor Least Squares (FF-LS) method for identification of time-varying hydrodynamics of a flexible cylinder under modulated VIV. The FF-LS method’s applicability to accurately identify time-varying hydrodynamic coefficients is demonstrated through an elastically mounted rigid cylinder under flow with a given modulated motion. Furthermore, we propose a framework to predict instantaneous amplitude (envelope) and frequency using time-varying hydrodynamic coefficients to establish their analytical relationship. This prediction method is further extended to a highly tensioned flexible cylinder through Fourier series expansion in the spatial domain. By performing the identification procedure for all sampled data of a flexible cylinder undergoing oscillatory flow, we obtain the corresponding time-varying hydrodynamics in the cross-flow direction considering the amplitude and frequency modulation. The results show that, under modulated VIV, hydrodynamic coefficients of the flexible cylinder also show time-varying characteristics. We further investigate differences between identified hydrodynamic coefficients and those obtained from the database of a cylinder with modulated motion under flow. Prediction results using these identified time-varying coefficients reveal that the time-varying excitation coefficients mainly influence the amplitude modulation, and the time-varying added-mass coefficients contain the major information of frequency modulation. These results further suggest including the temporal derivative of the instantaneous amplitude as one determining parameter in building databases to improve the prediction of modulated VIV.     

Interactions between a rectangular cylinder and a free-surface flow

The salient features of the interaction between a free-surface flow and a cylinder of rectangular cross-section are investigated and discussed. Laboratory-scale experiments are performed in a water channel under various flow conditions and elevations of the cylinder above the channel floor. The flow field is characterized on the basis of time-averaged and fluctuating local velocity measurements. Dynamic loadings on the cylinder are measured by two water-insulated dynamometers placed inside the cylinder structure. Starting from frequency and spectral analyses of the force signals, insights on the relationship between force dominant frequencies and the Strouhal number of the vortex shedding phenomenon are provided. Experimental results highlight the strong influence of the asymmetric configuration imposed by the two different boundary conditions (free surface and channel floor) on (i) the mean force coefficients and (ii) the vortex shedding frequencies. We provide an analysis of the nature of the dependence of average force coefficients on relevant dimensionless groups, i.e., the Reynolds number, normalized flow depth and cylinder submersion.     

Active vortex-induced vibration control of a circular cylinder at low Reynolds numbers using an adaptive fuzzy sliding mode controller

An adaptive fuzzy sliding mode control (AFSMC) scheme is applied to actively suppress the two-dimensional vortex-induced vibrations (VIV) of an elastically mounted circular cylinder, free to move in in-line and cross-flow directions. Laminar flow regime at Re=90, low non-dimensional mass with equal natural frequencies in both directions, and zero structural damping coefficients, are considered. The natural oscillator frequency is matched with the vortex shedding frequency of a stationary cylinder at Re=100. The strongly coupled unsteady fluid/cylinder interactions are captured by implementing the moving mesh technology through integration of an in-house developed User Define Function (UDF) into the main code of the commercial CFD solver Fluent. The AFSMC approach comprises of a fuzzy system designed to mimic an ideal sliding-mode controller, and a robust controller intended to compensate for the difference between the fuzzy controller and the ideal one. The fuzzy system parameters as well as the uncertainty bound of the robust controller are adaptively tuned online. A collaborative simulation scheme is realized by coupling the control model implemented in Matlab/Simulink to the plant model constructed in Fluent, aiming at determination of the transverse control force required for complete suppression of the cylinder streamwise and cross-flow oscillations. The simulation results demonstrate the high performance and effectiveness of the adopted control algorithm in attenuating the 2D-VIV of the elastic cylinder over a certain flow velocity range. Also, the enhanced transient performance of the AFSM control strategy in comparison with a conventional PID control law is demonstrated. Furthermore, the effect of control action on the time evolution of vortex shedding from the cylinder is discussed. In particular, it is observed that the coalesced vortices in the far wake region of the uncontrolled cylinder, featuring the C(2S)-type vortex shedding characteristic mode, are ultimately forced to switch to the classical von Kármán vortex street of 2S-type mode, displaying wake vortices of moderately weaker strengths very similar to those of the stationary cylinder. Lastly, robustness of AFSMC is verified against relatively large structural uncertainties as well as with respect to a moderate deviation in the uniform inlet flow velocity.     

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.     

Reduction in drag and vortex shedding frequency through porous sheath around a circular cylinder

A numerical study on the laminar vortex shedding and wake flow due to a porous‐wrapped solid circular cylinder has been made in this paper. The cylinder is horizontally placed, and is subjected to a uniform cross flow. The aim is to control the vortex shedding and drag force through a thin porous wrapper around a solid cylinder. The flow field is investigated for a wide range of Reynolds number in the laminar regime. The flow in the porous zone is governed by the Darcy–Brinkman–Forchheimer extended model and the Navier–Stokes equations in the fluid region. A control volume approach is adopted for computation of the governing equations along with a second‐order upwind scheme, which is used to discretize the convective terms inside the fluid region. The inclusion of a thin porous wrapper produces a significant reduction in drag and damps the oscillation compared with a solid cylinder. Dependence of Strouhal number and drag coefficient on porous layer thickness at different Reynolds number is analyzed. The dependence of Strouhal number and drag on the permeability of the medium is also examined. Copyright © 2009 John Wiley & Sons, Ltd.     

Plane problem of uniform flow of a two-layer fluid past a circular cylinder

An explicit solution is found for the problem of uniform horizontal flow of a two-layer fluid of infinite depth past a circular cylinder. The cylinder axis is perpendicular to the flow. The problem is solved within a linear formulation. The solution of the problem is expressed in the form of rapidly converging series with coefficients determined from a recurrence relation. The first seven terms of the series yield the values of the hydrodynamic loads with a relative accuracy of 10^–6. The results are in good agreement with the known values for similar problems in a homogeneous fluid. Tables of the lift and wave drag are given for homogeneous and two-layer fluids.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 91–97, January–February, 1996.     

A class of finite difference schemes for interface problems with an HOC approach

In this paper, we propose a new methodology for numerically solving elliptic and parabolic equations with discontinuous coefficients and singular source terms. This new scheme is obtained by clubbing a recently developed higher‐order compact methodology with special interface treatment for the points just next to the points of discontinuity. The overall order of accuracy of the scheme is at least second. We first formulate the scheme for one‐dimensional (1D) problems, and then extend it directly to two‐dimensional (2D) problems in polar coordinates. In the process, we also perform convergence and related analysis for both the cases. Finally, we show a new direction of implementing the methodology to 2D problems in cartesian coordinates. We then conduct numerous numerical studies on a number of problems, both for 1D and 2D cases, including the flow past circular cylinder governed by the incompressible Navier–Stokes equations. We compare our results with existing numerical and experimental results. In all the cases, our formulation is found to produce better results on coarser grids. For the circular cylinder problem, the scheme used is seen to capture all the flow characteristics including the famous von Kármán vortex street. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical simulation of Taylor Couette flow of Bingham fluids

The Bingham fluid flow between two concentric cylinders is studied using numerical simulation. The cylinders are assumed to rotate independently, and with an imposed axial sliding. The flow field is decomposed with linearity arguments of the base circular Couette shear flow and corresponding deviation field. The numerical methods are based on the expression of the deviation field in terms of complete sets of orthogonal functions and Chebyshev series. The Galerkin projection method is used with the pressure term being eliminated. The Adams Bashforth scheme is adopted for time marching. The results show that the vortices are squeezed toward the inner cylinder due to the effect of yield stress. When the outer cylinder is held stationary, the yield stress plays a role in weakening the vortex flow. However, for the co-rotation situation, the vortex flow is initially strengthened with an increase of yield stress, and then weakened as the yield stress is raised large enough. The annular unyielded regions emerge and stick to the outer cylinder. In case of Taylor Couette flow with an imposed axial sliding, a spiral vortex flow is visible with spiral unyielded region being obtained.     

Numerical study on the suppression of the vortex-induced vibration of an elastically mounted cylinder by a traveling wave wall

In the present paper, the commercial CFD code “Fluent” was employed to perform 2-D simulations of an entire process that included the flow around a fixed circular cylinder, the oscillating cylinder (vortex-induced vibration, VIV) and the oscillating cylinder subjected to shape control by a traveling wave wall (TWW) method. The study mainly focused on using the TWW control method to suppress the VIV of an elastically supported circular cylinder with two degrees of freedom at a low Reynolds number of 200. The cross flow (CF) and the inline flow (IL) displacements, the centroid motion trajectories and the lift and drag forces of the cylinder that changed with the frequency ratios were analyzed in detail. The results indicate that a series of small-scale vortices will be formed in the troughs of the traveling wave located on the rear part of the circular cylinder; these vortices can effectively control the flow separation from the cylinder surface, eliminate the oscillating wake and suppress the VIV of the cylinder. A TWW starting at the initial time or at some time halfway through the time interval can significantly suppress the CF and IL vibrations of the cylinder and can remarkably decrease the fluctuations of the lift coefficients and the average values of the drag coefficients; however, it will simultaneously dramatically increase the fluctuations of the drag coefficients.     

Unsteady natural convective flow past a moving vertical cylinder with heat and mass transfer

Transient natural convection boundary layer flow of an incompressible viscous fluid past an impulsively moving semi- infinite vertical cylinder is considered. The temperature and concentration of the cylinder surface are taken to be uniform. The unsteady, nonlinear and coupled governing equations of the flow are solved using an implicit finite difference scheme. The finite difference scheme is unconditionally stable and accurate. Numerical results are presented with various sets of parameters for both air and water. Transient effects of velocity, temperature and concentration profiles are analyzed. Local and average skin friction, rates of heat and mass transfer are shown graphically. Received on 1 November 1999     

Flow around a cylinder at the beginning of the critical region

Results of experiments with a turbulent flow around a transversely aligned circular cylinder located at identical distances from the walls of a rectangular channel are reported. Data on averaged velocity fields around the cylinder are obtained by means of particle image velocimetry (PIV). Based on these fields, the near wake behind the cylinder is studied, and the kinematic characteristics for flow regimes with and without cavitation are compared. Based on the vector fields of averaged velocity, the angles of separation of the boundary layer from the cylinder surface in the considered flow regimes are determined. The drag coefficients of the cylinder for different flow regimes are calculated. It is demonstrated that the vortex region behind the cylinder and the drag coefficient of the cylinder increase in the case with cavitation. It is also shown that vortex shedding from the cylinder may be irregular, despite the fact that this process is quasi-periodic for most of the time.     

Large Eddy Simulation of Flow around a Rectangular Cylinder Using the Finite Element Method

In previous papers, we proposed finite element schemes based on the Petrov-Galerkin weak formulation using exponential weighting functions for solving accurately, and in a stable manner, the flow field of an incompressible viscous fluid. In this paper, we present the Petrov-Galerkin finite element scheme for turbulent flow fields based on large eddy simulation using the standard Smagorinsky model with the Van Driest damping function. The filtered incompressible Navier-Stokes equations are numerically integrated in time by using a fractional step strategy with second-order accurate Adams-Bashforth explicit differencing for both convection an diffusion terms. In order to evaluate more accurately a mass matrix, the well-known multi-pass algorithm was also adopted in this study. Numerical results obtained are compared through flow around a rectangular cylinder at Re = 22,000 with the experimental data and other existing numerical data.     

Modeling of transverse self-oscillations of a circular cylinder in an incompressible fluid flow in a plane channel with circulation

Experimentally observed self-oscillations of a cylinder in a plane channel whose width is slightly greater than the cylinder diameter under the impact of the incoming fluid flow are modeled. Within the model of a nonseparated potential flow around the cylinder, the coefficients of added mass of the cylinder are calculated with the help of the generalized method of images. When the cylinder touches the channel wall, the circulation sign changes, and its value is determined by the boundary element method and the no-slip condition for the fluid at the contact point. The Joukowski force and the drag force proportional to the square of velocity are taken into account in the equations of motion of cylinder.