Flow Dynamics around Two Side by Side Circular Cylinders with Alternating Movements

The flow dynamics is analyzed through two-dimensional numerical simulations around two circular cylinders arranged side by side, with 4 combinations of alternating motions. All simulations are performed for Re = 1000, amplitude of oscillation (A) equal to 3, frequency ratio (fr) of 0.5, specific rotation (α) equal to 0.5 and different values of spacing ratio (L/D). It is verified that the combination of the type of movement, together with the position of one cylinder in relation to the other, exerts significant influence on the flow dynamics, as well as on the pressure distribution around the cylinder surface and on the average values of the fluid dynamics coefficients. The smallest value of the average pressure coefficient (Cp = -3.3), is obtained for the oscillating cylinder when placed side by side with the clockwise rotation cylinder, case 3 and L/D = 1.5. On the other hand, the lowest mean drag coefficient (Cd = 1.0788), is obtained for the cylinder with counterclockwise rotation, located in the lower position in relation to oscillating cylinder in the upper position, with spacing between them of 1.5. Furthermore, it is observed that the rotation movement is more effective in reducing drag than the rotation-oscillation movement, for the studied frequency ratio.

Analysis of Interaction of Plane Waves with Multiple Circular Cylinders

The interaction of water waves with multiple circular cylinders is analysed briefly in this paper. The formula obtained by Linton and Evans is improved to introduce a relation of phase between cylinders. The condition for the existence of the solution has been proved. The numerical results are compared with analytic solutions (Linton and Evans), numerical solutions and experimental data (Isaacson), and good agreement has been found.

Hydrodynamic interactions of water waves with a group of independently oscillating truncated circular cylinders

In this study, we examine the water wave radiation by arrays of truncated circular cylinders. Each cylinder can oscillate independently in any rigid oscillation mode with a prescribed amplitude, including translational and rotational modes such as surge, sway, heave, pitch, roll, and their combinations. Based on the eigenfunction expansion and Graf＇s addition theorem for Bessel functions, we developed an analytical method that includes the effects of evanescent modes in order to analyze such arrays of cylinders. To investigate the effects of several influential factors on convergence,our objective is to dramatically reduce the number of tests required and determine the influencing relationships between truncation number and convergence behavior for different factor combinations. We use the orthogonal test method to fulfill the objective. Lastly, we present our results regarding the effects of evanescent modes on hydrodynamic coefficients.

ON THE INSTABILITY OF WAKES BEHIND STATIONARY CIRCULAR CYLINDERS

The study on the formation of vortex streets behind stationary circular cylinders is of substantial sense in engineering, since vortex streets play the leading role in introduction of vibration, generation of noise and wake instability, etc.. In the present paper, the Orr-Sommerfeld equation combined with measured velocity profiles is used to investigate the type of instability behind stationary cylinders, which determines the mechanism of vortex formation. The numerical calculations for Reynolds numbers of 56-140 000 imply that there is a range around the end of the dead water region in cylinder wakes where the instability belongs to the absolute type. Beyond the range, the flows show to be of the convective type. On the other hand, the flows tend to be of the convective instability when Reynolds number is below the subcritical value of forming vortex streets. All of the correspondent Strouhal numbers agree with experimental data very well. The formation of vortex streets behind stationary cylinders is proposed to be caused by an absolute instability in the near wake. There is always an absolute instability region for the Reynolds numbers from 56-140,000. Further, the experimental manipulation of vortex streets according to the stability analysis mentioned above is proved to be very effective.

Three-Dimensional Instability of Flow Around Two Circular Cylinders in Tandem Arrangement

The spatial evolution of vortices and transition to three-dimensionality in the wake of two circular cylinders in tandem arrangement have been numerically studied. An improved virtual body method developed from the virtual boundary method is used here. A Reynolds number range between 220 and 270 has been considered, and the spacing between two cylinders is selected as L/D=3 and L/D=3.5. When L/D=3, the secondary vortices of Mode-A are seen to appear at Re=240 and persist over the range of the Reynolds number of 240～270. When L/D=3.5, the similar critical Reynolds number has been found at Re=250. No obvious discontinuity has been found in the Strouhal-Reynolds number relationship, and this is different from three-dimensional flow around a single cylinder at the critical Reynolds number. The spanwise wavelength is about four times the diameter of the cylinder, and it is the characteristic wavelength for Mode-A instability. This paper can give some foremost insight into the three-dimensional instability of flow by complicated geometrical configuration.

TORSION OF CIRCULAR CYLINDERS CONTAINING n CIRCULAR HOLES

In the present paper by using complex variable methods in linear elasticity and by-means of analytic continuation, the author obtains for this problem a complex torsional function, shear stress components, displacement components,the lorsional rigidity and shear stresses on boundaries expressed in terms of series.

A Finite Element Solution of Wave Forces on Submerged Horizontal Circular Cylinders

In this paper, a numerical model is established for estimating the wave forces on a submerged horizontal circular cylinder. For predicting the wave motion, a set of two dimensional Navier Stokes equations is solved numerically with a finite element method. In order to track the moving non linear wave surface boundary, the Navier Stokes equations are discretized in a moving mesh system. After each computational time step, the mesh is modified according to the changed wave surface boundary. In order to stabilize the numerical procedure, a three step finite element method is applied in the time integration. The water sloshing in a tank and wave propagation over a submerged bar are simulated for the first time to validate the present model. The computational results agree well with the analytical solution and the experimental data. Finally, the model is applied to the simulation of interaction between waves and a submerged horizontal circular cylinder. The effects of the KC number and the cylinder depth on the wave forces are studied.

Convective heat transfer from two rotating circular cylinders in tandem arrangement by using lattice Boltzmann method

The numerical investigation of the two-dimensional laminar flow past two ro- tating circular cylinders in the tandem arrangement is conducted by the lattice Boltzmann method. The numerical strategy is used for dealing with curved and moving boundaries of the second-order accuracy for velocity and temperature fields. The effects of various rotational speed ratios and gap spacing are studied with the Reynolds number of 100 and the Prandtl number of 0.71. A varied range of rotational speed ratios are investigated for four different gap spacing, i.e., 3.0, 1.5, 0.7, and 0.2. The results show that, for the first cylinder, the lift and drag coefficients for large gap spacing are similar to those for a single cylinder; for the second cylinder, the lift coefficient descends with the increase in the angular velocity for all gap spacing, while the drag coefficient ascends except for the gap spacing of 3.0. The results of the averaged periodic Nusselt number on the surface of the cylinders show that, for small distances between the cylinders and low angular velocities, conduction is a dominant mechanism of heat transfer, but for large distances and high angular velocities, convection is the main mechanism of heat transfer.

Numerical simulation of flow past twin near-wall circular cylinders in tandem arrangement at low Reynolds number

Fluid flow past twin circular cylinders in a tandem arrangement placed near a plane wall was investigated by means of numerical simulations. The two-dimensional Navier-Stokes equations were solved with a three-step finite element method at a relatively low Reynolds number of Re -- 200 for various dimensionless ratios of 0.25 ≤ G/D ≤2.0 and 1.0 ≤ L/D ≤ 4.0, where D is the cylinder diameter, L is the center-to-center distance between the two cylinders, and G is the gap between the lowest surface of the twin cylinders and the plane wall. The influences of G/D and L/D on the hydrodynamic force coefficients, Strouhal numbers, and vortex shedding modes were examined. Three different vortex shedding modes of the near wake were identified according to the numerical results. It was found that the hydrodynamic force coefficients and vortex shedding modes are quite different with respect to various combinations of G/D and L/D. For very small values of G/D, the vortex shedding is completely suppressed, resulting in the root mean square （RMS） values of drag and lift coefficients of both cylinders and the Strouhal number for the downstream cylinder being almost zero. The mean drag coefficient of the upstream cylinder is larger than that of the downstream cylinder for the same combination of G/D and L/D. It is also observed that change in the vortex shedding modes leads to a significant increase in the RMS values of drag and lift coefficients.

Flow characteristics at low Reynolds number around two in-line circular cylinders with slits

This study investigated numerically the characteristics of laminar flow around two identical circular cylinders placed in tandem, with slits of the same width through their respective axis. The center to center distance between the cylinders and the slit orientation were varied to study their effects on the flow structure, lift and drag, and vortex shedding characteristics. It was found that three flow regimes could be distinguished, the transitions between which could be indicated by the sudden changes in drag and lift. Asymmetrically, configured slits destabilized the stagnant region between cylinders;whereas in-line slits connect the two cylinders to act as a single elongated bluff body, even at large cylinder separation, by stabilizing the stagnant region in between. These in turn strongly modified the transition between flow regimes. Vortex shedding was also strongly influenced by both slit configuration and cylinder separation.

Identification of Internal Damage in Circular Cylinders through Laser Scanning of Vibrating Surfaces

With the aid of non-contact measurements of vibrating surfaces through laser scanning,operating deflection shapes(ODSs)with high spatial resolutions can be used to graphically characterize damage in plane structures.Although numerous damage identification approaches relying on laser-measured ODSs have been developed for plate-type structures,they cannot be directly applied to circular cylinders due to the gap between equations of motions of plates and circular cylinders.To fill this gap,a novel approach is proposed in this study for damage identification of circular cylinders.Damage-induced discontinuities of the derivatives of ODSs can be used to gra-phically manifest the occurrence of the damage,and characterize the location and size of the damage.The approach is experimentally validated on a specimen of the circular cylinder component,whose out-of-plane ODSs in an inspection region are acquired through laser scanning using a scanning laser vibrometer.The results suggest that the occurrence,location,and size of the internal damage of the circular cylinder can be identified.

On the spreading behavior of a droplet on a circular cylinder using the lattice Boltzmann method

The study of a droplet spreading on a circular cylinder under gravity was carried out using the pseudo-potential lattice Boltzmann high-density ratios multiphase model with a non-ideal Peng–Robinson equation of state. The calculation results indicate that the motion of the droplet on the cylinder can be divided into three stages: spreading, sliding, and aggregating.The contact length and contact time of a droplet on a cylindrical surface can be affected by factors such as the wettability gradient of the cylindrical wall, the Bond number, and droplet size. Furthermore, phase diagrams showing the relationship between Bond number, cylinder wall wettability gradient, and contact time as well as maximum contact length for three different droplet sizes are given. A theoretical foundation for additional research into the heat and mass transfer process between the droplet and the cylinder can be established by comprehending the variable rules of maximum contact length and contact time.

NUMERICAL SIMULATION OF FLOW OVER TWO CIRCULAR CYLINDERS IN TANDEM ARRANGEMENT

In this article,the 2-D unsteady viscous flow around two circular cylinders in a tandem arrangement is numerically simulated in order to study the characteristics of the flow in both laminar and turbulent regimes.The method applied alternatively is based on the finite volume method on a Cartesian-staggered grid.The great source term technique is employed to identify the cylinders placed in the flow field.To apply the boundary conditions,the ghost-cell technique is used.The implemented computational method is firstly validated through simulation of laminar and turbulent flows around a fixed circular cylinder.Finally,the flow around two circular cylinders in a tandem arrangement is simulated and analyzed.The flow visualization parameters,the Strouhal numbers,and drag and lift coefficients are comprehensively presented and compared for different cases in order to reveal the effect of the Reynolds number and gap spacing on the behavior of the flow.The obtained results have shown two completely distinct flow characteristics in laminar and turbulent regimes.

THREE-DIMENSIONAL FLOW AROUND TWO TANDEM CIRCULAR CYLINDERS WITH VARIOUS SPACING AT Re=220

The flow around two tandem circular cylinders was studied by a three-dimensional numerical simulation of the Navier-Stokes equations at Re=220 . The improved virtual boundary method was applied to model the no-slip boundary condition of the cylinders. The results show that as the spac ing ratio L/D≥4 , the three dimensionality occurs in the wake. When L/D≤3.5 the wake keeps a two-dimensional state at the Reynolds number Re=220 . The critical spacing for the appearance of three-dimensional instability obtained is at the range 3.5〈 L/D 〈 4, similar to the critical spacing found in two-dimensional case. Two sources of instability from upstream and downstream cylinder generate a complicat ed vortex structures in the wake, investigated by streamlines topology analysis in the streamwise plane. Many other interesting problems were also addressed in this paper.

Effect of Rotational Speed on the Stability of Two Rotating Side-by-side Circular Cylinders at Low Reynolds Number

Flow around two rotating side-by-side circular cylinders of equal diameter D is numerically studied at the Rey- nolds number 40〈 Re 〈200 and various rotation rate 8i. The incoming flow is assumed to be two-dimensional laminar flow. The governing equations are the incompressible Navier-Stokes equations and solved by the finite volume method （FVM）. The ratio of the center-to-center spacing to the cylinder diameter is T/D=2. The objective of the present work is to investigate the effect of rotational speed and Reynolds number on the stability of the flow. The simulation results are compared with the experimental data and a good agreement is achieved. The stability of the flow is analyzed by using the energy gradient theory, which produces the energy gradient function K to identify the region where the flow is the most prone to be destabilized and the degree of the destabilization. Numerical results reveal that K is the most significant at the separated shear layers of the cylinder pair. With Re in- creases, the length of the wake is shorter and the vortex shedding generally exhibits a symmetrical distribution for θi〈θcrit. It is also shown that the unsteady vortex shedding can be suppressed by rotating the cylinders in the counter-rotating mode.

Numerical investigation on fluid forces of piggyback circular cylinders in tandem arrangement at low Reynolds numbers

Numerical simulations of flows past the piggyback circular cylinders in tandem arrangement are performed by solving the variational multiscale formulation of the incompressible Navier-Stokes equations using in-house finite element method(FEM)codes.The effects of the gap-spacing-to-diameter(G/D)and the two diameter ratio(d/D)on the flow characteristics and the reductions of the root-mean-square(RMS)drag and lift coefficients are considered for Reynolds numbers(Res)are 100 and 200.The validation shows the fluid force coefficients obtained by the in-house FEM codes are in good agreement with the results in the existing literatures.The obtained results show that,with a proper placement of the smaller cylinder(d/D=0.2)behind the larger cylinder,the RMS drag and lift coefficients largely decrease compared to those of the single circular cylinder.When d/D=0.2,the largest reductions of the RMS lift coefficient of the larger cylinder and the RMS total lift coefficient appear at G/D=1.2 as Re=100 and at G/D=1.0 as Re=200.It is observed that the proper placement of the smaller cylinder causes the surrounding vorticity to take opposite sign with the vorticity in the outer region so as to suppress and postpone the vortex shedding in the wake,and that the different positions of the vortex shedding at two Res cause that the largest reductions of the RMS lift coefficient of the larger cylinder and the RMS total lift coefficient appear at different G/D as Re is different.When d/D varies,the variation of the RMS total lift coefficient behaves differently at two Res.It decreases with J/D increasing at Re=100,while it no longer monotonously varies with J/D,but reaches a minimum in the considered range of d/D at Re=200.Moreover,the larger d/D results in stronger suppression and postponement of the vortex shedding in the wake.

The hydrodynamic interactions of an array of truncated circular cylinders as each cylinder oscillates independently with different prescribed modes

An analytical method based on the eigenfunction expansion and the Graf＇s addition theorem for Bessel functions is developed to study the hydrodynamic interactions of an array of truncated circular cylinders with each cylinder oscillating independently in different prescribed modes. The hydrodynamic radiation and diffraction of linear waves by such an array of cylinders are investigated and the analytical solutions of the velocity potentials are obtained. After comparisons for degenerated cases and program verifications, several cases for an array of truncated cylinders with each cylinder oscillating independently in surge, sway, heave, roll, and pitch modes with different prescribed amplitudes, are studied and the hydrodynamic forces and moments acting on the cylinders are obtained.

THE UNSTABLE FLOW FROM THE GAP BETWEEN TWO CIRCULAR CYLINDERS

The interference of two circular cylinders has been researched for many years. In this study, the research work was concentrated on two cylinders in some special staggered arrangement. The velocity signal was measured with a hot wire anemometer and recorded with a TEAC portable data recorder. The relationship between spectrum and time was established by making 200 spectrum analysis in se- quence. The gap flow is unstable when two cylinders are arranged in L/D=2, T/D=1. Mainly, it can be looked as flow past a single blunt body and the Strouhal number is 0.15, The second peak arises in the power spectrum when the gap flow appears at irregular time interval. Sometimes it may be higher than the first one. The Strouhal num- ber corresponding to the second peak is 0.33. But at most of the time it is lower than the first one and even disap- peared. This is meaningful for exploring the mechanisms of interference induced oscillations in flow past two cylin- ders.

Large-eddy simulation of the flow past both finite and infinite circular cylinders at Re=3900

The flow past a finite circular cylinder with a height-to-diameter ratio of 1.5 and an infinite circular cylinder of the same diameter at a Reynolds number Re= 3 900 is investigated using the large eddy simulation（LES）. The objective of the present study is to explore the differences of the flow mechanisms between the finite and infinite circular cylinders. It is shown that the free end of the finite circular cylinders affects the wake region significantly. The mean drag coefficient and the fluctuating lift coefficient of the finite circular cylinder are smaller than those of the infinite circular cylinder. The three-dimensional separation and the separated shear layer instability of the finite circular cylinder can obviously be observed. The existence of an arch vortex in the average flow downstream of the free end is demonstrated.

A review on flow-induced vibration of offshore circular cylinders

As a fundamental fluid-structure interaction(FSI)phenomenon,vortex-induced vibrations(VIVs)of circular cylinders have been the center of the FSI research in the past several decades.Apart from its scientific significance in rich physics,VIVs are paid great attentions by offshore engineers,as they are encountered in many ocean engineering applications.Recently,with the development of research and application,wake-induced vibration(WIV)for multiple cylinders and galloping for VIV suppression attachments are attracting a growing research interest.All these phenomena are connected with the flow-induced vibration(FIV).In this paper,we review and give some discussions on the FIV of offshore circular cylinders,including the research progress on the basic VIV mechanism of an isolated rigid or flexible cylinder,interference of multiple cylinders concerning WIV of multiple cylinders,practical VIV suppression and unwanted galloping for cylinder of attachments.Finally,we draw concluding remarks,give some comments and propose future research prospects,especially on the major challenges as well as potentials in the offline/online modelling and prediction of real-scale offshore structures with high-fidelity CFD methods,new experimental facilities and applications of artificial intelligence tools.