NUMERICAL SIMULATION OF FLOW OVER TWO SIDE-BY-SIDE CIRCULAR CYLINDERS

In the present paper, the unsteady, viscous, incompressible and 2-D flow around two side-by-side circular cylinders was simulated using a Cartesian-staggered grid finite volume based method. A great-source term technique was employed to identify the solid bodies （cylinders） located in the flow field and boundary conditions were enforced by applying the ghost-cell technique. Finally, the characteristics of the flow around two side-by-side cylinders were comprehensively obtained through several computational simulations. The computational simulations were performed for different transverse gap ratios （1.5≤T/D≤4） in laminar （Re=100,200） and turbulent （Re=104） regimes, where T and D are the distance between the centers of cylinders and the diameter of cylinders, respectively. The Reynolds number is based on the diameter of cylinders,D. The pressure field and vorticity distributions along with the associated streamlines and the time histories of hydrodynamic forces were also calculated and analyzed for different gap ratios. Generally, different flow patterns were observed as the gap ratio and Reynolds number varied. Accordingly, the hydrodynamic forces showed irregular variations for small gaps while they took a regular pattern at higher spacing ratios.

Numerical Simulation on Flow Past Two Side-by-Side Inclined Circular Cylinders at Low Reynolds Number

A series of three-dimensional numerical simulations is carried out to investigate the effect of inclined angle on flow behavior behind two side-by-side inclined cylinders at low Reynolds number Re=100 and small spacing ratio T/D=1.5 (T is the center-to-center distance between two side-by-side cylinders, D is the diameter of cylinder). The instantaneous and time-averaged flow fields, force coefficients and Strouhal numbers are analyzed. Special attention is focused on the axial flow characteristics with variation of the inclined angle. The results show that the inclined angle has a significant effect on the gap flow behaviors behind two inclined cylinders. The vortex shedding behind two cylinders is suppressed with the increase of the inclined angle as well as the flip-flop gap flow. Moreover, the mean drag coefficient, root-mean-square lift coefficient and Strouhal numbers decrease monotonously with the increase of the inclined angle, which follows the independent principle at small inclined angles.

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.

A Review on Vibration Control of Multiple Cylinders Subjected to FlowInduced Vibrations

The fatigue damage caused by flow-induced vibration(FIV)is one of the major concerns for multiple cylindrical structures in many engineering applications.The FIV suppression is of great importance for the security of many cylindrical structures.Many active and passive control methods have been employed for the vibration suppression of an isolated cylinder undergoing vortex-induced vibrations(VIV).The FIV suppression methods are mainly extended to the multiple cylinders from the vibration control of the isolated cylinder.Due to the mutual interference between the multiple cylinders,the FIV mechanism is more complex than the VIV mechanism,which makes a great challenge for the FIV suppression.Some efforts have been devoted to vibration suppression of multiple cylinder systems undergoing FIV over the past two decades.The control methods,such as helical strakes,splitter plates,control rods and flexible sheets,are not always effective,depending on many influence factors,such as the spacing ratio,the arrangement geometrical shape,the flow velocity and the parameters of the vibration control devices.The FIV response,hydrodynamic features and wake patterns of the multiple cylinders equipped with vibration control devices are reviewed and summarized.The FIV suppression efficiency of the vibration control methods are analyzed and compared considering different influence factors.Further research on the FIV suppression of multiple cylinders is suggested to provide insight for the development of FIV control methods and promote engineering applications of FIV control methods.

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.

Magnetohydrodynamic Conjugate Free Convective Heat Transfer Analysis of an Isothermal Horizontal Circular Cylinder with Temperature Dependent Viscosity

Heat transfers due to MHD-conjugate free convection from the isothermal horizontal circular cylinder while viscosity is a function of temperature is investigated. The governing equations of the flow and connected boundary conditions are made dimensionless using a set of non-dimensional parameters. The governing equations are solved numerically using the finite difference method. Numerical results are obtained for various values of viscosity variation parameter, Prandtl number, magnetic parameter, and conjugate conduction parameter for the velocity and the temperature within the boundary layer as well as the skin friction coefficients and heat transfer rate along the surface.

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.

Use of Helical Strakes for FIV Suppression of Two Inclined Flexible Cylinders in A Side-by-Side Arrangement

The experimental studies on flow-induced vibrations(FIV) reduction of two side-by-side flexible cylinders inclined at 45° by using the helical strakes were carried out in a towing tank. The main aim of the experiment is to check whether the helical strakes with a pitch of 17.5 D and a height of 0.25 D, which is considered as the most effective vibration suppression device for the isolated cylinder undergoing vortex-shedding, still perform very well to reduce FIV of two inclined flexible cylinders in a side-by-side arrangement. The vibration of two identical inclined cylinders with a mass ratio of 1.90 and an aspect ratio of 350 was tested in the experiment. The center-to-center distance between the two cylinders was 3.0 D. The uniform flow was simulated by towing the cylinder models along the tank.The towing velocity varied from 0.05 to 1.0 m/s with an interval of 0.05 m/s. The maximum Reynolds number can be up to 1.6×104. Three cases were experimentally studied in this paper, including two side-by-side inclined smooth cylinders, only one smooth cylinder fitted with helical strakes in the two side-by-side inclined cylinders system and both two cylinders attached with helical strakes. The variations of displacement amplitude, dominant frequency, FIV suppression efficiency and dominant mode for the two side-by-side inclined cylinders with reduced velocity were shown and discussed.

Response of Two Unequal-Diameter Flexible Cylinders in A Side-by-Side Arrangement:Characteristics of FIV

Till now,little information is available on the flow-induced vibration(FIV)of multiple flexible cylinders with unequal diameters.Some FIV characteristics of unequal-diameter cylinders can be predicted based on the knowledge of equal-diameter cylinders,while there are still other features remaining unrevealed.In this paper,the FIV characteristics of two flexible cylinders with unequal diameters arranged side-by-side are experimentally investigated.The diameter ratio of the small cylinder(Small Cyl.)to the large cylinder(Large Cyl.)is nearly 0.5.The aspect ratios and mass ratios of the two flexible cylinders are 350/181 and 1.90/1.47,respectively.The centre-tocentre spacing ratio in the cross-flow(CF)direction is kept constant as 6.0 and the two cylinders can oscillate freely in both the CF and in-line(IL)directions.The towing velocity varies from 0.05 m/s to 1.00 m/s.The dominant modes and frequencies,CF and IL displacement amplitudes and response trajectories are discussed.Compared with the case of two identical cylinders in our previous study,the FIV responses demonstrate some similarities and differences.The similarities are as follows.Both cylinders exhibit multi-mode vibration features and they interact with each other.Meanwhile,the IL FIV shows a more complex behaviour than that in the CF direction.The difference is that as the diameter of one cylinder is increased,the effect on the smaller cylinder becomes more significant.For Large Cyl.,the FIV response is similar to its isolated counterpart,which indicates that Small Cyl.has a negligible effect on the FIV of the larger one.Whereas Large Cyl.perplexes the FIV of Small Cyl.during the vibration process.The spacing would change when both cylinders are oscillating.Proximity interference between the two cylinders and wake shielding effect of the Large Cyl.may occur.The dominant frequencies of Small Cyl.are reduced and the wake-induced flutter of Small Cyl.is observed from the response trajectories at different measuring points.

Application of Helical Strakes for Suppressing the Flow-Induced Vibration of Two Side-by-Side Long Flexible Cylinders

Helical strakes have been widely applied for suppressing the vibration of flexible cylinders undergoing vortexshedding in offshore engineering.However,most research works have concerned on the application of helical strakes for the isolated flexible cylinder subjected to vortex-induced vibration(VIV).The effectiveness of helical strakes attached to side-by-side flexible cylinders in vibration reduction is still unclear.In this paper,the response characteristics of two side-by-side flexible cylinders with and without helical strakes were experimentally investigated in a towing tank.The configuration of the helical strakes used in the experiment had a pitch of 17.5D and a height of 0.25D(where D is the cylinder diameter),which is usually considered the most effective for VIV suppression of isolated marine risers and tendons.The center-to-center distance of the two cylinders was 3.0D.The uniform flow with a velocity ranging from 0.05 m/s to 1.0 m/s was generated by towing the cylinder models along the tank.Experimental results,including the displacement amplitude,the dominant frequency,the dominant mode,and the mean drag force coefficient,were summarized and discussed.For the case where only one cylinder in the two-cylinder system had helical strakes,the experimental results indicated that helical strakes can remarkably reduce the flow-induced vibration(FIV)of the staked cylinder.For the case of two straked cylinders in a side-by-side arrangement,it was found that the performance of helical strakes in suppressing the FIV is as good as that for the isolated cylinder.

NUMERICAL COMPUTATION OF THE FLOW AROUND TWO SQUARE CYLINDERS ARRANGED SIDE-BY-SIDE

The numerical method is used to calculate the flow around two square cylinders arranged side-by-side and the mean and fluctuating aerodynamic forces, and Strouhal numbers and power spectrum of lift force and drag force are obtained. An improved MAC method proposed by Chen Suqin et al.,which uses three order upwind scheme to discretize the convection term and uses multigrid method to solve the Poisson equation for pressure is applied to simulate the flow around two square cylinders arranged side-by-side. Results show that the interference characteristic of two square cylinders arranged side-by-side is completely different with the different spacing ratio. When the spacing ratio is smaller than a certain critical value, the gap flow between two cylinders is biased to one side in a stable or unstable manner.

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.

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.

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.

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.

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.

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.

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.

Improved Circularity Metrology of Small Cylindrical Workpieces by the Segmenting-stitching Technique

To address the alignment and measuring force problem in the segmenting-stitching technique for the circularity metrology of small cylindrical workpieces(diameter less than 1.5 mm and length less than 10 mm),a magnet combination jig method is proposed.A small round magnet is attached between the round magnetic jig and small cylinder,and the other end of the small cylindrical workpiece is attached to some cylindrical magnets.Thus,the smaller cylinder can be put in the V-groove and measured successfully with the magnet combination.For verifying the advantage of the magnet combination jig,four measurement quality evaluations are proposed:the circumferential deviation of neighbor arc contours,radial deviation of neighbor arc contours,angle of inclination between the V-groove and small cylinder,and curvature of the obtained arc.The results show that the matching coefficient is enhanced by 98%,the Euclidean distance of overlap parts of neighbor arc contours is reduced by 68%,the position error is reduced 27%,and the average curvature of the arc contours is improved.It can be concluded that the measuring quality can be enhanced prominently by this magnet combination method for the segmenting-stitching method.

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.