S.C. Luo

A numerical study of flow past a rotating circular cylinder using a hybrid vortex scheme

The vortex shedding and wake development of a two-dimensional viscous incompressible flow generated by a circular cylinder which begins its rotation and translation impulsively in a stationary fluid is investigated by a hybrid vortex scheme at a Reynolds number of 1000. The rotational to translational speed ratio α varies from 0 to 6. The method used to calculate the flow can be considered as a combination of the diffusion-vortex method and the vortex-in-cell method. More specifically, the full flow field is divided into two regions: near the body surface the diffusion-vortex method is used to solve the Navier–Stokes equations, while the vortex-in-cell method is used in the exterior inviscid domain. Being more efficient, the present computation scheme is capable of extending the computation to a much larger dimensionless time than those reported in the literature. The time-dependent pressure, shear stress and velocity distributions, the Strouhal number of vortex shedding as well as the mean lift, drag, moment and power coefficients are determined together with the streamline and vorticity flow patterns. When comparison is possible, the present computations are found to compare favourably with published experimental and numerical results. The present results seem to indicate the existence of a critical α value of about 2 when a closed streamline circulating around the cylinder begins to appear. Below this critical α, Karman vortex shedding exists, separation points can be found, the mean lift and drag coefficients and Strouhal number increase almost linearly with α. Above α ≈ 2, the region enclosed by the dividing closed streamline grows in size, Karman vortex shedding ceases, the flow structure, pressure and shear stress distributions around the cylinder tend towards self-similarity with increase α, and lift and drag coefficients approach asymptotic values. The optimum lift to drag ratio occurs at α ≈ 2. The present investigation confirms Prandtls postulation of the presence of limiting lift force at high α, and thus the usefulness of the Magnus effect in lift generation is limited. The results show that the present method can be used to calculate not only the global characteristics of the separated flow, but also the precise evolution with time of the fine structure of the flow field.

Hysteresis phenomenon in the galloping oscillation of a square cylinder

Abstract It is well known that a square cylinder with one side normal to a uniform stream will gallop when a critical flow velocity is exceeded. It is also quite well known that there is a hysteresis phenomenon in the variation of the cylinders galloping amplitude with the flow velocity. However, little is known about the cause of this hysteresis phenomenon, and the objective of this paper is to study it more closely. In the present study, flow over a stationary square cylinder at different angle of attack ( α ) and at Reynolds number (Re) of 250 and 1000 was investigated numerically by using a 2-D hybrid vortex computation scheme. The study reveals that the well known point of inflection which exists in the side force ( C y ) versus α plots at high Reynolds number only occurs at Re=1000, α =4° in the present numerical simulation. Nonlinear analysis further reveals that this point of inflection is the cause of the hysteresis phenomenon. By further analysing the computed flow field, it is noted that at Re=1000, α =4°, intermittent flow reattachment takes place at alternate vortex shedding cycle on one side of the cylinder. This results in larger side force fluctuation, and it is conjectured that such large side force fluctuation affects the increasing trend of the side force with angle of attack, resulting in the point of inflection reported earlier. The above-mentioned alternate cycle flow reattachment was much less prominent at α =2° and 6° (Re=1000), and was not observed at Re=250. Finally, dye flow visualization was carried out in a recirculating water tunnel and the results at Re=1000 confirms the existence of the intermittent flow reattachment. However, in the experiment, flow reattachment does not take place in a very regular alternate cycle manner as in the computation. Instead, it occurs intermittently, possibly due to three-dimensional effects in real flow.

A HYBRID VORTEX METHOD FOR FLOWS OVER A BLUFF BODY

A hybrid vortex method was developed to simulate the two-dimensional viscous incompressible flows over a bluff body numerically. It is based on a combination of the diffusion–vortex method and the vortex-in-cell method by dividing the flow field into two regions. In the region near the body surface the diffusion–vortex method is used to solve the Navier–Stokes equations, while the vortex-in-cell method is used in the exterior domain. Comparison with results obtained by the finite difference method, other vortex methods and experiments shows that the present method is well adapted to calculate two-dimensional external flows at high Reynolds number. It is capable of calculating not only the global characteristics of the separated flow but also the evolution of the fine structure of the flow field with time precisely. The influence of the grid system and region decomposition on the results will also be discussed.

Aerodynamic stability of the downstream of two tandem square-section cylinders

Abstract The work reported in the present paper consists of three parts. In part one, the velocity distribution in the wake of a square cylinder at different distances from it (2⩽ x / D ⩽12) are measured and reported. Analytical expressions for the wake velocity distribution and for the correlation between wake half-width and downstream distance are obtained. The above expressions make it possible to estimate the wake velocity distribution without the availability of the actual experimental data. In part two, the lift and drag acting on the downstream of two cylinders are measured. The results are found to be in reasonable agreement (except in the range L / D =3–4 and T / D =2–3) with previous measurements, and are presented as contours of constant quantities, which make them useful to other researchers for quick information retrieval or estimation. Based on these steady flow results, the region where the downstream cylinder will become unstable to transverse galloping (static instability) are estimated and reported. In the next part, data are acquired with the downstream cylinder undergoing transverse oscillation. From the measurement of the phase angle between the body frequency component of the lift force and the cylinder displacement, the region where the downstream cylinder will be (dynamically) unstable to transverse galloping is estimated, and is found to be in good agreement with the estimation based on the steady flow results in the range L / D ⩽4. The variations of the mean drag as well as the Strouhal number and fluctuating lift and drag of the downstream cylinder with reduced velocity are also measured at different L / D and A / D , and possible explanations for the behaviour of the data are offered.

Numerical study of a linear shear flow past a rotating cylinder

Abstract The effects of shear rate on flow past a rotating circular cylinder in a linear shear flow have been investigated by using a hybrid vortex method at a Reynolds number of 1000. The velocity gradient of the shear flow K ranges from −0.3 to 0.3 and the rotational to translational speed ratio α is 0.5. The results show that the form of vortex shedding is controlled by the shear parameter K . The drag coefficient decreases with increasing | K |. On the other hand, the lift coefficient and Strouhal number increase as K increases. As K increases, the separation positions shift downstream, the wake becomes narrower and the amplitude of fluctuation of the instantaneous lift and drag coefficients decreases.

Discrete vortex simulation of the separated flow around a rotating circular cylinder at high Reynolds number

Abstract The separated flow around a rotating circular cylinder is investigated by the discrete vortex method combined with the boundary layer theory. The Keller Box method is used to solve the laminar boundary layer in order to determine the separation points on the upper and the lower sides of the rotating circular cylinder. The nascent vortices are then introduced near the separation points. A discrete circular vortex blob model, which has uniform vorticity distribution, is adopted to simulate the unsteady wake. Numerical experiments are conducted to investigate the cases in which the ratio of the speed at the cylinder surface to the speed at infinity is varied from 0 to 0.3 at a Reynolds number of 6 × 10 3 . The calculated values of the separation positions, the drag and lift force coefficients, the velocuty and the pressure distribution on the cylinder surface are found to agree well with the published experimental data.

Parallel vortex shedding at Re

The effects of the end conditions of a circular cylinder on its wake at a fairly high Reynolds number of Re = 1.57 x 10 4 were studied. The transverse control cylinder technique (TCCT) was previously reported to be able to induce parallel vortex shedding at Re = O(10 2 ). In the present work, experimental results showed that the TCCT is still effective in inducing parallel vortex shedding at Re = O(10 4 ). Initially, before the inclusion of the control cylinders, vortices shed by the main cylinder were curved (all shapes referred to are time-averaged shapes) owing to the influence of the cylinder end conditions. Later, two larger control cylinders of diameter D were included and were located normal and upstream of the main cylinder near its ends to change its end conditions. By manipulating the control distance (the gap between the control cylinders and the main cylinder), different vortex-shedding patterns could be induced. With both control cylinders fixed at the optimum control distance of L 1 = L 2 = L 0 = 1.26D, the main cylinder was induced to shed parallel vortices. For the cases of curved vortex shedding (without control cylinders) and parallel vortex shedding (with control cylinders at the optimum distance of L 1 = L 2 = L 0 = 1.26D), various aerodynamic parameters of the main cylinder were measured and compared

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A new finite-difference method is presented to solve the unsteady two-dimensional Navier-Stokes equations in the vorticity stream function form and tested for the flow around a cylinder at Reynolds number Re of 103–104. The simulation uses a body-fitting Cartesian coordinate system in the physical plane which is transformed by conformal mapping to a grid with uniform mesh sizes in the computational domain. A new mixed difference scheme coupling the 3rd-order upwind scheme with the 4th-order central scheme is used for the discretization of the vorticity transport equation, while a 2nd-order central scheme is used for the discretization of the stream function equation. Some numerical results for flow past a circular cylinder at Re = 1000 to 9500 and an elliptic cylinder with different angle of attack are given. This numerical method gives results comparable to those of previously published methods but does so using much less memory and computer time. The ease of setting boundary condition is another advantage of the present method. The influence of the initial condition and the grid system, time step is also discussed.