Capillary cavity flow past a circular cylinder

Cavity flow past a circular cylinder is considered accounting for the surface tension on the cavity boundary. The fluid is assumed to be inviscid and incompressible, and the flow is assumed to be irrotational. The solution is based on two derived governing expressions, which are the complex velocity and the derivative of the complex potential defined in an auxiliary parameter region. An integral equation in the velocity magnitude along the free surface is derived from the dynamic boundary condition. The Brillouin–Villat criterion is employed to determine the location of the point of flow separation. The cases of zero surface tension and zero cavitation number are obtained as limiting cases of the solution. Numerical results concerning the effects of surface tension and cavitation development on the cavity detachment, the drag force and the geometry of the free boundaries are presented over a wide range of the Weber and the cavitation numbers.     

On the unsteady rotational flow of a generalized Maxwell fluid through a circular cylinder

In this paper, the velocity field and the associated tangential stress corresponding to the rotational flow of a generalized Maxwell fluid within an infinite circular cylinder are determined by means of the Laplace and finite Hankel transforms. Initially, the fluid is at rest, and the motion is produced by the rotation of the cylinder about its axis with a unsteady angular velocity. The solutions that have been obtained are presented under series form in terms of the generalized G _a,b,c (, t)-functions. The similar solutions for the ordinary Maxwell and Newtonian fluids, performing the same motion, are obtained as special cases, when β → 1, respectively β → 1 and λ → 0, from general solutions. Finally, the solutions that have been obtained are compared by graphical illustrations, and the influence of the pertinent parameters on the fluid motion is also underlined by graphical illustrations.     

On the micropolar flow in a circular pipe: the effects of the viscosity coefficients

This paper considers the stationary flow of incompressible micropolar fluid through a thin cylindrical pipe governed by the pressure drop between pipe's ends. Its goal is to investigate the influence of the viscosity coefficients on the effective flow. Depending on the magnitude of viscosity coefficients with respect to the pipe's thickness, it derives different asymptotic models and discusses their properties.     

On the simulation of the flow around a circular cylinder at Re=140,000

The flow around a circular cylinder at Reynolds number of 1.4 × 10⁵ is examined with Reynolds-Averaged Navier–Stokes equations (RANS) and Scale-Resolving Simulation (SRS) methods. Such problem is in the upper limit of the flow regime where turbulent transition occurs in the free shear-layers and so the flow dynamics is dominated by the spatial development of vortex-shedding structure, and in particular by the Kelvin–Helmholtz rollers and turbulence onset. The objectives of this investigation are threefold: (i) determine the aptitude of distinct RANS and SRS models to simulate the correct flow regime; (ii) compare the predictions of selected methods with available experimental measurements; and (iii) examine key modelling and flow features that contribute to the observed results. The evaluated models range from RANS supplemented with linear, transition, and non-linear turbulent viscosity closures, to hybrid and bridging SRS methods. Bridging computations are conducted at various constant degrees of physical resolution (range of resolved scales). The results illustrate the complexity of predicting the present flow problem. It is shown that RANS and SRS formulations modelling turbulence in boundary-layers with the selected linear turbulent viscosity closures lead to a premature onset of turbulence which alters the flow regime of the simulations. Although the transition and non-linear RANS closures can predict the correct flow regime, the outcome of this study indicates that solely the bridging model at constant physical resolution is able to achieve an accurate and physics-based prediction of the flow dynamics. Nonetheless, the necessary degree of physical resolution makes the numerical requisites of such computations demanding.     

Heat transfer in a second-order fluid for flow around a circular cylinder

The temperature distribution within the thermal boundary layer region due to the flow of an incompressible second-order fluid around a heated circular cylinder, maintained at a constant temperature higher than that of the fluid at infinity, has been obtained near the forward stagnation point by series expansion. The graph of the Nusselt number Nu for the Prandtl number P = 25 and the Eckert number E = 0.1 indicates that the non-Newtonian effect is to increase the heat flux from the cylinder to the liquid in the region 0° ? θ ? 15.7° and to decrease it in the region 15.7° < θ ? 0₀ where θ is the angular distance on the cylinder measured from the forward stagnation point. The critical point θ₀ at which Nu = 0, that is, where the effect of the frictional heating balances the effect of the temperature difference and there is no heat flux either from the cylinder or from the liquid, shifts towards the forward stagnation point with the increase of non-Newtonian effects.     

The turbulent flow field around a circular cylinder

The flow field around a circular cylinder mounted vertically on a flat bottom has been investigated experimentally. This type of flow occurs in several technical applications, e.g. local scouring around bridge piers. Hydrogen bubble flow visualization was carried out for Reynolds numbers ranging from 6,600 to 65,000. The main flow characteristic upstream of the cylinder is a system of horse-shoe vortices which are shed quasi-periodically. The number of vortices depends on Reynolds number. The vortex system was found to be independent of the vortices that are shed in the wake of the cylinder. The topology of the separated flow contains several separation and attachment lines which are Reynolds number dependent. In the wake region different flow patterns exist for each constant Reynolds number.     

On the unsteady rotational flow of a fractional second grade fluid through a circular cylinder

Here the velocity field and the associated tangential stress corresponding to the rotational flow of a generalized second grade fluid within an infinite circular cylinder are determined by means of the Laplace and finite Hankel transforms. At time t=0 the fluid is at rest and the motion is produced by the rotation of the cylinder around its axis. The solutions that have been obtained are presented under series form in terms of the generalized G-functions. The similar solutions for ordinary second grade and Newtonian fluids are obtained from general solution for β→1, respectively, β→1 and α ₁→0. Finally, the influences of the pertinent parameters on the fluid motion, as well as a comparison between models, is underlined by graphical illustrations.     

On forced capillary-gravity waves in a circular cylinder

Capillary-gravity waves induced by the lateral oscillation of a cylindrical container are considered on Hocking's hypothesis that the surface slope at the contact line is proportional to the vertical velocity. This problem has been considered by Shen, Sun and Hsieh on Evans's hypothesis that the surface slope at the contact line is prescribed and proportional to the excitation. The latter condition, in contrast to that of Hocking, leaves the normal modes and resonant frequencies unchanged from those of the classical problem (for which the surface slope vanishes at the contact line), and is conservative (whereas Hocking's condition implies dissipation).     

Stable nonlinear waves in a poiseuille flow

Nonlinear Tolmin-Schlichting waves are studied [1–8]. The investigation is carried out by means of a modified Stuart-Watson method [1–3]. In the case of a rigid regime of excitation terms to the fifth order are taken into account in expansions with respect to the amplitude of self-excited oscillations. The stability of self-excited oscillations with respect to two- and three-dimensional disturbances is examined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 40–45, September–October, 1978.The author thanks S. Ya. Gertsenshtein for attention to the work and discussion of the results.     

Vortex shedding flow behind a slowly rotating circular cylinder

This paper investigates flow past a rotating circular cylinder at 3600?Re?5000 and α?2.5. The flow parameter α is the circumferential speed at the cylinder surface normalized by the free-stream velocity of the uniform cross-flow. With particle image velocimetry (PIV), vortex shedding from the cylinder is clearly observed at α<1.9. The vortex pattern is very similar to the vortex street behind a stationary circular cylinder; but with increasing cylinder rotation speed, the wake is observed to become increasing narrower and deflected sideways. Properties of large-scale vortices developed from the shear layers and shed into the wake are investigated with the vorticity field derived from the PIV data. The vortex formation length is found to decrease with increasing α. This leads to a slow increase in vortex shedding frequency with α. At α=0.65, vortex shedding is found to synchronize with cylinder rotation, with one vortex being shed every rotation cycle of the cylinder. Vortex dynamics are studied at this value of α with the phase-locked eduction technique. It is found that although the shear layers at two different sides of the cylinder possess unequal vorticity levels, alternating vortices subsequently shed from the cylinder to join the two trains of vortices in the vortex street pattern exhibit very little difference in vortex strength.     

Unsteady circulatory flow about a circular cylinder with suction

Summary The complete Navier-Stokes equations which describe the unsteady flow of a viscous incompressible fluid when an infinite circular cylinder is given an impulsive twist, and simultaneously a constant suction velocity is imposed on the cylinder, are integrated using Laplace transforms. It is found that points which are at a greater distance from the cylinder are nearer to steadiness than points which are closer to the cylinder. Unsteady flow through a concentric annulus has also been considered.     

Supersonic viscous perfect gas flow past a circular cylinder

The complete Navier-Stokes equations are used to calculate supersonic perfect gas flow past a circular isothermal cylinder by the method described in [1]. The effects of the Mach number M=2.5–10 and the Reynolds number Re=30-10⁵ on the flowfield structure and heat transfer to the cylinder wall are investigated. Special attention is paid to the study of the near wake and the local characteristics on the leeward side of the cylinder.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 107–115, November–December, 1993.     

Non-uniform suction control of flow around a circular cylinder

In the present study, numerical investigations were performed with optimisation to determine efficient non-uniform suction profiles to control the flow around a circular cylinder in the range of Reynolds numbers 4 < Re < 188.5. Several objectives were explored, namely the minimisation of the separation angle, total drag, and pressure drag. This was in an effort to determine the relationships between the characteristics of the uncontrolled flow and the parameters of the optimised suction control. A variety of non-uniform suction configurations were implemented and compared to the benchmark performance of uniform suction. It was determined that the best non-uniform suction profiles consisted of a distribution with a single locus and compact support. The centre of suction on the cylinder surface for the optimised control, and the quantity of suction necessary to achieve each objective, varied substantially with Reynolds number and also with the separation angle of the uncontrolled flows. These followed predictable relationships. Surprisingly, the location of optimised suction to eliminate separation did not follow the separation point as it moved with Re, but rather it moved in opposition to it towards the trailing edge of the cylinder. Non-uniform suction profiles were much more efficient at eliminating boundary layer separation, requiring the removal of less than half the volume of fluid as uniform control to achieve the same objective. Regardless of the method of control, less net suction was needed to minimise total drag than to eliminate separation, except at low Re. The results suggest that controlling the dynamic aspects of the flow has the most impact for reducing drag. This reinforces the usefulness of other studies that focus on the elimination of vortex shedding. The results show that the balance of drag components must be an important consideration when designing flow control systems and that, when done appropriately, substantial improvement can be seen in the flow characteristics.     

Synthetic jet control of separation in the flow over a circular cylinder

A synthetic jet generated by a non-sinusoidal waveform is used to control flow separation around a circular cylinder at Reynolds number 950. The synthetic jet is positioned at the rear stagnation point. The suction duty cycle factor defined as the ratio of the time duration of the suction cycle to the blowing cycle is introduced as the determining parameter. Increasing the suction duty cycle factor, the exit velocity and entrainment effect of the synthetic jet are enhanced, flow separation is delayed, and drag reduction by up to 29?% is achieved. Different mechanisms for separation control during both the blowing cycle and the suction cycle have been revealed. It is suggested that a better control effect can be obtained during the blowing cycle.     

Unsteady characteristics of the cavity flow around a rough circular cylinder

Effects of surface roughness on the unsteady cavitating flow around a two-dimensional circular cylinder were experimentally investigated at Reynolds numbers from 1.36 × 10⁵ to 1.78 × 10⁵. Two patterns of surface roughness were investigated, a double-cut pattern and a single-cut pattern. The cavity elongates with an increase of the surface roughness, especially in supercavitating flow. However, for some roughness parameters tested, the cavity length exhibits an extreme decrease. In a particular case of the double-cut pattern, there exists the minimum cavity behind the cylinder.     

Experimental investigation of the flow around a radially vibrating circular cylinder

This work aims to develop a process for controlling a cylinder wake, especially the von Karman vortex street, in such way so as to drastically reduce the drag coefficient. A new technique for influencing the cylinder wake is proposed in the present experimental study. The flow around a circular cylinder is perturbed by temporarily changing the cylinder diameter. Experiments have been performed for Reynolds numbers in the range Re=9,500 to Re=31,500. Three values of the controlling frequencies are considered: fs₁=0.41, fs₂=0.54 and fs₃=0.73, in addition to the stationary case corresponding to a non-deformable cylinder, fs₀=0. The visualisation flow shows that the pulsing motion of the cylinder walls greatly influences both the near and far wake dynamics. A decrease of the drag is expected.

Visual observations of the flow around a half-submerged oscillating circular cylinder

Visual observations are made on the flow around a horizontal circular cylinder which is half-submerged in still water and forced to oscillate vertically. The ends of the cylinder have great influence on the wave pattern and flow field. Progressive plane waves are generated at small forcing amplitudes, but cross-waves are superimposed on the progressive plane waves at large forcing amplitudes. The wavelength of the cross-waves in the direction parallel to the cylinder axis increases with the forcing amplitude. The crests of the cross-waves are in parallel lines which are oblique to the cylinder axis. The angle at which the parallel lines meet the cylinder axis decreases as the forcing amplitude is increased. Three kinds of steady flows are induced in the water: surface flow, undersurface flow, and vertical jet.     

Effect of blockage on critical parameters for flow past a circular cylinder

The effect of location of the lateral boundaries, of the computational domain, on the critical parameters for the instability of the flow past a circular cylinder is investigated. Linear stability analysis of the governing equations for incompressible flows is carried out via a stabilized finite element method to predict the primary instability of the wake. The generalized eigenvalue problem resulting from the finite element discretization of the equations is solved using a subspace iteration method to get the most unstable eigenmode. Computations are carried out for a large range of blockage, 0.005?D/H ?0.125, where D is the diameter of the cylinder and H is the lateral width of the domain. A non‐monotonic variation of the critical Re with the blockage is observed. It is found that as the blockage increases, the critical Re for the onset of the instability first decreases and then increases. However, a monotonic increase in the non‐dimensional shedding frequency at the onset of instability, with increase in blockage, is observed. The increased blockage damps out the low‐frequency modes giving way to higher frequency modes. The blockage is found to play an important role in the scatter in the data for the non‐dimensional vortex shedding frequency at the onset of the instability, from various researchers in the past. Copyright © 2005 John Wiley & Sons, Ltd.