3D‐Flow structures behind a circular cylinder with hemispherical head geometry

An experimental investigation of the flow around a finite circular cylinder mounted on a flat plate, see fig. 1, is reported. The aspect ratio L/D (with length L and diameter D) of the cylinder model is 2.0. The focus of this study is toward examining the complex separated flow structures and wake properties. Velocity and turbulence measurements have been carried out with a three component Laser Doppler anemometer (LDA) at the Reynolds number Re_D = 2.0 · 10⁵. The experimental results show complex 3D fluid motions in the separated flow region. They are induced by the superposition of three main vortical flows.     

Mechanics of transition in an axisymmetric laminar boundary layer on a circular cylinder

Measurements of the growth of artificially generated turbulent spots and intermittency distribution in the transition region on a circular cylinder in axial flow show that the instability Reynolds number of 11,000 has a marked effect on the properties. In particular, it is found that the spot production in the initial region when a single turbulent spot has not yet wrapped around the cylinder and the propagation is essentially two-dimensional, is significantly altered. But the transition in the downstream or latter region, where most of the turbulent spots propagate onedimensionally (like the turbulent plugs in a pipe), is not affected. When the radius Reynolds number is more than 11,000, the intermittency law in the initial region is essentially the same as in twodimensional flow on a flat plate and in the latter region it is the one-dimensional flow in a pipe, the demarcation between the two regions being quite sharp.     

Expansions at small Reynolds numbers for the flow past a porous circular cylinder

The purpose of this article is to use the method of matched asymptotic expansions (MMAE) in order to study the two-dimensional steady low Reynolds number flow of a viscous incompressible fluid past a porous circular cylinder. We assume that the flow inside the porous body is described by the continuity and Brinkman equations, and the velocity and boundary traction fields are continuous across the interface between the fluid and porous media. Formal expansions for the corresponding stream functions are used. We show that the force exerted by the exterior flow on the porous cylinder admits an asymptotic expansion with respect to low Reynolds numbers, whose terms depend on the characteristics of the porous cylinder. In addition, by considering Darcy's law for the flow inside the porous circular cylinder, an asymptotic formula for the force on the cylinder is obtained. Also, a porous circular cylinder with a rigid core inside is considered with Brinkman equation inside the porous region. Stress jump condition is used at the porous–liquid interface together with the continuity of velocity components and continuity of normal stress. Some particular cases, which refer to the low Reynolds number flow past a solid circular cylinder, have also been investigated.     

Influence of power-law index on transitional Reynolds numbers for flow over a semi-circular cylinder

In this work, the governing partial differential equations (continuity and Cauchy’s momentum equations) describing the flow of power-law type non-Newtonian fluids across a semi-circular cylinder (oriented with its curved surface in the upstream direction) have been solved numerically. In particular, consideration has been given to the delineation of the critical Reynolds numbers denoting the onset of flow separation from the surface of the cylinder and the onset of the laminar vortex shedding regime. This information is germane to establish the scaling of the macroscopic characteristics like drag coefficient and Strouhal number on the governing parameters, namely, Reynolds number and power-law index. The present results clearly suggest that the transitional Reynolds numbers show a strong dependence on the type (shear-thinning and shear-thickening) of fluid behavior as well as on the severity of the shear-dependence of the viscosity. With reference to the behavior seen in Newtonian fluids, the flow remains not only attached to the surface up to higher Reynolds numbers, but shear-thinning behavior also delays the onset of the laminar vortex shedding regime. As expected, shear-thickening fluids, of course, display the opposite characteristics.     

Axisymmetric flow over a backward-facing step in an annular pipe

The incompressible flow of a Newtonian fluid over a backward-facing step is investigated numerically. The geometry is an annular pipe in which the radius of the inner cylinder decreases suddenly. Keeping the radial expansion ratio fixed axisymmetric flows are computed for outlet radius ratios from 0.1 to 1 (ratio of the inner to the outer outlet radius). The Reynolds number at which the flow separates from the outer cylinder decreases as the outlet radius ratio decreases for constant inlet geometry. The growth with Reynolds number of the recirculation zone on the inner outlet cylinder just behind the step is strongly reduced when the recirculation zone on the outer cylinder is established. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Buoyancy-assisted flow of yield stress fluids past a cylinder: Effect of shape and channel confinement

The aiding-buoyancy mixed convection heat transfer in Bingham plastic fluids from an isothermal cylinder of elliptical and circular shape in a vertical adiabatic channel is numerically investigated. For a fixed shape of the elliptical cylinder E = 2 (ratio of major to minor axes), the effect of confinement is studied for three values of blockage ratio, B, defined as the ratio of the channel width to the circumference of the cylinder/π, as 6.5, 2.17 and 1.3. In order to delineate the role of cross-section of the cylinder, results are also presented here for a circular cylinder of the same heat transfer area as the elliptical cylinder. The results presented herein span the range of conditions as: Bingham number, 0 ≤ Bn ≤ 100, Reynolds number, 1 ≤ Re ≤ 40, and Prandtl number, 1 ≤ Pr ≤ 100 over the range of Richardson number Ri = 0 (pure forced convection) to Ri = 10. Extensive results on drag coefficient, local and surface averaged values of the Nusselt number and yield surfaces are presented herein to elucidate the combined effects of buoyancy, blockage ratio and fluid yield stress. The morphology of the yield surfaces shows that the unyielded plug regions formed upstream and downstream of the cylinder grow faster at low Reynolds numbers with the increasing yield stress effects under the weak buoyancy forces, i.e., small values of Grashof or Richardson number. The heat transfer enhancement is observed with the increasing channel-confinement due to the sharpening of the temperature gradients near the surface of the cylinder. The average Nusselt number shows a positive dependence on the Reynolds number, Prandtl number and Richardson number irrespective of the shape of the cylinder or the type of fluid. By employing the modified definitions of the dimensionless parameters (based on the two choices of the overall effective fluid velocity), predictive correlations have been established for estimating the value of the average Nusselt number in a new application.     

Numerical study on viscoelastic fluid flow past a rigid body

Viscoelastic non-Newtonian fluids can be achieved by adding a small amount of polymer additives to a Newtonian fluid. In this paper, numerical simulations are used to investigate the influence of such polymer additives on the behavior of flow past a circular cylinder. A numerical method is proposed that discretizes the non-linear viscoelastic system on a uniform Cartesian grid, with a penalization method to model the presence of the cylinder. The drag of the cylinder and the flow behavior under the effect of different Reynolds numbers ($\mathrm{Re}$), Weissenberg numbers (Wi) and polymer viscosity ratios (ε) are studied. Numerical results show that different flow characteristics are exhibited in different parameter zones. The polymer viscosity ratio plays an important role at low Weissenberg and Reynolds numbers, but as the Reynolds and Weissenberg numbers increase, the influence of ε weakens. The drag force of the cylinder is mostly affected by the Reynolds and Weissenberg numbers. At low Reynolds numbers, the drag of the cylinder and the flow fields are only affected by a large value of Wi when the elastic forces are strong. Non-trivial drag reduction occurs only when there is vortex shedding in the wake flow, whereas drag enhancement happens when the vortex shedding is inhibited.     

On the Influence of Thermal Convection in Classical Taylor‐Couette Flows

The presented work deals with the instabilities that occur in the flow of a viscous fluid between axisymmetric cylinders with a rotating inner and stationary outer cylinder. The results of a numerical study of convective flows are presented. The inner cylinder is rotating and heated from within, while the outer cylinder is stationary and cooled outside. Stationary horizontal endplates are used to seal the annulus, forming an enclosure. The working fluid is silikon oil M3. The flow of oil was rendered visible by injecting aluminium powder. By increasing the Reynolds number with angular velocity of the driving inner cylinder, the flow bifurcates into different types of instabilities. Investigation was aimed to find the values of critical Reynolds and Rayleigh numbers corresponding to the critical speeds and temperature differences at which these instabilities set in. The three‐dimensional problem was modelled numerically using software package FLUENT in which discretization is performed by means of finite volume techniques. Computational grid was created in preprocessor Gambit. Numerical experiments are conducted to determine the interdependence between the heat transfer mechanism and the structure of secondary flows     

Hydrodynamics of a particle impact on a wall

The problem of a particle impacting on a wall, a common phenomenon in particle-laden flows in the minerals and process industries, is investigated computationally using a spectral-element method with the grid adjusting to the movement of the particle towards the wall. Remeshing is required at regular intervals to avoid problems associated with mesh distortion and the constantly reducing maximum time-step associated with integration of the non-linear convective terms of the Navier–Stokes equations. Accurate interpolation between meshes is achieved using the same high-order interpolation employed by the spectral-element flow solver. This approach allows the full flow evolution to be followed from the initial approach, through impact and afterwards as the flow relaxes. The method is applied to the generic two-dimensional and three-dimensional bluff body geometries, the circular cylinder and the sphere. The principal case reported here is that of a particle colliding normally with a wall and sticking. For the circular cylinder, non-normal collisions are also considered. The impacts are studied for moderate Reynolds numbers up to approximately 1200. A cylindrical body impacting on a wall produces two vortices from its wake that convect away from the cylinder along the wall before stalling while lifting induced wall vorticity into the main flow. The situation for a sphere impact is similar, except in this case a vortex ring is formed from the wake vorticity. Again, secondary vorticity from the wall and particle plays a role. At higher Reynolds number, the secondary vorticity tends to form a semi-annular structure encircling the primary vortex core. At even higher Reynolds numbers, the secondary annular structure fragments into semi-discrete structures, which again encircle and orbit the primary core. Vorticity fields and passive tracer particles are used to characterize the interaction of the vortical structures. The evolution of the pressure and viscous drag coefficients during a collision are provided for a typical sphere impact. For a Reynolds number greater than approximately 1000 for a sphere and 400 for a cylinder, the primary vortex core produced by the impacting body undergoes a short-wavelength instability in the azimuthal/spanwise direction. Experimental visualisation using dye carried out in water is presented to validate the predictions.     

Unsteady heat transfer from a circular cylinder in a low Reynolds number flow

This paper examines the temperature distribution in a low Reynolds number flow past a circular cylinder following a sudden change in the temperature of the cylinder. Solutions describing the initial development of the temperature field and the final approach to the eventual steady state are obtained. Expressions for the Nusselt number for small and large values of time are determined.     

MILU-CG方法和绕旋转圆柱流动的数值研究

本文采用以修正的不完全LU分解作预处理器的共轭梯度法(MILU-CG),结合高阶隐式差分格式,改进了作者(1992)提出的基于区域分解、有限差分法与涡法杂交的数值方法(HDV).系统地研究了雷诺数Re=1000,200,旋转速度比α∈(0.5,3.25)范围内,绕旋转圆柱从突然起动到充分发展,长时间内尾流旋涡结构和阻力、升力系数的变化规律.计算所得流线与实验流场显示相比,完全吻合.首次揭示了临界状态时的旋涡结构特性,并指出最佳升阻比就在该状态附近得到.     

Improved stability techniques for the solution of Navier-Stokes equations

When solving the Navier-Stokes equations for transient incompressible viscous flow problems, one normally encounters a decrease in numerical stability of the time integration algorithm with an increase in Reynolds number. This instability cannot be easily overcome due to the non-linearities present. The present paper, using the finite element method to integrate the equations in the spacial dimension, incorporates a time-staggered semi-implicit fractional step technique to improve stability at the higher Reynolds numbers. Unlike the upwind or directional differencing schemes normally employed to increase numerical stability, the present scheme does not introduce numerical damping or artificial viscocity, and becomes more stable as the Reynolds number increases. Results for this scheme are compared with various explicit integration schemes for the case of flow around a circular cylinder at Reynolds numbers of 100 to 400. For comparable accuracy the time-staggered semi-implicit fractional step technique was found to be up to 25 times more efficient than the other explicit integration schemes.     

Magnetic field effects on Newtonian and non-Newtonian ferrofluid flow past a circular cylinder

The changes in the flow properties under the action of electromagnetic body forces are investigated numerically for ferrofluid flow past a circular cylinder. Ferrofluid is modeled as both a Newtonian and a non-Newtonian Power-Law fluid. Magnetic forces are applied by placing magnets at different locations on the surface of the cylinder. The magnetostatic effects on the structure of the wake region, on drag reduction and on vortex formation length and frequency are shown and compared in terms of Reynolds number, interaction parameter, Power-Law index and magnet location. It is shown that the increase in the interaction parameter reduces drag for both Newtonian and non-Newtonian model. This decrease is observed to be higher for shear thinning and lower for shear thickening fluid compared to Newtonian case. It is also shown that vortex street formation in the wake region behind the cylinder may be delayed under high magnetic effects. The Strouhal number is higher for shear thinning case at both low and high Reynolds numbers, and lower for shear thickening case at high Reynolds numbers, compared to Newtonian fluid. The vortex formation frequency also decreases under the action of the magnetic field in all cases, however the vortex formation length increases. Placing the magnet towards the front region of the cylinder increases considerably the drag coefficient for both Newtonian and non-Newtonian model. This increase in drag coefficient is higher in the shear thinning fluid and lower in the shear thickening fluid compared to the Newtonian case.     

Separation of streamlines for spatially periodic flow at non-zero Reynolds numbers

The flow generated by a small rotating circular cylinder at the center of a corrugated outer cylinder is considered. By using a Stokes expansion, the first order correction in the Reynolds numberR is found for the creeping flow solution. An approximate critical Reynolds numberR _c is found at which separation appears, and it is expressed in terms of the boundary parameters. Separation is found to occur in the concave regions of the boundary skewed opposite to the direction of rotation of the inner cylinder. By partially solving for the second order correction in the Stokes expansion, it is found that an increase inR causes an increase in the torque exerted on the outer boundary.This work was supported in part by a grant from NSERC.     

Numerical simulation of vortex induced vibrations and its control by suction and blowing

The vortex formation and shedding behind bluff structures is influenced by fluid flow parameters such as, Reynolds number, surface roughness, turbulence level, etc. and structural parameters such as, mass ratio, frequency ratio, damping ratio, etc. When a structure is flexibly mounted, the Kármán vortex street formed behind the structure gives rise to vortex induced oscillations. The control of these flow induced vibrations is of paramount practical importance for a wide range of designs. An analysis of flow patterns behind these structures would enable better understanding of wake properties and their control. In the present study, flow past a smooth circular cylinder is numerically simulated by coupling the mass, momentum conservation equations along with a dynamical evolution equation for the structure. An active flow control strategy based on zero net mass injection is designed and implemented to assess its efficacy. A three actuator system in the form of suction and blowing slots are positioned on the cylinder surface. A single blowing slot is located on the leeward side of the cylinder, while two suction slots are positioned at an angle α = 100°. This system is found to effectively annihilate the vortex induced oscillations, when the quantum of actuations is about three times the free stream velocity. The dynamic adaptability of the proposed control strategy and its ability to suppress vortex induced oscillations is verified. The exact quantum of actuation involved in wake control is achieved by integrating a control equation to decide the actuator response in the form of a closed loop feed back system. Simulations are extended to high Reynolds number flows by employing eddy viscosity based turbulence models. The three actuator system is found to effectively suppress vortex induced oscillations.     

Effect of aligned magnetic field on the steady viscous flow past a circular cylinder

The steady viscous incompressible and slightly conducting fluid flow around a circular cylinder with an aligned magnetic field is simulated for the range of Reynolds numbers 100 ? Re ? 500 using the Hartmann number, M. The multigrid method with defect correction technique is used to achieve the second order accurate solution of complete non-linear Navier–Stokes equations. The magnetic Reynolds number is assumed to be small. It is observed that volume of the separation bubble decreases and drag coefficient increases as M is increased. We noticed that the upstream base pressure increases slightly with increase of M whereas downstream base pressure decreases with increase of M. The effect of the magnetic field on the flow is discussed with contours of streamlines, vorticity, plots of surface pressure and surface vorticity.     

Simulation of the flow past a circular cylinder using an unsteady panel method

In the present work, an in-house UnSteady Double Wake Model (USDWM) is developed for simulating general flow problems behind bodies. The model is presented and used to simulate flows past a circular cylinder at subcritical, supercritical, and transcritical flows. The flow model is a two-dimensional panel method which uses the unsteady double wake technique to model flow separation and its dynamics. In the present work the separation location is obtained from experimental data and fixed in time. The highly unsteady flow field behind the cylinder is analyzed in detail. The results are compared with experiments and Unsteady Reynolds-Averaged Navier Stokes (URANS) simulations and show good agreement in terms of the vortex shedding characteristics, drag, and pressure coefficients for the different flow regimes.     

Viscoelastic flow in a curved channel: A similarity solution for the Oldroyd-B fluid

A similarity solution is used to analyse the flow of the Oldroyd fluid B, which includes the Newtonian and Maxwell fluids, in a curved channel modelled by the narrow annular region between two circular concentric cylinders of large radius. The solution is exact, including inertial forces. It is found that the non-Netonian kinematics are very similar to the Newtonian ones, although some stress components can become very large. At high Reynolds number a boundary layer is developed at the inner cylinder. The structure of this boundary layer is asymptotically analysed for the Newtonian fluid. Non-Newtonian stress boundary layers are also developed at the inner cylinder at large Reynolds numbers.     

Fast technique for solving the <Emphasis Type="Italic">N</Emphasis>-body problem in flow simulation by vortex methods

A fast algorithm is proposed for solving the N-body problem arising in flow simulation when the flow is represented as a set of many interacting vortex elements. The algorithm is used to compute the flow over a circular cylinder at high Reynolds numbers.     

Field descriptions for a steady,developing tube flow of vanishing Reynolds number

Numerical solutions for the stream function, vorticity, velocity, and pressure fields are presented for the case of a steady, laminar, isothermal, Newtonian flow developing from an initial slug flow in a circular cylinder of infinite length at zero Reynolds number.