Active control of cylinder wake

The objective of this paper is to develop an efficient active control algorithm for manipulating wake flows past a solid cylinder in an electrically low-conducting fluid (e.g. seawater). The intent is to avoid both vortex shedding and flow separation from the body. It is expected to reduce the mean drag significantly. This is achieved through the introduction of a Lorentz force in the azimuthal direction generated by an array of permanent magnets and electrodes located on the solid structure. With the use of a symmetric and static Lorentz force over the entire surface of the cylinder, the vortex shedding behind the cylinder weakens and eventually disappears completely when the Lorentz force is sufficiently large. The localized Lorentz force along the rear surface of the cylinder was also used to control the vortex shedding behind the cylinder. In this case, numerical results show that the efficiency of the localized Lorentz force in controlling the flow is to that of the Lorentz force distributed over the whole surface.     

Assessment of an improved turbulence model in simulating the unsteady flows around a D-shaped cylinder and an open cavity

Most engineering flows are still predicted by the conventional Reynolds-averaged Navier-Stokes method because of the low requirements of the computational quantities. However, the resolution capability of Reynolds-averaged Navier-Stokes models is still open to deliberation, especially in the recirculation and wake regions, where the vortical flows dominate. In the present work, an improved turbulence model derived from the original shear stress transport k-ω model is proposed and its superiority is assessed by our modeling the unsteady flows around a D-shaped cylinder and an open cavity, corresponding to two different Reynolds numbers. The results are compared with results from experiments and other turbulence models in terms of the flow morphology and mean velocity profiles. This shows that the predictive accuracy of the modified turbulence model is increased significantly in the bluff body wake flows and in the shear layer and separation flows of the cavity. Some special vortex structures can be captured in the open cavity, in which the secondary vortex emerging from the shear layer and the separation vortex near the trailing edge can induce large flow instability, and this phenomenon should be eliminated in engineering applications. It is believed that this improved turbulence model can be used for the more complex turbomachinery flows with better prediction of the hydrodynamic/aerodynamic performance and the unsteady vortical flows, which can provide some guidelines to design or optimize rotating machines.     

Flow separation behind ellipses at Reynolds numbers less than 10

Flow separation behind two-dimensional ellipses with aspect ratios ranging from 0, a flat plate, to 1, a circular cylinder, were investigated for Reynolds numbers less than 10 using both a cellular automata model and a commercial computational fluid dynamics software program. The relationship between the critical aspect ratio for flow separation and Reynolds number was determined to be linear for Reynolds numbers greater than one. At slower velocities, the critical aspect ratio decreases more quickly as the Reynolds number approaches zero. The critical Reynolds numbers estimated for flow separation behind a flat plate and circular cylinder agree with extrapolations from experimental observations. Fluctuations in the values of the stream function for laminar flow behind the ellipses were found at combinations of Reynolds number and aspect ratio near the critical values for separation.     

Modeling of flow separation of assist gas as applied to laser cutting of thick sheet metal

The present paper describes the results of mathematical modeling of supersonic flows of a viscous compressible gas, obtained by numerically solving three-dimensional full Navier–Stokes equations, and also the results of experiments with visualization of gas jet flows in channels geometrically similar to the laser cut. Separation of the gas flow from the cut front is predicted numerically and then validated by experiments on a model setup. The gas flow structure arising in a narrow channel behind a sonic (conical) or supersonic nozzle is described. Specific features of originating in the flow separation on a smooth surface in a narrow channel are examined, and mechanisms controlling the separation are proposed. Flow separation directly affects the changes in the shape and structure of striations and is the one of main reason for the worse quality of the laser cut surface. It is shown that the changes in the structures of striations over the thickness of the sheet being cut are closely related to aerodynamic features of jet flows of the assisting gas in the cut channel.     

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)     

Numerical simulation of flow past a sphere in vertical motion within a stratified fluid

In the present study we consider a viscous fluid, stratified by a diffusive saline agent and compute numerically the flow produced by a solid sphere moving vertically and uniformly. The governing equations describing this situation are solved on a variational grid. The results show the dependence of the boundary-layer separation point and the vanishing of vortices behind the sphere as the stratification increases at moderate Reynolds number flows. Details of the flow, density and pressure fields near the sphere are also shown. Important quantities for engineering use (drags, pressure and skin coefficients) are also computed and displayed in the Richardson vs. Reynolds number space. Comparison with experimental evidence shows and excellent agreement.     

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.     

A non-iterative immersed boundary-lattice Boltzmann method with boundary condition enforced for fluid–solid flows

A non-iterative immersed boundary lattice Boltzmann method (IB-LBM) is proposed in this work for the simulation of fluid–solid flows. In the scheme, the interface is implemented by the correction of the neighboring distribution functions, similar to that of the LBM. Such treatment of the boundary is contrary to the traditional methods, where the interface is usually modeled as a generator of external force. Therefore, an advantage of the present method is to remove the efforts to evaluate the IB force and then incorporate it into the governing equation. Furthermore, an adjustment parameter is introduced to the immersed boundary scheme, which ensures the interpolated distribution functions derive the desired velocity at the boundary. Compared with the solution of a large boundary matrix and the multiple force correction that generally used in the previous studies, the present method is simpler and efficient without any iterative procedures. Those above-mentioned features make the present scheme based on the correction of the distribution function, with the enforcement of no-slip boundary condition. Simulation of flow past a fixed cylinder shows that there is no penetration of streamlines to the cylinder surface, indicating a well enforcement of the no-slip boundary condition. This scheme is further validated in the flows of a cylinder oscillating in a quiescent fluid, circular and elliptical particles settling in a channel. The results have good agreement with those data available in the literature.     

Exact solutions of problems of the three-dimensional flow of ideal viscous incompressible fluids near cylindrical surfaces

Three-dimensional flows of an incompressible fluid, the parameters of which depend on two coordinates and time, are considered. The stream surfaces of such flows are cylindrical. The equations of continuity and the Navier-Stokes equations can be transformed to relations, one of which is the equation for the stream function the other is the integral of the equations relating the pressure and the stream function, and the third is a linear equation for the projection of the velocity vector onto the axis parallel to the generatrix of the cylindrical surfaces. The problems of modelling the flows are considered on the basis of the exact solutions of the Navier-Stokes equations and Euler's equations using examples. Relations for the distribution of the flow parameters in the channel created by hyperbolical cylinders are derived for the case of unsteady inviscid flow. The streamlines of these flows are situated on the side surfaces of the hyperbolical cylinders and intercept the generatrices of the cylinders at certain indirect angles. The flow around a circular cylinder and the flow of fluid inside an elliptic cylinder are considered in the case of steady inviscid flow. The streamlines on the circular cylinder are arranged transverse to the cylinder (the projection of the velocity vector onto the coordinate axis, parallel to the generatrix of the cylinder, is equal to zero). Far from the cylinder the streamlines are also situated on a cylindrical surfaces, but not transverse to the cylinder, making certain indirect angles with the generatrix. Viscous three-dimensional flows, possessing a certain symmetry, are considered. In the case of radial symmetry the streamlines are helical lines. The non-planar Couette flow between parallel moving planes is characterized by the fact that the velocity vectors, being situated in the same plane, are collinear, while the velocity vectors in parallel planes are not collinear. Relations for viscous steady three-dimensional flows, using well-known relations, obtained for the stream function of two-dimensional flows, are given.     

Lattice Boltzmann method for slip flow heat transfer in circular microtubes: Extended Graetz problem

Slip flow heat transfer in circular microtubes is of fundamental interest and practical importance. However, to the best knowledge of the present author, there is no open publication of developing simple and efficient lattice Boltzmann (LB) models on such topic. To bridge the gap, in this paper a simple LB model, which is based on our recent work [S. Chen, J. Tölke, M. Krafczyk, Simulation of buoyancy-driven flows in a vertical cylinder using a simple lattice Boltzmann model, Phys. Rev. E 79 (2009) 016704], is designed. In addition, the recently developed Langmuir slip model [S. Chen, Z.W. Tian, Simulation of thermal micro-flow using lattice Boltzmann method with Langmuir slip model, Int. J. Heat Fluid Flow 31 (2010) 227-235], which possesses a clear physical picture and keeps the Reynolds analogy, is extended to capture velocity slip as well as temperature jump in microtubes. The feasibility and capability of the present model are validated by the extended Graetz problem, which is a benchmark prototype for forced convection heat transfer in circular microtubes.     

A simple and efficient implicit direct forcing immersed boundary model for simulations of complex flow

This paper presents an implementation of an implicit immersed boundary (IB) method in a flow solver based on the fractional step method and the finite volume method for complex flows involving moving boundaries and complex geometries. In this implementation, a body force caused by the immersed body is first introduced into the N-S equation to model the effect of immersed boundary. However, the body force is not pre-calculated, but implicitly determined in such a way that the velocity at the immersed boundary interpolated from the corrected velocity field accurately satisfies the no-slip and no-penetration conditions. Then, the large-eddy simulation is applied in the solver, where the subgrid-scale stress is determined by the Smagorinsky–Lilly model. Near the immersed boundaries, the subgrid-scale stress is determined by a wall model where the wall shear stress is directly calculated from the Lagrangian force(which represents the action of fluid on solid) on the immersed boundary. Such treatment makes the simulations of high Reynolds number turbulent flows feasible with the IB method. The accuracy and capability of the present method are demonstrated by simulations of a variety of both two- and three-dimensional simulations, including laminar flow past static and oscillating cylinders, rotating hydrofoil and turbulent flow around a three-dimensional circular cylinder and a sphere. It shows that the present implementation provides an easy-to-use, inexpensive and accurate technique for computational fluid dynamics in industrially relevant problems.     

Nonsimilar aiding mixed convection along a moving cylinder

The work of Mahmood and Merkin (ZAMP 39:186–203, 1988) concerns the mixed convection flow along a stationary cylinder in a constant free stream. In the present note, we extend the above work to general situations involving a moving cylinder.     

Sensitivity Analysis of Promotion Opportunities in Graded Organizations

This paper extends earlier work on manpower mobility in hierarchical organizations and is concerned especially with the effects of changes in hiring and separation on opportunities for internal advancement. We make use of a fractional flow model of personnel to highlight the links between personnel flows and vacancy flows, and then derive formulae that can be used to simulate the impact of changes in grade-size targets, hiring policy and attrition rates on promotion opportunities for staff. The model is then illustrated by application to data on faculty staffing in a large university.     

Nonsimilar aiding mixed convection along a moving cylinder

The work of Mahmood and Merkin (ZAMP 39:186–203, 1988) concerns the mixed convection flow along a stationary cylinder in a constant free stream. In the present note, we extend the above work to general situations involving a moving cylinder.     

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     

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.     

Dissociation effect on the hypersonic flow past a circular cylinder

The effects of dissociation of air on hypersonic flow past a circular cylinder at zero angle of incidence are considered under the assumptions that the shock wave is in the shape of a circular cylinder, the density ratio across the shock is constant, the flow behind the shock is at constant density and dissociation occurs only behind the shock wave. In the present paper, the velocity, pressure and drag coefficients, vorticity, shock detachment distance, stagnation point velocity gradient and sonic points on the shock and the surface have been obtained in the presence of dissociation. The results have been compared with the corresponding results obtained in the case when dissociation dose not occur and the corresponding results in the case of the sphere in the presence of dissociation.     

Kinetic model of the Boltzmann equation with limiting gas flow regimes at low Knudsen numbers

A new model of the Boltzmann kinetic equation is constructed that describes both slow nonisothermal and Navier-Stokes continuum gas flows. The model is used to compute the slow nonisothermal flow past a circular cylinder. It is shown that the force exerted by the gas on the cylinder is affected by thermal stresses.     

Wakes and vortex streets behind a localized force: Numerical simulations

Two-dimensional wakes behind a body force acting inside a small circular area are investigated using direct numerical simulations. The flows induced by a single force are asymptotically related to the far-field wakes of a bluff body but belong to a wider class of flows because the problem contains an extra control parameter. Stable (almost parallel) wakes as well as regular vortex streets similar to those observed in the wakes of bluff bodies were obtained in our simulations. The behavior of the frequency of vortex shedding in the unstable wakes is described in detail for different values of the main control parameters of the flow, namely the amplitude of the forcing, the velocity of the stream, the size of the forcing area and the kinematic viscosity of fluid. Two different regimes of vortex shedding were observed in the space of these control parameters. Transition between the regimes is characterized by a rapid drop in frequency. The relation between the flows generated by a force and those past a circular cylinder is identified.