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A well-developed numerical scheme is used to simulate the steady current over a circular cylinder in proximity with a rigid plane at low Reynolds numbers. The numerical results, including the hydrodynamic forces acting on the cylinder and the flow fields, are obtained and discussed. The reduction of the vorticity generated at the cylinder surface of the gap side is attributed to the decrease of the amplitude of harmonic force components and eventually causes the complete suppression of the vortex shedding process. Particularly, a distinct flow scenario characterized by the agglomeration of two adjacent vortices takes place in the wake when the cylinder is positioned close to the free-slip wall just before the complete cessation of the vortex shedding. This finding might be served to explain the disappearance of regularly arranged vortices observed when the cylinder was towed above the stationary wall in the experiment. In contrast, the flow with a no-slip plane is also considered. The effective gap between the cylinder and the plane is reduced due to the presence of the boundary layer near the plane, and earlier cessation of vortex shedding is observed in comparison with that in the situations of free-slip plane.

A series of experiments was carried out to study the flow behaviour behind a rotationally oscillating cylinder at a low Reynolds number (Re=300) placed in a recirculation water channel. A stepper motor was used to rotate the cylinder clockwise- and- counterclockwise about its longitudinal axis at selected frequencies. The particle image velocimetry (PIV) technique was used to capture the flow field behind a rotationally oscillating cylinder. Instantaneous and timeaveraged flow fields such as the vorticity contours, streamline topologies and velocity distributions were analyzed. The effects of four rotation angle and frequency ratios F r (F r=f n/f v, the ratio of the forcing frequency f n to the natural vortex shedding frequency f v) on the wake in the lee of a rotationally oscillating cylinder were also examined. The significant wake modification was observed when the cylinder undergoes clockwise-and-counterclockwise motion with amplitude of π, especially in the range of 0.6≤F r≤1.0.

Theoretical characteristics of the flow in scrolls of hydraulic turbines whose cross-sectional dimensions and shapes are determined using the equations of the potential flow induced by a vortex sink cylinder of finite length located on an impermeable cylinder of infinite length in an ideal fluid are calculated. The theoretical distributions of the components of the velocity and the directions of its horizontal and vertical projections (vertical turbine) are determined and plotted. They are favorable for hydraulic turbines and are in good agreement with the values set at the stator inlet, which confirms the effectiveness of the new approach to studying potential flows whose velocity potential cannot be expressed analytically.

A first attempt is made for identifying the wake characteristics of circular cylinder confined by a wavy wall at laminar flow regime. Numerical study of flow characteristics past circular cylinder with wavy-wall confinement perpendicular to cylinder axis has been carried out in the range of Reynolds number 20–100. The finite volume-based CFD solver Ansys Fluent (Version 15.0) is used for computations. The results are presented in the form of streamline plots, mean drag co-efficient, flow separation angle and recirculation length. Wavy-wall confinement leads to highly significant changes in the cylinder wake such as the evolution of strong x-plane vortices, enhanced fluid mixing, wake suppression near the crest region and vortex stretching near the trough region on the downstream of the cylinder has been observed. Flow separation angle varies significantly along the axis of the cylinder. Increased wall shear stress on rear surface of the cylinder has also been observed. The part of vorticity magnitude as compared to strain rate has been distinguished and identified using vortex identification methods such as Q-criterion and Lambda-2 criterion.

A numerical analysis was carried out to examine the effect of pulsating flows around a semi-circular (heated) cylinder placed in a horizontal confined empty channel. The heat transfer induced as an outcome of non-zero mean sinusoidally varying flow past a semi-circular cylinder was investigated. For this purpose, computations are carried out for the following range of parameters: wall confinement (or blockage ratio, β) = 25%; Prandtl number (Pr) = 7 (water as a working fluid); Reynolds number (Re) = 10–100; Strouhal number (St) = 0–2; and amplitude of oscillation (A) = 0–0.6. The current situation is numerically investigated by solving the continuity, momentum and energy equations using the finite volume method—based solver Ansys Fluent. Results in terms of total drag coefficient and Nusselt number have been presented and discussed. The nature of flow for each considered case is reported. The flow (streamlines) and thermal (isothermal contours) patterns have been analyzed. The maximum augmentations of about 22 and 10% were obtained in drag coefficient and Nusselt number, respectively. It is noteworthy that amongst all the cases studied, an appreciable amount of augmentation is observed when St = 1 and A = 0.6 (with respect to the case of non-pulsating flow i.e. St = 0).

The flow past an in-line forced oscillating square cylinder at Reynolds number of 200 is studied using an in-house code, named constrained interpolation profile method developed in Zhejiang University (CIP-ZJU). The model is established in the Cartesian coordinate system using the CIP method to discretise the Navier-Stokes equations. The fluid-structure interaction is treated as a multiphase flow of the liquid and solid phases to be solved simultaneously. An immersed boundary method is used to deal with the boundary of the solid body. The CFD model is first applied to the computation of the flow past a fixed square cylinder for its validation. Computations are then performed for the flow past a square cylinder oscillating in the streamwise direction. Considerable attention is paid to the symmetric and anti-symmetric modes of the vortex shedding in the oscillating square cylinder wake. Various oscillation amplitudes and frequencies are simulated and their effects on the vortex shedding modes are analyzed via Lissajous patterns of the unsteady lift coefficient. The relationship among the lift coefficient, the drag coefficient and the lock-on range is also investigated quantitatively.

A numerical investigation was performed on the reduction of the fluid forces acting on the square cylinder in the laminar flow regime with a perforated plate. The effects of geometric parameters such as the distance between the square cylinder and the perforated plate on the wake of the square cylinder were discussed. Furthermore, the flow characteristics such as the drag coefficient, lift coefficient, Strouhal number and flow pattern were obtained. It can be concluded that the drag force of the square cylinder reduces to some extent due to the addition of the perforated plate. The flow structure varies when the perforated plate is located behind the square cylinder. Moreover, the recirculation zone augments with the increase of L/D, and the vortex trace on the upper and lower surface of the square cylinder moves gradually backwards until a stable recirculation zone formed between the square cylinder and the perforated plate.

The study focuses on the effect of gap spacing (g) ranging g = 1–7, Reynolds numbers (Re) ranging Re = 80–200 and the size of the control plate (w) varied from 0.1d to 1d (where d is the size of the main cylinder) on the flow around a square cylinder with an upstream control plate. Two-dimensional multiple-relaxation-time lattice Boltzmann method is used to find the optimum condition, where the maximum reduction in drag force and suppression of vortex shedding occurs. It is observed that the drag is reduced significantly and the fluctuating lift is also suppressed. The detailed wake structure mechanism within gap spacing and near wake vortex structures around and behind the main square cylinder in the presence of the control plate are studied and compared with a plain square cylinder. In this study, the optimum conditions for maximum drag reduction in terms of control plate width, gap spacings and Reynolds numbers are found. The single bluff body, shear layer reattachment, critical flow, two-row single bluff body, fully developed two-row vortex shedding and quasi-steady-flow patterns are found. The time-trace analysis of drag and lift coefficients, power spectra analysis of lift coefficients, variation in force statistics and inclination angles are discussed in detail for all observed flow patterns. The maximum reductions on the drag force are 99.82, 99.8, 99.8, 99.9, 99.98, 100.4, 100.1, 100.05 and 100.1% for Re = 80, 100, 120, 140, 150, 160, 180, 190 and 200, respectively.

The kinematic characteristics are considered of potential flow caused by an inflow cylinder of finite length, situated on an infinite impermeable cylinder filled with an ideal liquid. An algorithm is proposed for calculating the velocities along verticals that offer good determination accuracy. It is determined that flow characteristics confirm the correctness of analytical studies of potential flow created by an inflow cylinder of finite length, carried out by the author using his new approach for the investigation of potential flows having no analytical expression of the velocity-potential function. It is determined that the flow under consideration may be used to analyze hydraulic turbine spiral chambers.

Potential flow is considered in a cylindrical coordinate system (r, z, θ), caused by a vortex filament located on the z-axis and a finite length vortex inflow-cylinder of uniform intensity distribution located on an infinite impermeable cylinder, the centerline of which coincides with the z axis, in infinite space filled with an ideal liquid. Equipotential surface (line) equations and flow surfaces (lines) are given, along with relations for determining velocity components. It is shown that the flow lines caused by a vortex inflow-cylinder lie on the flow surfaces created generated by the inflow-cylinder. Equations are given that allow lines of total flow to be projected onto planes normal to the z axis using the finite difference method. It is noted that the shape of the flow lines on the respective flow surfaces depend only on the ratio of the vortex filament intensity to inflow-cylinder flow rate.

Three-stranded rope is widely used in fishing gear and mooring system. Results of numerical simulation are presented for flow around a three-stranded rope in uniform flow. The simulation was carried out to study the hydrodynamic characteristics of pressure and velocity fields of steady incompressible laminar and turbulent wakes behind a three-stranded rope. A three-cylinder configuration and single circular cylinder configuration are used to model the three-stranded rope in the two-dimensional simulation. The governing equations, Navier-Stokes equations, are solved by using two-dimensional finite volume method. The turbulence flow is simulated using Standard κ-e model and Shear-Stress Transport κ-ω (SST) model. The drag of the three-cylinder model and single cylinder model is calculated for different Reynolds numbers by using control volume analysis method. The pressure coefficient is also calculated for the turbulent model and laminar model based on the control surface method. From the comparison of the drag coefficient and the pressure of the single cylinder and three-cylinder models, it is found that the drag coefficients of the three-cylinder model are generally 1.3–1.5 times those of the single circular cylinder for different Reynolds numbers. Comparing the numerical results with water tank test data, the results of the three-cylinder model are closer to the experiment results than the single cylinder model results.

In this paper, large-eddy simulation (LES) has been performed to investigate the turbulent wake behind a wall-mounted square cylinder. The flow features a relatively high cylinder aspect ratio of 4, a Reynolds number of 12,000 (based on the free-stream velocity and cylinder side length), and a thin developing boundary layer with a thickness of only 18 % of the obstacle height. These characteristics of the flow impose challenges to LES for accurate simulation of large energetic eddies induced by the cylinder and their intense interactions with the thin developing boundary layer. The coherent flow structures around the cylinder have been studied based on the instantaneous and time-averaged resolved velocity and pressure fields. The local kinetic energy transfer between the resolved and subgrid scales and the streamwise evolution of the subgrid-scale viscosity have been investigated to provide physical insights into the subgrid-scale dynamics. The LES predictions of the flow statistics have been validated against a set of recently reported wind-tunnel experimental data.

Flow through rigid and emergent/submerged cylinder arrays are commonly found in several engineering application such as offshore structures, transmission lines, chimneys, array of silos and field array of trees. Various hydrodynamic phenomena may be occurring in the interaction between a flowing fluid and these structures. In this manuscript we focus on the study of flow structures in a channel partially obstructed by an array of equi-spaced, vertical, rigid, emergent, circular steel cylinders. Experimental results show that the presence of the cylinders array strongly affects the flow velocity distribution, forming a transversal sharp transition region at the interface between the obstructed and the unobstructed domains. At the interface, for the current and previous studies, it was observed that the flow distribution always resembles a boundary layer feature. This similarity in feature of the flow distribution as a boundary layer has led to adapting the universal law of the wall to describe the transversal profile of the mean flow velocity, considering, by analogy, the interface separating both domains as a virtual wall. The specific objectives addressed in this study is to propose and validate a new modified log-law predicting the representative transversal profile of the mean flow velocity at the interface between the obstructed and the unobstructed domains. The proposed analytical model is validated by a series of experiments carried out on a very large rectangular channel in the Department of Civil, Environmental, Building Engineering and Chemistry of the Technical University of Bari—Italy. The three-dimensional flow velocity components were measured using a 3D Acoustic Doppler Velocimeter ADV. As a result, it is observed that the measured and the predicted, applying the proposed modified log-law, mean flow velocity data have a perfect matching between them. Moreover, in the second part of the paper, detailed observations on the flow turbulence structure are analyzed and discussed.

It is demonstrated that for kinematically similar potential flows of an ideal liquid, the ratio of the velocities is inversely proportional to the ratio of the areas of the corresponding equipotential surfaces S 1/S 2 = K v , and directly proportional to the ratio of the flows. In that case when the flow rates of two flows are equal, the function of the velocity potential and the velocity of one flow can be expressed in terms of these characteristics multiplied by the dimensionless coefficient K v — the velocity correction of the other flow. Using the velocity correction K v , the flow caused by a cylinder flow of finite length, which is placed on an impervious cylinder in an infinite space filled with an ideal liquid is investigated in a cylindrical coordinate system. Analytical relationships are derived for the equipotential surfaces, and the flow and velocity surfaces; examples of the analysis are cited.

The flow past a finite circular cylinder with a height-to-diameter ratio of 1.5 and an infinite circular cylinder of the same diameter at a Reynolds number Re = 3 900 is investigated using the large eddy simulation (LES). The objective of the present study is to explore the differences of the flow mechanisms between the finite and infinite circular cylinders. It is shown that the free end of the finite circular cylinders affects the wake region significantly. The mean drag coefficient and the fluctuating lift coefficient of the finite circular cylinder are smaller than those of the infinite circular cylinder. The three-dimensional separation and the separated shear layer instability of the finite circular cylinder can obviously be observed. The existence of an arch vortex in the average flow downstream of the free end is demonstrated.

This paper studies the wall-bounded flow around a cylindrical at a high Reynolds numbers body in a determined computational domain, with simulations of the 3-D, turbulent concentric annulus flow in a straight pipe. Numerical results show that a reversing zone, appearing as a tongue zone with nested velocities higher than the surrounding area, exists behind the cylindrical body. The annulus space is a region of high velocity and low pressure. The zero velocity, of combined the velocity and the velocity, exists in the cross sections and no vortex shedding is formed behind the attaching cylinders. Among all investigated effecting factors, the diameters of the attaching and the main cylinders affect the wake feature behind the cylindrical body while the main cylinder length does not affect the distribution tendency of the flow field. The diameters of the main cylinder and the pipe affect the pressure values and the distribution tendencies on the main cylinder surface. Obviously, the increase of the pipe diameter reduces the drag coefficient of the cylindrical body and the increase of the diameter of the main cylinder increases the drag coefficient greatly. The numerical investigation of the concentric annulus flow provides foundations for further improvements of the intricate flow studies.

This paper reports on the time-dependent axisymmetric flow of a viscous, incompressible fluid along a moving circular cylinder having infinite extent. A mathematical account is given to unsteady motion, in which the governing non-dimensional equations are obtained in the presence of a velocity-slip boundary condition near the cylinder wall. In the case where the cylinder is started impulsively from rest in (initially) still air, the Bingham number is obtained by means of Laplace transform techniques with particular emphasis regarding the cylinder in motion with uniform velocity and acceleration. The effects of the momentum slip length parameter on the shear stress are determined and presented.

In this paper, two-dimensional numerical simulations of the incompressible flow around an elastically mounted rigid circular cylinder in cross-flow have been accomplished with the finite difference method. The bluff body immersed in the flow is modeled by the Immersed Boundary Methodology combined with the Virtual Physical Model. The motion of the cylinder is described by the harmonic structural model which is solved using a fourth order Runge–Kutta method. The numerical simulations were performed for Reynolds number 8,000 and 10,000 and for the reduced velocity in the range 1 ≤ V r ≤ 15. The vortex shedding process, the time evolution of the dynamic coefficients, the cylinder response and the power spectra of the lift coefficient and of the cylinder displacement were investigated. It was found a reasonable agreement with numerical results for R e = 8,000. On the other hand, for R e = 10,000, the present results as well as other numerical simulations failed when compared with the experiments in the capture of the so-called upper branch. The absence of that in LES simulations can be explained by the existence of discrepancies between the experiments and the assumptions adopted in the present methodology.

The vibrational behavior of a viscous nanoflow-conveying single-walled carbon nanotube (SWCNT) was investigated. The non-uniformity of the flow velocity distribution caused by the viscosity of fluid and the small-size effects on the flow field was considered. Euler-Bernoulli beam model was used to investigate flow-induced vibration of the nanotube, while the non-uniformity of the flow velocity and the small-size effects of the flow field were formulated through Knudsen number (K n ), as a discriminant parameter. For laminar flow in a circular nanotube, the momentum correction factor was developed as a function of K n . For K n = 0 (continuum flow), the momentum correction factor was found to be 1.33, which decreases by the increase in K n may even reach near 1 for the transition flow regime. We observed that for passage of viscous flow through a nanotube with the non-uniform flow velocity, the critical continuum flow velocity for divergence decreased considerably as opposed to those for the uniform flow velocity, while by increasing K n , the difference between the uniform and non-uniform flow models may be reduced. In the solution part, the differential transformation method (DTM) was used to solve the governing differential equations of motion.

We derive the streamfunction solution for flow in and around a viscous sphere suspended in an inviscid extensional flow with matched stress boundary conditions, which is a model for estimating the stresses on a tiny suspended organism by a nearby expanding and collapsing bubble. The boundary conditions are enforced in an easily resolvable form by expressing the surface stresses as sums of Legendre and Gegenbauer functions. The flow inside the sphere reflects a balance of exterior inertia with internal viscous forces, which together are shown to constitute the relevant flow Reynolds number. The solution is evaluated to examine the flow field inside this sphere as a potential source of damage to the organism.

Bistable flows around circular cylinders typically occur in the critical range of the Reynolds number (Re), due to the formation of a laminar separation bubble and its subsequent collapse on one side of the cylinder only. In turbulent flows, as well as on a rough cylinder at slightly higher Re, bistable flows tend to disappear. However, this paper gives experimental evidence of a new type of bistable flow, which is induced around a circular cylinder of finite length even at moderately high Re. Stiffening rings, applied along the height of a circular cylinder at a distance smaller than the diameter (d = 2/3D in the case of study), were found to be responsible for the phenomenon. This was demonstrated and then cross-checked by wind tunnel experiments on a H/D = 6.7 circular cylinder. The experiments were performed in two different wind tunnels, at WiSt (Ruhr University Bochum) and at CRIACIV (University of Florence). A numerical study of the latter experimental test case is also presented in this paper. A finite volume approach based on the iterative solution of the unsteady Reynolds-averaged Navier–Stokes equations has been used. Turbulence has been modelled using the SST model by Menter. The numerical results confirm the physical fundament of the phenomenon, which likely finds its explanation in the key role of the flow over the cylinder tip.

A discrete forcing based Cartesian grid method is presented. The non-staggered arrangement of velocity and pressure is considered. The pressure gradient in localized discrete form is added separately with the velocity making them explicitly coupled. The governing equation is time-integrated implicitly with both linearized and non-linear forms are investigated. Both linear and bi-linear reconstruction techniques are tested for extrapolation of velocity near a complex boundary. The present method is tested for vortical flow in an inclined cavity, flow past circular and inclined square cylinder. Both homogeneous and non-homogeneous Dirichlet forcing problems are tested. The parallelized version of the method is applied to 2D-to-3D transitional flow behind a single and multiple circular cylinders. The present numerical results compare well with the previously documented results.

Using ANSYS-CFX, a general purpose fluid dynamics program, the vortex-induced vibration (VIV) of a variable cross-section cylinder is simulated under uniform current with high Reynolds numbers. Large eddy simulation (LES) is conducted for studying the fluid-structure interaction. The vortex shedding in the wake, the motion trajectories of a cylinder, the variation of drag and lift forces on the cylinder are analyzed. The results show that the vortices of variable cross-section cylinder are chaotic and are varying along the cylinder. In places where cross-sections are changing significantly, the vortices are more irregular. The motion trail of the cylinder is almost the same but irregular. The drag and lift coefficients of the cylinder are varying with the changes of diameters.

An analysis of the physical processes in unsteady fl ow past a circular cylinder surrounded by a sheath with ports for bleeding of the medium has been made by a factorized fi nite-volume method on the basis of numerical solution of Navier–Stokes equations closed with the Menter sheer-stress-transfer model. It has been shown that such arrangement of a circular cylinder ensures stabilization of the wake of the cylinder, and also the reduction in its drag and cessation of the action of an alternating transverse force at Reynolds numbers higher than 105.

[EN] This paper presents a large eddy simulation of forced convection heat transfer in the flow around a surface-mounted finite-height circular cylinder. The study was carried out for a cylinder with height-to-diameter ratio of 2.5, a Reynolds number based on the cylinder diameter of 44 000 and a Prandtl number of 1. Only the surface of the cylinder is heated while the bottom wall and the inflow are kept at a lower fixed temperature. The approach flow boundary layer had a thickness of about 10% of the cylinder height. Local and averaged heat transfer coefficients are presented. The heat transfer coefficient is strongly affected by the free-end of the cylinder. As a result of the flow over the top being downwashed behind the cylinder, a vortex-shedding process does not occur in the upper part, leading to a lower value of the local heat transfer coefficient in that region. In the lower region, vortex-shedding takes place leading to higher values of the local heat transfer coefficient. The circumferentially averaged heat transfer coefficient is 20 % higher near the ground than near the top of the cylinder. The spreading and dilution of the mean temperature field in the wake of the cylinder are also discussed., The simulation was carried out using the supercomputing facilities of the Steinbuch Centre for Computing (SCC) of the Karlsruhe Institute of Technology. MGV has been partially supported by grant TRA2012-37714 of the Spanish Ministry of Economy and Competitiveness.

With the increase of petroleum and gas production in deep ocean, marine risers of circular cylinder shape are widely used in the offshore oil and gas platform. In order to research the hydrodynamic performance of marine risers, the dynamic mesh technique and User-Defined Function (UDF) are used to simulate the circular cylinder motion. The motion of a transversely oscillating circular cylinder in combination of uniform flow and oscillating flow is simulated. The uniform flow and oscillating flow both are in x direction. SIMPLE algorithm is used to solve the Navier-Stokes equations. The User-Defined Function is used to control the cylinder transverse vibration and the inlet flow. The lift and drag coefficient changing with time and the map of vorticity isolines at different phase angle are obtained. Force time histories are shown for uniform flow at Reynolds number (Re) of 200 and for the combination of uniform and oscillating flows. With the increase of amplitude of oscillating flow in combined flow, the change of lift amplitude is not sensitive to the the change of cylinder oscillating frequency. Lift amplitude increases with the increase of oscillating flow amplitude in the combined flow, but there is no definite periodicity of the lift coefficient. The drag and inertia force coefficients change when the maximum velocity of the oscillating flow increases in the combined flow. The vortex shedding near the circular cylinder shows different characteristics.

Unsteady nonisothermal traverse flow of an impurity-containing viscous fluid past a rotating circular cylinder has been investigated with account of the mechanical and thermal interaction of the carrier and dispersed phases. The processes occurring have been described mathematically with the Lagrange approach. The influence of the impurity on the flow pattern has been analyzed; the dependences of the drag coefficient, the lifting-force amplitude, and the Nusselt number of the cylinder on the relative rotational velocity of its surface have been determined.

Two-dimensional Stokes flow around a circular cylinder in a microchannel is investigated based on Stokes approximation. The cylinder with arbitrary radius translates along the centerline of the channel, and plane Poiseuille flow exists upstream and downstream from the cylinder. The translating velocity of the cylinder and the magnitude of the Poiseuille flow are arbitrary. The Stokes flow is examined analytically using Papkovich-Fadle eigenfunction expansion and least square method. The stream function and the pressure distribution of the flow field are obtained and shown for some typical cases. The force exerted on the cylinder and the pressure drop due to the cylinder are calculated as functions of the radius of the cylinder. For a small radius of the cylinder, the results of the force are coincident with previous asymptotic expressions for the force. For a given average velocity of the Poiseuille flow in the channel, translational drift velocity of the cylinder is determined as a function of blockage factor. The drift velocity is slightly lower than the mean velocity of the Poiseuille flow component projected by the cylinder. The induced pressure drop due to the drifting cylinder in the Poiseuille flow is quite small. When the cylinder translates in the stagnant channel, a series of Moffatt eddies appears far from the cylinder in the channel, as expected. The size of the primary eddy increases with the radius of the cylinder.

Two-dimensional numerical simulation is performed to understand the effect of flow pulsation on the flow and heat transfer from a heated square cylinder at Re = 100. Numerical calculations are carried out by using a finite volume method based on the pressure-implicit with splitting of operators algorithm in a collocated grid. The effects of flow pulsation amplitude (0.2 ≤ A ≤ 0.8) and frequency (0 ≤ f p ≤ 20 Hz) on the detailed kinematics of flow (streamlines, vorticity patterns), the macroscopic parameters (drag coefficient, vortex shedding frequency) and heat transfer enhancement are presented in detail. The Strouhal number of vortices shedding, drag coefficient for non-pulsating flow are compared with the previously published data, and good agreement is found. The lock-on phenomenon is observed for a square cylinder in the present flow pulsation. When the pulsating frequency is within the lock-on regime, time averaged drag coefficient and heat transfer from the square cylinder is substantially augmented, and when the pulsating frequency in about the natural vortex shedding frequency, the heat transfer is also substantially enhanced. In addition, the influence of the pulsating amplitude on the time averaged drag coefficient, heat transfer enhancement and lock-on occurrence is discussed in detail.

The characteristics of a uniform-shear flow over a circular cylinder are investigated numerically by using the alternative-direction implicit (ADI) algorithm and a fast Fourier transform (FFT) one in the exponential-polar coordinates for Re=150 and 0⩽K ⩽ 0.46. The diagram of lift-drag phase, implying the detail information about the fluctuations of drag and lift as well as the flow patterns in the wake and fluctuating pressure on the cylinder surface, is used to describe the effects of the shear rate on the flow. Results show that the upper (or lower) closed curve of a phase diagram corresponds to the first (or second) half shedding cycle. The lift-drag phase diagram will move down-left with the increase of shear rate K such that the lift is exerted from the upper side to the lower side, and the drag on the first half shedding cycle is smaller than that on the second half.

Fixed and forced moving circular cylinders in turbulent flows are studied by using the Large Eddy Simulation (LES) and two-equation based Detached Eddy Simulation (DES) turbulence models. The Cartesian cut cell approach is adopted to track the body surface across a stationary background grid covering the whole computational domain. A cell-centered finite volume method of second-order accuracy in both time and space is developed to solve the flow field in fluid cells, which is also modified accordingly in cut cells and merged cells. In order to compare different turbulence models, the current flow past a fixed circular cylinder at a moderate Reynolds number, Re = 3 900, is tested first. The model is also applied to the simulation of a forced oscillating circular cylinder in the turbulent flow, and the influences of different oscillation amplitudes, frequencies and free stream velocities are discussed. The numerical results indicate that the present numerical model based on the Cartesian cut cell approach is capable of solving the turbulent flow around a body undergoing motions, which is a foundation for the possible future study on wake induced oscillation and vortex induced vibration.

Direct Numerical Simulation of a linearly accelerating channel flow starting from an initially statistically steady turbulent flow has been performed. It is shown that the response of the accelerating flow is fundamentally the same as that of the step-change transient flow described in He and Seddighi (J Fluid Mech 715:60–102, 2013). The flow structure again behaves like a boundary layer bypass transition undergoing three distinct phases, namely, (i) initially (pre-transition), the flow is laminar-like and the pre-existing turbulent structures are modulated resulting in elongated streaks leading to a strong and continuous increase in the streamwise fluctuating velocity but little changes in the other two components; (ii) it then undergoes transition when isolated turbulent spots are generated which spread and merge with each other, and (iii) they eventually cover the entire surface of the wall when the flow is fully turbulent. The similarity between the turbulence responses in the two flows is significant noting the contrasting features of the two types of mean flow unsteadiness: in the step-change flow, a sharp boundary layer is resulted in nearly instantly on the wall which closely resembles the spatially developing boundary layer, whereas the linear flow acceleration causes a continuing change of velocity gradient adjacent to the wall which propagates into the flow field with time, resulting in a gradually-developing boundary layer. There are, however, quantitative differences in the detailed behavior of the two flows and especially the transition is much delayed in the accelerating flow. It is also shown that the late pre-transition and early transition stages in both flows are characterised by significantly increased inwards sweep events in the wall region and ejection events in the outer layer. The flatness of the wall-normal velocity increases markedly near the wall around the time of onset of transition as a consequence of the huge intermittency of the velocity fluctuations. That is, there are long periods of quiescent flow coupled with occasional turbulent bursts.

In order to investigate the scale effect of turbulent flow around a circular cylinder, two similarity numbers (criteria) based on turbulent kinetic and dissipation rates associated with the fluctuation characteristics of turbulence wake are deduced by analyzing the Reynolds averaged Navier-Stokes equations (RANS). The RNG k-ɛ models and finite volume method are used to solve the governing equations and the second-order implicit time and upwind space discretization algorithms are used to discrete the governing equations. A numerical computation of flow parameters around a two-dimensional circular cylinder with Reynolds numbers ranging from 102 to 107 is accomplished and the result indicates that the fluctuation of turbulence flow along the center line in the wake of circular cylinder can never be changed with increasing Reynolds numbers when Re ⩾ 3 × 106. This conclusion is useful for controlling the scale of numerical calculations and for applying model test data to engineering practice.

The flow over a circular cylinder at Reynolds number 2 × 104 was predicted numerically using the technique of large-eddy simulation (LES). Both incompressible and compressible flow formulations were used. The present results obtained at a low-Mach number (M = 0.2) revealed significant inaccuracies like spurious oscillations of the compressible flow solution. A detailed investigation of such phenomena was carried out. It was found that application of blended central-difference or linear-upwind schemes could damp artificial waves significantly. However, this type of schemes has a too dissipative nature compared to pure central-differences. The incompressible flow results were found to be consistent with the existing numerical studies as well as with the experimental data. Basic flow features and flow mechanics were found to be in good agreement with existing experimental data and consistent with previously obtained LES. Special emphasis was put on the spectral analysis. Here, the classical Fourier transform as well as the continuous wavelet transform were applied. Based on the latter, the separated shear-layer instability was precisely clarified. It was found that the Reynolds number dependency between vortex shedding and shear-layer instabilities had a power law relation with n = 0.5.

We show existence, uniqueness and spatial asymptotic behavior of a two-dimensional time-periodic flow around a cylinder that moves orthogonal to its axis, with a time-periodic velocity, v. The result is proved if the size of the data is sufficiently small, and the average of v over a period is not zero.

In this paper, 2-D computational analyses were conducted for unsteady high Reynolds number flows around a smooth circular cylinder in the supercritical and upper-transition flow regimes, i.e. 8.21×104

Wind tunnel experiments were performed to study the effect of passive flow control strategies on the wake and drag of a semicircular cylinder of infinite aspect ratio. High-resolution planar particle image velocimetry was used to obtain flow statistics around the semicircular cylinder at Reynolds number $$Re\approx 3.2\times 10^4$$ based on the cylinder diameter. The control mechanisms under consideration include rigid flaps of various lengths placed at the edges of the structure and a small slot along the symmetry plane of the cylinder. Mean velocity fields reveal the distinctive effects of each passive mechanism on the flow, such as velocity recovery, size of the recirculation bubble and location of the reattachment point. The distributions of turbulence kinetic energy and kinematic shear stress show the modulation of each passive control mechanism on the wake, including the onset and location of the maximum turbulence levels. Instantaneous and mean fields of swirling strength further highlight the role of the passive mechanisms in the vortex dynamics. Drag coefficient for the various cases was estimated indirectly from the flow measurements using a momentum balance. This approach shows that long flaps and slot were able to reduce drag with respect to the base case. The rigid flaps with length coincident with the diameter of the cylinder offered the best performance with drag reduction of $$\sim$$ 25 $$\%$$ .

The principle of velocity decomposition is used to combine field discretization and boundary-element techniques to solve for steady, viscous, external flows around bodies. The decomposition modifies the Navier---Stokes boundary-value problem and produces a Laplace problem for a viscous potential, and a new Navier---Stokes sub-problem that can be solved on the portion of the domain where the total velocity has rotation. The key development in the decomposition is the formulation for the boundary condition on the viscous potential that couples the two components of velocity. An iterative numerical scheme is described to solve the decomposed problem. Results are shown for the steady laminar flow over a sectional airfoil, a circular cylinder with separation, and the turbulent flow around a slender body-of-revolution. The results show the viscous potential is obtainable even for massively separated flows, and the field discretization must only encompass the vortical region of the total velocity.

The flow around a horizontal square cylinder with uniform suction or injection at the front and rear sides is considered in the present paper. The problem is investigated numerically with a finite volume method using the SIMPLE algorithm. This flow has been investigated in the past for Reynolds numbers greater than 70. In the present work, the investigation is extended to very low Reynolds numbers (up to 0.001, Stokes flow) including eight different cases concerning suction–injection at the two sides. It is found that the drag coefficient takes negative and zero values in many cases and varies linearly at low Re numbers. In all eight cases, the vortices around the cylinder have been calculated. It is found that at low Re numbers, some vortices are symmetrical both about the horizontal and vertical cylinder axes.

This work aims to investigate experimentally the transition of the aerodynamic forces on a cantilevered circular cylinder immersed in a thin boundary layer whose thickness is comparable to the cylinder diameter d. The aspect ratio H/d of the cylinder is 5, where H is the cylinder height. The Reynolds number Re, based on the freestream velocity (U ∞ ) and d, is varied from 0.68 × 105 to 6.12 × 105, covering the subcritical, critical and supercritical regimes. It has been found that the flow transition is non-uniform along the cylinder span, taking place at a smaller Re near the cylinder free end than near the base. Furthermore, the sectional drag coefficient of the cantilevered cylinder is smaller relative to that of a two-dimensional cylinder in the subcritical regime, but larger than the later in the supercritical regime. The sectional lift coefficient is not zero in the critical regime, with its maximum near the free end reaching almost four times of that near the base.

A compact difference scheme is developed for the streamfunction-velocity formulation of the steady incompressible Navier---Stokes equations in polar coordinates, which is of second-order accuracy and carries streamfunction and its first derivatives (velocities) as the unknown variables. Numerical examples, including the biharmonic problem with an analytic solution in the unit circular region, the flow past an impulsively started circular cylinder, the driven polar cavity flow and the wall-driven semi-circular cavity flow problems, are solved by the present method. Compared with the existing values by different available numerical methods and experiments in the literature, numerical results demonstrate the accuracy and efficiency of the currently proposed scheme.

Conjugate heat transfer around a circular cylinder with heat source was numerically investigated. Both the forced convection of water and conduction of carbon-steel were involved in the present simulation. A finite element formulation based on SIMPLE type algorithm was adopted for solving the incompressible Navier-Stokes equations coupled with energy equation. A conduction heat transfer problem inside the cylinder was trivially coupled with forced convection around the cylinder by using the Galerkin formulation of energy equation. The proposed algorithm was verified by solving the benchmark problem of conjugate heat transfer inside a cavity having a centered body. The effect of the Reynolds number on the temperature distribution on the cylinder surface and the maximum temperature inside the cylinder was examined. It was shown that the maximum temperature decreased as Reynolds number increased and that the position of the maximum temperature moved from the center to the rear part of the cylinder till Re = 20 and then moved back toward the center beyond Re = 20 since the reverse flow around the rear part of the cylinder became stronger as the Reynolds number further increased. Lastly, the maximum temperature of the cylinder with rotation was higher than that of the fixed one and the position of the maximum temperature inside the cylinder depended on the position and the strength of the dead zone.

The mixed convection boundary layer of a viscoelastic fluid past a circular cylinder with constant heat flux is discussed. The boundary layer equations are an order higher than those for the Newtonian (viscous) fluid and the adherence boundary conditions are insufficient to determine the solution of these equations completely. The governing non-similar partial differential equations are transformed into dimensionless forms and then solved numerically using the Keller-box method by augmenting an extra boundary condition at infinity. Numerical results obtained in the form of velocity distributions and temperature profiles are presented for a range of values of the dimensionless viscoelastic fluid parameter. It is found that for some values of the viscoelastic parameter and some negative values of the mixed convection parameter (opposing flow) the momentum boundary layer separates from the cylinder. Heating the cylinder delays separation and can, if the cylinder is warm enough, suppress the separation completely. Similar to the case of a Newtonian fluid, cooling the cylinder brings the separation point nearer to the lower stagnation point.

In this paper, we focus on the two-dimensional subsonic flow problem around an infinite long ramp. The flow is assumed to be steady, isentropic and irrotational, namely, the movement of the flow is described by a second elliptic equation. By the use of a separation variable method, Strum-Liouville theorem and scaling technique, we show that a nontrivial subsonic flow around the infinite long ramp does not exist under some certain assumptions on the potential flow with a low Mach number.

This paper presents the distribution of solute undergoing first order chemical reaction in axi-symmetric laminar boundary layer flow towards a stretching cylinder embedded in porous medium. Similarity transformations are used to convert the partial differential equations corresponding to the momentum and concentration equations into highly non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that velocity decreases with increasing permeability parameter. The skin friction as well as the mass transfer rate at the surface is larger for a cylinder compared to a flat plate.

Two-dimensional, steady, incompressible Navier-Stokes and energy equations are expressed in the stream function/vorticity formula- tion and solved numerically by finite difference method to study effects of buoyancy on fluid flow and heat transfer from a horizontal circular cylinder. The cylinder is exposed to approaching flow stream, for parallel (parallel flow) and opposing (contra flow) directions to the buoyant force. Two different thermal boundary conditions were considered at the cylinder surface: constant temperature (CT) and constant heat flux (CHF). The results elucidating the dependence of the flow and heat transfer characteristics on the Richardson number 02 Ri ≤≤ , Prandtl number 0 100 Pr ≤≤ and Reynolds number 0 40 Re ≤ ≤ are presented. Overall, for parallel flow regime, an increase in the Ri led to a raise in both Nusselt number and drag coefficient. However, for contra flow regime, these trends were reversed. For both regimes, the aforementioned behaviors were more pronounced for CT boundary condition than that for the CHF boundary con- dition.

The behavior of vortex-induced vibration of a two-degree-of-freedom cylinder near a deformable wall in steady flow is investigated experimentally. The typical phenomenon of the two-degree-of-freedom cylinder’s VIV is discussed. The influences of initial gap between the cylinder and the wall on the dynamic responses of the cylinder are analyzed. The comparison is made about dynamic responses of the cylinder with one and two degrees of freedom. Experimental results show that the vibration of the cylinder near a deformable wall with a small value of initial gap-to-diameter ratios can generally be divided into two phases. The initial gap-to-diameter ratios have a noticeable influence on the occurrence of transverse vibration. The transverse maximum amplitude of the cylinder with two degrees of freedom is larger than that of the cylinder with one degree of freedom under the condition with the same values of other parameters. However, the vibration frequency of the cylinder for the two degrees of freedom case is smaller than that for the one degree of freedom case at the same value of Vr number.

The governing differential equations (continuity, momentum and thermal energy) describing the two-dimensional steady flow of incompressible fluids have been solved numerically for the transverse flow over a semi-circular cylinder with its base aligned parallel to the flow. Based on the limited time-dependent simulations, the flow is shown to be steady up to Reynolds number of 120. Reported herein are extensive numerical results on the detailed flow and temperature fields characterized in terms of streamlines, iso-vorticity contours, surface pressure distribution, isotherms and local Nusselt number variation on the surface of bluff body. Also, included here are the values of macroscopic parameters like drag and lift coefficients and Nusselt number over the following ranges of governing dimensionless groups: 0.01 Re ≤120; 1 ≤ Pr ≤ 500 with the maximum value of Peclet number ≤4,000. Finally, the present numerical results are correlated using simple equations thereby enabling the interpolation of the present results for the intermediate values of the Reynolds and Prandtl numbers.

Two-dimensional oscillatory oblique stagnation-point flow towards a plane wall is investigated. The problem is a generalisation of the steady oblique stagnation-point flow examined by previous workers. Far from the wall, the flow is composed of an irrotational orthogonal stagnation-point flow with a time-periodic strength, a simple shear flow of constant vorticity, and a time-periodic uniform stream. An exact solution of the Navier–Stokes equations is sought for which the flow stream function depends linearly on the coordinate parallel to the wall. The problem formulation reduces to a coupled pair of partial differential equations in time and one spatial variable. The first equation describes the oscillatory orthogonal stagnation-point flow discussed by previous workers. The second equation, which couples to the first, describes the oblique component of the flow. A description of the flow velocity field, the instantaneous streamlines, and the particle paths is sought through numerical solutions of the governing equations and via asymptotic analysis.