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Two-dimensional flow around semi-circular cylinder at zero angle of attack and at Re = 50000 during the self-oscillatory regime has been extensively studied within the URANS method with the use of different-structure grids (multiblock, structured overlapping, unstructured composite), the SST turbulence model and its versions (1993) and (2003) considering the streamline curvature influence modified within the Rodi–Leschziner–Isaev approach and numerical different-approximation methods realized in two codes (VP2/3, Fluent). Experiments have been made on flow around a semi-circular cylinder in the wind tunnel of the Lomonosov Moscow State University, Institute of Mechanics to obtain data for verification of numerical predictions. The double-mode character of a periodic time history of a drag force caused by a periodically forming and disappearing jet flap and acting upon a body is explained. With increasing compressibility at a Mach number ranging from 0 to 0.5, it is observed that periodic flow around the semi-circular cylinder is restructured, and the time history of the drag force acting upon it is described by a dependence close to a sinusoidal one. It is found that, as the Mach number is increased, pressure field distortions in the form of concentric cylindrical waves propagating from the semi-circular cylinder and the vortex street behind it grow over the infrasonic range.

Large Eddy Simulations (LES) with Smagorinsky subgrid scale model have been performed for the flow past two circular cylinders in tandem placed in the vicinity of a horizontal plane wall at very small gap ratios, namely G ∕ D = 0 . 1 , 0 . 3 and 0.5, in three-dimension (3D). The ratio of cylinder center-to-center distance to cylinder diameter, or the pitch ratio, L ∕ D , considered in the simulations is L ∕ D = 2 and 5. This work serves as an extension of Abrahamsen Prsic et al. (2015). In essence, six sets of simulations have been performed in the subcritical Reynolds number regime at R e = 1 . 31 × 1 0 4 . Our major findings can be summarized as follows. (1) At both pitch ratios, the wall proximity has a decreasing effect on the mean drag coefficient of the upstream cylinder. At L ∕ D = 2 , the mean drag coefficient of the downstream cylinder is negative since it is located within the drag inversion separation distance. (2) At L ∕ D = 2 , a squarish cavity-like flow exists between the cylinders and the flow circulates within the cavity. A long lee-wake recirculation zone is found behind the downstream cylinder at G ∕ D = 0 . 1 . However, a much smaller lee-wake recirculation zone is noticed at L ∕ D = 5 with G ∕ D = 0 . 1 . (3) At L ∕ D = 2 , the reattachment is biased to the bottom shear layer due to the deflection from the plane wall, which leads to the formation of the slanted squarish cavity-like flow. At both pitch ratios, as G ∕ D becomes smaller, stronger vortices are found between the two cylinders. Less intense vortices are observed in the near wake of the downstream cylinder due to the vortex shedding suppression of the neighboring wall.

The selection of interface boundary conditions between porous-medium and clear-fluid regions is vital for the extensive range of applications in engineering. As such, present paper reports an analytically investigating Stokes flow over Reiner–Rivlin liquid sphere embedded in a porous medium filled with micropolar fluid using Brinkman’s model and assuming uniform flow away from the obstacle. The stream function solution of Brinkman equation is obtained for the flow in porous region, while for the inner flow field the solution is obtained by expanding the stream function in a power series of S . The flow fields are determined explicitly by matching the boundary conditions at the interface of porous region and the liquid sphere. Relevant quantities such as velocity and pressure on the surface of the liquid sphere are determined and exhibited graphically. The mathematical expression of separation parameter SEP is also calculated which shows that no flow separation occurs for the considered flow configuration and also validated by its pictorial presentation. The drag coefficient experienced by a liquid sphere embedded in a porous medium is evaluated. The useful features of the Stokes flow for numerous values of parameters are analyzed and discussed. The dependence of the drag force and stream line pattern on permeability parameter( η 2 ), viscosity ratio( λ ), micropolar parameter( m ), coupling number( N ), and dimensionless parameter S is presented graphically and discussed. The analysis also aims at the explanation of velocity overshoot behavior. Some previous noted results are then also obtained from the ongoing analysis.

Supersonic flow past a wavy cylinder has been investigated numerically using scale-adaptive simulation technique. The free-stream Reynolds number and Mach number for this supersonic flow are chosen as 2 × 105 and 1.7, respectively. For the sake of comparison and discussion, a corresponding circular cylinder for the same computational parameters also has been calculated. Unlike the subsonic operating condition, drag reduction and fluctuating lift suppression of wavy cylinder in supersonic flow are less dramatic. Results indicate that wavy surface as a flow control technique is invalid for supersonic flow over a circular cylinder. This is because the existence of bow shock-wave and no large-scale vortex shedding in the flow field of circular cylinder. Further, two different flow states have been found in the near wake of wavy cylinder. One is a quasi-steady flow state behind the nodal position with converged wake, and the other is an unsteady flow state behind the saddle position with obvious vortex street. Based on the analyses of flow patterns, pressure power spectral densities, and proper orthogonal decomposition of pressure fields, some novel characteristics of wavy cylinder in supersonic flow are systematically investigated.

The flow around a twisted elliptic cylinder is numerically calculated using large eddy simulation (LES) at the Reynolds number of 2 × 104, along with a circular cylinder for comparison. The mean drag coefficient and the fluctuating lift coefficient of the twisted cylinder are 27.99% and 94.01% lower, respectively, than that of the circular cylinder. The twisted surface leads to more stable wake, longer vortex formation length, higher base pressure and three-dimensional separation. In addition, cluster-based reduced-order modelling (CROM) is performed to analyze phase-dependent variations of the wake flow and evaluate the relationship between derived characteristic flow structures and their impact on forces. It captures the oscillatory behavior of Karman vortex shedding in the wake of the circular cylinder. Meanwhile, two flow regimes, anti-phased and in-phase-dominated vortex shedding, generated by the twisted cylinder are extracted and distinguished. The two regimes prevail alternately with changing probability of occurrence along the spanwise of the twisted cylinder, which can be attributed to the different separation angles. The in-phase-dominated vortex shedding inhibits the effect of Karman vortex shedding and is subjected to a lower force compared with the anti-phased vortex shedding.

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 numerical analysis is carried out to investigate the wake flow control behind a circular cylinder with corona discharge. The electrohydrodynamic flow is utilized to suppress the boundary layer separation and modify the vortical structures of the flow past a circular cylinder. Numerical simulations consist of the interaction between the electric and flow fields. In this article, the finite volume approach is employed to simulate the flow affected by EHD actuator. The effects of applied voltage, shape of the grounded electrode, location and radius of the discharge electrodes on the swirling flow patterns and drag reduction have been studied. The Reynolds numbers are considered from 4000 to 16000. The results shown that, the modification in EHD actuator design can be used to enhance the flow control effects. The present achievements indicate that, EHD-induced flow can significantly reduce the wake flow behind a circular cylinder. Moreover, the study suggested that this actuator can be applied to practical separation suppression and drag reduction. Furthermore, the predicted numerical results are in excellent agreement with the experimental data.

The flow dynamics over a vibrissa-shaped cylinder at the sub-critical Reynolds number of 1.8 × 104 are comparatively investigated using the large eddy simulation (LES) approach, with particular emphasis on the wake structure and self-induced force. Three reference configurations with the same hydrodynamic diameters, i.e., a circular cylinder, an elliptical cylinder and a wavy cylinder, are compared with the vibrissa-shaped cylinder configuration. The results demonstrate that the fluctuation of lift force for the vibrissa-shaped cylinder is reduced by approximately 79.2% compared with that for the circular cylinder, and the predicted RMS magnitudes for the four configurations agree reasonably well with the experimental data. For the vibrissa-shaped cylinder, only one sharp peak with relatively low magnitude is observed at the characteristic frequency f D / U 0 = 0.20 , and the wake shedding does not dominate the dynamics, while the vortex structures show significantly three-dimensional features. Meanwhile, the separation line of the recirculation zone shows a remarkable wavy structure that corresponds to the trailing geometrical surface with a spanwise shift of approximately a half-period of undulation. A proper orthogonal decomposition (POD) analysis is performed to explore the three-dimensional structures in the wake behind the vibrissa-shaped cylinder. The POD modes reveal a completely three-dimensional and periodically staggered arrangement along both the spanwise and streamwise directions. The spectra of the first two time coefficients reveal that the wake shedding processes on the nodal and saddle planes are not synchronous. Finally, the phase-averaging results show sequential processes of vortex shedding in the wake behind the vibrissa-shaped cylinder, and demonstrate marked differences between this and the other cylinders. Two symmetrical vortices are attached closely to the backward side of the vibrissa-shaped cylinder, resulting in smaller fluctuations of velocity and wall pressure, which in turn contribute to reducing the vortex-induced force and suppressing its vibrations.

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.

A numerical simulation of transverse flow-induced vibrations of a rotating circular cylinder is presented. Rotation rate and direction is imposed to be proportional either to the cylinder’s position or cylinder’s velocity. A 2D Lattice Boltzmann method is used to solve the flow dynamics and the cylinder is spring-mounted and free to undergo transverse vibrations. In all cases, non-dimensional mass is 12.7, Reynolds number 100, and zero damping is considered, so the analysis is focused on the role of the rotation law and the reduced velocity. Results are presented in terms of steady-state oscillations characterization (say amplitude and frequency), fluid forces on the cylinder, and wake-pattern topology. It is shown how the imposed rotation changes the cylinder’s response significantly, fluid forces on it and the flow field in the wake. Depending on the rotation law imposed flow-induced vibrations can be increased or diminished. The former can be of interest for energy harvesting purposes; whereas the later can be useful to avoid unwanted oscillations. When rotatory law is proportional to the cylinder’s position, a galloping-type response has been found. In this case, the cylinder’s amplitude can be reasonably well predicted with a quasi-steady theoretical model. For rotation proportional to the cylinder’s velocity only vortex-induced-type responses have been found.

Nonisothermal cross flow of a viscous incompressible fluid around a porous cylinder with a square cross section is considered. Main attention is paid when an impermeable core of the cylinder is surrounded with a porous layer. The full system of Navier–Stokes and energy equations is integrated numerically by the finite-volume method. The hydrodynamic interaction between the flow and the matrix of the porous layer is described by Darcy’s law. At moderate Reynolds numbers, the influence of the permeability of the porous layer on the nature of the flow and the heat exchange between the cylinder and the flow is studied. It is shown that, with increasing permeability, heat transfer from the cylinder increases mainly on its front side. From the analysis of the data obtained, an approximate formula for the mean Nusselt number as a function of the Reynolds and Darcy numbers is derived. The results of the calculation of hydrodynamic and thermal characteristics of the cross-flow around an impermeable and a fully permeable cylinder are also presented.

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.

In the present study, flow control mechanism of single groove on a circular cylinder surface is presented experimentally using Particle image velocimetry (PIV). A square shaped groove is patterned longitudinally on the surface of the cylinder with a diameter of 50 mm. The flow characteristics are studied as a function of angular position of the groove from the forward stagnation point of the cylinder within 0° ≤ θ ≤ 150°. In the current work, instantaneous and time-averaged flow data such as vorticity, ω streamline, Ψ streamwise, u / U o and transverse, v / U o velocity components, turbulent kinetic energy, TKE and RMS of streamwise, u rms and transverse, v rms velocity components are utilized in order to present the results of quantitative analyses. Furthermore, Strouhal numbers are calculated using Karman vortex shedding frequency, f k obtained from single point spectral analysis. It is concluded that a critical angular position of the groove, θ = 80° is observed. The flow separation is controlled within 0° ≤ θ θ = 80°, the flow separation starts to occur in the upstream direction. The instability within the shear layer is also induced on grooved side of the cylinder with frequencies different than Karman vortex shedding frequency, f k .

The effect of a cylindrical bluff body on the interface characteristics of stratified two-phase, oil-water, pipe flows is experimentally investigated with high speed Particle Image Velocimetry (PIV). The motivation was to study the feasibility of flow pattern map actuation by using a transverse cylinder immersed in water in the stratified pattern, and particularly the transition from separated to dispersed flows. The cylinder has a diameter of 5 mm and is located at 6.75 mm from the bottom of the pipe in a 37 mm ID acrylic test section. Velocity profiles were obtained in the middle plane of the pipe. For reference, single phase flows were also investigated for Reynolds numbers from 1550 to 3488. It was found that the flow behind the cylinder was similar to the two dimensional cases, while the presence of the lower pipe wall diverted the vorticity layers towards the top. In two-phase flows, the Froude number (from 1.4 to 1.8) and the depth of the cylinder submergence below the interface affected the generation of waves. For high Froude numbers and low depths of submergence the counter rotating von Karman vortices generated by the cylinder interacted with the interface. In this case, the vorticity clusters from the top of the cylinder were seen to attach at the wave crests. At high depths of submergence, a jet like flow appeared between the top of the cylinder and the interface. High speed imaging revealed that the presence of the cylinder reduced to lower mixture velocities the transition from separated to dual continuous flows where drops of one phase appear into the other.

Numerical investigation of heat transfer phenomena of low Reynolds number nano-fluid flow over an isothermal cylinder is presented in this paper. Steady state governing equations (continuity, N–S and energy equations) have been solved using finite volume method. Stationary heat transfer, and flow characteristics over the cylinder have been studied for water based copper nanofluid with different solid fraction values. The effect of volume fraction of nano- particles on the fluid flow and heat transfer were investigated numerically. It was found that at a given Nusselt number, drag coefficient, re-circulation length, and pressure coefficient increase by increasing the volume fraction of nano-particles.

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 turbulent structures formed in a Taylor–Couette (TC) flow established between two concentric counter-rotating cylinders were explored numerically. The shear Reynolds number was set to Reshear = 8000 and the radius ratio was set to ri/ro = 0.5. An optimal flow corresponding to the maximal angular velocity transport between the cylinders was selected for the TC flow. The mean velocity profile reached its steepest value near the cylinders in the optimal TC flow. The streamwise velocity correlations at the outer cylinder in the gap exceeded those at the inner cylinder. The large convective transport of angular velocity in the gap generated a maximal angular velocity flux to achieve the optimal flow. The angular velocity flux generated by the momentum source exceeded that generated by the momentum sink. The vorticity dispersion was larger near the inner cylinder than near the outer cylinder, but vorticity stretching near the outer cylinder exceeded than that near the inner cylinder. The skin fricti...

Finite container sizes in experiments and computer simulations impose artificial boundaries which do not exist when they are meant to mimic ambient fluid of infinite extent. We show here that this is the case with flows past an infinite cylinder placed in an infinite ambient fluid (Stokes’ paradox). Using a highly efficient and stable numerical method that is capable of handling computational domains several orders of magnitude larger than in previous studies, we provide a criterion for the minimum necessary extent around an object in order to provide accurate velocity and pressure fields, which are prerequisites for correct calculation of secondary quantities such as drag coefficient. The careful and extensive simulations performed suggest an improved relation for the drag coefficient as a function of Reynolds number, and identify the most suitable experimental data available in the literature.

Turbulent flow in the axial direction along a cylinder representing a monofilament yarn was reproduced for a relatively wide range of radius Reynolds numbers using direct numerical simulations. In the simulation of the thinnest cylinder, the friction coefficient agreed with a previously published formula. A pair of high- and low-speed streaks was detected around even the thinnest cylinder, whereby it was confirmed that turbulence was sustained according to the analysed turbulence statistics. Even when only a single pair of streaks around the cylinder was detected, the characteristics of the turbulence structures, such as the mean streak spacing based on the viscous length scale, were the same as those in flows over a flat plate. It was found that the friction coefficient changes in a way that maintains the structural characteristics of the flow, consistent with the view that universal characteristics of turbulence structures exist.

In the present study, a traveling wave wall (TWW) was employed to manipulate the vortex shedding behind a fixed circular cylinder based on a 2-D CFD numerical simulation method at a low Reynolds number of 200. The study mainly focused on four types of TWW propagation directions combined with nine different wave velocities to eliminate vortex shedding, and the lift and drag coefficients and vortex shedding modes at different propagation directions or velocities were analyzed in detail to access the effectiveness of the TWW flow control method. The control mechanism of eliminating wake stemming from the flow around a TWW-controlled circular cylinder was revealed by the boundary vorticity flux (BVF) and relative flow fields. The results show that the type of downstream propagating TWW can effectively eliminate the alternating wake. When the ratio of the wave velocity to the oncoming velocity is 2.0, the fluctuations of the lift coefficients descended to the lowest point. The averages of the drag coefficients decreased with increasing wave velocity and descended to the lowest point when the ratio of the wave velocity to the oncoming velocity was 5.0. Owing to the capture of small-scale vortices, there was a relatively larger level of vorticity in the wave valley of the TWW cylinder. The relative flow fields showed that the vortex shedding from the cylinder was completely eliminated and that the goal of eliminating the oscillating wake and suppressing the potential vortex-induced vibration (VIV) of flow around a cylinder was achieved.

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.

The dynamics of vortical structures in flow over a circular cylinder in the vicinity of a flat plate is investigated using particle image velocimetry (PIV). The cylinder is placed above the flat plate with its axis parallel to the wall and normal to the flow direction. The Reynolds number $Re_{D}$ based on the cylinder diameter $D$ is 1072 and the gap $G$ between the cylinder and the flat plate is varied from gap-to-diameter ratio $G/D=0$ to $G/D=3.0$. The flow statistics and vortex dynamics are strongly dependent on the gap ratio $G/D$. Statistics show that as the cylinder comes close to the wall ($G/D\leqslant 2.0$), the cylinder wake becomes more and more asymmetric and a boundary layer separation is induced on the flat plate downstream of the cylinder. The wake vortex shedding frequency increases with decreasing $G/D$ until a critical gap ratio (about $G/D=0.25$) below which the vortex shedding is irregular. The deflection of the gap flow away from the wall and its following interaction with the upper shear layer may be the cause of the higher shedding frequency. The vortex dynamics is investigated based on the phase-averaged flow field and virtual dye visualization in the instantaneous PIV velocity field. It is revealed that when the cylinder is close to the wall ($G/D=2.0$), the cylinder wake vortices can periodically induce secondary spanwise vortices near the wall. As the cylinder approaches the wall ($G/D=1.0$) the secondary vortex can directly interact with the lower wake vortex, and a further approaching of the cylinder ($G/D=0.5$) can result in more complex interactions among the secondary vortex, the lower wake vortex and the upper wake vortex. The breakdown of vortices into filamentary debris during vortex interactions is clearly revealed by the coloured virtual dye visualizations. For $G/D, the lower shear layer is strongly inhibited and only the upper shear layer can shed vortices. Investigation of the vortex formation, evolution and interaction in the flow promotes the understanding of the flow physics for different gap ratios.

The present paper deals with the numerical simulation of unsteady, two-dimensional laminar fluid flow past a circular cylinder. An unstructured grid finite volume method has been used, and the commercial CFD code ANSYS Fluent was employed to perform the simulations. Effects of injection of a second dissimilar fluid from two diametrically opposite peripheral slots on the cylinder are of prime interest in the study. Two distinct injection arrangements have been investigated–a co-counter flow arrangement, in which the injected fluid is aligned with the free stream flow, and a cross flow arrangement, in which the second fluid is injected perpendicular to the free stream flow direction. A parametric variation of the velocity of the injected stream in the downstream wake region of the cylinder have been studied qualitatively by observing the velocity, vorticity, and mass fraction contours. Effects of injection on the vortex shedding have also been studied by observing the variations of the Strouhal number. The two injection arrangements affected the vortex shedding in distinctly different manners. Effect of lateral walls on the flow dynamics were also investigated. The presence of lateral walls was found to delay the onset of aperiodic wake structures and to promote better mixing in the downstream wake of the cylinder. Proper orthogonal decomposition of the vorticity field was also performed in order to identify the dominant modes and their respective enstrophy contents. Significant differences in the modal structures were observed with increase in the value of the control parameter. At lower values, large scale POD modes dominate, while at higher values, the wake comprised of small scale structures, for both the flow arrangements. A gradual dominance of the injected stream on the free stream was also observed.

Within the framework of two-dimensional Euler equations, the stability is investigated of a system consisting of an inner unfastened round cylinder, an incompressible fluid flow around this cylinder with circular streamlines, and an outer fastened cylinder (vessel). An equation is obtained for the natural frequencies with different mean flows between the cylinders. Accurate solutions of this equation are derived and an analysis of these solutions is given. An energetic investigation of the loss of stability in the system is carried out.

In this paper, complicated hydrodynamics of a horizontal circular cylinder entering water is investigated numerically for low Froude numbers. A numerical approach is used to model the solid-liquid interactions in presence of a free-surface. The governing equations for the 3D incompressible fluid flow are continuity and Navier-Stokes equations along with an equation for the free surface advection. To track the free-surface motion, the fast-fictitious-domain method is integrated into the volume-of-fluid (VOF) technique. The governing equations are solved everywhere in the computational domain including the horizontal cylinder. A rigid body motion is applied to the region occupied by the circular cylinder. The no-slip boundary condition on the solid-liquid interface is exerted implicitly via increasing the viscosity of the region occupied by the solid. To validate the numerical scheme, the results are compared with those of the experiments available in the literature. The effects of cylinder diameter, length, impact velocity, and cylinder-water density ratio on the non-dimensional depth are also investigated.

Numerical solutions are presented for fluid flow past a rotating elliptic cylinder for different non-dimensional rotational rates (0.5, 1.0 and 1.5) and various axis ratios (0.1, 0.3, 0.5, 0.7 and 1.0). The two-dimensional, incompressible Navier–Stokes equations are solved using Immersed Boundary method on a non-body conforming Cartesian grid. Reynolds number based on the perimeter of the elliptic cylinder is 100. Periodic flow after an impulsive start of the elliptic cylinder is studied. Flow patterns and variation of aerodynamic force coefficients are reported for different set of parameters and it is observed to be very different from that of rotating circular cylinder. As the cylinder rotates, the trailing edge of the cylinder aids the flow while the leading edge deters the flow. This has significant effect on the wake region and vortex shedding pattern. Complex interactions between cylinder and shed vortices result in many interesting phenomenon, such as formation of hovering vortex. Parameters affecting the formation of hovering vortex and its underlying mechanism are analyzed. Aerodynamic force coefficients and vortex shedding frequencies are presented and it is observed that force coefficients have multiple amplitudes and frequencies.

The current research work investigates numerically the turbulent flow field characteristics around three dimensional circular cylinder of finite height at Reynolds number of 43000 using Detached Eddy Simulation (DES) turbulence model. Comparison of the numerical results with the experiment data has been taken place. The results reveals that the DES turbulence model is superior for predicting the flow past the circular cylinder of finite height at this Re. The numerical results of this study show the great potential of the presented DES for investigating the complicated flow structure in this case. DES is very accurate for predicting the flow characteristics in many sophisticated cases and can reduce the computational efforts during the simulation process in comparison with Large Eddy Simulation (LES) turbulence mathematical model.

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 steady axi-symmetric laminar boundary-layer slip flow of a viscous incompressible fluid and heat transfer towards a vertical stretching cylinder in the presence of a uniform magnetic field is investigated. It is assumed that the left surface of the cylinder is heated by a hot convective flow. Using a similarity transformation, the governing system of partial differential equations is first transformed into a system of coupled non-linear ordinary differential equations. The resulting intricate non-linear boundary value problem is solved numerically by the fourth-order Runge Kutta method with shooting iteration technique. The analytical solutions are presented for a special case. The effects of various physical parameters on velocity and temperature profiles are discussed through graphs. The values of skin friction coefficient and the Nusselt number are tabulated and examined. It is found that the thermal boundary layer thickness increases with the increase of velocity slip, magnetic field, surface convection parameter and curvature parameter and decreases with Prandtl number.

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 flow around an isolated cylinder with a Boger fluid was studied experimentally by partially immersing a small vertical cylinder in a test fluid contained in an annular tank slowly rotating on a turntable. To approximate isolation, the ratio of the tank width to cylinder diameter varied from 40/1 to 300/1, and Reynolds numbers ranged from 10−5 to 0.5. Drag was measured by a custom-made mechanical/optical system and the flow field was mapped using particle image velocimetry (PIV). The experimental liquids were two Newtonian fluids and two polyisobutylene/polybutene Boger fluids, and the cylinders had various diameters. The Newtonian drag data, corrected for end and wall effects, agree with Kaplun's low-Re asymptotic formula. Elasticity increased the drag, starting at a Deborah number of 0.6, by 50% at a De of 2.5, and by more at higher Deborah numbers. PIV measurements were made around a cylinder—upstream, downstream, and transversely—and at 180° from it. The velocity measurements showed that the wake increased with De, among other findings. To relate the increased drag to fluid elasticity, normal stresses due to elasticity were found from deformation rates derived from the PIV data, but these stresses appear to be insufficient to account for the effect.

In this work, the characteristics of flow over a circular cylinder with two filaments are numerically investigated. The circular cylinder is fixed, and the filaments with the same properties are symmetrically attached to the rear surface of the cylinder. Moreover, the leading ends of the filaments are fixed, and their trailing ends are free to flap in the wake of the cylinder. To implement numerical simulations, an improved immersed boundary-lattice Boltzmann, which is efficient for moving boundary problems, is employed. By fixing the length of two filaments, their influences on the flow control of the cylinder are examined systematically through varying the filament mass ( M r ) , the filament flexibility ( w r ) , and the attachment angle between two filaments (α). Moreover, the effect of flow viscosity is also examined. Based on the numerical results established, it is found that the fluctuation of lift force together with the mean drag force can be suppressed effectively. In the meanwhile, the flow control of two filaments is independent of Reynolds number. Particularly, the filaments with relatively low flexibility and large attachment angle can achieve high performance, which is caused by the vortex interaction between the cylinder and the filaments as well as the pressure redistribution along the surface of the cylinder.

Laminar flow over a twisted cylinder is numerically simulated at a Reynolds number of 100. The flow past a smooth cylinder is calculated for comparison. Jung and Yoon (J. Fluid Mech., 759, 2014) showed the considerable suppression of force coefficients at the subcritical Reynolds number of 3000. The present results verify that the twisted shape of the cylinder can be used to reduce the force coefficients at a low Reynolds number containing the laminar flow. This suppression of the force coefficients is supported by a longer vortex formation length produced by the twisted cylinder. We investigated the characteristics of the local force coefficients for a twisted cylinder. The simple periodic oscillation of the time histories of total and local lift coefficients for the twisted cylinder exhibits the same pattern as that of a smooth cylinder. However, the time history of drag for the twisted cylinder reveals the presence of multi-frequency oscillations, resulting in harmonic behavior of the power spectra. This is confirmed by a time sequence of the instantaneous flow fields during the half-period of the time histories of force coefficients. The nature of the three-dimensional (3-D) twisted shape forms the 3-D vortical structures along the spanwise direction, which leads to the harmonic behavior of the drag time trace power spectra.

Direct numerical simulation is performed for flow past an isolated cylinder at R e = 1 , 000 . The corners of the cylinder are rounded at different radii, with the non-dimensional radius of curvature varying from R + = R / D = 0.000 (square cylinder with sharp corners) to 0.500 (circular cylinder), in which R is the corner radius and D is the cylinder diameter. Our objective is to investigate the effect of the rounded corners on the development of the separated and transitional flow past the cylinder in terms of time-averaged statistics, time-dependent behavior, turbulent statistics and three-dimensional flow patterns. Numerical results reveal that the rounding of the corners significantly reduces the time-averaged drag and the force fluctuations. The wake flow downstream of the square cylinder recovers the slowest and has the largest wake width. However, the statistical quantities do not monotonically vary with the corner radius, but exhibit drastic variations between the cases of square cylinder and partially rounded cylinders, and between the latter and the circular cylinder. The free shear layer separated from the R + = 0.125 cylinder is the most stable in which the first roll up of the wake vortex occurs furthest from the cylinder and results in the largest recirculation bubble, whose size reduces as R + further increases. The coherent and incoherent Reynolds stresses are most pronounced in the near-wake close to the reattachment point, while also being noticeable in the shear layer for the square and R + = 0.125 cylinders. The wake vortices translate in the streamwise direction with a convection velocity that is almost constant at approximately 80% of the incoming flow velocity. These vortices exhibit nearly the same trajectory for the rounded cylinders and are furthest away from the wake centerline for the square one. The flow past the square cylinder is strongly three-dimensional as indicated by the significant primary and secondary enstrophy, while it is dominated by the primary enstrophy ( ω z 2 ) for the rounded cylinders.

In this work, the flow past surface-piercing cylinders with free lower ends is studied numerically with computational fluid dynamics (CFD) at varying aspect ratios (AR = H/D) from around 1 to 19, and compared against experimental measurement across the same range. Numerical and experimental work is carried out at Re = 2900 and Fr = 0.65. The aspect ratio of the cylinder is varied by raising and lowering the cylinder into the water. The resulting flow field and loads on the cylinder as a result of changing the cylinder’s depth of submergence are investigated in terms of drag, lift and frequency content. First, the effects of changing the aspect ratio are examined. CFD simulations demonstrate a reduced drag coefficient, consistent with the experimental measurements, as compared to a fully-submerged, infinite cylinder at the same Reynolds number. A significant reduction in the drag coefficient is observed at an aspect ratio of 2. For aspect ratios 3 and below, Karman vortex shedding is completely suppressed due to the dominance of free surface effects. With increasing aspect ratio the Strouhal number is found to approach 0.2. Second, the flow regime is investigated as a function of cylinder length for a cylinder with aspect ratio of 12. Different regions of vortex shedding are observed along the length of the cylinder, as demonstrated by lift forces, Strouhal numbers and CFD flow visualizations. Strouhal numbers below 0.2 were observed for regions near the free surface. Additionally, the drag coefficient was found to decrease near the free surface. This study over a wide range of aspect ratios exhibits the effects of a free surface, free end and also the length of the cylinder on both the flow regime and loading.

The topology and evolution of three-dimensional flow past a cylinder of slenderness ratio SR=1 mounted in a wind tunnel is examined for 0.1≤Re≤325 (based on the diameter of the cylinder) where steady-state solutions have been obtained. Direct numerical simulations were computed using an in-house parallel finite element code. The three-dimensional theory of separation is used to analyze and interpret the flow phenomena. Results indicate that symmetry breaking occurs at Re=1, while the first prominent structure is a horseshoe vortex downstream from the cylinder. At Re=150, two foci are observed, indicating the formation of two tornadolike vortices downstream. Concurrently, another horseshoe vortex is formed upstream from the cylinder. For higher Reynolds numbers, the flow downstream is segmented to upper and lower parts, whereas the topology of the flow on the solid boundaries remains unaltered. Pressure distributions show that pressure, the key physical parameter in the flow, decreases everywhere except im...

A series of experiments was conducted in a re-circulating water tunnel with a uniform flow profile, in which a flexible tension-dominated cylinder was held fixed at both ends and placed perpendicular to the incoming flow direction. The circular cylinder had an aspect ratio of L / D =67 and a low mass ratio of m *=0.43. Dynamic response of the system was studied in the reduced velocity range of U *=2.9–14.5 and Reynolds numbers of Re =315–1580. The oscillations of the cylinder in the inline (IL) and crossflow (CF) directions were captured using two synchronized high speed cameras. Continuous response of the cylinder was reconstructed from limited number of measurement points based on modal expansion theorem modified using Modal Assurance Criterion (MAC). The MAC enhanced the response reconstruction by adjusting the contributions from each structural mode. A distinct advantage of implementing the MAC in this method compared with the previously used methods was reconstructing the VIV response accurately when the experimental measurement points were clustered in a small region along the length of the cylinder. Mono- and multi-frequency excitation responses as well as transition from a low mode number to a higher one were observed. Flow forces acting on the cylinder were calculated and a consistent relation between the regions where the cylinder was being excited by the flow and the counterclockwise figure-eight trajectories of oscillations was observed.

Flow around a circular cylinder is a fundamental fluid mechanics problem of practical importance. The dynamic characteristics of the pressure and velocity fields of unsteady incompressible laminar and turbulent wakes behind a circular cylinder are investigated numerically and analyzed simulation. The governing equations, written in the velocity pressure formulation are solved using 2-D finite volume method. In the present work is based on the cylinder diameter 10 2 Reynolds number for flow analysis slow and also turbulent based on the diameter of the cylindrical Reynolds number 10 5 as well as for the analysis of the flow around a cylindrical has been considered. The aim of this research is to investigate the influence of Reynolds number on flow parameters and verify the correctness of the calculations carried out by the governing equations of fluid mechanicsflow. Research on the hydraulic parameters of the flow around a cylinder help of ANSYS software. The frequencies of the drag and lift oscillations obtained theoretically agree well with the experimental results. The pressure and drag coefficients for different Reynolds numbers were also computed and compared with experimental and other numerical results. Due to faster convergence, 2-D finite volume method is found very much prospective for turbulent flow as well as laminar flow.

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.

The problem of viscous incompressible flow past a periodic array of porous cylinders (a model of flow in an aerosol filter) is solved. The approximate periodic cell model of Kuwabara is used to formulate the fluid flow problem. The Stokes flow model is then adopted to model the flow outside the cylinder and the Darcy law of drag is applied to find the filtration velocity field inside the porous cylinder. The boundary value problems for biharmonic and Laplace equations for stream functions outside and inside the porous cylinder are solved using a boundary elements method. A good agreement of numerical and analytical models is shown. The analytical formulas for the integrals in the expressions for the stream function, vorticity and Cartesian velocity components are obtained. It is shown that the use of analytical integration gives considerable advantage in computing time.

Wake and heat transfer characteristics around a heated circular cylinder were studied numerically in this paper. Heat transfer from a heated cylinder to the freestream flow was in mixed convection regime, with the free convection-bouyancy driven flow in opposite direction to the forced convection-main flow. Numerical simulations were performed for three Reynolds numbers of 100, 135 and 200, with the Richardson (Ri = Gr/Re2) numbers varied from 0 to 1. Results showed that buoyancy force significantly altered wake formation behind the heated cylinder, further resulted in increasing drag and decreasing Nusselt number.

A novel two dimensional pure-Lagrangian vortex method based on instantaneous vorticity conserved boundary conditions (IVCBC) has been applied to investigate the hydrodynamic coefficients and patterns flow around two circular cylinders in side-by-side arrangements with pitch ratios T / D =1.1–7 at a high Reynolds number Re =6×10 4 . The benchmark case of viscous flow around a circular cylinder was first carried out to validate the novel vortex method. Then simulations of the flow around two side by side circular cylinders were performed. A new scheme was proposed to distinguish the wide wake (WW) and narrow wake (NW) by judging the velocity direction of a specific point in the gap flow. The hydrodynamic coefficients and Strouhal numbers were thoroughly studied as a function of the pitch ratios. A total of five kinds of flow patterns were identified. During the investigation of biased flow, an intermediate frequency between frequencies of NW and WW was found and approached to that of a single cylinder. The results show good agreement with the previously published experimental and numerical data.

The heat transfer and flow characteristics of a rectangular channel with a small scale slit-vent circular cylinder are numerically investigated by Large Eddy Simulation (LES). The small scale circular cylinder is used as vortex generator and located in the boundary layer. The gap ratio G/D (the distance between the lower of the cylinder and the bottom of the channel G to the cylinder diameter D) varies from 0.5 to 6.0. The Reynolds number based on the bulk velocity and half height of the channel is 3745. The influence of gap ratio on cylinder wake and flow structure near the bottom of the channel is probed. Then, the effect of the cylinder wake on the flow and heat transfer features of the channel is revealed. Compared with the result of the rectangular channel without cylinder, it can be found that the interaction between the wake of cylinder and the boundary layer can significantly improve the heat transfer performance of the channel. Compared with the result of the rectangular channel with a reference cylinder whose diameter is the same as the slit-vent cylinder and without slit-vent, it can be found that the impinging jet derived from the slit-vent can further strengthen the interaction between the wake from the lower cylinder and the boundary layer when the gap ratio is less than 2.0. When the gap ratio is more than 2.0, the overall thermal performance of rectangular channel with the slit-vent cylinder is improved, and the constraint of the channel bottom on the wake of the cylinder is gradually weakened. Meantime, the disturbance caused by the wake of the slit-vent cylinder wears off, which leads the synthesis thermal coefficient η lower. The impinging jet has obvious influence on the stability of cylinder wake which related to the features of flow and heat transfer of the channel.

In the present study heat transfer and entropy generation analysis of boundary layer flow of an incompressible viscous fluid over hyperbolic stretching cylinder are taken into account. The governing nonlinear partial differential equations are normalized by using suitable transformations. The numerical results are obtained for the partial differential equations by a finite difference scheme known as Keller box method. The influence of emerging parameters namely curvature parameter and Prandtl number on velocity and temperature profiles, skin friction coefficient and the Nusselt number is presented through graphs. A comparison for the flat plate case is given and developed code is validated. It is seen that curvature parameter has dominant effect on the flow and heat transfer characteristics. The increment in the curvature of the hyperbolic stretching cylinder increases both the momentum and thermal boundary layers. Also skin friction coefficient at the surface of cylinder decreases but Nusselt number shows opposite results. Temperature distribution is decreasing by increasing Prandtl number. Moreover, the effects of different physical parameters on entropy generation number and Bejan number are shown graphically.

In order to offer a detailed explanation for heat transfer enhancement caused by the instability, a computational model for offset cylinder arrays was established by using a compound grid system. The fully implicit forms of continuous equation, unsteady Navier–Stokes equations and energy equation were finite-differenced. The numerical results demonstrate that cylinder row pitch plays an important role on the flow effects, which enhance or deteriorate the heat transfer on cylinder surfaces. Among these flow effects, the acceleration effect and the instability effect are the main factors for enhancing the downstream cylinders. Moreover, heat transfer enhancement caused by the flow instability is an effective way to reach the aim of reducing flow resistance and promoting heat transfer.

This research presents a computational fluid dynamics study for simulating a curved cylinder in ocean currents. A rigid curved cylindrical geometry with two bending directions was modelled in uniform and logarithmic flow profiles at a maximum Reynolds number of 1.5 × 105; the Realizable k–epsilon formulation is used as the turbulence closure model. An analysis of force coefficients and vortex structure are presented. The results show that a curved cylindrical structure will have different hydrodynamic behaviour depending on the oncoming flow direction. Bending the cylinder in a direction which is opposite to the predominant flow direction is recommended, as the maximum forcing amplitude is reduced in this case.

The flow field and wall shear stresses around a wall-mounted cylinder for a Reynolds number of R e D = 39000 , based on the diameter of the cylinder and the bulk velocity, was investigated applying Large-Eddy Simulation (LES). We used a Finite-Volume method on a Cartesian grid with staggered arrangement of the variables. The curved surface of the cylinder has been approximated by a conservative second order Immersed Boundary method. We carefully validate our simulation in terms of grid resolution, inflow condition and contribution of subgrid scale stresses. Around the cylinder, local grid refinement provides spacings of 7.5 wall units in horizontal and 1.9 wall unit in vertical direction based on the the wall shear stress of the oncoming flow. Thus, the contributions of the modeled subgrid scale stresses remain small compared to other stresses and the flow variables converge with grid resolution. We demonstrate that the flow structure and predicted wall shear stresses strongly depend on the inflow condition, which has to take into account turbulent fluctuations and the secondary flow, if present. A maximum amplification factor of the time-averaged wall shear stress of 12.0 with respect to the one in the oncoming flow field shows up in the lateral front of the cylinder. Instantaneous wall shear stresses however reach a maximum amplification factor of up to 40 in the wake of the cylinder.

Generating an adverse pressure gradient (APG), using a rotating cylinder in the proximity of a plane wall under a laminar freestream flow, is studied numerically in this work. The magnitude of the generated APG is a function of the gap, G, between the cylinder and the wall, and the rotational speed of the cylinder, Ω. The flow in such a configuration is characterized by periodic transient vortex shedding at high Reynolds number. A numerical model for the computation of the transient flow for this configuration is developed using the ANSYS CFD simulation tool. The model is validated against published experimental and numerical data for similar flow configurations and excellent agreement is observed. A parametric study is carried out for different combinations of G and Ω for two different Reynolds numbers of 200 and 1000 to examine the development of the resulting separation bubble due to the generated APG. The mechanism of the boundary layer separation over the plane wall and the corresponding wake dynamics is investigated. Results are presented in terms of the distribution of the pressure coefficient as well as skin friction coefficient along the wall and flow patterns around and downstream of the cylinder in the proximity of the wall. The results of these computations confirm that using a rotating cylinder over a plane wall in a freestream flow is an effective technique to generate a controlled range of adverse pressure gradients.

The characteristics of the flow field of a circular cylinder having a small vertical plate at the upstream side are investigated by measuring the fluid force on the circular cylinder and by visualizing the flow field using particle image velocimetry. The experimental parameters are the width ratios (H/B = 0.2–0.6) of the vertical plates to the circular cylinder's diameter, and the gap ratios (G/B = 0–3) between the circular cylinder and the vertical plate. The drag reduction rate and Strouhal number of the circular cylinder increased and then decreased with G/B in the case of the same H/B. The drag reduction rate increased with H/B in the case of the same G/B. In the case of a circular cylinder having a small vertical plate, the stagnation regions are represented on the upstream and downstream sides of the circular cylinder, and the size of that region on the upstream side increased with H/B.

The effect of a uniform through-surface flow (velocity$U_{b}$) on a rigid and stationary cylinder and sphere (radius$a$) fixed in a free stream (velocity$U_{\infty }$) is analysed analytically and numerically. The flow is characterised by a dimensionless blow velocity${\it\Lambda}\,(=U_{b}/U_{\infty })$and Reynolds number$Re\,(=2aU_{\infty }/{\it\nu}$, where${\it\nu}$is the kinematic viscosity). High resolution numerical calculations are compared against theoretical predictions over the range$-3\leqslant {\it\Lambda}\leqslant 3$and$Re=1,10,100$for planar flow past a cylinder and axisymmetric flow past a sphere. For$-{\it\Lambda}\gg 1$, the flow is viscously dominated in a thin boundary layer of thickness${\it\nu}/|U_{b}|$adjacent to the rigid surface which develops in a time${\it\nu}/U_{b}^{2}$; the surface vorticity scales as$Re|{\it\Lambda}|U_{\infty }/a$for a cylinder and sphere. A boundary layer analysis is developed to analyse the unsteady viscous forces. Numerical results show that the surface pressure and vorticity distribution within the boundary layer agrees with a steady state analysis. The flow downstream of the body is irrotational so the wake volume flux,$Q_{w}$, is zero and the drag force is$F_{D}=-{\it\rho}U_{\infty }Q_{b}$, where${\it\rho}$is the density of the fluid and$Q_{b}$is the normal flux through the body surface. The drag coefficient is therefore$-2{\rm\pi}{\it\Lambda}$or$-8{\it\Lambda}$for a cylinder or sphere, respectively. A dissipation argument is applied to analyse the drag force; the rate of working of the drag force is balanced by viscous dissipation, flux of stagnation pressure and rate of work by viscous stresses due to sucking. At large$Re|{\it\Lambda}|$, the drag force is largely determined by viscous dissipation for a cylinder, with a weak contribution by the normal viscous stresses, while for a sphere, only$3/4$of the drag force is determined by viscous dissipation with the remaining$1/4$due to the flux of stagnation pressure through the sphere surface. When${\it\Lambda}\gg 1$, the boundary layer thickness initially grows linearly with time as vorticity is blown away from the rigid surface. The vorticity in the boundary layer is weakly dependent on viscous effects and scales as$U_{\infty }/a{\it\Lambda}$or$U_{\infty }/a{\it\Lambda}^{3/2}$for a cylinder and sphere, respectively. For large blow velocity, the vorticity is swept into two well-separated shear layers and the maximum vorticity decreases due to diffusion. The drag force is related to the vorticity distribution on the body surface and an approximate expression can be derived by considering the first term of a Fourier expansion in the surface vorticity. It is found that the drag coefficient$C_{D}$for a cylinder (corrected for flow boundedness) is weakly dependent on${\it\Lambda}$while for a sphere,$C_{D}$decreases with${\it\Lambda}$.