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Extensive numerical experiments were carried out to study the effect of cylinder heating on the characteristics of the flow and heat transfer in a two-dimensional horizontal laminar flow of air past a heated circular cylinder for the range of Reynolds numbers $0.001 \le Re \le 170$. The fluid was treated as incompressible (density is independent of the pressure) while the variation of the fluid properties with temperature was taken into account. By including the transient density term of the continutiy equation, which was neglected in a previous study by Lange et al.(IJHMT, 41(22), 1998), we were able to predict correctly the vortex shedding frequency at various overheat ratios using an incompressible flow solver. The effect of dynamic viscosity and density variations on the flow dynamics occurring with the cylinder heating was analyzed separately. Another emphasis of the work was to investigate the physical mechanism behind the ``effective Reynolds number'' concept widely applied in engineering correlations. Similarity was discovered for the distribution of the local dimensionless viscous force, the vorticity and the Nusselt number at the cylinder surface and the pressure force in the rear part of the cylinder. Two characteristic temperatures, T_{ef\!f} = T_\infty + 0.28(T_W-T_\infty) for the flow dynamics and T_{f} = T_\infty + 0.5(T_W-T_\infty) for the heat transfer, were identified.

The unsteady problem of two parallel circular cylinders, moving in an inviscid fluid, is analyzed analytically by exploring a conformal mapping. Exact solutions are obtained for the flow induced and the hydrodynamic forces acting on them, as the two circular cylinders, with any radii and at any locations, expand (contract) and translate arbitrarily at time dependent speeds. As the two bodies are far apart, the solutions of the flow and forces reduce to those for a single circular cylinder moving in an unbounded inviscid flow. The force components along the line of centers are inversely proportional to the distance between them, whereas the force components perpendicular to the line of centers are inversely proportional to the square of the distance between them. Numerical analyses are performed for the two circular cylinders deforming and translating at constant speeds and in various ways, as well as a circular cylinder falling to a wall. It has been noticed that they are attracted to each other, as one of them expands and the other contracts, or as they translate perpendicular to the line of centers; whereas they are repelled from each other, as both of them expand, contract, or as they translate along the line of centers. The force on one of them increases with the size and speed of the other, as well as their proximity.

The drag force experienced by a circular cylinder in a two-dimensional (2D) flow is investigated experimentally. Both horizontal and vertical soap film tunnels are used to set up the 2D flow with Reynolds numbers Re ranging from 35 to 560 (based on the diameter of the circular cylinder). Momentum defect measurements are used to obtain the time averaged drag coefficients, via laser Doppler velocimetry. It is found that the drag curve is in good agreement with the 2D computations of Henderson [Phys. Fluids 7, 2102 (1995)]. Two separate three-dimensional instabilities of the natural wake at Re≅180 and 260 are not observed in the present data. Flow visualization of the characteristic wake patterns behind a circular cylinder, as Reynolds number increases, is also presented.

A model for the evolution of a thin liquid coating on a horizontal cylinder is presented. The cylinder rotates about its axis, carrying liquid around its circumference. For a viscous coating, this leads to formation of a relatively thick coating where the cylinder surface moves upward. The model is based on lubrication theory, as the coating is thin compared to the cylinder radius, and includes the effects of cylinder rotation, gravity, surface tension, and flow along the cylinder axis. A two-dimensional numerical scheme based on finite differences is produced, for investigation of the case when axial flow is neglected. This numerical scheme is validated in appropriate limiting cases. Coating cross sections are obtained over a range of cylinder rotation rates, for realistic parameter values. These show a transition from pendant drops hanging beneath the cylinder to a nearly uniform coating wrapped around it as rotation rate is increased.

This paper examines in detail the flow structure and associated wall pressure fluctuations caused by the injection of a round, turbulent jet into a turbulent boundary layer. The velocity ratio, r, ratio of mean jet velocity to the mean cross flow, varies from 0.5 to 2.5 and the Reynolds number based on the cross flow speed and jet diameter is 1.9×104. Particle image velocimetry is used to measure the flow and flush mounted pressure sensors installed at several locations used to determine the wall pressure. The results consist of sample instantaneous flow structures, distributions of mean velocity, vorticity and turbulence intensity, as well as wall pressure spectra. The flow structure depends strongly on the velocity ratio and there are two distinctly different regions. At low velocity ratios, namely r 2, the near-wall flow behind the jet resembles a Karman vortex street and the wall-normal vortical structures contain cross flow boundary layer vorticity. Autospectra of the pressure signals show that the effect of the jet is mainly in the 15–100 Hz range. At r 2, the wall pressure levels reach a plateau demonstrating the diminishing effect of the jet on the near-wall flow. Consistent with the flow structure, the highest wall pressure fluctuations occur off the jet centerline for r 2. Also, the advection speed of near-wall vortical structures increase with r at r 2 it is a constant.

Three-dimensional, time-dependent solutions of flow and heat transfer past a circular cylinder with a periodic array of circular fins is obtained using an accurate and efficient spectral multidomain methodology. A Fourier expansion with a corresponding uniform grid is used along the circumferential direction. A spectral multidomain method with Chebyshev collocation is used along the r–z plane to handle the periodic array of circular fins attached to the surface of the cylinder. At a Reynolds number of 300 based on the cylinder diameter, results for the finned cylinder are compared with those of a smooth cylinder in order to see the effects of the presence of the fin array on flow and heat transfer. Detailed structure of fluid flow and temperature fields are obtained as a function of time to investigate how the fin array changes heat transfer mechanism related to the vortical structure in the wake region.

The fluctuating wall pressure on a circular cylinder in cross flow has been investigated experimentally in a water tunnel to examine the effect of yaw angle on the spectral characteristics of the wall pressure field and to provide insight into the periodic and turbulent structures of the flow. Wall pressure was measured at five azimuthal positions around the periphery of the cylinder for seven yaw angles from α=90° (normal flow) to α=0° (axial flow) at three subcritical Reynolds numbers (ReD=7200, 13 500, 27 600). As the yaw angle is varied from α=90° to 0°, large systematic and nonmonotonic variations in both the narrowband (periodic vortex shedding) and broadband (turbulent) spectral levels occur. The results provide additional insight into the structural characteristics of the yawed cylinder flow regimes over that which has been identified previously through measurements of mean wall forces and flow field characteristics. Significant Reynolds number effects were also observed over the range of the measurements, particularly at small yaw angles, that may indicate fundamental shifts in the structure of the wake or underlying regime transition mechanisms. Possible effects due to vortex-induced cylinder vibrations are not entirely clear but predominantly confined to the larger yaw angles. Simultaneous wall pressure, cylinder vibration, radiated acoustic pressure, and wake velocity measurements are required to appropriately isolate the various potential contributions to the wall pressure field and thus provide a clearer understanding of the underlying boundary layer separation, transitional wake, and fluid-structural coupling mechanisms.

This paper reports velocity measurements of slow flow through a model brush. The flow field was created in the annulus between two concentric cylinders, which was filled with a viscous oil. The inner cylinder was stationary and the outer one was installed on a turntable and rotated at a constant speed. A brush was modeled by an array of uniformly spaced rods mounted horizontally onto the inner cylinder. With a generous gap between the rod ends and the outer cylinder, the flow outside the array was circular Couette flow. Three brushes were made and the external shear flow penetrated these because the solid volume fractions were small, namely, 0.025, 0.05, and 0.10. Particle image velocimetry was used to study the velocity field in the penetration region, and from these measurements the velocity at the interface, “the slip velocity,” was determined. The slip velocity was found to be close to the value predicted by Brinkman’s equation, and to be higher than velocities found previously for rod arrays in other...

Control of flow-induced forces on a circular cylinder using a detached splitter plate is numerically studied for laminar flow. A splitter plate with the same length as the cylinder diameter is placed horizontally in the wake region. Suppressing the vortex shedding, the plate significantly reduces drag force and lift fluctuation; there exists an optimal location of the plate for maximum reduction. However, they sharply increase as the plate is placed further downstream of the optimal location. This trend is consistent with the experimental observation currently available in the case of turbulent wake.

The instability giving rise to the Karman vortex street in a flow past a circular cylinder is responsible for the occurrence of large amplitude oscillations in the lift. In this work, we seek to control the instability via active feedback control by means of transverse displacements of the solid structure. Our investigation is based on Foppl’s four-dimensional potential flow model of point vortices. A feedback controller capable of manipulating the flow in order to maintain zero lift at all times is derived analytically by using perturbation methods and asymptotic expansions. We then apply the controller to the viscous flow by direct numerical simulation of the flow based on the two-dimensional Navier–Stokes equations and show that our control algorithm is capable of keeping the lift close to zero in the impulsively started viscous flow and, therefore, controlling vortex shedding. Computations are carried out at the Reynolds numbers Re=100 and Re=200.

The wake transition regime in square cylinder flow is investigated experimentally. Mode A and B transitions similar to those captured in circular cylinder flows are found to exist in this regime and by using dye- and laser-induced fluorescence visualization, the spanwise and streamwise vortex structures are captured. Upon comparison with their corresponding modes in circular cylinder flows, some differences are noted. Most notably, the critical Reynolds numbers at which Mode A and B occur for square cylinder flows were estimated to be approximately 160 and 200, respectively, and are lower than those found in circular cylinder flows, which are generally agreed to be approximately 188–190 and 230–260, respectively. Also, the spanwise wavelengths for the two modes in square cylinder flows (5.2 Ds and 1.2 Ds for Modes A and B, respectively) are longer than their counterparts in circular cylinder flows (3–4Do and 0.8–1Do, respectively). Furthermore, by using a hot wire to measure the shedding frequency, it was...

A known bifurcation scenario describing the development and interaction of Mode A and Mode B vortex shedding modes of a circular cylinder wake is extended to predict the Strouhal–Reynolds number profile over the three-dimensional transitions. The mode amplitudes are described by coupled Landau equations and, with frequency information being included by the addition of complex coefficients, the model predicts the discontinuous nature of the Strouhal–Reynolds number shedding profile of the circular cylinder wake throughout the laminar three-dimensional transition regime. The model coefficients are determined from computations of the three-dimensional modes of a circular cylinder wake.

A linear stability analysis has been implemented for the Taylor–Dean flow between porous concentric rotating cylinders when radial flow is present. The stability equations with respect to both axisymmetric and nonaxisymmetric disturbances are derived and solved by a direct numerical procedure. Both types of radial flows, inward and outward flows, are considered. A parametric study covering wide ranges of α, the radial Reynolds number based on the radial velocity at the inner cylinder and inner radius, and β, a parameter characterizing the ratio of average pumping velocity due to azimuthal Poiseuille flow and rotation velocity due to inner cylinder rotation, is conducted for the situation of practical interest where the outer cylinder is stationary and the inner cylinder is rotating. The area where the onset mode is nonaxisymmetric is shown in the plane (β,α). A critical curve is discovered that the most stable state always occurs at the point on this curve for an assigned value of α. Moreover, a discontinuity of the critical axial wavenumber happens when the parameters α or β cross this curve. The critical mode transition of the onset of instability is demonstrated in detail and results for the variations of the critical Taylor number and axial wavenumber are presented. It is found that the superimposed radial flow may produce a stabilizing or destabilizing effect depending heavily on the value of β related to the basic state.

Results are presented for the flow of homogeneous, concentrated, oil-in-water emulsions subjected to a shear flow between rotating, horizontal concentric cylinders. Nuclear magnetic resonance imaging (NMRI) was used to measure velocity profiles. This technique allows velocity profiles to be measured noninvasively within a flowing, concentrated emulsion. It was observed that below a critical velocity, in a portion of the gap, the fluid moves in a direction opposite to the outer, rotating cylinder. Above this critical velocity, the emulsion corotates with the outer cylinder. Theoretical analysis suggests that the transitions are driven by buoyancy effects. The corotating and counter-rotating flow states at different rotation speeds can be characterized by a single dimensionless parameter Γ, which relates buoyancy and viscous effects.

Three-dimensional, time-dependent, nonlinear flow dynamics within a cylinder with sidewall mass injection are investigated. A nonaxisymmetric transient injection velocity, prescribed along the sidewall boundary of a long, narrow, half-open cylinder, induces a low Mach number, high Reynolds number flow. The injection drives nearly planar axial acoustic disturbances, which interact with the injected fluid to produce the azimuthal component of vorticity on the sidewall in an inviscid manner. A smaller, but important azimuthally dependent transient disturbance, driven by the nonaxisymmetric injection disturbance leads to the axial component of vorticity on the cylinder sidewall. Both components of vorticity are shown to convect toward the center of the cylinder, diffuse radially, and convect downstream. Other results show that the axial component of vorticity produced along the sidewall is largest near the maximum of a mass source distribution in the azimuthal dimension. The amplitude of the axial vorticity c...

A two-dimensional numerical study on the laminar flow past a circular cylinder rotating with a constant angular velocity was carried out. The objectives were to obtain a consistent set of data for the drag and lift coefficients for a wide range of rotation rates not available in the literature and a deeper insight into the flow field and vortex development behind the cylinder. First, a wide range of Reynolds numbers (0.01⩽Re⩽45) and rotation rates (0⩽α⩽6) were considered for the steady flow regime, where α is the circumferential velocity at the cylinder surface normalized by the free-stream velocity. Furthermore, unsteady flow calculations were carried out for one characteristic Reynolds number (Re=100) in the typical two-dimensional (2D) vortex shedding regime with α varying in the range 0⩽α⩽2. Additionally, the investigations were extended to very high rotation rates (α⩽12) for which no data exist in the literature. The numerical investigations were based on a finite-volume flow solver enhanced by multi...

Rotating, barotropic flow past a circular cylinder with circulation in the presence of a piecewise constant distribution of potential vorticity is considered. For a given cylinder radius, linear theory is used to show that there exists a unique value of the circulation for which the downstream wake vanishes. The cylinder experiences zero drag for such flows. A numerical method, based on contour dynamics, is then used to compute steady, nonlinear, waveless flows past the cylinder. For a given upstream velocity and different choices of the cylinder radius, waveless potential vorticity interface profiles are presented and corresponding values of the circulation calculated. Possible applications to propagating geophysical vortices are discussed, including the computation of nonlinear solutions which may be interpreted as freely propagating vortices.

Effects of rotary oscillation on unsteady laminar flow past a circular cylinder have been investigated in this study. Numerical simulations are performed for the flow at Re=100 in the range of 0.2⩽Ω⩽2.5 and 0.02⩽Stf⩽0.8, where Ω and Stf are, respectively, the maximum rotational speed and forcing oscillation frequency normalized by the free-stream velocity and cylinder diameter. Results show that the rotary oscillation has significant effects on the flow. The lock-on frequency range becomes wider as the rotational speed increases. In a non lock-on region, modulations in the velocity, lift and drag signals occur and the modulation frequency is expressed as a linear combination of the forcing frequency and vortex-shedding frequency. Also, the mechanism for the modulation phenomenon is presented in terms of the vortex merging process. Finally, it is found that the mean drag and amplitude of the lift fluctuations show local minima near the boundary between the lock-on and non lock-on regions.

Gravity-driven soap-film channels offer a convenient way to study two-dimensional hydrodynamics in the laboratory. With recently developed quantitative soap-film diagnostic techniques, velocity and thickness field information can be acquired to provide a complete description of the flow. We present a study of soap-film flow in a state-of-the-art tilted soap-film tunnel which can sustain a mean freestream velocity about 0.5 m/s with velocity fluctuations on the order of 1%. Our investigation concentrates on the evolution of the velocity and thickness profiles with downstream distance. We observe a hydrodynamically fully developed flow within a substantial range of distances and compare our results with the analytical solution based on the assumptions of linear air drag and constant film thickness. We find air drag to be the dominant dissipative mechanism in the flow, although the role of internal viscous dissipation is also apparent. Direct measurements of the air drag coefficient are in good agreement with the values inferred from the analytical solution.

A direct numerical simulation is applied to investigate three-dimensional unsteady flow characteristics around a finite wall-mounted square cylinder with an aspect ratio of 7 at a Reynolds number (Re) of 40-250. Determination of Re for the onset of vortex shedding and Re influence on the wake structure and integral parameters are the major objectives of the current research. The results show that the vortex shedding inception occurs within the range of 75 200.

In this paper, we report two novel theoretical approaches to examine a fast-developing flow in a thin fluid gap, which is widely observed in industrial applications and biological systems. The problem is featured by a very small Reynolds number and Strouhal number, making the fluid convective acceleration negligible, while its local acceleration is not. We have developed an exact solution for this problem which shows that the flow starts with an inviscid limit when the viscous effect has no time to appear and is followed by a subsequent developing flow, in which the viscous effect continues to penetrate into the entire fluid gap. An approximate solution is also developed using a boundary layer integral method. This solution precisely captures the general behavior of the transient fluid flow process and agrees very well with the exact solution. We also performed numerical simulation using Ansys-CFX. Excellent agreement between the analytical and the numerical solutions is obtained, indicating the validity ...

A semi-analytical model is presented for pressure-driven flow through a channel, where local pressure loss is incurred at a sudden change in the boundary condition: from no-slip to partial-slip. Assuming low-Reynolds-number incompressible flow and periodic stick–slip wall patterning, the problems for parallel-plate and circular channels are solved using the methods of eigenfunction expansion and point match. The present study aims to examine in detail how the flow will evolve, on passing through the cross section at which the change in the slip condition occurs, from a no-slip parabolic profile to a less sheared profile with a boundary slip. The present problem is germane to, among other applications, flow through a channel bounded by superhydrophobic surfaces, which intrinsically comprise an array of no-slip and partial-slip segments. Results are presented to show that the sudden change in the boundary condition will result in additional resistance to the flow. Near the point on the wall where a slip cha...

A new geometric disturbance giving the reductions of the drag and lift fluctuations for bluff body flows has been proposed by applying the asymmetry to a symmetric wavy (SW) geometry. This asymmetric wavy (ASW) disturbance is applied on a circular cylinder to identify its effect on the flow control, forming the asymmetric wavy (ASW) cylinder. The turbulent flow over an ASW cylinder is investigated at a subcritical Reynolds number of 3000 using large eddy simulation based on the finite volume method. The findings of the present study identify that the ASW disturbance achieves more reductions in the mean drag and the lift fluctuation than the optimal wavy cylinder. The branch-like formation of the additional streamwise and transverse vorticities observed in the ASW cylinder are dissipated farther upstream than the symmetric wavy (SW) cylinder, resulting in wider regions of the zero vorticities in the near-wake. The ASW cylinder formed the asymmetric distribution of flow and the extent of the coherent flow farther downstream. The vortex formation length of the ASW cylinder reveals the asymmetric distribution along the span and is much longer than that of the smooth and SW cylinders. This comparison of the vortex formation length also proves the capacity of the ASW geometric disturbance to reduce the drag and lift fluctuation than the SW cylinder.

The initial development of the two dimensional viscous, incompressible flow induced by an impulsively started circular cylinder which performs time dependent sinusoidal rotational oscillations about its axis is investigated numerically. The investigation is based on the solutions of stream function-vorticity formulation of Navier-Stokes equations on non-uniform polar grids using higher order compact formulation. The numerical method is validated by comparing the computed results with existing experimental and numerical results for Reynolds numbers Re = 150 and 500. The effects of forced oscillation frequency f and peak rotation rate αm on the early development of the flow structure in the near wake region are discussed. Results are given for the initial development with time of the flow structure at the rear of the cylinder at Re = 200. The details of the formation, movement, closure points, and strengths of the vortices behind the cylinder are presented. The velocity profiles at different locations and vorticity profiles at the surface of the cylinder are also shown. The effect of increase in αm on the timing of the formation of the vortices, the closed wake length, and the thickness of the boundary layer is investigated.

In this paper, an incompressible two-dimensional shear flow past a square cylinder problem is investigated numerically using a higher order compact finite difference scheme. Simulations are presented for three sets of Reynolds numbers, 100, 200, and 500, with various shear parameter (K) values ranging from 0.0 to 0.4. The purpose of the present study is to elaborate the influence of shear rate on the vortex shedding phenomenon behind the square cylinder. The results presented here show that the vortex shedding phenomenon strongly depends on Re as well as K. The strength and size of vortices shed behind the cylinder vary as a function of Re and K. When K is larger than a critical value, the vortex shedding phenomenon has completely disappeared depending on the Reynolds number. Apart from the numerical study, a thorough theoretical investigation has been done by using a topology based structural bifurcation analysis for unsteady flow separations from the walls of the cylinder. Through this analysis, we stud...

Large-eddy simulations were used to investigate the supercritical aerodynamics of a square cylinder with rounded corners in comparison with those in the subcritical regime. First, the numerical methods, especially the dynamic mixed model, were validated on the basis of their prediction of supercritical flows past a circular cylinder. Then, the supercritical flows past a rounded-corner square cylinder were simulated and systematically clarified. Strong Reynolds number (Re) effects existed in the forces and local pressures as Re increased from o(104) to o(106). Changeover of flow patterns occurred as Re increased. At the supercritical Re, the free stream overall flowed along the cross sections of the cylinder, separated from the leeward corners and generated Karman vortices behind the cylinder. This pattern resulted in a much smaller recirculation region behind the cylinder compared with the subcritical flow. At the micro level, the flow experienced laminar separation and flow reattachment near the frontal ...

Eddy-resolving numerical simulations are conducted to investigate the dynamics of the large-scale coherent structures around a circular cylinder in an open channel under very shallow flow conditions where the bed friction significantly affects the wake structure. Results are reported for three test cases, for which the ratio between the cylinder diameter, D, and the channel depth, H, is D/H = 10, 25, and 50, respectively. Simulation results show that a horseshoe vortex system forms in all test cases and the dynamics of the necklace vortices is similar to that during the breakaway sub-regime observed for cases when a laminar horseshoe vortex forms around the base of the cylinder. Given the shallow conditions and turbulence in the incoming channel flow, the necklace vortices occupy a large fraction of the flow depth (they penetrate until the free surface in the shallower cases with D/H = 25 and 50). The oscillations of the necklace vortices become less regular with increasing polar angle magnitude and can i...

This article presents a two-dimensional numerical study of the unsteady laminar flow from a square cylinder in presence of multiple small control cylinders. The cylinders are placed in an unconfined medium at low Reynolds numbers (Re = 100 and 160). Different flow phenomena are captured for the gap spacings (g = s/D, where s is the surface-to-surface distance between the main cylinder and small control cylinders and D is the size of the main cylinder) between 0.25 – 3 and angle of attack (θ) ranging from 300 to 1800. Numerical calculations are performed by using a lattice Boltzmann method. In this paper, the important flow physics of different observed flow patterns in terms of instantaneous vorticity contours visualization, time-trace analysis of drag and lift coefficients and power spectra analysis of lift coefficient are presented and discussed. Drag reduction and suppression of vortex shedding is also discussed in detail and compared with the available experimental and numerical results qualitatively as well as quantitatively. In addition, the mean drag coefficient, Strouhal number, root-mean-square values of the drag and lift coefficients are determined and compared with a single square cylinder without small control cylinders. We found that the drag is reduced 99.8% and 97.6% for (θ, g) = (300, 3) at Re = 100 and 160, respectively.

The stability analysis is presented for a thin viscous liquid film flowing inside a uniformly heated horizontal cylinder that is rotating about its axis. The free surface evolution equation for the liquid-gas interface is obtained by simplifying the Navier-Stokes and energy equations within the lubrication approximation. Various dimensionless numbers are obtained that quantify the effect of gravity, viscous drag, inertia, surface tension, and thermocapillary stress. The film thickness evolution equation is solved numerically to obtain two-dimensional, steady state solutions neglecting axial variations. A liquid pool forms at the bottom of the cylinder when gravity dominates other forces. This liquid pool is shifted in the direction of rotation when inertia or viscous drag is increased. Small axial perturbations are then imposed to the steady solutions to study their stability behavior. It is found that the inertia and capillary pressure destabilize whereas the gravity and thermocapillary stress stabilize ...

Laminar boundary layers with fully developed uniform shear cross flows are considered. The first streamwise laminar flow is a Blasius boundary layer flow, the second is uniform shear flow over a semi-infinite plate, and the third is the flow induced by a power-law stretching surface. In the first two cases, the effect of streamwise plate motion is taken into account by the parameter λ. In each case, the similarity solutions reduce the governing boundary layer equations to a primary ordinary differential equation for the streamwise flow and a secondary linear equation coupled to the primary solution for the cross flow. It is found that an infinity of solutions exist in each problem and the unique solution in each case is found by applying the Glauert criterion. In some instances, a simple exact solution for the cross flow is presented. Results for the wall shear stresses and velocity profiles are given in graphical form.

The effect of steady base suction and blowing on the stability and dynamics of the cylinder wake is investigated at low Reynolds numbers, using numerical simulation and stability analysis. Simulation results show that, in the supercritical Reynolds number regime (Re>47), slight blowing or high enough suction stabilizes the wake; in the subcritical regime, suction destabilizes the wake and results in vortex shedding, whereas blowing has no detectable effect on the flow stability. At supercritical Reynolds numbers, the transition from unsteady to steady flow at a critical suction flow rate is accompanied by simultaneous symmetry breaking, resulting in strongly asymmetric steady flow. For finite flow domain, the flow undergoes another transition from steady asymmetric to steady symmetric flow at even higher suction flow rates. The dynamics of vortex shedding in the controlled flow can be strongly modified, in comparison to the uncontrolled flow. Global stability analysis confirms the results of numerical sim...

We consider the flow within a rotating horizontal cylinder containing a small amount of a very viscous liquid which completely coats the cylinder surface. We show that, under creeping flow conditions, the addition of the hydrostatic pressure term to the standard lubrication equation leads to film thickness profiles which, over a broad range of parameters, are in close agreement with those obtained experimentally, as well as via the solution to the full Stokes equations.

The flow in the gap between an inner rotating cylinder concentric with an outer stationary cylinder with an imposed pressure-driven axial flow was studied experimentally using particle image velocimetry (PIV) in a meridional plane of the annulus. The radius ratio was η=0.83 and the aspect ratio was Γ=47. Velocity vector fields for nonwavy toroidal and helical vortices show the axial flow winding around vortices. When the axially averaged axial velocity profile is removed from the velocity field in a meridional plane, the velocity field looks much like it would with no imposed axial flow except that the vortices translate axially and the distortion of the azimuthal velocity contours in meridional plane related to the vortices is shifted axially by the axial flow. The velocity vector fields for wavy vortices also show axial flow winding around the vortices. Again, removing the axial velocity profile results in a flow that appears similar to that with no axial flow. The path of the vortices is generally axial, but the vortices periodically move retrograde to the imposed axial flow due to the waviness of the vortices. The axial velocity of helical vortices, both nonwavy and wavy, is twice the rotational frequency of the inner cylinder indicating a coupling between the axial translation of the vortices and the cylinder rotation. Little fluid transport between vortices occurs for nonwavy vortices, but there is substantial transport between vortices for wavy vortex flow, much like supercritical cylindrical Couette flow with no axial flow.

The flow field around a sphere falling at its terminal velocity in a column of viscoelastic non-shear-thinning fluid is experimentally measured with digital particle image velocimetry. The working fluid is an extensively characterized, monodisperse, polystyrene based Boger fluid. The sphere radius relative to the radius of the column of fluid is small (a/rc=0.083). The Weissenberg number (λUt/a) ranges from 0.5 to 14 over which the sphere experiences a drag increase up to 8 times that of the Newtonian flow. The flow field is investigated in detail for We 0.5 to 2.5. A length and width scale is defined for the wake. Over this range of We the wake is found to grow linearly with We and become self-similar in a transverse cross-section of the axial component of the velocity. Streamlines along with extension and rotation rates along those streamlines are also determined.

The present study numerically investigates two-dimensional laminar flow past a circular cylinder rotating with a constant angular velocity, for the purpose of controlling vortex shedding and understanding the underlying flow mechanism. Numerical simulations are performed for flows with Re=60, 100, and 160 in the range of 0⩽α⩽2.5, where α is the circumferential speed at the cylinder surface normalized by the free-stream velocity. Results show that the rotation of a cylinder can suppress vortex shedding effectively. Vortex shedding exists at low rotational speeds and completely disappears at α>αL, where αL is the critical rotational speed which shows a logarithmic dependence on Re. The Strouhal number remains nearly constant regardless of α while vortex shedding exists. With increasing α, the mean lift increases linearly and the mean drag decreases, which differ significantly from those predicted by the potential flow theory. On the other hand, the amplitude of lift fluctuation stays nearly constant with in...

Time-dependent flow dynamics within a cylinder with sidewall mass injection are investigated. A time-dependent injection velocity, prescribed along the sidewall boundary of a long, narrow, half-open cylinder, induces a low Mach number, high Reynolds number flow. The injection is the source of planar acoustic disturbances which interact with the injected fluid to produce vorticity on the sidewall in an inviscid manner. The analysis of these flow processes is based on the Navier–Stokes equations, which are reduced to simpler forms using a multiple-scale asymptotic analysis. The equations that arise from the analysis describe the leading-order vorticity dynamics. These nonlinear equations possess both wave and diffusion properties and are solved in an initial value sense. The results show that the vorticity produced at the sidewall convects toward the center of the cylinder, diffuses radially, and convects downstream.

The flow around a circular cylinder (diameter d) was investigated, behind which a short thin splitter plate with a chord of 1.0d was inserted horizontally as an interference element. The plate was traversed upstream along the wake; hence its relative position is defined by gap G from the cylinder base to the plate tip and by level Z from the wake centerline. The variation in both base suction coefficient and Strouhal number with G/d significantly depends on Z/d. In the circular cylinder case with Z/d=0.5–1.3, as the plate approaches the cylinder, the base suction coefficient exhibits a critical fall in a similar fashion to Roshko’s experiment where Z/d=0. Interestingly, however, unlike his experiment, the Strouhal number exceeds the natural one for some range of G/d beyond the critical gap. To further examine the flow mechanism, a similar situation was investigated by using a rectangular cylinder (height h, depth 0.1h) in place of the circular cylinder. A rise in the Strouhal number is observed for Z/h=1....

Direct numerical simulations of two-dimensional (2D) and 3-D unsteady flow around a square cylinder for moderate Reynolds numbers (Re=150–500) are performed, employing an implicit fractional step method finite-volume code with second-order accuracy in space and time. The simulations, which are carried out with a blockage ratio of 5.6%, indicate a transition from 2-D to 3-D shedding flow between Re=150 and Re=200. Both spanwise instability modes, A and B, are present in the wake transitional process, similar to the flow around a circular cylinder. However, seemingly in contrast to a circular cylinder, the transitional flow around a square cylinder exhibits a phenomenon of distinct low-frequency force pulsations (Re=200–300). For 3-D simulations, the Strouhal number and the mean drag coefficient are in general agreement with existing experiments. Between Re=300 and 500, an increase in the spanwise coupling of fluctuating forces is indicated. The influence of the spanwise aspect ratio using periodic boundary conditions, a finer grid, and a finer time step is also investigated.

This work numerically investigates laminar plane twin-jet flows with side-wall confinement. Time-dependent computations on the full physical domain are performed in light of the possible emergence of flow unsteadiness and an asymmetric pattern. Of particular concern is how wall-confinement and jet momentum influence the transition of flow patterns. Results presented herein provide further insight into the complexities involving issues such as the variety of flow structure and the related bifurcations, jet–jet and jet–wall interactions, and flow instability involved in the confined twin-jet flow field.

The problem of the rotatory oscillation of an axi-symmetric body in an axi-symmetric, viscous, incompressible flow at low Reynolds number has been studied. In contrast to the steady rotation of a body, which involves solving the Laplace equation, the study of an oscillating body requires solution of the Helmholtz equation which results from the simplification of the unsteady Stokes equations. In the present work, we have numerically evaluated the local stresses and torques on a selection of free, oscillating, axi-symmetric bodies in the continuum regime in an axi-symmetric viscous incompressible flow. The Helmholtz equation was solved by a Green’s function technique. The accuracy of the technique is tested against known solutions for a sphere, a prolate spheroid, a thin disk, and an infinitely long cylinder. Good agreements have been obtained. Finite cylinders have been studied and the edge correction factors for the circular disk geometry, that are basic to oscillating disk viscometers, have been calculated. It has been found that the calculated edge correction factors, based on the ratios of the real parts of the actual torques (calculated from this work) to the ideal torques, agree to within 1% to 10% with the reported values obtained by Clark et al. [Physica A 89, 539 (1977)] using the theory of Kestin and Wang [J. Appl. Mech. 24, 197 (1957)]. However, since the ratios of the real parts and the ratios of the imaginary parts of the torques do not coincide, the edge correction factors depend upon which ratio is used.

Three-dimensional internal flow dynamics are studied in a cylinder with mass injection from the sidewall. A time-dependent, harmonic, non-axisymmetric axial velocity disturbance is imposed on the endwall of the cylinder to create a non-axisymmetric velocity field. An asymptotic analysis is used to reduce the Navier-Stokes equations to more elementary forms in two regions adjacent to the endwall with distinct physical characteristics: an incompressible, inviscid and irrotational core near the endwall, and an incompressible viscous boundary layer containing all three components of vorticity adjacent to the sidewall. Solutions to these equations for disturbance frequencies associated with the lowest order axial acoustic modes show that the non-axisymmetric nature of the flow is confined to the core region adjacent to the endwall with a characteristic axial dimension on the order of the cylinder radius. Within the region, axial, radial, and azimuthal velocities exist. These non-axisymmetric effects decay expo...

We study experimentally the parallel flow in a Hele–Shaw cell of two immiscible fluids, a gas and a viscous liquid, driven by a given pressure gradient. We observe that the interface is destabilized above a critical value of the gas flow and that waves grow and propagate along the cell. The experimental threshold corresponds to a velocity difference of the two fluids in good agreement with the inviscid Kelvin–Helmholtz instability, while the wave velocity corresponds to a pure viscous theory deriving from Darcy’s law. We report our experimental results and analyze this instability by the study of a new equation where the viscous effects are added to the Euler equation through a unique drag term. The predictions made from the linear stability analysis of this equation agree with the experimental measurements.

In this paper an extensive investigation is done of the linear stability of a film falling down a vertical rotating cylinder. Two cases are considered: flow in the outside and flow in the inside of the cylinder. To this end, a system of differential equations which describe the instability is solved numerically with the Runge–Kutta fourth and sixth order methods. We show that in different circumstances the azimuthal disturbances become the most unstable when the rotation is taken into account. Moreover, a splitting of the azimuthal modes appears due to the Coriolis force. In the case of flow in the inside there is a threshold in the centrifugal force above which the flow is linearly stable. Besides, new results for the nonrotating case are also obtained.

In this manuscript a taxonomy of potential/complex-lamellar decompositions will be developed for describing the flow of an incompressible viscous fluid. Since these decompositions are not unique, they are best defined by their governing equations and not by their individual components. Within this framework we will construct a number of decompositions, both classical and contemporary, inviscid and viscous. Finally, we will use these results to derive the conditions under which an unsteady flow is circulation preserving. First, using a decomposition based on the Lighthill–Darwin–Hawthorne drift function, we will show that a flow ceases to be circulation preserving when the cross product of its circulation and drift function gradients are not harmonic. Then we will show that an unsteady flow can be circulation preserving only when it is an irrotational one as well.

The unsteady flow of a homogeneous viscous fluid past a straight circular cylinder (radius l*) confined between two infinite parallel plates (a distance d* apart) relative to a rapidly rotating frame is considered. The cylinder is impulsively started from rest to a uniform velocity. The unsteady form of the boundary-layer equations for a rotating fluid is used to examine the flow Rossby number Ro∼O(E1/2), where E≪1 is the Ekman number. A range of values of the non-dimensional parameter N=lE1/2/Ro (where l=l*/d*) is considered. For 0⩽N

In this paper we present the results of an experimental study of wavy rivulet flow along the lower side of an inclined cylinder. The influence of the inclination angle of the cylinder, mode of irrigation and flow rate on the hydrodynamical characteristics is investigated. It is shown that the rivulet flow is unstable. As a consequence the nonlinear waves appear on a rivulet surface. The different types of surface waves are described. For the purpose of a detailed study of the wave characteristics, a method of superimposed oscillations is applied. New regularities of wave motion were found in comparison to the case of liquid film flow. The critical conditions for liquid ejection from the rivulet are determined.

We study the instantaneous Stokes flow near the apex of a corner of angle 2α formed by two plane stress free surfaces. The fluid is under the action of gravity with g↘ parallel to the bisecting plane, and surface tension is neglected. For 2α≳126.28°, the dominant term of the solution as the distance r to the apex tends to zero does not depend on gravity and has the character of a self‐similar solution of the second kind; the exponent of r cannot be obtained on dimensional grounds and the scale of the coefficient depends on the far flow field. Within this angular domain, the instantaneous flow is deeply related to the (steady) flow in a rigid corner known since Moffatt [J. Fluid Mech. 18, 1 (1964)] and, as in that case, there may be eddies in the flow. The situation is substantially different for 2α

The linear stability of an inviscid, axisymmetric and rotating columnar flow in a finite length pipe is studied. A well posed model of the unsteady motion of swirling flows with compatible boundary conditions that may reflect the physical situation is formulated. A linearized set of equations for the development of infinitesimal axially‐symmetric disturbances imposed on a base rotating columnar flow is derived. Then, a general mode of axisymmetric disturbances, that is not limited to the axial‐Fourier mode, is introduced and an eigenvalue problem is obtained. Benjamin’s critical state concept is extended to the case of a rotating flow in a finite length pipe. It is found that a neutral mode of disturbance exists at the critical state. In the case of a solid body rotating flow with a uniform axial velocity component, analytical solution of the eigenvalue problem is found. It is demonstrated that the flow changes its stability characteristics as the swirl changes around the critical level. When the flow is ...

Planar flow induced in a viscous fluid by a small cylinder oscillating in the direction normal to its axis is modeled theoretically and reproduced experimentally. In the model, a line force dipole (force doublet) was used as the source of motion. In an initially quiescent unbounded fluid this source produces zero net momentum and generates symmetrical quadrupolar flow consisting of two dipolar vorticity fronts propagating in opposite directions from the source. For starting flow at low Reynolds numbers, a second‐order unsteady solution is obtained in terms of a power series of the Reynolds number, Re=Q/4πν2, where Q is the forcing amplitude and ν is the kinematic viscosity. This solution demonstrates that, as time t→∞, the flow in the vicinity of the source becomes steady and radial. To describe this steady asymptote, the Jeffery–Hamel nonlinear solution for radial flow is used. A particular solution is derived using the nondimensional intensity Re of the force dipole as a governing parameter. It is shown...

In this paper, laminar flow past a rotating circular cylinder placed in a compressible uniform stream is investigated via a two-dimensional numerical simulation and the compressibility effects due to the combination of the free-stream and cylinder rotation on the flow pattern such as forming, shedding, and removing of vortices and also the lift and drag coefficients are studied. The numerical simulation of the flow is based on the discretization of convective fluxes of the unsteady Navier-Stokes equations by second-order Roe’s scheme and an explicit finite volume method. Because of the importance of the time dependent parameters in the solution, the second-order time accurate is applied by a dual time stepping approach. In order to validate the operation of a computer program, some results are compared with previous experimental and numerical data. The results of this study show that the effects due to flow compressibility such as normal shock wave caused the interesting variations on the flow around the ...