Phase-averaging in the turbulent far-wake

The dominant peak in the spectrum of the lateral velocity fluctuation in the turbulent far-wake of a circular cylinder can be used to describe the organised motion in this region, in much the same way as phase-averaging has been used to study the organised motion in the near-wake.     

Investigating swirl and tumble using two prototype inlet port designs by means of multi-planar PIV

Flow structures created during the intake stroke of an engine were investigated by means of multi-planar particle image velocimetry (PIV). A unique water-analogue engine model has been developed, where all essential parts and parameters, such as the cylinder head, valve timing, piston geometry and motion, etc. can easily be modified. Two cylinder heads with geometrically different inlet ports were investigated and experiments were performed with both moving and fixed valves. Three-dimensional visualisations of the flow field, mode decomposition through proper orthogonal decomposition, circulation as well as classical statistics were obtained and evaluated in order to gain an understanding of the flow structures, i.e. tumble and swirl, created by the two cylinder heads. It was clearly shown that one of the cylinder heads created a strong swirling motion in the cylinder. Three different fixed valve positions were investigated and the fully opened valve gave the strongest large-scale structures, whereas with smaller openings a larger amount of the kinetic energy was converted into small-scale turbulence. Results showed a more organised and stable flow field consisting of a well-defined swirl motion occupying the whole cylinder at the end of the intake stroke when the valves were fixed at the highest position. The moving valve case gave results similar to the fully open case but with slightly higher turbulence. Cycle-to-cycle variations were found to be less pronounced for these two cases as compared to the smaller fixed valve lifts. The second cylinder head showed a flow field that was more turbulent and much less coherent. Statistical analysis showed that this had a direct effect on cyclic variations in the flow where this head showed more profound variations.     

On the orbital motion of a rotating inner cylinder in annular flow

In this paper, numerical calculations have been performed to analyse the influence of the orbital motion of an inner cylinder on annular flow and the forces exerted by the fluid on the inner cylinder when it is rotating eccentrically. The flow considered is fully developed laminar flow driven by axial pressure gradient. It is shown that the drag of the annular flow decreases initially and then increases with the enhancement of orbital motion, when it has the same direction as the inner cylinder rotation. If the eccentricity and rotation speed of the inner cylinder keep unchanged (with respect to the absolute frame of reference), and the orbital motion is strong enough that the azimuthal component (with respect to the orbit of the orbital motion) of the flow‐induced force on the inner cylinder goes to zero, the flow drag nearly reaches its minimum value. When only an external torque is imposed to drive the eccentric rotation of the inner cylinder, orbital motion may occur and, in general, has the same direction as the inner cylinder rotation. Under this condition, whether the inner cylinder can have a steady motion state with force equilibrium, and even what type of motion state it can have, is related to the linear density of the inner cylinder. Copyright © 2006 John Wiley & Sons, Ltd.     

Numerical study of the suppression mechanism of vortex-induced vibration by symmetric Lorentz forces

In this paper, the electro-magnetic control of vortex-induced vibration (VIV) of a circular cylinder is investigated numerically based on the stream function–vorticity equations in the exponential–polar coordinates attached on the moving cylinder for Re=150. The effects of the instantaneous wake geometries and the corresponding cylinder motion on the hydrodynamic forces for one entire period of vortex shedding are discussed using a drag–lift phase diagram. The drag–lift diagram is composed of the upper and lower closed curves due to the contributions of the vortex shedding but is magnified, translated and turned under the action of the cylinder motion. The Lorentz force for controlling the vibration cylinder is classified into the field Lorentz force and the wall Lorentz force. The symmetric field Lorentz force will symmetrize the flow passing over the cylinder and decreases the lift oscillation, which, in turn, suppresses the VIV, whereas the wall Lorentz force has no effect on the lift. The cylinder vibration increases as the work performed by the lift dominates the energy transfer. Otherwise, the cylinder vibration decreases. If the net transferred energy per motion is equal to zero, the cylinder will vibrate steadily or be fixed.     

Boundary layer on the moving surface of a cylinder

A study is made of the problem of the boundary layer on a cylinder with a moving surface when the cylinder moves with constant velocity in an incompressible fluid. Expressions are obtained for the distributions of the frictional stress on the surface of the cylinder and the coordinate of the singular point in the solution of the boundary layer equations that indicates the appearance of a region of reverse flow for different values of the relative velocity of the motion of the surface of the cylinder. Numerical calculations have been made of the work of the force of friction associated with displacement of the cylinder, the work expended on the motion of its surface, and, in the case of flow separation, the work of the pressure forces (it being assumed here that the pressure and friction on the wall behind the singular point are constant and equal to the pressure and friction at the singular point).     

Average wavelength of organised structures in the turbulent far wake of a cylinder

The average wavelength of organised structures in the far wake of a circular cylinder is inferred from several different estimates based primarily on wind tunnel measurements. Spectra of the lateral velocity fluctuation and cross-spectra between this fluctuation and the temperature fluctuation, at either the same point or at a different point in space, provide relatively unambiguous estimates of the average wavelength of the structures. Dye photographs in a water tunnel provide a less accurate estimate of the average wavelength of the structures. However, all estimates indicate that the average wavelength increases with streamwise distance, at a rate consistent with the self-preserving growth of the wake.     

Motion of a circular cylinder in a viscous liquid between parallel plates

The two-dimensional motion of a cylinder in a viscous fluid between two parallel walls of a vertical channel is studied. It is found that when the cylinder moves very closely along one of the channel walls, it always rotates in the direction opposite to that of contact rolling along the nearest wall. When the cylinder is away from the walls, its rotation depends on the Reynolds number of the flow. In this study two numerical methods were used. One is for the unsteady motion of a sedimenting cylinder initially released from a position close to one of the channel walls, where the Navier-Stokes equations are solved for the fluid and Newton's equations of motion are solved for the rigid cylinder. The other method is for the steady flow in which a cylinder is fixed in a uniform flow field where the channel walls are sliding past the cylinder at the speed of the approaching flow, or equivalently a cylinder is moving with a constant velocity in a quiescent fluid. The flow field, the drag, the side force (lift), and the torque experienced by the cylinder are studied in detail. The effects of the cylinder location in the channel, the size of the channel relative to the cylinder diameter, and the Reynolds number of the flow are examined. In the limit when the cylinder is translating very closely along one of the walls, the flow in the gap between the cylinder and the wall is solved analytically using lubrication theory, and the numerical solution in the other region is used to piece together the whole flow field.This research was supported by NSF DMR91-20668 through the Laboratory for Research on the Structure of Matter at the University of Pennsylvania and from the Research Foundation of the University of Pennsylvania.     

FREE SURFACE WAVE INTERACTION WITH A HORIZONTAL CYLINDER

Classes of vortex formation from a horizontal cylinder adjacent to an undulating free-surface wave are characterized using high-image-density particle image velocimetry. Instantaneous representations of the velocity field, streamline topology and vorticity patterns yield insight into the origin of unsteady loading of the cylinder. For sufficiently deep submergence of the cylinder, the orbital nature of the wave motion results in multiple sites of vortex development, i.e., onset of vorticity concentrations, along the surface of the cylinder, followed by distinctive types of shedding from the cylinder. All of these concentrations of vorticity then exhibit orbital motion about the cylinder. Their contributions to the instantaneous values of the force coefficients are assessed by calculating moments of vorticity. It is shown that large contributions to the moments and their rate of change with time can occur for those vorticity concentrations having relatively small amplitude orbital trajectories. In a limiting case, collision with the surface of the cylinder can occur. Such vortex–cylinder interactions exhibit abrupt changes in the streamline topology during the wave cycle, including abrupt switching of the location of saddle points in the wave. The effect of nominal depth of submergence of the cylinder is characterized in terms of the time history of patterns of vorticity generated from the cylinder and the free surface. Generally speaking, generic types of vorticity concentrations are formed from the cylinder during the cycle of the wave motion for all values of submergence. The proximity of the free surface, however, can exert a remarkable influence on the initial formation, the eventual strength, and the subsequent motion of concentrations of vorticity. For sufficiently shallow submergence, large-scale vortex formation from the upper surface of the cylinder is inhibited and, in contrast, that from the lower surface of the cylinder is intensified. Moreover, decreasing the depth of submergence retards the orbital migration of previously shed concentrations of vorticity about the cylinder.     

The boundary layer on the free surface of a hollow vortex

Several problems are known which are associated with the circular motion of a viscous incompressible fluid with a rotating cylinder[l, 2]. In the present paper we consider the case of unsteady circular motion of a viscous fluid with a cavity in the fluid.     

Obtaining phase averaged turbulence properties in the near wake of a circular cylinder at high Reynolds number using POD

The flow past a circular cylinder at high Reynolds number is studied by means of PIV, 3C-PIV and Time-Resolved PIV techniques. One of the goals of this study was to allow comparisons with numerical simulations on a domain identical to that of the experiment. For this reason, the cylinder was placed in a confined environment, with a high blockage and a low aspect ratio, thereby allowing computations on a mesh of reasonable size, and avoiding “infinite conditions”. This paper deals with the decomposition of the flow in a coherent and random parts. To this aim, phase averaged quantities were first obtained using the wall pressure signal on the cylinder as a trigger signal. This was achieved using both conditional sampling and LSE with similar results. This decomposition is then analysed using the Time Resolved PIV measurements, as well as by comparison of the contributions of the organised and turbulent fluctuations to the time-independent Reynolds stress tensor with those estimated from velocity spectra by interpolation and integration of the continuous part. In agreement with other studies, it is found that the contribution of the turbulent motion is overestimated as a result of the occurence of phase jitter between the trigger and velocity signal. A POD analysis was then performed to extract the coherent motion and to compare this decomposition with that obtained by phase averaging. Similarly to the phase averaging, the POD allows the decomposition of the time-independent stress tensor as the sum of two contributions corresponding to the first N modes, and the rest of the modes. This decomposition is then analysed by comparing these contributions to those obtained from the velocity spectra, according to the value N chosen. It is found that these contributions are strongly dependent on N, and the contribution of the first modes greatly overestimate the coherent motion if N is too large. In order to obtain a good decomposition of the flow in coherent and random parts, the difficulty in this case lies in the choice of the modes. Finally, the POD coefficients of the first two modes are used instead of the pressure signal to determine the phase of the vortex shedding, and the phase averaging is reconsidered. It is found that the phase averaged vortices are less smeared by the averaging process, the turbulent stresses better follow the evolution of the vortices, and the contributions of both coherent and turbulent fluctuations are found to agree well with those evaluated from the velocity spectra. This enhancement is obtained because the phase angle is determined directly from the velocity fields to be averaged, thereby reducing the phase-jitter effect. A comparison with a detached eddy simulation is also briefly shown and demonstrates the high level of agreement obtainable between simulation and experiment, as well as confirming the enhancement of the phase averaging using this procedure.     

Dynamics of the rolling and sliding of an elongated cylinder

A snap of a finger on an elongated cylinder produces on it a surprising fast spinning motion during which its mass center rises with very large oscillations. After that, the mass center goes to a long quasi-stationary oscillations state and eventually goes down very slowly. To explain this behavior we present a theoretical and numerical analysis of the dynamics of a spinning elongated cylinder moving with a single point of contact on a horizontal plane under the action of gravity. The study has been made taking into account the rolling and sliding dissipation as well as the Kutta–Joukowski airflow effect. The results of the simulations are in agreement qualitatively with the observed real motion.     

Translational motion of a cylinder below the free surface of a fluid

A method of solving the problem of the translational motion of a cylinder of given shape below the free surface of an infinitely deep heavy fluid is developed. As distinct from existing techniques, the method permits the obtaining of a solution which becomes exact as the Froude number increases without bound. The solution of the problem of the motion of a circular cylinder is considered in detail. Suggestions are made concerning the characteristic properties of an exact solution of the general problem.Kazan'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 9–22, November–December, 1996.     

Flow control using bifrequency motion

We used a second-order approximation for the periodic lift coefficient of a circular cylinder under monofrequency and bifrequency cross-flow motions. Two lock-in modes exist under monofrequency fundamental (i.e., near the Strouhal number) motion. In the first mode, the work is done by the flow on the cylinder, whereas in the second mode the work is done by the cylinder on the flow. Under monofrequency superharmonic (i.e., near three times the Strouhal number) motion, the work is always done on the flow. We then replaced the monofrequency motions by a bifrequency one, consisting of a fundamental term combined with a small-magnitude superharmonic term. We examined the effect of the magnitude and phase of the superharmonic motion term on the two modes of lock-in which we obtained when only the fundamental motion term is applied, considering two different frequencies that belonged to the two lock-in modes. Under the bifrequency motion, the work can be done on the flow or on the cylinder. This can be controlled using the superharmonic motion term, even when its magnitude is 5% of magnitude of the fundamental motion term. Other flow variables, such as the magnification of the lift, can be remarkably altered through the added superharmonic motion term. The phase of the third superharmonic lift-coefficient component relative to the fundamental one is the most responsive variable to the phase of the superharmonic motion component relative to the fundamental one.     

Formation of a cavity in the initial stage of motion of a circular cylinder in a fluid with a constant acceleration

This paper considers the joint motion of an ideal fluid and a circular cylinder completely immersed in it at small times. It is assumed that the cylinder, which was initially at rest, moves in a horizontal direction with a constant acceleration. The dynamics of the internal and external free boundaries of the fluid at small times is studied. An asymptotic analysis of the form of the internal free surface near the separation points is performed. It is shown that at high acceleration of the circular cylinder, a large cavity is formed behind, with a strong perturbation of the external free surface of the fluid over the surface of the cylinder.     

Brachistochrone for a rolling cylinder

The motion of a heavy homogeneous cylinder is considered as a no-slip rolling along the desired curve. We obtain a functional in the form of the total time of the cylinder rolling and solve the corresponding variational problem of minimizing this functional. We obtain an algebraic equation for the directional line of steepest descent, brachistochrone, in parametric form. We use the equation of motion of the cylinder with constraint reaction to determine the conditions of implementation of its pure rolling without separation and slip with respect to the brachistochrone.     

A quasi-static approach to the stability of the path of heavy bodies falling within a viscous fluid

We consider the gravity-driven motion of a heavy two-dimensional rigid body freely falling in a viscous fluid. We introduce a quasi-static linear model of the forces and torques induced by the possible changes in the body velocity, or by the occurrence of a nonzero incidence angle or a spanwise rotation of the body. The coefficients involved in this model are accurately computed over a full range of Reynolds number by numerically resolving the Navier–Stokes equations, considering three elementary situations where the motion of the body is prescribed. The falling body is found to exhibit three distinct eigenmodes which are always damped in the case of a thin plate with uniform mass loading or a circular cylinder, but may be amplified for other geometries, such as in the case of a square cylinder.     

Wake dynamics of external flow past a curved circular cylinder with the free-stream aligned to the plane of curvature

The fundamental mechanism of vortex shedding past a curved cylinder has been investigated at a Reynolds number of 100 using three-dimensional spectral/hp computations. Two different configurations are presented herein: in both cases the main component of the geometry is a circular cylinder whose centreline is a quarter of a ring and the inflow direction is parallel to the plane of curvature. In the first set of simulations the cylinder is forced to transversely oscillate at a fixed amplitude, while the oscillation frequency has been varied around the Strouhal value. Both geometries exhibit in-phase vortex shedding, with the vortex cores bent according to the body's curvature, although the wake topology is markedly different. In particular, the configuration that was found to suppress the vortex shedding in absence of forced motion exhibits now a primary instability in the near wake. A second set of simulations has been performed imposing an oscillatory roll to the curved cylinder, which is forced to rotate transversely around the axis of its bottom section. This case shows entirely different wake features from the previous one: the vortex shedding appears to be out-of-phase along the body's span, with straight cores that tend to twist after being shed and manifest a secondary spanwise instability. Further, the damping effect stemming from the transverse planar motion of the part of the cylinder parallel to the flow is no longer present, leading to a positive energy transfer from the fluid to the structure.     

Initial stage of the circular cylindermotion in a fluid after an impact with the formation of a cavity

The joint motion of an ideal fluid and a submerged circular cylinder is considered in the initial stage after an impact. The dynamics of separation points on the inner free boundary (cavity boundary) and the shapes of the inner and outer free boundaries of the fluid are determined. An asymptotic analysis of the inner free boundary near the separation points is made. The effects of the Froude number, the pressure difference, and the cylinder immersion depth are investigated.     

Motion of a cylinder below the free surface of a fluid at large froude numbers

A method of solving the problem of the motion of a cylinder of given shape below the free surface of an infinitely deep heavy fluid is perfected for large Froude numbers. The motion of a circular cylinder is investigated at small distances from the free surface. Solutions of the problem are given for cylinders with noncircular cross-sections. Kazan. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 34–45, July–August, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (projects Nos. 99-01-00169 and 99-01-00173).     

Influence of general rotation on the transfer of torsional vibrations through axisymmetric layers of viscous liquid

A study is made of the motion of a viscous incompressible liquid in a gap between a cylinder of finite length and a jacket that contains it. The motion is due to small torsional vibrations of the jacket, whereas the complete system rotates uniformly around the common symmetry axis. The equation is linearized under the assumption that the Rossby number is small. Three problems are considered: the one-dimensional problem of vibrational motion in the cylindrical gap, the self-similar problem for the flow in the end interdisk gaps, and the two-dimensional problem that describes the flow in the corner region. It is established that the superposition of the general rotation makes the damping properties of the liquid layers between the jacket and the ends of the cylinder much less good. The influence of boundary effects is clarified.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 26–31, May–June, 1991.