Dynamics of the viscous interaction of a ring vortex with a flat screen

A separation turbulent flow has been mathematically simulated on the basis of numerical solution of nonstationary Navier-Stokes equations for determining the dynamics of viscous interaction of a ring vortex with a flat screen. The problem was solved for an axisymmetric turbulent flow at Reynolds numbers falling within the range 10⁵–10⁷. On the basis of the calculation data obtained, the interaction of a ring vortex with a turbulent flow induced on the screen and with the secondary ring vortices was investigated. The data obtained are in qualitative agreement with the analogous data obtained by other authors with the use of the discrete-vortex method and the boundary-layer theory as well as with the available experimental and calculation data obtained for a laminar flow. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 1, pp. 184–190, January–February, 2008.     

Flow visualization studies of vortices

An actual vortex in the Kármán vortex street downstream of a circular cylinder has a core of finite dimension which increases downstream. The circulation of the vortex is nearly constant. The ratiob/a which is 0.281 according to the theory of Kármán, grows from 0.2 to 0.4 in the near wake. In the flow about a circular cylinder rotating in a uniform flow, a Kármán vortex street, Görtler-type vortices and Taylor vortices are generated at the same time. In the flow about a circular cylinder impulsively started with a constant velocity, the primary twin vortices behind the cylinder induce secondary twin vortices near the separation point. At the beginning of the motion, the separation does not occur even though a reverse flow is observed in the boundary layer. Mutual slip-through of a pair of vortex rings was achieved by increasing the Reynolds number. A vortex ring rebounds from a plane surface due to the separation of the flow on the surface induced by the vortex ring, and the secondary vortex ring is formed from the separated shear layer.     

Vortex motion in the early stages of unsteady flow around a circular cylinder

In this paper, processes in the early stages of vortex motion and the development of flow structure behind an impulsively-started circular cylinder at high Reynolds number are investigated by combining the discrete vortex model with boundary layer theory, considering the separation of incoming flow boundary layer and rear shear layer in the recirculating flow region. The development of flow structure and vortex motion, particularly the formation and development of secondary vortex and a pair of secondary vortices and their effect on the flow field are calculated. The results clearly show that the flow structure and vortices motion went through a series of complicated processes before the symmetric main vortices change into asymmetric: development of main vortices induces secondary vortices; growth of the secondary vortices causes the main vortex sheets to break off and causes the symmetric main vortices to become “free” vortices, while a pair of secondary vortices is formed; then the vortex sheets, after breaking off, gradually extend downstream and the structure of a pair of secondary vortices becomes relaxed. These features of vortex motion look very much like the observed features in some available flow field visualizations. The action of the secondary vortices causes the main vortex sheets to break off and converts the main vortices into free vortices. This should be the immediate cause leading to the instability of the motion of the symmetric main vortices. The flow field structure such as the separation position of boundary layer and rear shear layer, the unsteady pressure distributions and the drag coefficient are calculated. Comparison with other results or experiments is also made. This work was presented at the First Asian Congress of Fluid Mechanics, Bangalore in December 1980.     

Vortex simulation for non-axisymmetric collision of a vortex ring with solid particles

This study is concerned with the numerical simulation for the non-axisymmetric collision between a vortex ring and solid particles. The vortex ring convects with its self-induced velocity in a quiescent air, and the half part collides with spherical glass particles. The vortex method for gas-particle two-phase flow proposed by the authors in a prior paper is used for the simulation. The Reynolds number of the vortex ring is 2600, and the particle diameter is 50 μm. The Stokes number, defined as the ratio of the particle response time to the characteristic time of the vortex ring, is 0.74. The simulation clarifies that the particles induce the vortices, having an axis parallel to the convection direction of the vortex ring, inside the vortex ring and that pairs of the positive and negative vortex tubes appear. It also highlights that highly organized three-dimensional vortical structures composed of the streamwise vortices yield the rapid deformation and collapse of the vortex ring.     

Simulating three-dimensional vortex motion by a vortex blob method

A three-dimensional vortex blob method was applied to calculate several vortex motions: the deformation of pseudo-elliptic vortex rings, the jet issuing from the pseudo-elliptic nozzle into flow of uniform velocity, the unsteady separated flow around a circular disk with an angle of attack, and the interaction of several vortex rings which approximately reproduced the Kolmogorov spectrum. In the first three cases, the viscous diffusion of vorticity was included. The pseudo-elliptic vortex rings experienced axis switching and split into a few deformed vortex rings. Rolling-up vortices in the pseudo-elliptic jet had a symmetric arrangement in the minor-axis plane and an antisymmetric arrangement in the major-axis plane in the developing region; further downstream, the vortices were arranged antisymmetrically in both planes. The wake behind the disk normal to the main flow reproduced the spiral and columnar modes of instability. A problem in the three-dimensional vortex method is that vorticity tends to diverge at a stage of evolution of the vortex motions. An approximate method of avoiding the divergence of vorticity is proposed.     

Accelerating the annihilation of an optical vortex dipole in a Gaussian beam

When a Gaussian beam with two oppositely charged vortices propagates in free space, these two vortices will move around on the transverse beam plane. They may either move toward each other and annihilate each other spontaneously or survive all the way depending on the conditions. Here, we investigate how to force vortex dipoles to annihilate. We find that the background phase function created by two oppositely charged vortices during beam propagation can cause the vortices to move together and annihilate each other. The background phase function on a transverse plane just beyond the point where a dipole annihilated is continuous and retains the potential that forces a dipole to annihilate. We use this background phase function to accelerate the annihilation of vortex dipoles. Numerical results are provided to show the acceleration of dipole annihilation in a Gaussian beam, using such a background phase function.     

Wind pressure features of large-span flat roof in different wind fields induced by conical vortex

The wind pressure features on a large-span flat roof in uniform flow field and turbulent field induced by conical vortex were studied, through wind tunnel tests. From the comparison of the mean and fluctuating wind pressure distributions on a flat roof in different wind fields induced by conical vortex, results indicate that the mean suction dominates in the smooth flow, whereas the fluctuating suction is more obvious in the turbulent flow. The probability density function for the pressure fluctuations under different approaching flows is analyzed. The two-peaked distribution, peculiar to turbulent flow field, is observed on the curve of probability density. The fluctuating pressures at reattachment points are larger under the turbulent flow. This indicates a more intense reattachment, which may cause overturning moment for roof-mounted items. Point vortex, RanKine vortex, and simplified Cook expression are applied to fit the pressure profiles beneath conical vortices, respectively. The results have shown that the RanKine vortex model and simplified Cook expression were applicable to forecast the wind pressure profiles beneath conical vortices, while point vortex underestimated the real wind suction. The wind pressure distributions in turbulent fields induced by different wind angles were contrasted, when the approaching flow is along the diagonal of the roof, the intensity of the vortex pairs is almost equal, with obvious reattachment. When the approaching flow deviate from the diagonal of the roof, the lateral turbulent component spins the vortex more quickly; this induces larger mean suctions beneath windward vortices. Smaller suctions are observed beneath the leeward vortex, due to less vorticity being converted to vortex motion from the freestream.     

Calculation of a separated low-velocity air flow past a profile with vortex cells

Solving two-dimensional Navier-Stokes equations on multiblock different-scale computational grids by a finite-volume method, we carry out numerical simulation of laminar low-velocity air flow past a profile with passive vortex cells. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 6, pp. 1116–1120, November–December, 1998.     

Fluid dynamics of a quantized vortex filament in a hole

The behavior of nucleated vortex loops and of remanent vortex filaments in idealized circular and slit-like orifices has been investigated by direct computation. It is found that such vortices can be stretched by the diverging flow on the exit side of the orifice. The energy needed to stretch the vortex is abstracted from the flow field and observed as dissipation. This occurs in the form of discrete phase-slip events in the case of nucleated vortex loops, and in the form of multiple-phase-slip cascades when a remanent vortex is involved.     

Traveling vortex breakdown

A new type of propagating perturbations on a vortex filament-traveling vortex breakdown-has been observed experimentally. A method of controlled external action on a vortex flow with known parameters is used. Data are obtained on the absolute propagation velocity of the perturbations as a function of the conditions in the vortex chamber, which determine the vortex characteristics. Pis’ma Zh. Tekh. Fiz. 23, 24–28 (November 26, 1997)     

Existence of extra vortex and twin vortex of anomalous mode in Taylor vortex flow with a small aspect ratio

Summary This experimental work on Taylor vortex flow in a gap with a small aspect ratio is concerned with two extra vortices and a twin vortex system, each of which depends on an anomalous cell of the anomalous mode. Extra vortices are smaller than other vortices such as defined cells. At any Reynolds number and aspect ratio extra vortices can be found at the corner of the end plate and inner rotating cylinder and at the corner of the end plate and outer stationary cylinder. For a one-cell flow (anomalous one-cell mode) in a symmetric system, an outer extra vortex develops and grows to the same size as the main cell, only in an aspect ratio of less than one. A twin vortex is observed to form when two vortices are aligned in the direction of the radius. There are three flow fields on the end plate; two are extra vortex flows and the other is the main cell flow. The flow direction of the anomalous cell is from the inner cylinder to the outer one, at the end plate opposite of the flow direction of the normal cell.Nomenclature R ₁ Radius of inner cylinder (2R ₁=40.19±0.006 mm) - R ₂ Radius of outer cylinder (2R ₂=60.11±0.024 mm) - R _r Radius ratio (R ₁/R ₂=0.669) - d Clearance between cylinders (R ₂–R ₁=9.96±0.025 mm) - L Height of working fluid - Aspect ratio=L/d - Rotational angular speed - Kinematic viscosity - Re Reynolds number=R ₁ d/ Other nomenclature is defined as it appears     

Regimes of flow past a vortex generator

A complete parametric investigation of the development of multi-vortex regimes in a wake past simple vortex generator has been carried out. It is established that the vortex structure in the wake is much more complicated than a simple monopole tip vortex. The vortices were studied by stereoscopic particle image velocimetry (SPIV). Based on the obtained SPIV data, a map of the regimes of flow past the vortex generator has been constructed. One region with a developed stable multivortex system on this map reaches the vicinity of the optimum angle of attack of the vortex generator.     

Identification of the vortex mechanism of front stabilization in modeling of asymmetric flow of an incompressible fluid along a cylinder with a protruding disk

Based on numerical solution of the Navier—Stokes equations by the finite-difference method and physical modeling in a wind tunnel of laminar flow along a cylinder with a protruding disk the vortex mechanism of front stabilization and reduction in the drag of blunt bodies is investigated.     

Instability of Quantized Vortices Attached to Oscillating Boundaries in Superfluid 4He

The motion of quantized vortices is studied using a vibrating wire in superfluid ⁴He. A vortex filtering method provides a superfluid practically free of remanent vortices in which the vibration of a wire cannot generate turbulence. Vortex lines are produced by cooling through the superfluid transition and remain forming bridges between a wire and a surrounding wall. Bridged remanent vortices increase the resonance frequency of a vibrating wire: the rate of an increase due to the remanent vortices is constant in a laminar flow regime and steeply increases in a turbulent flow regime with increasing wire velocity. These results suggest that oscillation of the bridged vortices provides a linear contribution to the wire vibration in the laminar flow regime, until instability occurs in the oscillation of the vortices, causing turbulence.      

Circular vortex formation in a pulsed jet penetrating through a filter layer

A method for the formation of a laminar circular vortex is proposed that excludes the interaction of a pulsed jet with the nozzle edge. Another method is suggested for visualization of the gas flow and measurement of the gas velocity distribution in a jet penetrating through a filter layer. Critical conditions for the formation of a circular vortex are established, determining the jet power as a function of the thickness of a flat filter layer formed by granulated silica gel. It is shown that a mechanism of the laminar circular vortex formation is controlled only by the gas flow acceleration in the jet.     

Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams

Two forms of the transverse energy circulation within plane-polarized paraxial light beams are specified: one inherent in wave-front singularities (optical vortices) and the other peculiar to astigmatism and asymmetry of beams with a smooth wave front. As quantitative measures of these energy flow components, the concepts of vortex and asymmetry parts of a beam's orbital angular momentum are introduced and their definitions are proposed on the basis of beam intensity moments. The properties and physical meaning of these concepts are analyzed, and their use for the study of transformations of optical vortices is demonstrated.     

A vortex method for separated flow around an airfoil with a detached spoiler

A discrete vortex method based on no-slip condition is developed for simulating unsteady separated flows around an airfoil with a detached spoiler. For flow separated at each sharp edge, such as the spoiler tips and the trailing edge of the airfoil, a vortex sheet is used to feed discrete vortices at each time step. The length, inclination and strength of each sheet is determined by the continuity equation, the momentum principle and a Kutta pressure condition such that the flow, net force and pressure difference across the vortex sheet are all zero. The separation on the airfoil upper surface is simulated by discrete vortices shed from a fixed separation point. The flow patterns behind a detached spoiler at different time steps are obtained and compared with those of the conventional spoiler. Reasonable agreements are found between the predicted pressure distributions and experimental measurements. The computed results show that base-venting changes the flow field around the spoiler and reduces the adverse effect in lift experienced by the airfoil when the spoiler undergoes a rapid deployment.     

The flow structure of a puff

From time-resolved stereoscopic particle image velocimetry measurements over the entire circular cross section of a pipe, a first-of-its-kind quasi-instantaneous three-dimensional velocity field of a turbulent puff at a low Reynolds number is reconstructed. At the trailing edge of the puff, where the laminar flow undergoes transition to turbulence, pairs of counterrotating streamwise vortices are observed that form the legs of large hairpin vortices. At the upstream end of the puff, a quasi-periodic regeneration of streamwise vortices takes place. Initially, the vortex structure resembles a travelling wave solution, but as the vortices propagate into the turbulent region of the puff, they continue to develop into strong hairpin vortices. These hairpin vortices extract so much energy from the mean flow that they cannot be sustained. This structure provides a possible explanation for the intermittent character of the puffs in pipe flow at low Reynolds numbers.     

Modeling of vortex structures on the lateral surface of a cylinder in a longitudinal flow

The problem of generation of vortex structures by ejection of a jet through an annular slot on a cylindrical surface in a longitudinal flow is considered. Results of modeling of large-scale vortices and their effect on local characteristics of the wall boundary layer are presented. The modeling is based on numerical integration of the Navier-Stokes equations in an axisymmetric formulation. An unsteady-state flow with separation and entrainment of vortices by the main stream is obtained. The decrease in the friction drag achievable in devices of this kind is estimated.Academic Scientific Complex A. V. Luikov Heat and Mass Transfer Institute, Academy of Sciences of Belarus, Minsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66, No. 5, pp. 527–533, May, 1994.