Evolution of global enstrophy in cylinder wake controlled by Lorentz force

The Okubo-Weiss function is correlated with the fluid particle compression, deformation and vorticity, which provides a simple way to characterize different regions of a flow-field. In the present paper, it shows mathematically that the global integration of Okubo-Weiss function is always equal to zero for a two dimensional incompressible flow with no-slip boundaries. To validate the conclusion, a flow passing a circular cylinder con- trolled by the electromagnetic force is calculated numerically as an example. Distributions of global enstrophy, total squared strain and Okubo-Weiss function in the controlled flow field are discussed. The influence of Lorentz force on the distribution is analyzed.

CENTRIFUGAL INSTABILITY AND THE RIB VORTICES IN THE CYLINDER WAKE

The physical mechanism for generation of streamwise vortices (or rib vortices) in the cylinder wake was numerically investigated with a finite-difference scheme. Rayleigh's theory of centrifugal instability for inviscid axisymmetric flow was extended to analyze the 2-D primary flows. Centrifugal instability occurs when Ray greater than 0. Stability analyses were carried out with this discriminant for primary flows at different time levels in a half shedding period of the von Karman (or vK) vortices. Unstable areas were identified and the locations of rib vortices were coincident well with the unstable areas within the first wavelength of vK vortices behind the cylinder. The numerical results also show that rib vortices experience amplification in this region. (Edited author abstract) 17 Refs.

WKBJ analysis in the periodic wake of a cylinder

The nature of the three-dimensional transition arising in the flow past a cylinder is investigated by apply- ing the Lifschitz-Hameiri theory along special Lagrangian trajectories existing in its wake. Results show that the yon K^rm^n street is unstable with regard to short-wavelength perturbations. The asymptotic analysis predicts the possible existence of both synchronous （as modes A and B） and asynchronous （as mode C） instabilities, each associated to specific Lagrangian orbits. The proposed study provides useful qualitative information on the origin of the different modes but no quantitative agreement between the growth rates predicted by the asymptotic analysis and by a global stability analysis is observed. The reasons for such mismatch are briefly discussed and possible improvements to the present analysis are sug- gested.

Three-Dimensional Direct Numerical Simulation of Flow past A Near-Wall Circular Cylinder:Combined Effects of Gap Ratio and Boundary Layer Thickness on Flow Profiles and Pressure Distribution

Three-dimensional direct numerical simulations of the wake flow downstream of a near-wall circular cylinder at different gap ratios and boundary layer thicknesses are carried out by using the iterative immersed boundary method.The non-dimensional gap between the cylinder and the wall,G/D=0.2,0.6 and 1.0,the non-dimensional boundary layer thickness,δ/D=0.0,0.7 and 1.6,the Reynolds number,Re=350,and the aspect ratio of the cylinder,L/D=25are adopted.High-resolution visualizations of the complex vortex structures at differentδ/D and G/D are presented.The transition of the streamwise vortex mode,the combined effects ofδ/D and G/D on the flow statistics,the pressure and shear stress distribution and the hydrodynamic forces are analyzed.Results show that with decreasing G/D and increasingδ/D,the gap flow and its vortex-shedding are significantly weakened,together with an elongated wake and an enlarged low-velocity area near the wall,leading to the wake mode transition from the two-sided to one-sided vortex-shedding.Different relative positions of the cylinder regarding the boundary layer alter the flow features of the shear layers.With an increase inδ/D,the front stagnation point shifts to the upper surface,and the distance between the flow divergence point and the maximum pressure position increases.The mean drag coefficient and r.m.s.values of drag and lift coefficients decrease with a decrease in G/D and an increase inδ/D,while the mean lift coefficient increases with decreasing G/D but decreases with increasingδ/D.

ON THE INSTABILITY OF WAKES BEHIND STATIONARY CIRCULAR CYLINDERS

The study on the formation of vortex streets behind stationary circular cylinders is of substantial sense in engineering, since vortex streets play the leading role in introduction of vibration, generation of noise and wake instability, etc.. In the present paper, the Orr-Sommerfeld equation combined with measured velocity profiles is used to investigate the type of instability behind stationary cylinders, which determines the mechanism of vortex formation. The numerical calculations for Reynolds numbers of 56-140 000 imply that there is a range around the end of the dead water region in cylinder wakes where the instability belongs to the absolute type. Beyond the range, the flows show to be of the convective type. On the other hand, the flows tend to be of the convective instability when Reynolds number is below the subcritical value of forming vortex streets. All of the correspondent Strouhal numbers agree with experimental data very well. The formation of vortex streets behind stationary cylinders is proposed to be caused by an absolute instability in the near wake. There is always an absolute instability region for the Reynolds numbers from 56-140,000. Further, the experimental manipulation of vortex streets according to the stability analysis mentioned above is proved to be very effective.

A note on the numerical simulations of flow past a wavy square-section cylinder

The flow past a square-section cylinder with a geometric disturbance is investigated by numerical simulations. The extra terms, due to the introduction of mapping transformation simulating the effect of disturbance into the transformed Navier-Stokes equations, are correctly derived, and the incorrect ones in the previous literature are pointed out and analyzed. Furthermore, the relationship between the vorticity, especially on the cylinder surface, and the disturbance is derived and explained theoretically. The computations are performed at two Reynolds numbers of 100 and 180 and three amplitudes of waviness of 0.006, 0.025 and 0.167 with another aim to explore the effects of different Reynolds numbers and disturbance on the vortex dynamics in the wake and forces on the body. Numerical results have shown that, at the mild waviness of 0.025, the Kairmain vortex shedding is suppressed completely for Re = 100, while the forced vortex dislocation is appeared in the near wake at the Reynolds number of 180. The drag reduction is up to 21.6% at Re = 100 and 25.7% at Re = 180 for the high waviness of 0.167 compared with the non-wavy cylinder. The lift and the Strouhal number varied with different Reynolds numbers and the wave steepness are also obtained.

Experimental Study of Flow around a Circular Cylinder inside a Bubble Plume

This study experimentally explores the flow around a cylinder with circular cross-section placed inside a bubble plume. Small gas bubbles with diameter smaller than 0.06 mm are released from electrodes on the bottom of a water tank by electrolysis of water. The bubbles induce water flow around them as they rise because of buoyancy. Inside the generated bubble plume, a cylinder with diameter D of 30 mm is placed at 6.5D above the electrodes. The bubbles and water flow around the cylinder are visualized, and the bubble velocity distribution is measured. The experiments elucidate the bubble behavior around the cylinder, the separated shear layers originating at the cylinder surface, their roll-up, the bubble entrainment in the resultant large-scale eddies behind the cylinder, and the vortex shedding from the cylinder.

Electro–magnetic control of shear flow over a cylinder for drag reduction and lift enhancement

In this paper, the electro-magnetic control of a cylinder wake in shear flow is investigated numerically. The effects of the shear rate and Lorentz force on the cylinder wake, the distribution of hydrodynamic force, and the drag/lift phase diagram are discussed in detail. It is revealed that Lorentz force can be classified into the field Lorentz force and the wall Lorentz force and they affect the drag and lift forces independently. The drag/lift phase diagram with a shape of ＂8＂ consists of two closed curves, which correspond to the halves of the shedding cycle dominated by the upper and lower vortices respectively. The free stream shear （K 〉 0） induces the diagram to move downward and leftward, so that the average lift force directs toward the downside. With the upper Lorentz force, the diagram moves downwards and to the right by the field Lorentz force, thus resulting in the drag increase and the lift reduction, whereas it moves upward and to the left by the wall Lorentz force, leading to the drag reduction and the lift increase. Finally the diagram is dominated by the wall Lorentz force, thus moving upward and leftward. Therefore the upper Lorentz force, which enhances the lift force, can be used to overcome the lift loss due to the free stream shear, which is also obtained in the experiment.

Underlay mechanism in lift-drag phase diagrams for shear flow over cylinder

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

The influences of wall Lorentz force and field Lorentz force on the cylinder drag reduction

In this paper,the effects of Lorentz force on drag reduction for a circular cylinder have been studied experimentally and numerically.Based on its effects on drag reduction,the Lorentz force is found to be classified into two parts：one acts directly on the cylinder,named as the wall Lorentz force,and the other called the field Lorentz force acts on the fluid inside the boundary layer.The wall Lorentz force leads to the generation of a thrust,whereas the field Lorentz force results in drag increase.Since the former dominates the drag variation,the drag would reduce accordingly and even turn into negative （thrust） with the application of Lorentz force.

Hydrodynamic characteristics and noise reduction mechanism of a wave leading hydrofoil placed in the wake of a cylinder

We have investigated the hydrodynamic and acoustic performance of a hydrofoil with a wave leading edge that is being ingested in a cylindrical wake,to explore the interaction and noise reduction mechanism with the use of near flow field and far field noise decoupled prediction methods of large eddy simulation(LES)and Ffowcs Williams-Hawkings(FW-H).Our results indicate that the wave leading edge has minimal effect on the hydrodynamic performance,however,it has demonstrated the ability to significantly improve the acoustic performance.Through the comparison of sound pressure level(SPL)and acoustic directivity,we have observed that the wave leading edge can significantly reduce the broadband noise in the far field.This is due to its ability to break the large-scale structure of the incoming flow,which weakens the direct impact and therefore reduces the tone noise.Additionally,the interaction between the broken vortex and the boundary layer around the hydrofoil surface is weakened,leading to a reduction in surface pressure pulsation and broadband noise intensity.The wave structure primarily affects the flow structure near the leading edge,resulting in a reduction in flow disturbance and sound source intensity,and an improvement in the acoustic feedback loop between the foil and the fore-cylinder.

Experimental Research on the Mechanism of Lift Amplification and Vibration Suppression of Lorentz Force

The Lorentz force generated by electromagnetic field on the surface of the cylinder in the electrolyte solution may modify the structure of the flow boundary layer effectively. The transient control process of Lorentz force is investigated experimentally for lift amplification and vibration suppression. The experiments are conducted in a rotating annular tank filled with a low-conducting electrolyte. A cylinder with an electro-magnetic actuator is placed into the electrolyte. The lift force of cylinder is measured using the strain gages attached to a fixed beam, and the flow fields are visualized by the dye markers. The results show that the upper vortex on the cylinder is suppressed, and the wake becomes a line and leans to the lower side under the action of upside Lorentz force while the lower vortex on the cylinder is suppressed and limited in a small region. Therefore, the value of lift increases with the variation of flow field. However, the vortexes on the cylinder are suppressed fully under the action of symmetrical Lorentz force which leads to the suppression of lift oscillation and then the vibration of cylinder are suppressed fully.

Molecular tagging techniques and their applications to the study of complex thermal flow phenomena

This review article reports the recent progress in the development of a new group of molecule-based flow diagnostic techniques, which include molecular tag- ging velocimetry （MTV） and molecular tagging thermometry （MTT）, for both qualitative flow visualization of thermally induced flow structures and quantitative whole-field mea- surements of flow velocity and temperature distributions. The MTV and MTT techniques can also be easily combined to result in a so-called molecular tagging velocimetry and ther- mometry （MTV＆T） technique, which is capble of achieving simultaneous measurements of flow velocity and temperature distribution in fluid flows. Instead of using tiny particles, the molecular tagging techniques （MTV, MTT, and MTV＆T） use phosphorescent molecules, which can be turned into long-lasting glowing marks upon excitation by photons of appropriate wavelength, as the tracers for the flow veloc- ity and temperature measurements. The unique attraction and implementation of the molecular tagging techniques are demonstrated by three application examples, which include： （1） to quantify the unsteady heat transfer process from a heated cylinder to the surrounding fluid flow in order to exam- ine the thermal effects on the wake instabilities behind the heated cylinder operating in mixed and forced heat convec- tion regimes, （2） to reveal the time evolution of unsteady heat transfer and phase changing process inside micro-sized, icing water droplets in order to elucidate the underlying physics pertinent to aircraft icing phenomena, and （3） to achievesimultaneous droplet size, velocity and temperature measure- ments of ＂in-flight＂ droplets to characterize the dynamic and thermodynamic behaviors of flying droplets in spray flows.

Experimental investigation on coherent structures at early stage of boundary layer bypass transition induced by wake impingement

The early stage of a boundary layer bypass transition induced by the direct impingement of a circular cylinder wake is experimentally investigated in water tunnel,with the primary interest in both the evolution of coherent structures and their effects on the disturbance growth inside the boundary layer.It is found that spanwise vortices with small scale first form in the near-wall region around the leading-edge,which are either the residual of the wake rollers cut by the leading-edge or the high-order structures induced by the wake rollers.The formation of these spanwise vortices leads to the first rapid disturbance growth inside the boundary layer.On the other hand,streamwise vortices,which result from the impingement of longitudinal braids onto the leading-edge,are also observed inside the boundary layer.They lead to the three dimensional destabilization and the subsequent dispersion of spanwise vortices,and soon become the most dominant coherent structures inside the transitional boundary layer.It is suggested that the formation and evolution of these streamwise vortices contribute to the secondary disturbance growth stage and thus promote the completion of the transition process.The difference between the present transition scenario triggered by direct wake impingement and that by indirect wake-vortex inducement is further discussed.

Some studies on mechanics of continuous mediums viewed as differential manifolds

The continuous mediums are divided into two kinds according to their geometrical configurations,the first one is related to Euclidian manifolds and the other one to Riemannian manifolds/surfaces in the point of view of the modern geometry.Two kinds of finite deformation theories with respect to Euclidian and Riemannian manifolds have been developed in the present paper.Both kinds of theories include the definitions of initial and current physical and parametric configurations,deformation gradient tensors with properties,deformation descriptions,transport theories and governing equations of nature conservation laws.The essential property of the theory with respect to Euclidian manifolds is that the curvilinear coordinates corresponding to the current physical configurations include time explicitly through which the geometrically irregular and time varying physical configurations can be mapped in the diffeomorphism manner to the regular and fixed domains in the parametric space.It is quite essential to the study of the relationships between geometries and mechanics.The theory with respect to Riemannian manifolds provides the systemic ideas and methods to study the deformations of continuous mediums whose geometrical configurations can be considered as general surfaces.The essential property of the theory with respect to Riemannian manifolds is that the thickness variation of a patch of continuous medium is represented by the surface density and its governing equation is rigorously deduced.As some applications,wakes of cylinders with deformable boundaries on the plane,incompressible wakes of a circular cylinder on fixed surfaces and axisymmetric finite deformations of an elastic membrane are numerically studied.

Particle Image Velocimetry Measurement of Flow Across Tube Bundle in Waste Heat Boiler

In the present paper the experimental investigations of flow across staggered tube bundles in waste heat boiler are conducted by mans of PIV (Particle Image Velocimetry) system. Flow visualization and velocity distribution of the wake between different cylinders are measured in detail. It is concluded that there are still Von Karman vortices in the wake and the phenomena of vortex shedding, pairing, merging are observed in the flow. The Von Karman vortices can’t fully developed because of the existence of the downstream cylinder There is interaction between main streams and vortices, and the development of the vortex is enhanced by this interaction. Meanwhile some statistical results are performed. The distribution of correlated variables of the velocity fluctuations u’ u’, u’ v’, v’ v’ and the space correlation coefficients are obtained.