On the vorticity characteristics of lobe-forced mixer at different configurations

Lobe-forced mixer is one typical example of the passive flow controllers owing to its corrugated trailing edge. Besides the spanwise Kelvin–Helmholtz vortex shedding, streamwise vortices are also generated within its mixing layer. The geometrical configuration of the lobe significantly affects these two types of vortices, which in turn affects the mixing performance of the mixer. In the present investigation, characteristics of mixers with five different configurations were examined and evaluated for two velocity ratios (r = 1, 0.4). The mixers have only one lobe in order to eliminate any possible interactions between neighboring vortices generated by the adjacent lobes. Hot-wire anemometer was used to examine the Kelvin–Helmholtz vortices via the spectrum analysis while laser Doppler anemometer was employed to examine the streamwise vortices. It was found that there were two main frequencies for the Kelvin–Helmholtz vortices in the wake of the mixer; and the Strouhal numbers approached their respective maximum values at high Reynolds number. The rectangular mixer had similar mixing performance with the semicircular one; and both of them were better than the triangular mixer. The scalloping modification enhanced mixing by generating additional streamwise vortices while the scarfing modification could not improve the mixing performance.     

Dynamics of hairpin vortices generated by a mixing tab in a channel flow

To better understand mixing by hairpin vortices, time-series particle image velocimetry (PIV) was applied to the wake of a trapezoidal-shaped passive mixing tab mounted at the bottom of a square turbulent channel (Re _h =2,080 based on the tab height). Instantaneous velocity/vorticity fields were obtained in sequences of 10 Hz in the tab wake in the center plane (x–y) and in a plane (x–z) parallel to the wall. Periodically-shed hairpin vortices were clearly identified and seen to rise as they advected downstream. Experimental evidence shows that the vortex-induced ejection of the near-wall viscous fluid to the immediate upstream is important to the dynamics of hairpin vortices. It can increase the strength of the hairpin vortices in the near tab region and cause generation of secondary hairpin vortices further downstream when the hairpin heads are farther away from the wall. Measurements also reveal the existence of a type of new secondary vortice with the opposite-sign spanwise vorticity. The distribution of vortex loci in the x–y plane shows that the hairpin vortices and the reverse vortices are spatially segregated in distinct layers. Turbulence statistics, including mean velocity profiles, Reynolds stresses, and turbulent kinetic energy dissipation rate distributions, were obtained from the PIV data. These statistical quantities clearly reveal imprints of the identified vortex structures and provide insight into mixing effectiveness. Received: 24 February 2000/Accepted: 24 October 2000     

The nature of near-wall convection velocity in turbulent channel flow

A novel notion of turbulent structure the local cascade structure-is introduced to study the convection phenomenon in a turbulent channel flow. A space-time cross-correlation method is used to calculate the convection velocity. It is found that there are two characteristic convection speeds near the wall, one associated with small-scale streaks of a lower speed and another with streamwise vortices and hairpin vortices of a higher speed. The new concept of turbulent structure is powerful to illustrate the dominant role of coherent structures in the near-wall convection, and to reveal also the nature of the convection-the propagation of patterns of velocity fluctuations-which is scale-dependent.     

On the formation of Taylor–G?rtler vortices in RMF-driven spin-up flows

This paper is concerned with a liquid metal flow driven by a rotating magnetic field inside a stationary cylinder. We consider especially the secondary meridional flow during the time when the fluid spins up from rest. The developing flow is investigated experimentally and by direct numerical simulations. The vertical profiles of the axial velocity are measured by means of the ultrasound Doppler velocimetry. Evolving instabilities in the form of Taylor–G?rtler vortices have been observed just above the instability threshold (Ta ≥ 1.5· Ta ^cr). The rotational symmetry may survive over a distinct time even if a first Taylor–G?rtler vortex pair has been formed as closed rings along the cylinder perimeter. The transition to a three-dimensional flow in the side layers results from the advection or a precession and splitting of the Taylor–G?rtler vortex rings. The predictable behaviour of the Taylor–G?rtler vortices disappears with increasing magnetic field strength. The numerical simulations agree very well with the flow measurements.     

Measurement of parallel blade–vortex interaction at low Reynolds numbers

In this study parallel blade–vortex interaction for a Schmidt-propeller configuration has been examined using particle image velocimetry (PIV). This tandem configuration consists of a leading airfoil (forefoil), used to generate a vortical wake of leading-edge vortices (LEVs) and trailing-edge vortices (TEVs) through a pitching or plunging motion, and a trailing airfoil (hindfoil), held fixed with a specified angle of attack and vertical spacing in its wake. The hindfoil incidence (loading) and not the vertical spacing to the incoming vortical wake has been found to dictate the nature of the interaction (inviscid vs. viscous). For cases where the vortex–blade offset is small and the hindfoil is loaded, vortex distortion and vortex-induced separations are observed. By tracking the circulation of the LEV and TEV, it has been found that the vortices are strengthened for the tandem arrangement and in certain cases dissipate quicker in the wake when interacting with the hindfoil. Time-averaged forces obtained using a standard control-volume analysis are then obtained and used to evaluate these vortex-interaction cases. A subsequent analysis of the varying pressure distribution over the suction side of the hindfoil is performed by integrating the Navier–Stokes equations through the velocity field. This allows for a direct comparison of the vortex-induced loading for the various configurations.     

An analog of the Bernoulli and Cauchy-Lagrange integrals for a time-dependent vortex flow of an ideal incompressible fluid

An expression with a constant value over all space (including multiply connected domains) relating the pressure function to the square of the velocity and the characteristics of the traveling vortices is derived for a time-dependent ideal incompressible fluid flow with nonzero vorticity. When there are bodies in the flow, they must also be represented in the form of traveling vortices. For steady-state flow the formula obtained goes over into the Bernoulli integral and for time-dependent irrotational flow into the Cauchy-Lagrange integral. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 31–41, January–February, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 98-01-00156 and project No. 96-15-9603 for the support of leading science schools).     

An unsteady point vortex method for coupled fluid–solid problems

A method is proposed for the study of the two-dimensional coupled motion of a general sharp-edged solid body and a surrounding inviscid flow. The formation of vorticity at the body’s edges is accounted for by the shedding at each corner of point vortices whose intensity is adjusted at each time step to satisfy the regularity condition on the flow at the generating corner. The irreversible nature of vortex shedding is included in the model by requiring the vortices’ intensity to vary monotonically in time. A conservation of linear momentum argument is provided for the equation of motion of these point vortices (Brown–Michael equation). The forces and torques applied on the solid body are computed as explicit functions of the solid body velocity and the vortices’ position and intensity, thereby providing an explicit formulation of the vortex–solid coupled problem as a set of non-linear ordinary differential equations. The example of a falling card in a fluid initially at rest is then studied using this method. The stability of broadside-on fall is analysed and the shedding of vorticity from both plate edges is shown to destabilize this position, consistent with experimental studies and numerical simulations of this problem. The reduced-order representation of the fluid motion in terms of point vortices is used to understand the physical origin of this destabilization.      

A structural model for the vortex tubes of isotropic turbulence

A class of exact solutions of the Navier–Stokes equations is introduced to model the fine-scale, tubular structures of isotropic turbulence. The model vortices exhibit slow algebraic fall-off of the induced velocity, and accurately reproduce the velocity signatures observed in DNS and experiments. The proposed model has interesting implications for the theoretical analysis of turbulence, supporting the view that the inertial range energy scaling may have a link with the near-singular velocity field induced by vortex tubes produced by the roll-up of vortex sheets.      

Vortex stretching and filaments

This paper presents a new technique to produce controlled stretched vortices. Intense elliptical vortices are created by stretching of an initial vorticity sheet. The initial vorticity comes from a laminar boundary layer flow and the stretching is parallel to the vorticity vectors. This low velocity flow enables direct observation of the formation and destabilization of vortices. Visualizations are combined with quasi-instantaneous measurements of a full velocity profile. The velocity profile is obtained with an ultrasonic pulsed Doppler velocimeter. The evolution of the central diameter of the vortices is related to the stretching. It is observed that destabilization occurs by pairing of two vortices, by hairpin deformation, and by breakdown of vortices into a “coil shape”.     

The flow in a planar-radial vortex chamber. 2. Vortex structure of the flow

A vortex structure of an air flow with a characteristic size of vortices comparable with the primary vortex size was observed in a vortex chamber of planar-radial geometry for the first time. The vortex component of the flow velocity along the chamber radius and its axis was calculated. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 41–49, January–February, 2000.     

Direct simulation of isolated elliptic vortices and of their radiated noise

The aerodynamic evolution and the acoustic radiation of elliptic vortices with various aspect ratios and moderate Mach numbers are investigated by solving numerically the full compressible Navier–Stokes equations. Three behaviours are observed according to the aspect ratio σ = a/b where a and b are the major and minor semi-axes of the vortices. At the small aspect ratio σ = 1.2, the vortex rotates at a constant angular velocity and radiates like a rotating quadrupole. At the moderate aspect ratio σ = 5, the vortex is initially unstable. However the growth of instability waves is inhibited by the return to axisymmetry which decreases its aspect ratio. The noise level becomes lower with time and the radiation frequency increases. For vortices with larger aspect ratios σ ≥ 6, the return to axisymmetry does not occur quickly enough to stop the growth of instabilities, which splits the vortices. Various mergers are then found to occur. For instance in the case σ = 6, several successive switches between an elliptic state and a configuration of two co-rotating vortices are observed. The present results show that the initial value of the aspect ratio yields the relative weight between the return to axisymmetry which stabilizes the vortex and the growth of instabilities which tends to split it. Moreover the noise generated by the vortices is also calculated using the analytical solution derived by Howe (J. Fluid Mech. 71:625–673, 1975) and is compared with the reference solution provided by the direct computation. This solution is found to be valid for σ = 1.2. An extended solution is proposed for higher aspect ratios. Finally, the pressure field appears weakly affected by the switches between the two unstable configurations in the case σ = 6, which underlines the difficulty to detect the split or the merger of vortices from the radiated pressure. This study also shows that elliptic vortices can be used as a basic configuration of aerodynamic noise generation.      

Laminar co-rotating Batchelor vortex merging

The dynamics of laminar co-rotating vortex pairs without axial flow have been recently thoroughly studied through theoretical, experimental and numerical studies, which revealed different instabilities contributing to the decay of the vortices. In this paper, the objective is to extend the analysis to the case of co-rotating vortices with axial flow at low Reynolds numbers. A high-order incompressible Navier–Stokes flow solver is used. The momentum equations are spatially discretized on a staggered mesh by finite differences and all derivatives are evaluated with 10th order compact finite difference schemes with RK-4 temporal discretization. The initial condition is a linear superposition of two co-rotating circular Batchelor vortices with q = 1. It is found that there is an initial evolution that resembles the evolution that single q = 1 vortices go through. Azimuthal disturbances grow and result in the appearance of large-scale helical sheets of vorticity. With the development of these instability waves, the axial velocity deficit is weakened. The redistribution of both angular and axial momentum between the core and the surroundings drives the vortex core to a more stable configuration, with a higher q value. After these processes, the evolution is somewhat similar to a pair of co-rotating Lamb–Oseen vortices. A three-dimensional instability develops, with a large band of unstable modes, with the most amplified mode corresponding scaling with the vortex initial separation distance. P. J. S. A. Ferreira de Sousa wishes to acknowledge the support of FCT—SFRH/BD/1129/2000 and SFRH/BPD/21778/2005.     

Transition of boundary layer flows in the presence of Goertler vortices

Transition of boundary layer flows in the presence of longitudinal counter-rotating Goertler vortices was experimentally investigated on a concave surface of 1.0 m radius of curvature in a perspex (plexiglass) curved rectangular duct connected to a low speed wind tunnel for a free-stream velocity range of 5.7–11.8 m/s. Quantitative measurements were carried out using a single sensor hot-wire anemometer, while the boundary layer transitions were detected using frequency spectrum method. The results confirm that in the presence of Goertler vortices, transition is initiated at the boundary layer upwash regions, and also agree well with the predicted values obtained using the two existing empirical transition criteria for concave surface boundary layer flows.     

Characteristics of air and water velocity fields during natural convection

Air and water velocity fields have been simulated during natural convection, using a two-dimensional volume of fluid (VOF) model. The results have shown that during unstable thermal stratification, the root-mean-square (RMS) airside velocities are an order of magnitude higher than the RMS waterside velocities, whereas, during the stable thermal stratification, the velocity magnitudes are comparable for air and water sides. Furthermore, the magnitude of the air velocity changed more rapidly with the change in the bulk air–water temperature difference than the water velocity, indicating that the air velocities are more sensitive to the bulk air and water temperature difference than the water velocities. A physical model of the heat and mass transfer across the air–water interface is defined. According to this model, the vortices on the air and water sides play an important role in enhancing the heat and mass transfer. Due to the significance of the flow velocities in the transport process, it has been proposed that the correlations for the heat and mass transfer during natural convection should be improved by incorporating the flow velocity as a parameter.     

Microscopic particle image velocimetry measurements of transition to turbulence in microscale capillaries

The character of transitional capillary flow is investigated using pressure-drop measurements and instantaneous velocity fields acquired by microscopic PIV in the streamwise–wall-normal plane of a 536 μm capillary over the Reynolds-number range 1,800 ≤ Re ≤ 3,400 in increments of 100. The pressure-drop measurements reveal a deviation from laminar behavior at Re = 1,900 with the differences between the measured and the predicted laminar-flow pressure drop increasing with increasing Re. These observations are consistent with the characteristics of the mean velocity profiles which begin to deviate from the parabolic laminar profile at Re = 1,900, interpreted as the onset of transition, by becoming increasingly flatter and fuller with increasing Re. A fully-turbulent state is attained at Re ≅ 3,400 where the mean velocity profile collapses onto the mean profile of fully-developed turbulent pipe flow from an existing direct numerical simulation at Re = 5,300. Examination of the instantaneous velocity fields acquired by micro-PIV in the range 1,900 ≤ Re < 3,400 reveal that transitional flows at the microscale are composed of a subset of velocity fields illustrating a purely laminar behavior and a subset of fields that capture significant departure from laminar behavior. The fraction of velocity fields displaying non-laminar behavior increases with increasing Re, consistent with past observations of a growing number of intermittent turbulent spots bounded by nominally laminar flow in macroscale pipe flow with increasing Re. Instantaneous velocity fields that are non-laminar in character consistently contain multiple spanwise vortices that appear to streamwise-align to form larger-scale interfaces that incline slightly away from the wall. The characteristics of these “trains” of vortices are reminiscent of the spatial features of hairpin-like vortices and hairpin vortex packets often observed in fully-turbulent wall-bounded flow at both the macro- and micro-scales. Finally, single-point statistics computed from the non-laminar subsets at each transitional Re, including root-mean-square velocities and the Reynolds shear stress, reveal a gradual and smooth maturation of the patches of disordered motion toward a fully-turbulent state with increasing Re.     

Time resolved flow-field measurements of a turbulent mixing layer over a rectangular cavity

High Reynolds number, low Mach number, turbulent shear flow past a rectangular, shallow cavity has been experimentally investigated with the use of dual-camera cinematographic particle image velocimetry (CPIV). The CPIV had a 3 kHz sampling rate, which was sufficient to monitor the time evolution of large-scale vortices as they formed, evolved downstream and impinged on the downstream cavity wall. The time-averaged flow properties (velocity and vorticity fields, streamwise velocity profiles and momentum and vorticity thickness) were in agreement with previous cavity flow studies under similar operating conditions. The time-resolved results show that the separated shear layer quickly rolled-up and formed eddies immediately downstream of the separation point. The vortices convect downstream at approximately half the free-stream speed. Vorticity strength intermittency as the structures approach the downstream edge suggests an increase in the three-dimensionality of the flow. Time-resolved correlations reveal that the in-plane coherence of the vortices decays within 2–3 structure diameters, and quasi-periodic flow features are present with a vortex passage frequency of ~1 kHz. The power spectra of the vertical velocity fluctuations within the shear layer revealed a peak at a non-dimensional frequency corresponding to that predicted using linear, inviscid instability theory.     

Effect of wing–wake interaction on aerodynamic force generation on a 2D flapping wing

This paper is motivated by the works of Dickinson et al. (Science 284:1954–1960, 1999) and Sun and Tang (J Exp Biol 205:55–70, 2002) which provided two different perspectives on the influence of wing–wake interaction (or wake capture) on lift generation during flapping motion. Dickinson et al. (Science 284:1954–1960, 1999) hypothesize that wake capture is responsible for the additional lift generated at the early phase of each stroke, while Sun and Tang (J Exp Biol 205:55–70, 2002) believe otherwise. Here, we take a more fundamental approach to study the effect of wing–wake interaction on the aerodynamic force generation by carrying out simultaneous force and flow field measurements on a two-dimensional wing subjected to two different types of motion. In one of the motions, the wing at a fixed angle of attack was made to follow a motion profile described by “acceleration-constant velocity-deceleration”. Here, the wing was first linearly accelerated from rest to a predetermined maximum velocity and remains at that speed for set duration before linearly decelerating to a stop. The acceleration and deceleration phase each accounted for only 10% of the stroke, and the stroke covered a total distance of three chord lengths. In another motion, the wing was subjected to the same above-mentioned movement, but in a back and forth manner over twenty strokes. Results show that there are two possible outcomes of wing–wake interaction. The first outcome occurs when the wing encounters a pair of counter-rotating wake vortices on the reverse stroke, and the induced velocity of these vortices impinges directly on the windward side of the wing, resulting in a higher oncoming flow to the wing, which translates into a higher lift. Another outcome is when the wing encounters one vortex on the reverse stroke, and the close proximity of this vortex to the windward surface of the wing, coupled with the vortex suction effect (caused by low pressure region at the center of the vortex), causes the net force on the wing to decrease momentarily. These results suggest that wing–wake interaction does not always lead to lift enhancement, and it can also cause lift reduction. As to which outcome prevails depend very much on the flapping motion and the timing of the reverse stroke.     

Internal waves induced by potential vortices

A linearized equation of the internal waves developing in an ideal stratified gas under the action of potential vortices concentrated in a vertical cylinder is obtained. The Cauchy problem for the internal wave equation with right side depending on the vortex intensity is solved by the integral transform method. In the case of a vortex filament the exact solution is found. Approximate formulas are obtained on the basis of the steady-phase method when the vorticity is exponentially stratified along the vertical. Expressions for the phase velocity and amplitude of the radial wave traveling away from the cylindrical vortex are found. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 118–123, January–February, 1998. The work was carried out with the support of the Russian Foundation for Fundamental Research (project No. 96-01-04599).     

Two-dimensional gas vortices and twisted gas jets

This paper studies an invariant solution of rank one of the equations of motion of a polytropic gas that describes two-dimensional gas vortices and twisted gas jets. Flow types are classified according to the governing parameter: vortices in the form of sources and sinks, unlimited expansion, and collapse. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 71–81, May–June, 2009.