Secondary Vortex Pair Research Articles

Effects of aspect ratio on shock-cylinder interaction

Interaction of a planar shock wave with a discontinuous \(\hbox {SF}_6\) elliptic gas cylinder surrounded by air is investigated. Special attention is given to the effects of aspect ratio on wave pattern, interface evolution, and material mixing. An ideal discontinuous two-dimensional gas cylinder is created by the soap film technique in experiments, and the shocked flow is captured by schlieren photography combined with a high-speed video camera. The surface of the gas cylinder is clear enough to observe the shock motions, and the distinct interface boundaries allow us to extract more details. As aspect ratio varies, the shock focusing process is quite different. For the prolate gas cylinder, an inward jet is produced although an internal shock focusing firstly occurs. The inward jet has never been observed in membraneless prolate ellipse experiments probably because the inward jet is so faint due to less vorticity generation on membraneless interface that it is difficult to be observed. For the oblate gas cylinder, a secondary vortex pair, which has not been described clearly in previous work, is derived from the downstream interface. The material lines at early stages are extracted from experiments, which grow faster as aspect ratio increases. The interfacial area, the mean volume fraction and the mixing rate are presented from computations, and the results show that the increase of aspect ratio promotes the mixing between gases.

Numerical investigation on vortex dipole interacting with concave walls of different curvatures

Immersed boundary lattice Boltzmann method is adopted to simulate Lamb vortex dipole colliding with concave walls of different curvatures. We introduce the single-relaxation-time lattice Boltzmann method and a variant of the immersed boundary method (IBM). The present IBM avoids the penetration phenomenon of streamlines through the solid wall. The formation of Lamb vortex dipole is simulated subsequently. Focusing on dipole-wall interactions, vortex dipoles colliding with concave walls of different curvatures at three Reynolds numbers Re = 800, 1600 and 2400 are simulated. Circulation and the track of the positive monopole from initial vortex dipole are used to investigate the features of dynamics process. The results show that the circulation ratio of the secondary vortex pair reduces as the curvature of the concave wall decreases. The results also indicate that there exists certain threshold of curvature, out of which the dynamic characteristics of the vorticity field changes apparently.

Boundary layer transition mechanisms behind a micro-ramp

The early stage of three-dimensional laminar-to-turbulent transition behind a micro-ramp is studied in the incompressible regime using tomographic particle image velocimetry. Experiments are conducted at supercritical micro-ramp height $h$ based Reynolds number $Re_{h}=1170$. The measurement domain encompasses 6 ramp widths spanwise and 73 ramp heights streamwise. The mean flow topology reveals the underlying vortex structure of the wake flow with multiple pairs of streamwise counter-rotating vortices visualized by streamwise vorticity. The primary pair generates a vigorous upwash motion in the symmetry plane with a pronounced momentum deficit. A secondary vortex pair is induced closer to the wall. The tertiary and even further vortices maintain a streamwise orientation, but are produced progressively outwards of the secondary pair and follow a wedge-type pattern. The instantaneous flow pattern reveals that the earliest unstable mode of the wake features arc-like Kelvin–Helmholtz (K–H) vortices in the separated shear layer. Under the influence of the K–H vortices, the wake exhibits a high level of fluctuations with a pulsatile mode for the streamwise momentum deficit. The K–H vortices are lifted up due to the upwash induced by the quasi-streamwise vortex pair, while they appear to undergo pairing, distortion and finally breakdown. Immediately downstream, a streamwise interval of relatively low vortical activity separates the end of the K–H region from the formation of new hairpin vortices close to the wall. The latter vortex structures originate from the region of maximum wall shear, induced by the secondary vortex pair causing strong ejection events which transport low-speed flow upwards. The whole pattern features a cascade of hairpin vortices along a turbulent/non-turbulent interface. The wedge-shaped cascade signifies the formation of a turbulent wedge. The turbulent properties of the wake are inspected with the spatial distribution of the velocity fluctuations and turbulence production in the developing boundary layer. Inside the wedge region, the velocity fluctuations approach quasi-spanwise homogeneity, indicating the development towards a turbulent boundary layer. The wedge interface is characterized by a localized higher level of velocity fluctuations and turbulence production, associated to the deflection of the shear layer close to the wall and the onset of coherent hairpin vortices inducing localized large-scale ejections.

Modification of vortex dynamics and transport properties of transitional axisymmetric jets using zero-net-mass-flux actuation

We study the near field of a zero-net-mass-flux (ZNMF) actuated round jet using direct numerical simulations. The Reynolds number of the jet ReD = 2000 and three ZNMF actuators are used, evenly distributed over a circle, and directed towards the main jet. The actuators are triggered in phase, and have a relatively low momentum coefficient of Cμ = 0.0049 each. We study four different control frequencies with Strouhal numbers ranging from StD = 0.165 to StD = 1.32; next to that, also two uncontrolled baseline cases are included in the study. We find that this type of ZNMF actuation leads to strong deformations of the near-field jet region that are very similar to those observed for non-circular jets. At the end of the jet's potential core (x/D = 5), the jet-column cross section is deformed into a hexagram-like geometry that results from strong modifications of the vortex structures. Two mechanisms lead to these modifications, i.e., (i) self-deformation of the jet's primary vortex rings started by distortions in their azimuthal curvature by the actuation, and (ii) production of side jets by the development and subsequent detachment of secondary streamwise vortex pairs. Further downstream (x/D = 10), the jet transforms into a triangular pattern, as the sharp corner regions of the hexagram entrain fluid and spread. We further investigate the global characteristics of the actuated jets. In particular when using the jet preferred frequency, i.e., StD = 0.33, parameters such as entrainment, centerline decay rate, and mean turbulent kinetic energy are significantly increased. Furthermore, high frequency actuation, i.e., StD = 1.32, is found to suppress the mechanisms leading to large scale structure growth and turbulent kinetic energy production. The simulations further include a passive scalar equation, and passive scalar mixing is also quantified and visualized.

Stability study of flow in a 90° bend based on the energy gradient theory

The energy gradient theory is used to analyze numerical simulation of the flow in a 90 degree bend with square cross-section. The Reynolds number based on the cross-sectional width and the averaged velocity is 158, 394 and 790, respectively. It is found that at Re = 790, the value of the energy gradient function K increases with the fluid entering the curved section, causing flow instability and forming a pair of secondary vortices; then the secondary vortices gradually stabilizes and the value of K decreases. At the exit of the bend, the total pressure distribution in the cross-section presents serious distortion, which leads to a transition of two vortices to four vortices. With the flow ahead, the maximum of K rises again, resulting in the transition of four vortices to eight vortices. At the low Reynolds number (Re = 158 and Re = 394), there is only one pair of vortices due to the low value of K, which are stable. This study shows that the occurrence of instability is closely related to the evolution of energy gradient function K.

Impact of a vortex dipole with a semi-infinite rigid plate

The physics of a two-dimensional vortex dipole impinging on the tip of a semi-infinite rigid plate is numerically examined. The dipole trajectory is initially orthogonal to the plate and aligned with its tip. The impact behavior is examined for three dipole Reynolds numbers. As the dipole approaches, vorticity is induced along the plate, as in the case of a dipole approaching a full wall, and is additionally shed from the tip. Upon impact, the dipole effectively splits, with half of it interacting with the vorticity induced on the plate and the other half with the vorticity shed from the tip. Each half of the original dipole forms a new secondary vortex pair whose behavior depends upon the Reynolds number of the original dipole. Contingent upon the rate of momentum diffusion, these secondary (and tertiary) vortex pairs may return and impact the plate again. Herein, we detail the interaction of the dipole impact at various Reynolds numbers, with a focus on the vortex dynamics and the distributed load imposed on the rigid plate by the fluid.

Effect of High-Amplitude Forcing on Turbulent Combustion Intensity and Vortex Core Precession in a Strongly Swirling Lifted Propane/Air Flame

The present work reports stereoscopic particle image velocimetry (PIV) measurements in a strongly swirling nonreacting jet and partially premixed lifted flame. The spatial distributions of the average velocity and components of turbulent kinetic energy were calculated from the measured ensembles of the instantaneous velocity fields. A pronounced bubble-type vortex breakdown was observed for the studied flows. Based on proper orthogonal decomposition (POD) of the PIV data and on estimates of velocity fluctuation spectra by a laser Doppler velocimetry (LDV) probe, it was concluded that the combustion did not fundamentally affect the type of coherent structures in the strongly swirling flow: a pair of secondary helical vortices was induced by a precessing vortex core in both cases. Because a strongly swirling jet flow is usually insensitive to weak forcing, strong perturbations were superimposed on the flow bulk velocity to force the formation of ring-like vortices in the flow and to investigate the possible outcomes on the turbulent combustion process. The forcing frequency was below that of the precession. Based on the CH* chemiluminescence signal, it was observed that the forcing provided an increase in the turbulent combustion rate near the flame onset, as the entrainment of ambient air to the rich mixture must have increased. Moreover, for a forcing amplitude typically above the magnitude of reverse flow inside the bubble-type recirculation zone, a dramatic suppression of the vortex core precession took place in the reacting case. This effect was accompanied by a quasi-periodical vanishing of the recirculation zone due to interaction of the forced ring-like vortices with the lifted flame.

Pulsed-Jet Ejector Thrust Augumentor Characteristics

An experimental study is carried out to investigate the characteristics of a pulsed-jet ejector thrust augmentor that is suitable for use in vertical take-off and landing aircraft. Phase-locked particle image velocimetry is used to obtain the detailed spatio-temporal evolution of the ejector flowfield. Experiments were carried out to determine the conditions formaximum thrust augmentation. In the presence of the ejector, the pulsed-jet primary vortex induces a secondary vortex at the ejector wall. The peak vorticity magnitude of the primary vortex was found to be at a maximum at the condition of maximum thrust augmentation. The presence of this primary and secondary vortex pair results in enhancedmass entrainment andmixing, which, in turn, produces increased thrust augmentation. The nonmonotonic variation of the thrust augmentation ratio with the ejector area ratio (ejector inlet area/nozzle exit area) is largely determined by the peak vorticity magnitude of the primary-vortex ring and the secondary vortex.

Parallel DNS for vortex structure of late stages of flow transition

A new DNS using compact high order scheme and MPI parallel computation has been conducted with 1920 × 241 × 128 grid points for non-linear stages of flow transition. The coherent vortex structure of the late flow transition stages and the mechanism of formation of single vortex ring, multiple vortex rings, and small length scales are discussed. The ring-like vortex formation from the Λ-vortex is the result of the interaction of two pairs of counter-rotating primary and secondary streamwise vortices. The formation of the multiple ring structure follows the first Helmholtz vortex conservation law. A bridge must be formed to link two Λ-vortex legs. The bridge finally develops as a new ring. This process keeps going onto form a multiple ring structure. The U-shaped vortices are part of existing coherent large vortex structure. Actually, the U-shaped vortex, which is a third level vortex, serves as a second neck to supply vorticity to the multiple rings. The multiple ring-like vortex structure is found quite stable and can travel for a long distance. The “hairpin vortex breakdown” does not happen. The small vortices can be found on the bottom of the boundary layer near the wall surface. It is believed that the small vortices are generated by the interaction of higher level vortices with the solid wall, but not by the “vortex breakdown”.

Numerical study of turbulent heat and fluid flow in a straight square duct at higher Reynolds numbers

This paper presents the large eddy simulation (LES) results of turbulent heat and fluid flows in a straight square duct (SSD) at higher Reynolds numbers ranged from 10 4 to 10 6 , which are based on the bulk mean velocity and the duct cross-sectional side length. A sub-grid model is proposed, which assumes that the sub-grid stress and heat flux are, respectively, proportional to the temporal increments of the filtered strain rate and temperature gradient, with the proportional coefficient determined by calibrating the friction factor. The temperature was taken as passive due to the neglect of buoyancy effect. The Taylor and Kolmogorov scales in the SSD are predicted and the results show that the LES results are better than c-DNS results. The LES results can explain why the c-DNS is applicable to the problem at a moderate Re, and reveal that the largest relative deviation of the overall mean Nusselt number is less than 10% as compared with existing experimental correlations. With the rise of Reynolds number, the mean secondary vortex pairs move towards the corners and have smaller size, while smaller vortices also occur in the instantaneous secondary flow. Empirical mode decomposition (EMD) was carried out to analyze the fluctuation of the x -averaged cross-sectional origin temperature at Re = 10 5 .

Direct numerical simulation of turbulent Taylor–Couette flow

Direct numerical simulation (DNS) is used to investigate turbulent Taylor–Couette (TC) flow. A simulation was run for a Reynolds number of 3200 in an apparatus with a radius ratio of η = 0.617 and an aspect ratio of 4.58, which assumed a vortex pair wavelength of 2.29. Results reported include the mean velocity, velocity fluctuation intensities, Reynolds stress budgets, and visualizations of the instantaneous velocity fluctuation field. Secondary near-wall vortex pairs are observed near to the cylinder in addition to the Taylor vortex (TV) motion. Weaker evidence of secondary vortices is found at the outer cylinder where a banded structure has been identified. The azimuthal wall shear stress component shows large peaks and valleys at stagnation points on the surface of both cylinders where flow from neighbouring vortices impacts on the respective wall. These stagnation points correspond to locations where the secondary vortices have been identified. The effect of the mean TV motion is reflected in the Reynolds stress budgets which are similar to but more complex than those of two-dimensional boundary layers. Visualization of the turbulent velocity fluctuations reveals near-wall streaks at the inner cylinder.

Electroosmotic effect on flows in a serpentine microchannel with varying zeta potential

Electroosmosis is widely observed in different micro-scale flows. Flow modification due to electroosmosis is important for applications related to fuel cells such as micro direct methanol fuel cells and micro-scale devices. Mechanism for delivering methanol into the micro-fuel cell is very important process affecting its power density and often they need to be stand alone systems with no external pumps or other ancillary devices to eliminate the parasitic power loss accounting from fuel feed. In this study, numerical simulation has been carried out for the electroosmotic effect on pressure-driven flows in a serpentine microchannel whose side walls are subjected to variable zeta potentials. It is observed that for a non-uniform zeta potential, the secondary vortex pair and their strength of motion generated by electroosmosis is modified asymmetrically, corresponding to the degree of the variation in and the magnitude of the zeta potential. It is also found that the flow profiles are quite different for variable zeta potentials as compared to a constant zeta potential applied on the channel walls. The flow phenomena at the bend of the serpentine channel has also been investigated, and flow control is possible by regulating the applied zeta potential on the channel walls. It is observed that vortices shift in a clockwise direction as the applied zeta potential is increased on the walls of the serpentine channel. Formation of additional vortices has also been observed for very low values of applied zeta potential.

Measurement of mean rotation and strain-rate tensors by using stereoscopic PIV

A technique is described for measuring the mean velocity gradient (rate-of-displacement) tensor by using a conventional stereoscopic particle image velocimetry (SPIV) system. Planar measurement of the mean vorticity vector, rate-of-rotation and rate-of-strain tensors and the production of turbulent kinetic energy can be accomplished. Parameters of the Q criterion and negative λ2 techniques used for vortex identification can be evaluated in the mean flow field. Experimental data obtained for a circular turbulent jet issuing normal to a crossflow in a low speed wind tunnel for a jet-to-crossflow velocity ratio of 3.3 are presented to show the applicability of the proposed technique. The results reveal the presence of a secondary counter-rotating vortex pair (SCVP) which is located within the jet core and has a sense of rotation opposite to that of the primary one (PCVP). Consistency of the measurements is verified by the agreement of data obtained in two perpendicular planes. Accuracy of the data is discussed and algebraic relations for some measurement uncertainties are presented.

Three-dimensional flow in cavity at yaw

This study introduces a “building block” prototype model of three-dimensional (3-D) flows about protrusions and cavities with an arbitrary angle between the external flow and rigid elements. The considered flow in a 3-D cavity has the lid of cavity moving along the lid diagonal (Case A). The proposed case is taken as a typical representative of essentially 3-D highly separated vortical flows having simple single-block rectangular geometry of computational domain. This 3-D lid-driven cavity flow is studied by numerical solution of the 3-D viscous Navier–Stocks equations using FLUENT software with second-order upwind schemes for convective terms. Computational results are compared to the classical benchmark case where the lid moves in the direction parallel to the cavity side walls (Case B).The volume and plane integrals of momentum in the direction of lid motion and perpendicular to it are introduced to compare cases in a quantitative way. The integral momentum of the secondary flow (transverse to the lid motion) appears to be about an order of magnitude larger than that in Case B. In the proposed flow, the number and strength of secondary vortices depend substantially on the Re number of the flow whereas in Case B only one pair of secondary vortices appears for arbitrary Re number. For a rectangular 3-D 3:1:1 cavity, the integral momentum of the secondary flow in Case A is an order of magnitude larger than that in the Case B. The flowfield in Case A includes a curvilinear separation line and non-symmetrical vortices.

Coherent Helical Structures in Swirl Flows

A nonstationary flow with rotating helical filaments formed in the region of swirl flow breakdown has been studied using the method of phase averaging of the output signal of a laser Doppler velocimeter. Vortices in the measured flow field were separated using the λ2 technique based on an analysis of the velocity gradient tensor. It is shown for the first time that precession of the central monopolar vortex is accompanied by the formation of a pair of secondary vortices with the opposite directions of circulation, which form a helical dipole structure.

A pressure probe for the detection of the flow direction close to walls. Case study: flow through a bend

We report on the development of a new pressure probe that detects the flow direction in wall-bound flow. Two pressure differences are measured and combined in a pressure coefficient which is proportional to the flow direction in a ±20° range. The probe is applied to the secondary flow vortex pair generated in a 90° pipe bend, with excellent results. The vortex pair, and its downstream decay, are identified. Furthermore, the stability of the vortex pair is found to depend sensitively on the upstream conditions. When these are fixed, the vortices stay put; in other words they are spatially stabilized. The consequences for installation effects on flow metering are discussed.

Spatially-resolved heat transfer and flow structure in a rectangular channel with pin fins

Spatially-resolved Nusselt numbers and flow structural characteristics are presented for a stationary channel with an aspect ratio of 8 and a staggered array of pin fins between two of the surfaces. Local Nusselt numbers, measured on one endwall, are highest beneath primary and secondary horseshoe vortices located just upstream of individual pins, beneath pin wakes, and downstream of the pins, in regions where shear layers are positioned between the wakes behind the pins and the higher speed flow away from an individual pin. Also important are intense, highly unsteady secondary flows and vortex pairs (evident in flow visualizations and time-averaged surveys), which increase secondary advection and turbulent transport over the entire channel cross-section.

Flow structure due to dimple depressions on a channel surface

Instantaneous, dynamic and time-averaged characteristics of the vortex structures which are shed from the dimples placed on one wall of a channel are described. The dimpled test surface contains 13 staggered rows of dimples in the streamwise direction, where each dimple has a print diameter of 5.08 cm, and a ratio of depth to print diameter of 0.2. Considered are Reynolds numbers (based on channel height) ReH from 600 to 11 000, and ratios of channel height to dimple print diameter H/D of 0.25, 0.50, and 1.00. For all three H/D, a primary vortex pair is periodically shed from the central portion of each dimple, including a large upwash region. This shedding occurs periodically and continuously, and is followed by inflow advection into the dimple cavity. The frequency of these events appears to scale on time-averaged bulk velocity and dimple print diameter, which gives nondimensional frequencies of 2.2–3.0 for all three H/D values considered. As H/D decreases, (i) the strength of the primary vortex pair increases, and (ii) two additional secondary vortex pairs (which form near the spanwise edges of each dimple) become significantly stronger, larger in cross section, and more apparent in flow visualization images and in surveys of time-averaged, streamwise vorticity. The locations of these primary and secondary vortex pairs near the dimpled surface coincide closely with locations where normalized Reynolds normal stress is augmented. This evidences an important connection between the vortices, Reynolds normal stress, and mixing. The large-scale unsteadiness associated with this mixing is then more pronounced, and encompasses larger portions of the vortex structure (and thus extends over larger volumes) as H/D increases from 0.25 to 1.0.

Linear interaction of a cylindrical entropy spot with a shock

The interaction of a cylindrical element of hot or cold gas (the “entropy spot”) with a shock wave is considered. An exact solution in the limit of weak spot amplitudes is elaborated, using the linear interaction analysis theory and the procedure of decomposition proposed by Ribner (Technical Report No. 1164, NACA, 1953). The method is applied to an entropy spot with a Gaussian profile. Results are presented for a wide range of shock Mach numbers, with a special interest at M1=2. The resulting vorticity field consists of a pair of primary counter-rotating vortices, as well as a pair of secondary vortices of opposite sign and weaker amplitude. An expression for the circulation in half a plane is derived and compared to existing results. The pressure field consists of a cylindrical acoustic wave which propagates away from the transmitted spot and an evanescent nonpropagative field confined behind the shock. For a hot spot, the cylindrical wave is a rarefaction wave on its forward front and a compression wave on its upstream propagating parts, and the nonpropagative field corresponds to a pressure deficit. The structure of the transmitted spot and the shock deformation are also discussed. The linear solution is compared with numerical simulation results for M1=2 and M1=4. The comparison shows qualitative and quantitative agreement when linear as well as nonlinear spot amplitudes are considered. Finally, the method is applied to the case of a constant spot with a tophat profile, and the results are compared to the case of a Gaussian spot. This paper also contains in the Appendix a general formulation of the linear interaction problem for the three kinds of plane waves (entropy, vorticity, and pressure waves) impinging upon a shock.

Numerical simulations of a mixed layer in a stably stratified fluid

We investigate numerically the generation and evolution of a mixed layer in a stably stratified Boussinesq fluid. Momentum injection is driven by a forcing term introduced in the equations of motions. As in experimental situations where the energy input is due to an oscillating grid, the forcing is localized in a thin horizontal layer at the top of the domain and it does not cause a mean flow. Typical Reynolds numbers based on the Taylor microscale are of the order of 30⩽ Re λ ⩽100 . At moderate Reynolds numbers, the entrainment is produced by an advection-diffusion process of the temperature field. Downwards directed jets generated by the forcing deform the isotherms and create thin vertical structure where the temperature is nearly constant. At the boundaries of these jets, typical horizontal scales are much smaller than those imposed by the external forcing with the consequence that the thermal diffusion time becomes comparable to the dynamical one. As a result, the temperature is well mixed over a few dynamical times. This process can be described using a model of temperature advection which yields the observed scaling law of the entrainment versus the Richardson number. At higher Reynolds numbers in 2D the jets become unstable and produce pairs of secondary vortices which propagate downwards. This process is reminiscent of the classical picture of mixing due to the interaction of vortex rings with the interface which separates the mixed from the underlying quiescent fluid. After some time, these vortices start to interact together resulting in horizontal mixing of the fluid on a time scale comparable with that observed in the moderate Reynolds case.