Generation Of Secondary Vortices Research Articles

Effect of leading and secondary vortices on the propulsion performance of an undulating swimmer in the periodic vortex street

Aquatic animals have evolved diverse swimming techniques. They have demonstrated abilities to harness energy from vortices, particularly the Kármán vortex street, resulting in enhanced thrust. However, gaps remain in comprehensively understanding the factors influencing this increased thrust and the specific hydrodynamic characteristics involved. In this study, we studied an undulating foil downstream a circular cylinder to further understand the flow control mechanism involved in optimizing energy capture from hydrodynamic disturbances. We utilised numerical simulations with a moving adaptive mesh in laminar flow. We found that the leading vortex and secondary vortex at the foil's leading edge, originating from the Kármán vortex, played a crucial role in thrust enhancement. The undulating foil was more efficient in capturing energy from the Kármán vortex street than a stationary foil. When the foil was nearer to the cylinder, the energy capture was more evident, leading to intricate vortex patterns and easier leading vortex and secondary vortex generation. The foil's lift initially rose with closer proximity but decreased with increased distance. Our results showed that for minimal drag and optimal lift, the cylindrical body's position is closely tied to the interaction between the Kármán vortex street and the undulating foil. These insights can be applied in applications of designing efficient propulsion systems for underwater vehicles and optimising energy harnessing mechanisms in marine environments.

A high-resolution numerical investigation of unsteady wake vortices for coaxial rotors in hover

High-resolution numerical simulations for wake vortical flows have long been a challenge in rotor aerodynamics. A novel spectrum-optimized sixth-order Weighted Essentially Non-Oscillatory (WENO) scheme is proposed to discretize inviscid fluxes on moving overset grids, and the Improved Delayed Detached Eddy Simulation (IDDES) is employed to resolve turbulent vortices. The integration of these methods facilitates a comprehensive numerical investigation into the unsteady vortical flows over coaxial rotors in hover. The results highlight the substantial improvement in numerical resolution, in terms of both spatial structure and temporal evolution of unsteady multiscale wake vortices. Coaxial rotors in hover manifest three primary scales of wake vortex structures: (A) the helical evolution of primary blade tip vortices and the periodic occurrence of strong Blade-Vortex Interactions (BVI); (B) the continuous shedding of small-scale horseshoe-shaped vortices from the trailing edges of rotor blades, forming the vortex sheets; (C) the emergence of small-scale secondary vortex braids induced by interactions between rotor tip vortices and the vortex sheets. These vortex structures and their interactions cause high-frequency oscillations in rotor disk loads and induce unsteady perturbations in the local flow field. Interactions among these primary vortices, coupled with the generation of secondary vortices, result in the dissipation, distortion, and breakup of the rotor tip vortices, ultimately forming a vortex soup. Notably, a substantial quantity of seemingly weak small-scale secondary vortex braids significantly contribute to energy dissipation during the evolution of wake vortices for coaxial rotors in hover.

On the propeller wake evolution using large eddy simulations and physics-informed space-time decomposition

A novel modal analysis methodology, denoted as the physics informed sparsity-promoting dynamic mode decomposition (pi-SPDMD) model, was introduced for the reduction and reconstruction analysis of intricate propeller wake flows, aiming to provide insight into the inherent flow structures spanning diverse temporal and spatial scales. Large-Eddy Simulation (LES) was employed to numerically model the wake dynamics of a four-bladed propeller, providing a comprehensive resolution from the proximate to the distant wake regions. The findings indicate that the pi-SPDMD model enhances the efficiency of the sparse-promoting algorithm, producing modes that gravitate towards stability, and the resulting decomposition maintains commendable physical fidelity. Integrating the results from the LES solution and the modal decomposition of pi-SPDMD, the tip vortex exhibits a uniform topological configuration with notable coherence in the proximate domain. In this region, the large-scale vortex is the dominant feature of the propeller wake, and there is a marked intermittency in the turbulence. In the mid-field, the tip vortex system transitions into fine-scale vortices, rapidly diminishing in coherence due to the onset of elliptic instability and subsequent secondary vortex generation. As the tip vortex structures related to physical quantities become fully discretized, the small-scale turbulent patterns quickly intermingle, leading to a more homogeneous distribution in the distant wake.

Comparative study on the wake dynamics of pump-jet and ducted propeller based on dynamic mode decomposition

A comparative study on the wake dynamics of a pump-jet propulsor (PJP) and a ducted propeller (DP) is conducted to investigate the effects of the pre-swirl stator and corresponding stator–rotor interaction on the wake evolution and destabilization mechanisms of a PJP system. The flow field analysis, vortex structure identification, and dynamic mode decomposition (DMD) analysis are carried out based on the numerical results obtained from delayed detached eddy simulations. The numerical hydrodynamic loading and flow field of the PJP are compared with experimental results, and they are in good agreement. Compared with the DP, the stator trailing vortices of the PJP interact with the rotor trailing vortices as well as the hub vortex, accelerating their diffusion and viscous dissipation. The pre-swirl stator triggers the generation of secondary vortices and moderates the spiral behavior of tip leakage vortices, which dominates the wake instability of PJP. The DMD analysis revealed that the wake field evolution is primarily characterized by the different mode structures at blade passing frequency and its multiples, especially in the PJP due to its strong stator–rotor interaction. The modal energy decays faster in the PJP wake field owing to its more turbulent and earlier instability. The hub vortex plays an important role in the wake dynamics of the DP.

Long-wave deformation of in-ground-effect wake vortex under crosswind condition

The in-ground-effect (IGE) aircraft wake vortex poses great hazards to airplanes. Especially when the vortex column is deformed with a long wavelength, the vortex core position is harder to determine, and thus, the IGE wake vortex is essential to air traffic safety and requires more detailed research. In this study, to account for the effects of roll-up-induced structures, the wake vortex pair was initialized using the vortex sheet model proposed by Lin et al. [1]. The asymmetrical wing loading effect on IGE wake evolution was considered for the first time. The Large Eddy Simulation results showed that the crosswind strengthened the upwind vortex, while the long-term wake vortex evolution was not significantly influenced by the wind. Most importantly, in certain crosswind conditions, the wake vortex deformed sinusoidally and linked with its mirror counterpart. From a linear stability analysis, it was found that this long-wave deformation could only occur on the upwind side owing to the redistribution of the strain field caused by the near-ground wind shear. Due to secondary vortex generation, the deformation was suppressed and a low growth rate of α≈0.41 was recorded for the long-wave instability.

Vortex collision against static and spinning round cylinders: A lattice Boltzmann study

In this paper, the flow physics generated by the collision of a vortex dipole that moves against a spinning round cylinder is investigated numerically. Fluid dynamics is predicted by a combined central-moments-based lattice Boltzmann-immersed boundary method. First, the model is validated against well established consolidated benchmark problems, showing very high accuracy properties. Then, results from a comprehensive numerical campaign are presented. A wide set of values of the Reynolds number (Re) is investigated, ranging from 10 to 1000. The cylinder is forced to spin around its centre with different angular velocities, which are obtained by varying the spinning number (Sp) between 0 (corresponding to the static case) and 0.75. The generation of secondary vortices as a consequence of the impact is elucidated and linked to the time evolution of the kinetic energy, enstrophy and hydrodynamic forces. Interestingly, we find that the flow physics changes drastically when Re≥250, independently from the value of Sp. Through a closer look at the vorticity field, we find that the impact creates two primary–secondary structures and a second impingement takes place when Re≥250. Interestingly, the normalised drag force (Cd) is found to constantly fluctuates around a mean value. Oscillations are due to the vorticity created by the rotation of the cylinder and are more emphasised as Sp grows. Specifically, Cd can achieve marked negative values as a consequence of the velocity field created by the cylinder during its rotation.

Wake instabilities of a pre-swirl stator pump-jet propulsor

The wake of a pump-jet propulsor (PJP) with a pre-swirl stator is investigated using stress-blended eddy simulations. The flow field is analyzed in detail through a systematic comparison of the wake morphology under different loading conditions, allowing the destabilization process and the mechanism of wake instabilities to be inspected. To further examine the evolution of the vortices, as well as their interaction and destabilization, the pressure fluctuations and spectra of turbulent kinetic energy are considered. The mean loads are in good agreement with experimental results. The PJP flow field has a complex vortical system, the evolution of which determines the wake instabilities. The tip clearance leakage vortex first exhibits short-wave instabilities, and the destabilization process then accelerates under the effects of duct shed vortices, which promote the generation of secondary vortices. The secondary vortices further enhance the destabilization process and lead to chaotic evolution. The stator blade root vortices are strongly affected by the rotor blade root vortices, causing an exchange of vorticity that depends on the relative intensity of the two sets of root vortices. The instability of the hub vortices is apparently related to the upstream vortices. The correlation between the tip clearance leakage vortices and the instability of hub vortices is very weak.

Effect of impinging jet pulsation on primary and secondary vortex characteristics

In this study, the effect of impinging air jet pulsation on the generation of toroidal (“primary”) vortices near to the nozzle exit, their subsequent downstream evolution, the creation of “secondary” vortices and their interaction along the radial wall jet was investigated. Experiments were performed using particle image velocimetry and data analysis was based on the determined instantaneous vorticity and swirling strength fields. Reynolds numbers based on the average jet exit velocity were Re=4606, 8024 and 13,513, whereas jet pulsation Strouhal numbers ranged from 2.0×10−3 to 15.6×10−3. The present results showed that jet pulsation significantly affected both the primary and the secondary vortex numbers, areas, and strengths. However, the actual change in vortex strength depended on the phase and the jet Reynolds number. Secondary vortex strengths increased up to twice the value obtained for the steady jet case. However, no enhancement was measured when the Strouhal number exceeded 8.5×10−3. Conditionally averaged data indicated that secondary vortex generation in the pulsating jet is similar as for the baseline steady jet case. The different contributions to the averaged vorticity equation showed that the mean vortex stretching term strengthened primary and secondary vortices. Further away from the stagnation point, wall-normal diffusion of fluctuating, azimuthal vorticity weakened the vortices.

Wall-mounted flexible plates in a two-dimensional channel trigger early flow instabilities.

A high level of mixing by passive means is a desirable feature in microchannels for various applications, and use of flexible obstacles (or plates) is one of the prime choices in that regard. To gain further insight, we carry out two-dimensional numerical simulations for flow past one or two flexible plates anchored to a channel's opposite walls using a fluid-structure interaction framework. For the inlet flow Reynolds number vs the Strouhal number plane, we observe a sudden flow change from a laminar to a time-periodic vortex shedding state when flexible plates are present in the channel. We found the critical Reynolds number to be Re_{cr}≈370 when a single plate is anchored on the channel wall and Re_{cr}≈290 or even lower when two plates are anchored. With an increase in the inlet flow Reynolds number (up to 3200), we found that vortices detach regularly at the plates' tips, which causes the flow to meander in the channel. In a two-plate anchored configuration, primary vortices generated at the first plate are constrained by the second plate and result in an energetic secondary vortex generation in the downstream side. The overall flow features and the energy dissipation in the channel are mainly controlled by the separation gap between the plates. At high-inlet-flow Reynolds numbers (≥1600), the probability density function (F) of the kinetic energy dissipation in a flexible plate configuration shows a stretched exponential shape in the form F(Z)∼1/sqrt[Z]e^{-pZ^{q}}, where Z is the normalized kinetic energy dissipation and the constants p=0.89 and q=0.86. The observed increase in energy dissipation comes at the cost of an increase in pressure loss in the channel, and we found that the loss is inversely related to the plates' separation gap. From our simulations, we found that if high mixing levels are desired, then two flexible plates anchored to the channel walls is a better choice than a channel flow without obstacles or flow past a single plate. The two-plate configuration with zero separation gap between the plates is best suited to achieve a high mixing level.

Numerical Simulation of Drag Reduction in Microgrooved Substrates Using Lattice-Boltzmann Method

We study drag reduction of a uniform flow over a flat surface due to a series of rectangular microgrooves created on the surface. The results reveal that making grooves on the surface usually leads to the generation of secondary vortices inside the grooves that, in turn, decreases the friction drag force and increases the pressure drag force. By increasing the thickness of the grooves to the thickness of the obstacle, the pressure drag increases due to the enhancement of the generated vortices and the occurrence of separation phenomenon and the friction drag reduces due to a decrease of the velocity gradient on the surface. In addition, by increasing the grooves depth ratio, the pressure drag coefficient decreases and the friction drag coefficient increases. However, the impact of the pressure drag coefficient is higher than that of the friction drag coefficient. From a specific point, increasing the groove depth ratio does not effect on decreasing the total pressure drag of the plate. Therefore, creating the grooves in flat surfaces would reduce the total drag coefficient of the plate if the thickness of the grooves does not exceed a specific size and the depth of the grooves is chosen to be sufficiently large. The lattice-Boltzmann method (LBM) is used and the optimal reduction of the drag coefficient is calculated. It is found that for the width ratio equal to 0.19 and the groove depth ratio equal to 0.2548, about 7% decrease is achieved for the average total drag.

Axisymmetric jet impingement on a dimpled surface: Effect of impingement location on flow field characteristics

Few studies have investigated the flow characteristics of jets impinging on dimpled surfaces that may increase or decrease their heat transfer capabilities. Here, particle image velocimetry (PIV) measurements have been performed on a round jet (diameter D) impinging on a surface having large spherical dimples (opening size d), D/d = 0.83. In particular, the effect of jet impingement location on the flow field was investigated. Impingement of the jet centered on the “dimple” as well as on the flat surface between the dimples (“isthmus”), was compared to impingement on a smooth surface. Measurements were performed at three Reynolds numbers, ⟨Re⟩ = 1,352, 6,268 and 12,342 at a stand-off distance of 4.8D. Results showed that the flow field in the developing wall jet strongly changed for “isthmus” impingement while for “dimple” and “smooth” impingement it was similar. However, outer-layer self-similarity was not attained in the developing wall jet. Furthermore, secondary vortex generation as a result of primary vortex impingement, was the same for “smooth” and “dimple” impingement while for “isthmus” impingement, secondary vortices were created through the generation of an unsteady separation bubble.

Drag reduction using metallic engineered surfaces with highly ordered hierarchical topographies: nanostructures on micro-riblets

Durable drag-reduction surfaces have recently received much attention, due to energy-saving and power-consumption issues associated with harsh environment applications, such as those experienced by piping infrastructure, ships, aviation, underwater vehicles, and high-speed ground vehicles. In this study, a durable, metallic surface with highly ordered hierarchical structures was used to enhance drag-reduction properties, by combining two passive drag-reduction strategies: an air-layer effect induced by nanostructures and secondary vortex generation by micro-riblet structures. The nanostructures and micro-riblet structures were designed to increase slip length. The top–down fabrication method used to form the metallic hierarchical structures combined laser interference lithography, photolithography, thermal reflow, nanoimprinting, and pulse-reverse-current electrochemical deposition. The surfaces were formed from nickel, which has high hardness and corrosion resistance, making it suitable for use in harsh environments. The drag-reduction properties of various metal surfaces were investigated based on the surface structure: a bare surface, a nanostructured surface, a micro-riblet surface, and a hierarchically structured surface of nanostructures on micro-riblets.

On hairpin vortices induced by circular synthetic jets in laminar and turbulent boundary layers

Numerical simulations are carried out to investigate the hairpin vortices induced by single circular synthetic jets (SJ) in a laminar boundary layer (LBL) and a turbulent boundary layer (TBL) over a flat plate. Both boundary layers have the same freestream velocity 0.1m/s. The momentum-thickness based Reynolds number is Reθ=180 in the LBL and Reθ=420 in the TBL. In both cases, the synthetic jet actuator (SJA) operates under the same conditions, i.e. the jet-to-freestream velocity ratio VR=0.17 and the dimensionless stroke length L=1.7. For the TBL simulation, large eddy simulation (LES) is used. The generation and evolution of the SJ-induced hairpin vortices and their accompanying vortex structures in both boundary layers are compared. It is found that in the TBL the hairpin vortex travels faster and is in a more bent shape than in the LBL. In addition, the hairpin vortex in the TBL is asymmetric, oscillates laterally, and dissipates fast, whereas it is symmetric and persistent in the LBL. Secondary vortices are observed in both cases. It is found the SJA ingestion also contributes to the generation of secondary vortices, and plays a major role in the TBL. The influence of hairpin vortices on both boundary layers is also examined in the context of flow separation control, through the investigation of the boundary layers’ velocity profile, wall shear stress, and shape factor. The change of velocity and velocity gradient profiles due to the passage of hairpin vortices reveals that the influence of the hairpin vortex on the TBL is wider but much weaker than on the LBL. The current results suggest that a much stronger SJ is required for the current TBL in order to achieve similar flow separation control effect to that in the LBL.

Experimental investigation of the wall shear stress and the vortex dynamics in a circular impinging jet

The wall shear stress and the vortex dynamics in a circular impinging jet are investigated experimentally for Re = 1,260 and 2,450. The wall shear stress is obtained at different radial locations from the stagnation point using the polarographic method. The velocity field is given from the time resolved particle image velocimetry (TR‐PIV) technique in both the free jet region and near the wall in the impinging region. The distribution of the momentum thickness is also inspected from the jet exit toward the impinged wall. It is found that the wall shear stress is correlated with the large-scale vortex passing. Both the primary vortices and the secondary structures strongly affect the variation of the wall shear stress. The maximum mean wall shear stress is obtained just upstream from the secondary vortex generation where the primary structures impinge the wall. Spectral analysis and cross-correlations between the wall shear stress fluctuations show that the vortex passing influences the wall shear stress at different locations simultaneously. Analysis of cross-correlations between temporal fluctuations of the wall shear stress and the transverse vorticity brings out the role of different vortical structures on the wall shear stress distribution for the two Reynolds numbers.

Geometrical influence on mixing in helical porous membrane microcontactors

The goal of gas–liquid micromixing has led to develop various kinds of passive micromixer configurations, which can be used for many microfluidics applications. This work details gas–liquid contacting using porous helical microchannels. An experimental and numerical design methodology for different geometrical configurations is presented which systematically integrates computational fluid dynamics (CFD) with an optimization methodology based on the use of design of experiments (DOE) method. The methodology investigates the effect of geometric parameters on the mixing performance of helical membrane microchannel that has design characteristics based on the generation of secondary vortices. The methodology has been applied on different designs of helical hollow fiber geometry at several Reynolds numbers. The geometric features of this microchannel geometry have been optimized and their effects on mixing are evaluated. The flux enhancement and degree of mixing are the performance criteria to define the efficiency of the gas–liquid microchannel contactor for different design requirements. Due to its ease of fabrication, efficiency and operational flexibility, helical membrane micromixers are favorable for gas–liquid contacting, water oxygenation, pervaporation, etc.

Early induction of secondary vortices for micromixing enhancement

In the present work a new type of micromixer has been proposed and its mixing characteristic has been analyzed. The micromixer can be viewed as a U-tube with a side inlet. Here micromixing is enhanced by the secondary vortex generation induced by the curvature of the tube. The flow in the mixer geometry is investigated theoretically to understand micro-mixing using computational fluid dynamics (CFD). For this we use the Navier–Stokes equations coupled with species transport. Mixing is quantified using mixing quality which is a measure of the uniformity of the concentration in a given geometry. Special attention is paid to the occurrence of the secondary vortices close to the mid point of the outer wall and its role in mixing. Simulations are also done to study the flow in U shaped channels. The simulation results show that the new design leads to an early introduction of secondary vortices than a simple U tube. Thus in the new design the secondary vortices are induced at a Re = 120 as opposed to the classical value of Re = 400 (when there is no side inlet) reported in the literature. Mixing is studied for different diffusivities and combination of inlet velocities. We also compare the performance of our design with the classical T and Y mixers. The early induction implies that we can have good mixing at low Re. Consequently, when used as a micro-reactor we can combine good mixing with high residence times to obtain good conversions in our system.

Measurements of Wake Vortices Interacting with the Ground

Although wake vortices are known to decay more rapidly near the ground than away from the ground, the details of the ground interaction are not well understood. Propeller anemometer arrays located under the approach path have been used to study vortex transport and provide some information about the vortex interaction with the ground, such as the generation of secondary vortices via boundary-layer detachment. A propeller anemometer array at John F. Kennedy International Airport using 8.5-m poles was augmented with 1) a sonic anemometer measuring three-dimensional wind and temperature at 10 Hz and 2) a vertical array of vertical wind and crosswind anemometers, mounted at four additional levels (4.2, 3.2, 1.05, and 0.5 m). The sonic anemometer gave 1) measurements of turbulence inside the vortex flowfield and 2) indications of vertical variations in the ambient headwind and temperature, which were brought down to the measurement level by the descent of the vortex recirculation oval. In general, under conditions of low to moderate turbulence, the turbulence level inside the wake vortex flowfield is greater than that in the ambient wind. The vertical anemometer array showed that the crosswind profile under a wake vortex in ground effect has a very thin boundary layer, much thinner than that of the ambient wind. It also provided some details concerning the wind profile of the secondary vortex.

Elliptic Instability of Counter-Rotating Vortices: Experiment and Direct Numerical Simulation

The short-wavelength elliptic instability of a pair of closely spaced counter-rotating vortices is analyzed using water tank experiments and direct numerical simulations. Qualitative and quantitative comparison shows excellent agreement and validates each of these complementary approaches. Both sets of results are used to give a detailed description of the instability characteristics. In the initial phase, the vortices are subject to a three-dimensional perturbation of their internal structure, with a wavelength scaling on the vortex core size and a distinct phase relationship between the two vortices. In the nonlinear evolution of the  ow, the growth of the perturbations leads to the generation of secondary vortices and the breakdown of the initial pair into small-scale turbulence, accompanied by a rapid decrease of the average circulation. The growth rate of the instability is found to be higher than the one of the well-known Crow instability. The interaction between both mechanisms is also investigated, and an even faster decay of circulation is observed than for the cases where each instability acts alone. The relevance of these results for realistic aircraft trailing wakes is discussed.

Numerical Simulation of Aircraft Trailing Vortices Interacting with Ambient Shear or Ground

A two-dimensional algorithm, based on the continuous vortex sheet method, is proposed for modeling the evolution and propagation of aircraft trailing vortices in a sheared environment. Among the phenomena discussed are the generation of secondary vortices, shear-layer instabilities, and interactions of trailing vortices with atmospheric and ground shear layers. Numerical simulations are produced by a code written as an interactive-graphics application for the Windows platform

The oblique ascent of a viscous vortex pair toward a free surface

The problem of a vortex pair, rising obliquely at an angle of 45° toward a deformable free surface in a viscous, incompressible fluid, is solved with the aid of the Navier—Stokes equations. The full nonlinear boundary conditions at the free surface are applied. The oblique interaction of the vortex pair with the free surface results in a number of novel features that have not been observed for the special case of a vertical rise, reported earlier. These features include the directional change of trajectories near the free surface and the occurrence of waves driven by the vortex pair. Moreover, surface tension can completely change the flow characteristics such as the direction of the trajectories and the generation of secondary vortices. Numerical solutions are presented for selected Reynolds, Froude, and Weber numbers.