Oblique Vortex Research Articles

Wall shear stress and wall heat flux in a supersonic turbulent boundary layer

We report the characteristics of wall shear stress (WSS) and wall heat flux (WHF) from direct numerical simulation (DNS) of a spatially developing zero-pressure-gradient supersonic turbulent boundary layer at a free-stream Mach number M∞ = 2.25 and a Reynolds number Reτ = 769 with a cold-wall thermal condition (a ratio of wall temperature to recovery temperature Tw/Tr = 0.75). A comparative analysis is performed on statistical data, including fluctuation intensity, probability density function, frequency spectra, and space–time correlation. The root mean square fluctuations of the WHF exhibit a logarithmic dependence on Reτ similar to that for the WSS, the main difference being a larger constant. Unlike the WSS, the probability density function of the WHF does not follow a lognormal distribution. The results suggest that the WHF contains more energy in the higher frequencies and propagates downstream faster than the WSS. A detailed conditional analysis comparing the flow structures responsible for extreme positive and negative fluctuation events of the WSS and WHF is performed for the first time, to the best of our knowledge. The conditioned results for the WSS exhibit closer structural similarities with the incompressible DNS analysis documented by Pan and Kwon [“Extremely high wall-shear stress events in a turbulent boundary layer,” J. Phys.: Conf. Ser. 1001, 012004 (2018)] and Guerrero et al. [“Extreme wall shear stress events in turbulent pipe flows: Spatial characteristics of coherent motions,” J. Fluid Mech. 904, A18 (2020)]. Importantly, the conditionally averaged flow fields of the WHF exhibit a different mechanism, where the extreme positive and negative events are generated by a characteristic two-layer structure of temperature fluctuations under the action of a strong Q4 event or a pair of strong oblique vortices. Nevertheless, we use the bi-dimensional empirical decomposition method to split the fluctuating velocity and temperature structures into four different modes with specific spanwise length scales, and we quantify their influence on the mean WSS and WHF generation. It is shown that the mean WSS is mainly related to small-scale structures in the near-wall region, whereas the mean WHF is associated with the combined action of near-wall small-scale structures and large-scale structures in the logarithmic and outer regions.

Precursors of backflow events and their relationship with the near-wall self-sustaining process

This study examines the precursors and consequences of rare backflow events at the wall using direct numerical simulation of turbulent pipe flow with a high spatiotemporal resolution. The results obtained from conditionally averaged fields reveal that the precursor of a backflow event is the asymmetric collision between a high- and a low-speed streak (LSS) associated with the sinuous mode of the streaks. As the collision occurs, a lifted shear layer with high local azimuthal enstrophy is formed at the trailing end of the LSS. Subsequently, a spanwise or an oblique vortex spontaneously arises. The dominant nonlinear mechanism by which this vortex is engendered is enstrophy intensification due to direct stretching of the lifted vorticity lines in the azimuthal direction. As time progresses, this vortex tilts and orientates towards the streamwise direction and, as its enstrophy increases, it induces the breakdown of the LSS located below it. Subsequently, this vortical structure advects as a quasi-streamwise vortex, as it tilts and stretches with time. As a result, it is shown that reverse flow events at the wall are the signature of the nonlinear mechanism of the self-sustaining process occurring at the near-wall region. Additionally, each backflow event has been tracked in space and time, showing that approximately 50 % of these events are followed by at least one additional vortex generation that gives rise to new backflow events. It is also found that up to a maximum of seven regenerations occur after a backflow event has appeared for the first time.

Sheltering electroconvective instability in a weak electrolyte

Sheltering vortices by shear flow is a common method in plasma and neutral fluids and has recently been successfully applied to control ionic fluids. This work proposes a new chemical sheltering vortex method for electroconvective instability (ECI) based on the Onsager chemical effect. We reveal unique ECI behaviors in a weak electrolyte with the Onsager effect, including the vortex height selection, overlimiting transport, and vortex structure. Due to the strong electric field strength in the electric double layer, the Onsager effect in a weak electrolyte causes neutral molecules to generate additional free ions, which weakens the thickness of the extended space charge layer and causes the fluid to transition from a chaotic ECI to a steady ECI. Consequently, the Onsager effect shelters ECI without an oblique vortex, which is significantly different from the shear flow effect [Kwak et al., “Sheltering the perturbed vortical layer of electroconvection under shear flow,” J. Fluid Mech. 813, 799 (2017)]. We believe that the proposed chemical control strategy can be an alternative candidate for ionic fluids.

Three-dimensional numerical investigation on flow past two side-by-side curved cylinders

Three-dimensional numerical simulations of flow past two side-by-side convex curved cylinders are performed for various spacing ratios (1.25 ≤ L/D ≤ 5) and Reynolds numbers (100 ≤ Re ≤ 500). A comprehensive investigation of the effects of spacing ratio and Reynolds number on the wake flow features, pressure coefficients and axial flow velocity is conducted. Four flow patterns: a single bluff body pattern, biased flow pattern, coupling vortex shedding pattern and co-shedding pattern are identified for the vertical straight sections. The flows along the curved sections of two cylinders are classified into five flow regimes: normal shedding, vortex dislocation, oblique shedding, non-shedding and instability of shear layer regimes. It is revealed that at L/D = 1.5, the switchover of the gap flow deflection along the curved spans leads to the oblique vortex shedding pattern for Re = 100 and 300. The Reynolds stress intensity, vortex strength, and the mean pressure coefficient are found to be reduced significantly from the vertical to the horizontal sections of the cylinders. With the increase of the spacing ratio, the axial flow velocity increases along the curved span of two cylinder, whereas the absolute value of base coefficient decreases.

On the three-dimensional features of a confined slug bubble in a flowing square capillary

The motion of long bubbles in tubular capillaries has typically been described by bulk characteristics. However, the dynamics of slug bubbles in square capillaries are more complex due to a corner flow and a thin film flow. The physics can be correctly explained by elucidating local 3D features of the two-phase flow field. To this aim, an experimental study based on particle tracking velocimetry (PTV) and a numerical simulation based on the volume-of-fluid method were conducted to investigate the dynamics of slug bubbles rising in a flowing square capillary with a cross-sectional area of 3 × 3 mm2. To precisely analyze the phases' interaction, interfacial flow data were mapped onto a radial-tangential coordinate system on central and diagonal planes. The simulated interface topology and velocity fields show a good agreement with the experimental PTV data on the central plane, with an absolute error of less than 1.2% for terminal bubble speed. Tangential speeds show their maxima occurring in the channel corners, where pressure is maximum. The thin liquid film flow that occurs where the bubble approaches the wall applies noticeable shear stress on the channel walls, where high and low-pressure regions are generated. Structures of vortices inside the bubble were identified using isosurfaces of the Q-criterion, and their cores were detected based on the parallel vector method. Results reveal a dominant vortex ring adjacent to the liquid film flow and two oblique vortex tubes close to the bubble's nose.

Oblique and streamwise vortex paths in a plane Couette flow using a RNL system

This paper revisits oblique wave and streamwise vortex scenarios in a plane Couette flow using restricted nonlinear simulations, where only a single Fourier mode for perturbation is retained. It is shown that this restriction of full dynamics gives a good approximation of the two subcritical paths. In particular, critical energy thresholds and edge states compare favorably with results obtained using direct numerical simulations by Duguet et al. (Phys. Rev. E 82 (2010), 026316).

Method for Accountting the Effect of End Washers on the Flow Around the Wing with Spanwise Profiles

Purpose of research is to develop a method for accounting for the influence of end washers on the flow of wings with an arbitrary distribution of fillets over the span.Methods. The installation of end washers significantly improves the aerodynamics of the wing, increasing lift and reducing inductive resistance. The theory of a continuous vortex surface is applied to simulate the effect of end washers on the flow of a volumetric wing. In accordance with it, oblique horseshoe-shaped vortices that model the upper and lower sides of the wing are continuously distributed along the longitudinal panels, into which the half-span of the wing is divided. The bearing parts of each horseshoe-shaped vortex lie in planes parallel to the plane of the wing chords and pass through the points and the middle section of the panel at which the induced velocities are calculated. The free vortices of the wing descend from its ends from the upper and lower surfaces at an angle to the plane of the chords.Results. An algorithm has been developed for calculating the intensity of vortices from the non-permeability condition, taking into account the attached and free vortices of the wing and the end-washer vortices. The vortex densities included in this condition are represented by trigonometric series. The developed method takes into account the geometry of the profile and end washers, the shape of the wing in the plan. The vortices induce an additional velocity at the points on the surface of the wing. To calculate their values, the Biot-savard formula on vortex influence is used.Conclusion. A method for calculating the aerodynamic characteristics of a volumetric wing with end washers has been developed from the unified positions of the theory of a continuous vortex surface. The calculations take into account the geometry of the washers and profile, the shape of the wing in the plan. The method is universal and can be used for wings without washers, including for thin ones.

High fill factor microlens array fabrication using direct laser writing and its application in wavefront detection

We fabricate 100% fill factor microlens arrays (MLAs) using femtosecond laser direct writing. The array consists of periodical hexagonal plano-convex microlens units with a diameter of 9 µm. The focusing efficiency of each microlens is measured to be 92%. Combined with a CCD camera, the MLA works as a Shack-Hartmann wavefront sensor. We use it to detect wavefronts of both oblique incident plane beams and vortex beams. The experimental results match well with theoretical ones.

Wake events during early three-dimensional transition of a circular cylinder placed in shear flow

Three-dimensional (3D) direct numerical simulations are carried out for shear flows past a circular cylinder in the early 2D (two-dimensional)–3D transition regime. The effect of incoming shear is buried in a source term employing a velocity transformation. Wake transition events are inspected for both planar and span-wise shear flows. Parallel, time-mean-symmetric shedding for planar shear and oblique vortex shedding for span-wise shear are observed with a near wake roll-up vortical structure. Vortex splits and dislocations are found without any order in time for moderate shear, while they give way to visibly higher levels of instabilities at higher shear rates. Mode “B” instabilities are noted for planar shear, while opposite streamwise vortices align in parallel horizontal layers for span-wise shear. Local Strouhal frequency (Stz) drops inside a span-wise cell for span-wise shear with finite jumps across cell boundaries. Wavelet multiresolution analysis indicates a strong flushing effect, triggered by vortex dislocations, which gives rise to a new frequency event. The dominant span-wise mode indicates periodic forcing of mode “A” instabilities at a rate close to the inverse of local Strouhal number. In contrast, the streamwise velocity modes result in a global span-wise similarity. Intrinsic secondary instabilities play a vital role in span-wise shear cases. The addition of planar shear makes the downstream defect layer nearly span-wise-invariant. However, the velocity defect is entirely controlled by the span-wise shear. The momentum thickness exhibits streamwise growth, similar to the Blasius profile. The shape factor of such profiles indicates a delay in laminar–turbulent transition for span-wise shear.

Direct Numerical Simulations of Horizontally Oblique Flows Past Three-Dimensional Circular Cylinder Near a Plane Boundary

Abstract Understanding hydrodynamics of a free-spanning pipeline subjected to omni-directional flows is important to engineering design. In this study, horizontally oblique flows past a three-dimensional circular cylinder in the vicinity of a plane boundary are numerically investigated using direct numerical simulations. Parametric studies are carried out at the normal Reynolds number of 500, a fixed gap-to-diameter ratio of 0.8 and five flow inclination angles (α) ranging from 0 deg to 60 deg with an increment of 15 deg. Two distinct vortex-shedding modes are observed: parallel (α ≤ 15 deg) and oblique (α ≥ 30 deg) vortex shedding. The wake evolution is further divided into two or three stages depending on α. The occurrence of the oblique vortex shedding is accompanied by the base pressure gradient along the cylinder span and the resultant axial flows near the cylinder base. The total hydrodynamic drag and lift force coefficients decrease from being the parallel mode to the oblique mode, owing to the intensified three-dimensionality of wake flows and the phase differences in the spanwise vortex shedding. The independence principle (IP) is found to be valid in predicting hydrodynamic forces and wake patterns when α ≤ 15 deg. This IP might produce unacceptable errors when α > 15 deg. In comparison with the mean drag force, the fluctuating lift force is more sensitive to the inclination angle. The IP validity range is substantially smaller than that in the case of flow past a wall-free cylinder. Such finding would be practically useful for vortex-induced vibration prediction.

Wake behind a concave curved cylinder

The wake behind a concave, curved cylinder configuration is investigated at different Reynolds numbers. Distinctly different wake flow regimes were observed in the computed flow field, including oblique vortex shedding and dislocations. The crucial influence of a straight vertical extension is explored.

Distribution of gyrotactic micro-organisms in complex three-dimensional flows. Part 1. Horizontal shear flow past a vertical circular cylinder

As a first step towards understanding the distribution of swimming micro-organisms in flowing shallow water containing vegetation, we formulate a continuum model for dilute suspensions in horizontal shear flow, with a maximum Reynolds number of 100, past a single, rigid, vertical, circular cylinder that extends from a flat horizontal bed and penetrates the free water surface. A numerical platform was developed to solve this problem, in four stages: first, a scheme for computation of the flow field; second, a solver for the Fokker–Planck equation governing the probability distribution of the swimming direction of gyrotactic cells under the combined action of gravity, ambient vorticity and rotational diffusion; third, the construction of a database for the mean swimming velocity and the translational diffusivity tensor as functions of the three vorticity components, using parameters appropriate for the swimming alga, Chlamydomonas nivalis; fourth, a solver for the three-dimensional concentration distribution of the gyrotactic micro-organisms. Upstream of the cylinder, the cells are confined to a vertical strip of width equal to the cylinder diameter, which enables us to visualise mixing in the wake. The flow downstream of the cylinder is divided into three zones: parallel vortex shedding in the top zone near the water surface, oblique vortex shedding in the middle zone and quasi-steady flow in the bottom zone. Secondary (vertical) flow occurs just upstream and downstream of the cylinder. Frequency spectra of the velocity components in the wake of the cylinder show two dominant frequencies of vortex shedding, in the parallel- and oblique-shedding zones respectively, together with a low frequency, equal to the difference between those two frequencies, that corresponds to a beating modulation. The concentration distribution is calculated for both active particles and passive, non-swimming, particles for comparison. The concentration distribution is very similar for both active and passive particles, except near the top surface, where upswimming causes the concentration of active particles to reach values greater than in the upstream strip, and in a thin boundary layer on the downstream surface of the cylinder, where a high concentration of active particles occurs as a result of radial swimming.

Elliptical vortex and oblique vortex lattice in the FeSe superconductor based on the nematicity and mixed superconducting orders

The electronic nematic phase is characterized as an ordered state of matter with rotational symmetry breaking, and has been well studied in the quantum Hall system and the high-Tc superconductors, regardless of cuprate or pnictide family. The nematic state in high-Tc systems often relates to the structural transition or electronic instability in the normal phase. Nevertheless, the electronic states below the superconducting transition temperature is still an open question. With high-resolution scanning tunneling microscope measurements, direct observation of vortex core in FeSe thin films revealed the nematic superconducting state by Song et al. Here, motivated by the experiment, we construct the extended Ginzburg–Landau free energy to describe the elliptical vortex, where a mixed s-wave and d-wave superconducting order is coupled to the nematic order. The nematic order induces the mixture of two superconducting orders and enhances the anisotropic interaction between the two superconducting orders, resulting in a symmetry breaking from C4 to C2. Consequently, the vortex cores are stretched into an elliptical shape. In the equilibrium state, the elliptical vortices assemble a lozenge-like vortex lattice, being well consistent with experimental results.

Control of a three-dimensional turbulent shear layer by means of oblique vortices

The effect of local forcing on the separated, three-dimensional shear layer downstream of a backward-facing step is investigated by means of large-eddy simulation for a Reynolds number based on the step height of 10,700. The step edge is either oriented normal to the approaching turbulent boundary layer or swept at an angle of $$40^\circ $$ . Oblique vortices with different orientation and spacing are generated by wavelike suction and blowing of fluid through an edge parallel slot. The vortices exhibit a complex three-dimensional structure, but they can be characterized by a wavevector in a horizontal section plane. In order to determine the step-normal component of the wavevector, a method is developed based on phase averages. The dependence of the wavevector on the forcing parameters can be described in terms of a dispersion relation, the structure of which indicates that the disturbances are mainly convected through the fluid. The introduced vortices reduce the size of the recirculation region by up to 38%. In both the planar and the swept case, the most efficient of the studied forcings consists of vortices which propagate in a direction that deviates by more than $$50^\circ $$ from the step normal. These vortices exhibit a spacing in the order of 2.5 step heights. The upstream shift of the reattachment line can be explained by increased mixing and momentum transport inside the shear layer which is reflected in high levels of the Reynolds shear stress $$-\rho \overline{u'v'}$$ . The position of the maximum of the coherent shear stress is found to depend linearly on the wavelength, similar to two-dimensional free shear layers.

Unstructured Cartesian refinement with sharp interface immersed boundary method for 3D unsteady incompressible flows

A novel numerical method is developed for solving the 3D, unsteady, incompressible Navier–Stokes equations on locally refined fully unstructured Cartesian grids in domains with arbitrarily complex immersed boundaries. Owing to the utilization of the fractional step method on an unstructured Cartesian hybrid staggered/non-staggered grid layout, flux mismatch and pressure discontinuity issues are avoided and the divergence free constraint is inherently satisfied to machine zero. Auxiliary/hanging nodes are used to facilitate the discretization of the governing equations. The second-order accuracy of the solver is ensured by using multi-dimension Lagrange interpolation operators and appropriate differencing schemes at the interface of regions with different levels of refinement. The sharp interface immersed boundary method is augmented with local near-boundary refinement to handle arbitrarily complex boundaries. The discrete momentum equation is solved with the matrix free Newton–Krylov method and the Krylov-subspace method is employed to solve the Poisson equation. The second-order accuracy of the proposed method on unstructured Cartesian grids is demonstrated by solving the Poisson equation with a known analytical solution. A number of three-dimensional laminar flow simulations of increasing complexity illustrate the ability of the method to handle flows across a range of Reynolds numbers and flow regimes. Laminar steady and unsteady flows past a sphere and the oblique vortex shedding from a circular cylinder mounted between two end walls demonstrate the accuracy, the efficiency and the smooth transition of scales and coherent structures across refinement levels. Large-eddy simulation (LES) past a miniature wind turbine rotor, parameterized using the actuator line approach, indicates the ability of the fully unstructured solver to simulate complex turbulent flows. Finally, a geometry resolving LES of turbulent flow past a complete hydrokinetic turbine illustrates the potential of the method to simulate turbulent flows past geometrically complex bodies on locally refined meshes. In all the cases, the results are found to be in very good agreement with published data and savings in computational resources are achieved.

Effect of spanwise shear on flow past a square cylinder at intermediate Reynolds numbers

Three-dimensional numerical simulation of flow past a square cylinder with linear spanwise shear has been performed in the Reynolds numbers range of 165-250. Navier-Stokes equations are discretized using second order central differencing for both advection and diffusion terms, explicitly marching in time using the second order Adams-Bashforth scheme. The solution methodology used is the Simplified Marker and Cell algorithm. Spanwise shear is simulated by providing a linear variation in the inlet velocity profile along the spanwise direction and the resulting wake characteristics are compared with uniform inflow. Presence of mode-A, mode-B, and large scale vortical irregularities of two-sided symmetrical vortex dislocations is detected when the inflow is uniform. With shear, oblique and cellular vortex shedding are identified for the square cylinder. Shedding frequency of the vortices varies in a stepwise manner along the span, giving rise to local cells of constant frequency. Constant frequency cell sizes are found to be longer for a square cylinder in shear flow as compared to the circular one. Spanwise shear leads to vortex splitting and one-sided vortex dislocation, contrary to the naturally occurring two-sided vortex dislocation for uniform flow. Reynolds number dependence of spanwise shear flow is studied by comparing wake dynamics at three mid-span Reynolds numbers of 165, 200, and 250 with a shear parameter of 0.025. With an increase in the average Reynolds number, cell sizes decrease and dislocations become irregular in space and time. Simulations with three different shear parameters of 0.0125, 0.025, and 0.05 have been carried out for an average Reynolds number of 250. With an increase in the shear parameter, the frequency of occurrence of vortex dislocations increases in the wake. In addition, obliqueness of the primary vortices and the number of cells also show an increase.

Vibrations of a cylinder in a uniform flow in the presence of a no-slip side-wall

A circular cylinder placed in a uniform flow, and that spans the entire length between two side walls, may experience either parallel or oblique vortex shedding depending on the end conditions. It was shown by Mittal and Sidharth (2014) that the spatio-temporal periodicity of the oblique vortex shedding results in constant-in-time force experienced by the cylinder. On the contrary, parallel vortex shedding leads to fluid force that fluctuates with time. The free vibrations of a circular cylinder, in the presence of a wall, are investigated. For comparison, computations with end walls, where a slip condition on velocity is specified, are also carried out. The Reynolds number, based on the diameter of the cylinder and free-stream speed of the flow, is Re=100. The initial condition for the free vibrations is the fully developed unsteady flow past a stationary cylinder with oblique shedding. It is found that as the amplitude of vibration of the cylinder builds up, the vortices shed from the cylinder align with its axis leading to parallel shedding. The response of the cylinder is associated with two branches: initial and lower. On the lower branch, the response of the cylinder is virtually identical from two- and three-dimensional computations. The flow as well as the response is different on the initial branch and outside the synchronization regime. Forced vibrations confirm the phenomena.

Steady forces on a cylinder with oblique vortex shedding

We present a curious situation of a fluid-flow wherein the body experiences non-fluctuating fluid-flow force despite being associated with an unsteady flow comprising of sustained vortex shedding. The flow past a circular cylinder at Re=100 is investigated. It is shown that the spatio-temporal periodicity of the oblique vortex shedding results in constant-in-time force experienced by a cylinder placed in uniform flow. On the contrary, parallel vortex shedding leads to fluid force that fluctuates with time. It is found that, both, the parallel and oblique shedding are linearly unstable eigenmodes of the Re=100 steady flow past a cylinder.

Numerical investigation of oblique shock wave/vortex interaction

The purpose of the present study was to investigate the interaction between stream-wise vortices with oblique shock fronts of various intensities. A three-dimensional, Navier–Stokes solution of the problem with an orthogonal grid incorporating a RANS approach with a RNG k–ɛ turbulence model was used to simulate earlier experimental studies of the problem. The accuracy of the computational study was examined by comparing the results to the previous experiments of oblique shock vortex interactions using three different shock wave intensities leading to weak, moderate and strong interactions as identified in our previous experimental investigations. Similar to the experimental findings, the weak and the moderate interactions did not result in vortex breakdown as the vortex was seen to deflect in the direction of the main flow downstream of the shock with lowered intensity. Computational simulation of the strong interaction case however, confirms presence of a supersonic vortex breakdown having many of the characteristics of subsonic vortex breakdown. The flow field generated by the strong interaction is characterized by the formation of a bulged forward shock structure followed by a rapid expansion of the vortex core, formation of a stagnation point on the vortex axis and appearance of a reversed flow region in a recirculation zone. The vortex was modeled by implementing the experimentally measured vortex properties at the inlet, namely total and static pressures, while constant total temperature was assumed to calculate the velocity, and components of the Mach number. Inlet values for turbulent kinetic energy and turbulent dissipation rate were calculated from assumed values of turbulence intensity.

Effect of steady rotation on low Reynolds number vortex shedding behind a circular cylinder

In this paper control of oblique vortex shedding in the wake behind a straight circular cylinder is explored experimentally and computationally. Towards this, steady rotation of the cylinder about its axis is used as a control device. Some limited studies are also performed with a stepped circular cylinder, where at the step the flow is inevitably three-dimensional irrespective of the rotation rate. When there is no rotation, the vortex shedding pattern is three dimensional as described in many previous studies. With a non-zero rotation rate, it is demonstrated experimentally as well as numerically that the shedding pattern becomes more and more two-dimensional. At sufficiently high rotation rates, the vortex shedding is completely suppressed.