Steady Vortex Research Articles

Effects of flow unsteadiness and chemical kinetics on the reaction yield in a T-microreactor

Experimental flow visualizations and velocity measurements are used jointly with numerical simulations to investigate the mixing and monitor the reaction progress in the periodic flow regimes occurring in a T-shaped microreactor. We considered the effects of different kinetic constants, with very different characteristic chemical time scales resulting in a wide range of Damköhler numbers.A remarkable agreement between experiments and simulations is found both in terms of flow pattern and reaction progress. Two different flow regimes are present for increasing Reynolds number. The first is the periodic asymmetric regime, characterized by the shedding of vorticity-blobs along the mixing channel leading to a further increase of the mixing performance compared to the steady engulfment regime. The second regime is the periodic asymmetric one, which is mainly a poorly mixed segregated regime with periodic oscillation at the interface between the two reactants. The mixing degree significantly increases in the unsteady asymmetric regime, whereas it predictably drops down in the unsteady symmetric regime. In the periodic asymmetric regime the reaction yield follows the same function of the Damköhler number, describing the residence to chemical time-scale ratio, and of a non-dimensional kinetic constant, taking into account also fluid properties, previously proposed for the steady vortex and engulfment regimes. In the periodic symmetric regime, the reaction yield is found to depend only on the Damköhler number, with the same dependence previously highlighted for the steady segregated regime.

Автоколивання потоку при обтіканні кругового циліндра зі спліттером

The problem of generation of self-sustained oscillations in the flow past a circular cylinder with a splitter plate is solved numerically. We investigate both the transient process and the steady periodic vortex shedding behind the cylinder. The evolution of the vorticity field is shown for various length of the splitter plate. It is demonstrated that the splitter oriented along the flow direction significantly reduces the forces applied to the cylinder. With increasing splitter length the average drag decreases monotonically but the amplitudes of oscillation of the forces applied to the body change nonmonotonically. In this paper we offer our explanation of this phenomenon. It is shown that when turning the splitter plate at some angle from the flow direction the process of vortex formation and shedding behind the cylinder is no longer strictly regular and periodic.

Vortex dynamics of supercritical carbon dioxide flow past a heated circular cylinder at low Reynolds numbers

The vortex dynamics in the steady regime and laminar vortex shedding regime with Reynolds number (Re) ranging from 15 to 150 are systematically investigated for supercritical carbon dioxide (SCO2) through a high-resolution numerical method in this paper. Numerical results of constant-property air are validated with the available experimental and numerical data from various angles. Excellent agreements are found between the present work and the previous studies. By comparing one vortex shedding process between SCO2 and conventional air, it is found that for SCO2 the period from the initial growth state of one vortex to its dominant state of inducing a new counter-rotating vortex on the other side of the body wake is accelerated, which contributes to the higher Strouhal frequency of SCO2 to a certain extent. By analyzing the development of lift coefficient history and the instantaneous vorticity near the onset of vortex shedding, transition from the steady separated flow to the primary wake instability for SCO2 is found between Re of 28 and 29, exactly 28.2 predicted by the intersection of the fitting curves of the base suction, much lower than the classical value (∼ 47). The wake bubble in the steady regime enlarges in size as Re increases, while in the laminar shedding regime the mean recirculation region decreases with Re. The distributions of local quantities, such as pressure coefficient, friction coefficient, and Nusselt number along the circumference, are presented to understand the development of the flow. The two dimensionality of the wake is confirmed at Re of 150 by comparing with the three-dimensional calculation. A new three-term correlation is proposed to represent the Strouhal–Reynolds number relation for SCO2 in parallel shedding mode.

On desingularization of steady vortex for the lake equations

Abstract In this paper, we constructed a family of steady vortex solutions for the lake equations with a general vorticity function, which constitutes a desingularization of a singular vortex. The precise localization of the asymptotic singular vortex is shown to be the deepest position of the lake. We also study global nonlinear stability for these solutions. Some qualitative and asymptotic properties are also established.

Stability of a horizontal vortex in weakly stratified flow

A horizontal vortex in a moving stratified flow will have the density field overturn along the axis of the vortex. Gravity distorts this steady vortex, ultimately leading to three instabilities. The twirling and rolling instabilities are strong for small Froude number and small pitch. The streaming instability is strong for large pitch and is independent of Froude number.

Numerical investigation of flow around a square cylinder in accelerated flow

To investigate the flow field evolution and resultant aerodynamic characteristics of a square cylinder during flow acceleration, large-eddy simulations were undertaken to simulate flow with a dimensionless acceleration rate ap of 0.0048. The adopted ap resembles that is likely to be experienced during a severe downburst wind storm. The tested incidence angle α ranges from 0° to 45° and the time-dependent Reynolds number Re [Re = U(t)D/v, where U(t) is the time-dependent inflow velocity and D and v are the cylinder length and the kinematic viscosity, respectively] varies from 0 to 5 × 104 throughout the simulation. Results revealed that the flow around a square cylinder in accelerated flow evolves through three distinct temporal flow phases: namely, Phase I (Ia and Ib) where no vortex shedding (the instantaneous lift force through this period is zero) is observed, Phase II, where periodic vortex shedding and associated lift force oscillations are initiated and enhanced, and Phase III where stable vortex shedding occurs. Phase I can be further broken down into Phase Ia, which is characterized by laminar shear layer separation and the existence of steady recirculation vortices in the near wake region, and Phase Ib (only present at α = 0° and 45°) which is distinguished by the presence of quasi-steady recirculation vortices behind the cylinder. Aside from the variation of flow patterns, the transient lift and drag coefficients and the wind pressure distributions, as well as the spatial evolution of three-dimensional flow structures and pressure distributions, are also elucidated in detail.

The propagation and decay of a coastal vortex on a shelf

A coastal eddy is modelled as a barotropic vortex propagating along a coastal shelf. If the vortex speed matches the phase speed of any coastal trapped shelf wave modes, a shelf wave wake is generated leading to a flux of energy from the vortex into the wave field. Using a simple shelf geometry, we determine analytic expressions for the wave wake and the leading-order flux of wave energy. By considering the balance of energy between the vortex and wave field, this energy flux is then used to make analytic predictions for the evolution of the vortex speed and radius under the assumption that the vortex structure remains self-similar. These predictions are examined in the asymptotic limit of small rotation rate and shelf slope and tested against numerical simulations. If the vortex speed does not match the phase speed of any shelf wave, steady vortex solutions are expected to exist. We present a numerical approach for finding these nonlinear solutions and examine the parameter dependence of their structure.

Numerical investigation of lagrangian coherent structures in steady rotation vortex shedding control

In this paper, vortex shedding and suppression are numerically investigated as autonomous and non-autonomous dynamical systems respectively. Lagrangian coherent structures (LCSs) are used as a numerical tool to analyze these systems. These structures are ridges of Finite time Lyapunov exponent (FTLE) which act as material surfaces that are transport barriers within the flow. Initially, the utility of LCSs is explored for revealing the coherent structures of these systems. Finally, an active flow control method, steady rotation is applied to the non-autonomous dynamical system with different speed ratios to mitigate vortex shedding magnitude. This will eventually turn the system into an autonomous system. Fixed saddle points, separation profiles essentially as unstable time variant manifolds attached to cylinder wall and evolution of other unstable manifolds with variant speed ratios are analyzed with reference to LCSs. It is revealed that speed ratio of 2.1 fully suppresses the von Karman vortex street at Reynolds number of 100 and system turns into an autonomous dynamical system with fixed saddle points and time-invariant manifolds.

Internal structure of localized quantized vortex tangles

In this study, we numerically investigate the internal structure of localized quantum turbulence in superfluid $^4$He at zero temperature with the expectation of self-similarity in the real space. In our previous study, we collected the statistics of vortex rings emitted from a localized vortex tangle. As a result, the power law between the minimum size of detectable vortex rings and the emission frequency is obtained, which suggests that the vortex tangle has self-similarity in the real space [Nakagawa $et$ $al.$, Phys. Rev. B $\boldsymbol{101}$, 184515 (2020)]. In this work, we study the fractal dimension and vortex length distribution of localized vortex tangles, which can show their self-similar structure. We generate statistically steady and localized vortex tangles by injecting vortex rings with a fixed size. We used two types of injection methods that produce anisotropic or isotropic tangles. The injected vortex rings develop into a localized vortex tangle consisting of vortex rings of various sizes through reconnections (fusions and splitting of vortices). The fractal dimension is an increasing function of the vortex line density and becomes saturated to a value of approximately 1.8, as the density increases sufficiently. The behavior of the fractal dimension was independent of the anisotropy of the vortex tangles. The vortex length distribution indicates the number of vortex rings of each size that are distributed in a tangle. The distribution of the anisotropic vortex tangle shows the power law in the range above the injected vortex size, although the distribution of the isotropic vortex does not.

Experimental characterization of mixing and flow field in the liquid plugs of gas\u2013liquid flow in a helically coiled reactor

Flow mixing of two miscible liquids with the addition of gas bubbles is a process often found in industrial chemical apparatus for the production of primary matter. The ongoing optimization of such processes also involves the transformation of batch to continuous mode operation. In that case, the use of helically coiled tubes is an interesting alternative, since those reactors have narrow residence time distributions, very good radial mixing properties and excellent mass transfer can be realized between gases and liquids. For these reasons, in this study the mixing of two miscible liquids with addition of air bubbles in gas–liquid flows has been characterized in a horizontal helically coiled reactor in the laminar flow regime at {text{Re}}_{{{text{total}}}} = 300 ldots 1088. Eight different superficial liquid velocities and five superficial gas velocities were investigated. In order to characterize mixing in the liquid plugs between two bubbles, laser-induced fluorescence of resorufin was used and particle image velocimetry has been employed to characterize the flow field. Pseudo-3D-visualizations of the resorufin concentration and the Q-criterion, representing the mixing efficiency and vorticity, respectively, were established for individual liquid plugs from the time-resolved measurement results. A time-resolved mixing coefficient, as well as a mean mixing coefficient obtained from multiple liquid plugs, is calculated from the fluorescence images for all examined flow conditions. The experimental results clearly show an increase in the mixing coefficient compared to single-phase conditions, caused by the bubbles. However, distinct mixing pattern, depending on the flow structure, can be recognized on different locations inside the liquid plug. Compared to a stationary case without air bubbles, mixing is worse behind the bubbles and increases inside the plug, reaching a maximum mixing coefficient in front of the next bubble. Overall the mixing coefficient is always increased by the presence of the bubbles. Pseudo-3D-visualizations of the Q-criterion and the vorticity show the presence of secondary vortices right in front of the bubbles, shifted to the outer tube walls, and in addition to the steady Dean vortices. In small plugs, these secondary vortices appear in the whole plug and increase the mixing coefficient drastically.Graphical

Group Analysis of the Plane Steady Vortex Submodel of Ideal Gas with Varying Entropy

The submodel of ideal gas motion being invariant with respect to the time translation and the space translation by one direct has 4 integrals in the case of vortex flows with the varying entropy. The system of nonlinear differential equations of the third order with one arbitrary element was obtained for a stream function and a specific volume. This element contains from the state equation and arbitrary functions of the integrals. The equivalent transformations were found for arbitrary element. The problem of the group classification was solved when admitted algebra was expanded for 8 cases of arbitrary element. The optimal systems of dissimilar subalgebras were obtained for the Lie algebras from the group classification. The example of the invariant vortex motion from the point source or sink was done. The regular partial invariant submodel was considered for the 2-dimensional subalgebra. It describes the turn of a vortex flow in the strip and on the plane with asymptotes for the stream line.

Confined vortex surface and irreversibility. 1. Properties of exact solution

We revise the steady vortex surface theory following the recent finding of asymmetric vortex sheets (Migdal, 2021). These surfaces avoid the Kelvin–Helmholtz instability by adjusting their discontinuity and shape. The vorticity collapses to the sheet only in an exceptional case considered long ago by Burgers and Townsend, where it decays as a Gaussian on both sides of the sheet. In generic asymmetric vortex sheets (Shariff, 2021), vorticity leaks to one side or another, making such sheets inadequate for vortex sheet statistics and anomalous dissipation. We conjecture that the vorticity in a turbulent flow collapses on a special kind of surface (confined vortex surface or CVS), satisfying some equations involving the tangent components of the local strain tensor. The most important qualitative observation is that the inequality needed for this solution’s stability breaks the Euler dynamics’ time reversibility. We interpret this as dynamic irreversibility. We have also represented the enstrophy as a surface integral, conserved in the Navier–Stokes equation in the turbulent limit, with vortex stretching and viscous diffusion terms exactly canceling each other on the CVS surfaces. We have studied the CVS equations for the cylindrical vortex surface for an arbitrary constant background strain with two different eigenvalues. This equation reduces to a particular version of the stationary Birkhoff–Rott equation for the 2D flow with an extra nonanalytic term. We study some general properties of this equation and reduce its solution to a fixed point of a map on a sphere, guaranteed to exist by the Brouwer theorem.

The steady vortex and enhanced drag effects of dandelion seeds immersed in low-Reynolds-number flow

Dandelion seeds can stably diffuse owing to the dominant drag rather than the lift-based mechanism of the streamlined leaves of the plant, where this is known to favor their long-distance dispersal with the steady vortex attached. However, the generation mechanism of the vortex and the aerodynamic force exerted on the seeds through multiple filaments remain unknown. Clarifying these subjects may help realize the optimal performance of porous structures under different flight conditions. This study conducts numerical simulations to illuminate the influence of gaps and the Reynolds number (Re) on the wake structures and consequent drag force of dandelion seeds. We fabricate the seeds into circular disks composed of evenly distributed square cylinders placed in a vertical flow field with Re of 100 and 400, with the porosity of the pappus (ε) ranging from 0.887 to 0.964. We explain the geometric properties of the attached, steady vortex rings and clarify their generation mechanism, i.e., the base bleed and convection effects competed with vorticity generation, based on which the gaps are confirmed to delay chaotic vortices from occurring compared with the solid case. The weakened leeward pressure is critical for the increase in the drag coefficient to reach the peak level. The enhanced drag coefficient is several times higher than that in the solid case, endowing the seeds with a high loading capacity, and the porosity corresponding to its peak is beneficial for the structural design. These conclusions provide positive insights into the design of ventilated aircrafts with optimal long-distance dispersal performance.

Direct numerical simulation of control of oblique breakdown in a supersonic boundary layer using a local cooling strip

Control of oblique breakdown in a supersonic boundary layer at Mach 2.0 using a local cooling strip is investigated by direct numerical simulation. Previous studies have indicated that wall cooling can stabilize first-mode disturbances, but no study has yet investigated the use of local cooling to control oblique breakdown in a supersonic boundary layer. In the present work, local cooling strips with various temperatures and widths are utilized at different locations to control oblique breakdown. Insight is obtained into the stabilizing effect of a cooling wall on the evolution of various disturbances in the streamwise direction. A local cooling strip controls oblique breakdown mainly by suppressing the amplification of the fundamental oblique waves in the streamwise direction, and it is found that this suppressive effect is enhanced by increasing the width and decreasing the temperature of the strip. The stabilizing effect of a local cooling strip on higher-harmonic modes is reinforced when the strip is located farther downstream, although this effect is negligible when compared with the stabilizing effect on the fundamental oblique waves. When the cooling strip is placed in the midstream area, where the steady vortex mode is amplified to the order of the fundamental oblique waves, outstanding performance in suppressing transition is found. Furthermore, in addition to the stabilizing effect of the cooling wall on the fundamental oblique waves, the boundary layer is stabilized by rapid growth of higher-spanwise-wavenumber steady modes. Eventually, oblique breakdown is suppressed and substantial improvements in the skin-friction coefficient are also obtained.

Vortex breakdown mechanics of a laminar confined swirling flow with large expansion ratio using a non-uniform finite difference approximation

Abrupt expansions are a very frequent geometry in mechanical engineering systems, i.e. in combustion chambers, valves, heat exchangers or impinging cooling devices. However, despite the large number of devices that use this geometry, the expanded flow behaviour still needs further research to understand and predict the full system performance. This paper presents the application of the non-uniform finite difference approximation method developed in Sanmiguel et al. for the numerical characterisation of a confined swirling laminar jet discharging with a large expansion ratio. This investigation can be considered an extension of previous work by Revuelta, but now a swirling flow is generated by a rotating pipe upstream the expansion. The structures found when a fully-developed rotating Hagen-Poiseuille flow discharges into a much larger pipe section are summarised in a bifurcation diagram, whose coordinates are the Reynolds number of the jet ( Rej) and the swirl parameter ( L), for which the time-dependent, axisymmetric and incompressible Navier-Stokes equations are integrated numerically. For values of the jet Reynolds number below 200, there is a critical value of the swirl parameter above which stable vortex breakdown appears. For values of the Reynolds number above 200, three different behaviours are observed, and each performance appears for a critical value of the swirl parameter. When increasing the swirl parameter from zero, the flow becomes axisymmetrically unstable, showing an oscillatory behaviour. If further increasing the swirl intensity, the oscillatory flow coexists with a vortex breakdown bubble and, finally, a steady vortex breakdown is reached. The expansion ratio ε considered in all the simulations is 1[Formula: see text]. In previous literature, the exactness of the limiting critical Rej and L values that define these behaviours has been found to be influenced by the variability in the inlet profile conditions, which affects the expanded flow. This enhances the importance in the present investigation to accurately simulate the discharge pipe inlet profiles.

3D Instability of a Toroidal Flow in the Liquid Partially Covered by a Solid Film

The structure of a steady radial thermocapillary flow from the local heat source in cylindrical geometry has been studied numerically. The up boundary of the liquid was partially covered by the stationary film of an insoluble surfactant, pushed to the wall of the cavity. The calculations are fulfilled on the base of interfacial hydrodynamics equations by using mathematical package “Comsol Multiphysics”. It is shown that the effect of a radial flow symmetry breakdown appears as a result of convective instability, so that the initial poloidal rotation of the liquid transforms into the azimuthal plane. The system of inclined steady volumetric vortices is formed under the film of surfactant. The inclination angle of the plane of rotation in dependence on the intensity of radial thermocapillary flow is studied. It is shown that the azimuthal vorticity can be regulated by the power of point-heat source and by free surface area. The increase of heating intensity leads to the growth of the azimuthal vorticity. Thus, the initially radially symmetric toroidal flow is divided into two parts with the origination of vortices in the azimuthal plane under the film.

Evolution of instability modes in Mach 10 frozen and chemically reacting boundary layers by means of non-linear parabolized stability equations

The physical mechanisms and laminar-to-turbulent transition scenarios characterizing hypersonic flows are not yet completely identified and well described as in low-supersonic and subsonic regimes. Particularly, there is a lack of knowledge about the role chemistry plays and the effects that high temperature has on the transition non-linear stages. In this study, transition in a Mach 10 adiabatic flat-plate boundary layer is investigated by means of non-linear parabolized stability equations, considering both frozen and chemical non-equilibrium (CNE) flow assumptions. A tendency to switch from a H- to a K-type transition scenario at the increment of the primary-mode initial amplitude is found, similar to what occurs in subsonic and low-supersonic regimes. Secondary-waves' initial amplitudes do not affect directly the occurring breakdown type, but they significantly influence the evolution of the higher harmonics, in particular the generation of streamwise steady vortices. Chemical reactions play an indirect role in transition through the determination of the laminar base flow and the linear stability characteristics of the primary instability. Excitation of secondary modes is weaker in CNE than in frozen conditions, but qualitatively similar. Contrary to previous studies, assuming frozen perturbations in a chemically reacting base flow is found to have a significant effect on the higher-harmonics amplitudes, in particular on the relative evolution of the secondary modes.

The decay of Hill's vortex in a rotating flow

Abstract

Comparison between the Lagrangian and Eulerian Approach in Simulation of Free Surface Air-Core Vortices

The problematic consequences regarding formation of air-core vortices at the intakes and the drastic necessity of a thorough investigation into the phenomenon has resulted in particular attention being placed on Computational Fluid Dynamics (CFD) as an economically viable method. Two main approaches could be taken using CFD, namely the Eulerian and Lagrangian methods each of which is characterized by specific advantages and disadvantages. Whereas many researchers have used the Eulerian approach for vortex simulation, the Lagrangian approach has not been found in the literature. The present study dealt with the comparison of the Lagrangian and Eulerian approaches in the simulation of vortex flow. Simulations based on both approaches were carried out by solving the Navier–Stokes equations accompanied by the LES turbulence model. The results of the numerical model were evaluated in accordance with a physical model for steady vortex flow using particle image velocimetry (PIV), revealing that both approaches are sufficiently capable of simulating the vortex flow but with the difference that the Lagrangian method has greater computational cost with less accuracy.

Control of Shock-Induced Separation of a Turbulent Boundary Layer Using Air-Jet Vortex Generators

An experimental analysis was carried out to study the control effectiveness and turbulence behavior of an array of steady air-jet vortex generators on a shock-induced boundary-layer separation. Control was applied to a 24° compression-ramp interaction at Mach 2.52 and . A parametric study varying the jet spacing revealed that an adequate interaction between the vortices is essential for effective control, and the most favorable control effect was achieved with a jet spacing of . This case was analyzed in more detail using particle image velocimetry. The results reveal a strong corrugation of the separation zone due to the injection of the jets with a substantial reduction in its area along the entire spanwise extent of the air-jet array, compared with the uncontrolled case. Measurements of velocity fluctuations along the interaction region also show that the jet injection results in a reduction in turbulent intensity after reattachment, contributing to an overall reduction in amplification factor across the interaction region. The expected increase in turbulent mixing, which is essentially responsible for the control effect, was confirmed in the region in-between jet injection and separation shock. Farther away from the surface, the flow is not affected, which reduces potential drag penalties.