Nonstationary Vortex Research Articles

Modeling and simulation of one- and two-row six-bladed ducted fans

The problem of simulation of efficient ducted fan type propulsors is considered. From experience of operation of twin blades in fantails of helicopters, it is known that this configuration creates less noise compared to a uniform arrangement of the blades around the circumference. However, the flow behind such fan is less uniform than that of a conventional ducted fan. For multicopter-type unmanned aircraft and air taxis, the key problem is flight in take-off and landing modes as well as acoustic and vortex fields created by propulsors in these modes. The decrease in the noise level in propellers with twin blades can potentially be accompanied by an increase in non-stationary vortex effects on the aircraft as well as a decrease in specific thrust. The objectives were to develop a method for simulation of ducted fan propellers in the takeoff and landing mode, to determine the optimal angle between the blades, and to compare a ducted fan with twin X-shaped blades to conventional blade position. Turbulent flows were calculated using transient Reynold-averaged Navier-Stokes equations, complemented by SST turbulence model, and large eddy simulation with WALE subgrid viscosity model. The calculations used the modification γ–Reθ Transition SST of the Langtry-Menter turbulence model, where there are relations for the intermittency criterion, which made it possible to consider the laminar-turbulent transition and the appearance of thin laminar separation bubbles that affect both the thrust of the propeller and the non-uniformity of the flow behind it. Testing was carried out on four-bladed propellers according to the known results of the TsAGI reference experiments. Testing of the γ–Reθ Transition SST Langtry-Menter turbulence model showed that it reproduces the dependence of the thrust coefficient and power factor on the blade angle better than the standard SST model. Calculations have shown that there is a clearly defined optimum angle between the paired blades. A comparison of three-bladed, six-bladed single and six-bladed propellers with twin blades showed that the latter option has slightly better thrust characteristics and creates a significantly lower noise level on the ground. The studied characteristics of ducted fans demonstrate the prospects for the use of propellers with twin blades in aircraft with vertical takeoff and landing. The developed numerical method can be directly used for industrial calculations of propellers and fans.

The convective instability of the boundary-layer flow over a rotating cone in and out of a uniform magnetic field

We present convective instability analyses of the boundary-layer flows originated over cones (with half-angle ψ≤90∘) rotating in an otherwise still conducting fluid. A uniform magnetic field (with magnetic strength parameter, m≥0) is acting normally on the surface of each cone. In the non-magnetic case of cones, comparison of present results with existing experimental and theoretical studies lead *to propose that onset of instabilities may be attributed to crossflow (type I) modes and streamline curvature (type II) modes for broad cones (with ψ≥40∘) and more slender cones (with ψ≤15∘), respectively. For slender cones with half-angle ψ in the vicinity of 25° the presented results validate the hypothesis of centrifugal (type III) modes ( discovered by Garrett et al. (2014)). In the magnetic case, increasing magnetic strength m∈(0,11] considerably delays the onset of instabilities (due to both type I and type II modes) over each rotating cone with fixed ψ. The stabilising influence of magnetism is in agreement with the meagrely available theoretical studies for magnetic rotating disk case ψ=90∘. In addition, our results lead to suggest that streamline curvature mode over each cone with fixed half-angle ψ become sensitive with increasing m. A minimum m0∈[0,11] exists for each fixed half-angle ψ0≤90∘ such that whenever m≥m0 the onset of instabilities (in the sense of minimum critical Reynolds numbers) over every cone with half-angle (ψ≤ψ0) are commenced by type II mode instead of type I mode whilst the aforementioned conjecture of stabilising effect of magnetism is not violated in the considered range of parameters. Under non-stationary vortices assumption with magnetism, we show that crossflow modes travelling at around 75% of the cone surface are likely to be selected in applications where smooth and frictionless surfaces are used. This finding is in complete agreement with the non-magnetic case of rotating cone in existing studies.

Визуализация смерчеобразных структур с целью совершенствования систем охлаждения электротехнических устройств

Визуализация смерчеобразных структур с целью совершенствования систем охлаждения электротехнических устройств

Non-stationary vortex streets in shear flows

Spatially periodic vortex systems that form due to unstable shear flows are called vortex streets. A number of exact and asymptotic solutions of two-dimensional hydrodynamic equations describing nonstationary vortex streets have been constructed. It is shown that the superposition of the flow with a constant horizontal shear and its perturbations in the form of a nonmodal wave provides an exact solution that describes a nonstationary vortex street with rotating elliptic current lines. The width of the zone occupied by such a vortex street has been determined. The equation of separatrix separating vortex cells with closed current lines from an external meandering flow has been obtained. The influence of the quasi-two-dimensional compressibility and beta effect on the dynamics of vortex streets has been studied based on the potential vorticity transport equation. The solutions describing the formation of vortex streets during the development of an unstable zonal periodic flow and a free shear layer have been constructed using a longwave approximation.

Nonstationary Vortex Streets in Shear Flows

Spatially periodic vortex systems that form due to unstable shear flows are called vortex streets. A number of exact and asymptotic solutions of two-dimensional hydrodynamic equations describing nonstationary vortex streets have been constructed. It is shown that the superposition of the flow with a constant horizontal shear and its perturbations in the form of a nonmodal wave provides an exact solution that describes a nonstationary vortex street with rotating elliptic current lines. The width of the zone occupied by such a vortex street has been determined. The equation of separatrix separating vortex cells with closed current lines from an external meandering flow has been obtained. The influence of the quasi-two-dimensional compressibility and beta effect on the dynamics of vortex streets has been studied based on the potential vorticity transport equation. The solutions describing the formation of vortex streets during the development of an unstable zonal periodic flow and a free shear layer have been constructed using a longwave approximation.

Redchyts Evaluation of aerodynamic and thermal loads on the HYPERLOOP capsule fuselage in a partly evacuated tube

Aerodynamics occupies an important place in the design of high-speed ground transportation systems. When a vehicle is moving at a speed above 500 km/h under atmospheric pressure, the main energy is spent to overcome the aerodynamic drag. Creating a rarefied atmosphere inside a sealed pipe in order to significantly reduce energy loss is one of the key ideas of the HYPERLOOP project [1].The paper assesses the aerodynamic and thermal loads on the HYPERLOOP capsule fuselage in a partly evacuated tube based on the numerical solution of the Navier-Stokes equations of compressible flow closed by a differential turbulence model [2-4]. Numerical modeling was carried out with the help of the computational fluid dynamics software developed by the scientific researchers of the Institute of Transport Systems and Technologies of the National Academy of Sciences of Ukraine [5].It was shown that even under conditions of low air pressure in a partly evacuated tube the high-speed movement of the HYPERLOOP capsule will be accompanied by the formation of local supersonic zones, shock waves and non-stationary vortex systems. The structure of the flow essentially depends on geometry of the streamlined capsule and the speed of its movement.It was found that the flow structure and the values of aerodynamic dimensionless coefficients weakly depend on the pressure in the partly evacuated tube. Thus, the aerodynamic forces acting on the HYPERLOOP capsule at the same speeds are almost directly proportional to the pressure value in the tube.A certain problem in the design of the HYPERLOOP type high-speed vehicles will be the aerodynamic heating of the capsule fuselage. When the capsule moves at transonic speed the temperature of the outer surface of the capsule will be 60÷900 C. This heat load can have a negative impact on the performance of onboard power supply and control systems, as well as on the ensuring of the passengers’ comfort on the way.

A Double Screw Spiral as a Possible Mechanism of Wall-Free Nonstationary Air Vortex Generation

In this work, our discovery for the first time of a two-spiral nonstationary structure of interacting vortex filaments preceding the generation of a wall-free nonstationary air vortex is described.

Measurement of Velocity Fields of Nonstationary Air Vortices by Anemometry Using Particle Images

We consider aspects of using the method of anemometry on particle images to measure the velocity fields of nonstationary air vortices. To prevent the loss of a cross-pair when a particle passes through a light curtain, a method is proposed for determining the time delay between frames. Methods for measuring the velocity fields of nonstationary air vortices are described taking into account the vertical velocity of particles when the actual velocity is reproduced from the measured horizontal projection in the case of using a two-dimensional (single-chamber) type of anemometry method.

Bound states of dark solitons and vortices in trapped multidimensional Bose-Einstein condensates

We report on the existence and stability of multidimensional bound solitonic states in harmonically-trapped scalar Bose-Einstein condensates. Their equilibrium separation, as a measure of the strength of the soliton-soliton or the solitonic vortex-vortex interaction, is provided for varying chemical potential $\mu$. Static bound dark solitons are shown to be dynamically stable in elongated condensates within a range of intermediate (repulsive) interparticle-interaction strength. Beyond this range the snaking instability manifests during the time evolution of the planar solitons and produces the decay into non-stationary vortex states. A subsequent dynamical recurrence of solitons and vortices can be observed at low $\mu$. At equilibrium, the bifurcations of bound dark solitons are bound solitonic vortices. Among them, both two-open and two-ring vortex lines are demonstrated to exist with both counter- and co-rotating steady velocity fields. The latter flow configurations evolve, for high chemical potential, into a stationary 3D-chain-shaped vortex and a three vortex-antivortex-vortex ring sequence that arrest the otherwise increasing angular or linear momentum respectively. As a common feature to the bifurcated vortex states, their excitation spectra present unstable modes with associated oscillatory dynamics.

Advection of passive scalars induced by a bay-trapped nonstationary vortex

A simple model of fluid particle advection induced by the interaction of a point vortex and incident plane flow occurring near a curved boundary is analyzed. The use of the curved boundary in this case is aimed at mimicking the geometry of an isolated bay of a circular shape. An introduction of such a boundary to the model results in the appearance of retention zones, where the vortex can be permanently trapped being either stationary or periodically oscillating. When stationary, it induces a steady velocity field that in turn ensures regular advection of nearby fluid particles. When the vortex oscillates periodically, the induced velocity field turns unsteady leading to the manifestation of chaotic advection of fluid particles. We show that the size of the fluid region engaged into chaotic advection increases almost monotonically with the increased magnitude of the vortex oscillations provided the magnitude remains relatively small. The monotonicity is accounted for the fact that the frequency of the vortex oscillations incommensurable with the proper frequency of fluid particle rotations in the steady state. Another point of interest is that it is demonstrated that bounded regions, in which the vortex may be trapped, can appear even at a significant distance from the bay. Making use of a Lagrangian indicator, examples of fluid particle advection induced by the periodic motion of the vortex inside the bay are adduced.

Stable Vortex Clusters in Two-Dimensional Bose-Einstein Condensates with Spatially Modulated Defocusing Nonlinearity

We investigate the vortex dynamic behavior of Bose-Einstein condensate in a spatially two-dimensional harmonic potential with spatially modulated defocusing nonlinearity. Kinds of exact vortex solutions of the Gross-Pitaevskii equation are obtained by designing various laser potentials which can be experimentally realized. In particular, we demonstrate that the spatially modulated defocusing nonlinearity supports stable vortex clusters. For the stationary vortex solutions, the vortex clusters are dynamically stable, and the circulation direction of each vortex and vortex core positions remain unchanged. However, for the non-stationary vortex solutions, stable and unstable vortex clusters exist. For the stable vortex clusters, the vortex core positions are constant during dynamical evolution, while the phase increase directions vary periodically. Additionally, corresponding to the unstable vortex clusters, vortices disappear and appear periodically in the condensate.

An Exact Non-stationary Vortex Solution of the Plane Flow and Brownian Motion

An Exact Non-stationary Vortex Solution of the Plane Flow and Brownian Motion

Vortices in Bose-Einstein condensates with PT -symmetric gain and loss

We investigate vortex excitations in dilute Bose-Einstein condensates in the presence of complex $\mathcal{PT}$-symmetric potentials. These complex potentials are used to describe a balanced gain and loss of particles and allow an easier calculation of stationary states in open systems than in a full dynamical calculation including the whole environment. We examine the conditions under which stationary vortex states can exist and consider transitions from vortex to nonvortex states. In addition, we study the influences of $\mathcal{PT}$ symmetry on the dynamics of nonstationary vortex states placed at off-center positions.

The Choice of Turbulence Models for Steam Jets

The noise from the steam dumping is a serious problem for many industries. For example, the popping of pressure relief valves of power boilers causes a temporal sound level overshoot over the admissible one up to 30-40 dBA in a radius of several kilometers. Mathematical modeling is an important tool for studying the outflow steam jets. Knowing processes of steam efflux into the atmosphere allows us correctly to calculate noise levels at a distance from them on the one hand and on the other hand to realize measures for sound attenuation. The study of mechanisms of noise generation by jets had begun in the end of 1940s and had been generally related to investigations of air jets and exhaust gas jets of aircrafts. The choice of turbulence models for steam jets has been studied insufficiently until recently. The significant subject of the steam jet simulation is the choice of the turbulence model. There are about a dozen mathematical models of turbulence, which are implemented in different software packages. In the case of simulation of turbulent flows with transient large scale vortex structures, it is ineffective and impossible to solve Reynolds averaged Navier-Stokes equations closed using semi empirical turbulence model or by means of the direct numerical simulation (DNS). Simulation of three dimensional and nonstationary vortices is carried out using a Large Eddy Simulation (LES) method in which the idea of the formal mathematical differentiation of coarse and fine structures by means of either operation, for example the filtration operation, is recommended. It is noted that, based on the LES method, it is possible to compute the coherent vortex structures, and the applicability of the model for prediction of noise generated by steam jets. LES model describes noise generation processes from steam jet more correct.

Concentrated air and fire vortices: Physical modeling (a Review)

The experimental works devoted to studying the generation and dynamics of concentrated air and fire vortices are reviewed. The main characteristics of stationary and nonstationary vortices, as well as free and confined air and fire vortices, are considered.

Numerical modeling of heat and mass transfer processes upon the flowing of regular structures by gas-droplet stream

Approximate models are developed for calculating heat and mass transfer processes in gas-drop flows that pass over a regular packed bed with cylindrical elements. A number of different flow regimes are considered: flat laminar flow, the formation of the stationary vortex behind packing element and formation of nonstationary vortex wake. Criterial equations for calculating corresponding mass transfer parameters are obtained.

Heat transfer and thermohydrodynamic fluctuations in aluminum–air fuel cell

Numerical simulation and experimental investigation of processes of conjugate heat transfer, hydrodynamics, and electrochemical kinetics in an alkaline aluminum–air fuel cell are performed. A mathematical model of hydrodynamics, heat and mass transfer, and electrochemical kinetics in an alkaline aluminum–air fuel cell with regard to the temperature dependence of electrochemical kinetics of electrodes, the ohmic heat losses, the thermogravimetric convection in electrolyte, and water evaporation from the cathode surface is proposed. Three-dimensional nonstationary vortex structures producing temperature fluctuations of the hydrodynamic nature are developed in the region of the electrolyte chamber with unstable electrolyte stratification, which is above the heated electrodes. It is shown that the thermohydrodynamic temperature fluctuations cause fluctuations of net power of the fuel cell during discharge.

Diagnostics of bubble-mode vortex breakdown in swirling flow in a large-aspect-ratio cylinder

We report for the first time on the possible formation of regions with counterflow (bubble-mode vortex breakdown or explosion) at the center of strongly swirling flow generated by a rotating endwall in a large-aspect-ratio cylindrical cavity filled with a liquid medium. Previously, the possibility of bubble-mode breakdown was studied in detail for cylindrical cavities of moderate aspect ratio (length to radius ratios up to H/R ∼ 3.5), while flows in large-aspect-ratio cylinders were only associated with regimes of self-organized helical vortex multiplets. In the present study, a regime with nonstationary bubble-mode vortex breakdown has been observed in a cylindrical cavity with H/R = 4.5.

Nonstationary cylindrical vortex in an ideal fluid

Equations of rotationally symmetric motion of an ideal incompressible fluid are considered. A class of solutions to these equations, described by a hyperbolic equation of the fourth order with one space variable, for which an initial boundary-value problem is formulated, is distinguished. The new class of exact solutions of the Euler equations was used to describe the a nonstationary cylindrical vortex in an ideal fluid.

The Integral Formula for Pressure Field in the Nonstationary Barotropic Flows of Viscous Fluid

An integral expression of pressure via dynamical characteristics of the vortex and velocity fields for viscous fluid is presented. This expression may be considered as an analog (or generalization) of the Bernoulli equation for nonstationary vortex flows of ideal or viscous fluids, including the case of an external nonconservative mass force. The presented formulas are useful for calculating the pressure field when meshless vortex methods are applied for the flow simulation.