Vortex-free Flow Research Articles

Towards High-Speed And High-Resolution Real-Time Optical Flow Particle Image Velocimetry

One of the major advantages of Optical Flow PIV (Particle Image Velocimetry) algorithms over Cross-Correlation PIV is their scalability leading to potentially very high computational speeds. This is confirmed in this study using different GPUs (Graphics Processor Unit) and different image sizes. The other advantage is the possibility of obtaining dense velocity fields of up to one vector per pixel. It is well known that particle seeding plays a crucial role in the results of standard particle image velocimetry based on cross-correlation algorithms. Its influence on the quality of the optical flow algorithm is not as well established. In this article the influence of particle concentration is quantified by introducing a criterion considering the proportion of “active” pixels in a snapshot. It is shown that it is possible to optimize particle concentration to maximize the percentage of active pixels, leading to better spatial resolution, down to one vector per pixel. The principle is validated on a vortex-free flow and applied to the complex 3D flow downstream a backward-facing step.

Verification of the Mathematical Model for Calculating the Air Flow Velocity Fields for Displacing Ventilation of Rooms of Complex Configuration

Statement of the problem. The purpose of the article is to verify the developed mathematical model of conformal mapping of air flows, which constructs air velocity fields during displacement ventilation of rooms of complex configuration with partitions. Results. An experimental setup has been developed to study the physical model of a room with partitions, which allows performing physical modeling of air flows. The comparison of analytical and experimental results of calculating the air velocity in randomly selected points of the studied area is carried out. Conclusions. The verification results show that the developed model, with a sufficiently high accuracy, allows one to determine the air flow velocity with a vortex-free flow and its insignificant disturbance. An increase in the speed and deviation of the flow trajectory from the level lines leads to an increase in the calculation error.

Начально-краевая задача о течении в кровеносном сосуде

The solution of the initial boundary value problem for a system of two quasi-linear hyperbolic equations, which describes a rotationally symmetric vortex-free flow of a viscous incompressible fluid in an infinite cylindrical domain (pipe, blood vessel) is constructed. It is assumed that the side surface of the domain is a free (soft, compliant) boundary on which the kinematic condition is set. The dynamic condition at the boundary is modeled by some constitutive relation – the dependence of the pressure P on the cross-sectional area S of the cylindrical domain. To study the flow an asymptotic model based on the shallow water theory is used. When constructing the solution of the initial-boundary (as well as initial and boundary) problem for a system of two quasilinear partial differential equations of the first order, the hodograph method based on the conservation law is used. A variant of the polynomial constitutive relation is chosen for the study: P~S2β (β>0). In the case of the initial data problem which specified at the initial time the Riemann-Green function, allowing to construct an implicit analytical solution, and an algorithm (numerical) for constructing an explicit solution of the original problem are given. The main attention is focused on the special case P~S2, for which all the formulas necessary to construct a solution are written in explicit form. For P~S2, several variants of conditions (initial and boundary value) are considered for the initial boundary value problem, which allow us to trace the evolution of the solution in detail. Numerical calculations demonstrating the motion of shock waves and wave fronts are given. The results obtained, in practice, can be used to describe flows in blood vessels, as well as reliable tests for testing compu tational algorithms intended to solve such problems, in particular, systems of quasi-linear hyperbolic equations.

Simulation of Biological Wastewater Treatment in Aerotanks with Moving Biocenosis

Purpose. The main purpose of the article is to develop a numerical model for the analysis of the process of biological wastewater treatment in a reactor with a mobile biocenosis. Methodology. For mathematical modeling of the process of biological wastewater treatment in a reactor with a moving biocenosis, a hydrodynamic model of a non-viscous vortex-free flow is used. We calculated the boundary conditions for the modeling equation on the surfaces of the bioreactor, solid walls, and the upper surface; at the inlet boundary; at the outlet boundary from the building. To calculate the process of movement of activated sludge and substrate in the bioreactor, a mass transfer model is used, which takes into account the convective-diffusion movement of the substrate and activated sludge. The process of biological water purification in that part of the bioreactor where there are no mobile biocenosis carriers will be calculated based on the Monod model. The process of biological water purification in the part of the bioreactor where there are mobile carriers is calculated on the basis of an empirical model in three stages. The first stage is determined using the Harremoes model. At the second stage, the rate of substrate «consumption» in the biofilm is calculated. At the third stage, the change in the substrate concentration in the zone where the biocenosis carriers are located is determined due to convective movement, substrate diffusion in the flow and its destruction in the biofilm on the carriers. The chaotic motion of biocenosis carriers in the reactor is modeled based on the parabolic diffusion equation. Finite-difference schemes are used for numerical integration of modeling equations. Findings. The software implementation of the constructed numerical model is carried out. A computational experiment to determine the efficiency of biological wastewater treatment in different parts of the bioreactor was conducted. Originality. An effective multifactorial numerical model has been created, which allows quick analysis of the efficiency of biological wastewater treatment in an aeration tank with mobile biocenosis carriers. Practical value. The created two-dimensional numerical model can be used for serial calculations at the stage of designing biological wastewater treatment systems and analysis of the efficiency of bioreactors under different operating conditions.

MATHEMATICAL DESIGN OF THE SHAFT FURNACES WITH MATERIALS MELTING

The authors have formed the objective of stationary heat exchange in shaft grate-fired furnaces in which the reason of processed materials movement is their melting. In this case the energy transfer specific feature manifests itself, namely the process intensity is largely determined by the speed of material flow, which in turn, substantially depends on particles melting tempo. Since iterative approach is the only way for reconciliation of the contradictions, in mathematical formulation of the tasks in general it is necessary to rely on idealization of certain phenomena. In particular, certain idealizations are necessary due to insufficient number of theoretical explanations of certain issues, i.e., mathematical theory of solid materials movement in the shaft furnaces. The vortexfree flow was used at description of layer gas mechanics.

Modeling and Optimization of Y-Type Micromixers

A trend in the global technological progress in the last few decades is the development of microsystem technology, microelectromechanical systems and corresponding technologies. Fluid mixing is an extremely important process widely used in various microfluidic devices (chemical microreactors, chemical and biological analyzers, drug delivery systems, etc.). To increase the mixing rate, it is necessary to use special devices: micromixers. This paper presents the results of a hydrodynamic simulation of Y-shaped micromixers. Flows are analyzed for both low and moderate Reynolds numbers. The passive and active mixers are considered. The dependence of the mixing efficiency on the Reynolds and Péclet numbers, as well as the possibility of using the hydrophobic and ultra-hydrophobic coatings is analyzed. Five different flow regimes were identified: (1) stationary vortex-free flow (Re < 5); (2) stationary symmetric vortex flow with two horseshoe vortices (5 < Re < 150); (3) stationary asymmetric vortex flow (150 < Re < 240); (4) non-stationary periodic flow (240 < Re < 400); and (5) stochastic flow (Re > 400). The maximum mixing efficiency was obtained for stationary asymmetric vortex flow.

Study of fluid flow in micromixer with symmetrical and asymmetrical inlet conditions

Flow regimes and mixing pattern in a T-type micromixer at high Reynolds numbers were studied by numerical solution of the Navier-Stokes equations and by micro-PIV and micro-LIF experimental measurement. The Reynolds number was varied from one to one thousand. The cross section of the mixing channel was 200 μm×400 μm and its length was 3000 μm. Five different flow regimes were identified: (i) stationary vortex-free flow (Re < 5); (ii) stationary symmetric vortex flow with two horseshoe vortices (5 < Re < 150); (iii) stationary asymmetric vortex flow (150 < Re < 240); (iv) nonstationary periodic flow (240 < Re < 400); (v) stochastic flow (Re >400). Maximum mixing efficiency was obtained for stationary asymmetric vortex flow. In this case, an S-shaped vortex structure formed in the flow field. Also the numerical investigation of flow and mixing in the T-shaped micromixer with asymmetrical inlet conditions for different Reynolds numbers was carried out. The good agreement between calculation and experiment was obtained as a result.

Investigation of slip boundary conditions in the T-shaped microchannel

Flow regimes and mixing performance in a T-type micromixer at high Reynolds numbers were studied by numerical solution of the Navier–Stokes equations. The Reynolds number was varied from 1 to 1000. The cross section of the mixing channel was 100μm×200μm, and its length was 1400μm. The transverse inlet channels were symmetric about the mixing channel, and their cross-section was 100μm×100μm, and the total length was 800μm. Five different flow regimes were identified: (i) stationary vortex-free flow (Re<5); (ii) stationary symmetric vortex flow with two horseshoe vortices (5<Re<150); (iii) stationary asymmetric vortex flow (150<Re<240); (iv) non-stationary periodic flow (240<Re<400); and (v) stochastic flow (Re>400). Maximum mixing efficiency is obtained for nonstationary asymmetric vortex flow. In this case, an S-shaped vortex structure is formed in the flow field. The effect of the slip conditions on the flow pattern and mixing efficiency is studied. The slip length varied from 1 to 70μm in the calculations. It was shown that the mixing can be controlled by hydrophobic coating.

Superfluid Vortex Front atT→0: Decoupling from the Reference Frame

Steady-state turbulent motion is created in superfluid (3)He-B at low temperatures in the form of a turbulent vortex front, which moves axially along a rotating cylindrical container of (3)He-B and replaces vortex-free flow with vortex lines at constant density. We present the first measurements on the thermal signal from dissipation as a function of time, recorded at 0.2T(c) during the front motion, which is monitored using NMR techniques. Both the measurements and the numerical calculations of the vortex dynamics show that at low temperatures the density of the propagating vortices falls well below the equilibrium value, i.e., the superfluid rotates at a smaller angular velocity than the container. This is the first evidence for the decoupling of the superfluid from the container reference frame in the zero-temperature limit.

Flow Structure and Heat Transfer in a Stagnation Flow CVD Reactor

An experimental study is undertaken to investigate the flow structure and heat transfer in a stagnation flow chemical vapor deposition (CVD) reactor at atmospheric pressure. It is critical to develop models that predict flow patterns in such a reactor to achieve uniform deposition across the substrate. Free convection can negatively affect the gas flow as cold inlet gas impinges on the heated substrate, leading to vortices and disturbances in the normal flow path. This experimental research will be used to understand the buoyancy-induced and momentum driven flow structure encountered in an impinging jet CVD reactor. Investigations are conducted for various operating and design parameters. A modified stagnation flow reactor is built where the height between the inlet and substrate is reduced when compared with a prototypical stagnation flow reactor. By operating such a reactor at certain Reynolds and Grashof numbers, it is feasible to sustain smooth and vortex free flow at atmospheric pressure. The modified stagnation flow reactor is compared with other stagnation flow geometries with either a varied inlet length or varied heights between the inlet and substrate. Comparisons are made to understand the impact of such geometric changes on the flow structure and the thermal boundary layer. In addition, heat transfer correlations are obtained for the substrate temperature. Overall, the results obtained provide guidelines for curbing the effects of buoyancy and for improving the flow field to obtain greater film uniformity when operating a stagnation flow CVD reactor at atmospheric pressure.

Aerodynamic effects of inferior turbinate surgery on nasal airflow--a computational fluid dynamics model

Turbinate reduction surgery may be indicated for inferior turbinate enlargement when conservative treatment fails. The aim of this study was to evaluate the effects of inferior turbinate surgery on nasal aerodynamics using computational fluid dynamics (CFD) simulations. CFD simulations were performed for the normal nose, enlarged inferior turbinate and following three surgical procedures: (1) resection of the lower third free edge of the inferior turbinate, (2) excision of the head of the inferior turbinate and (3) radical inferior turbinate resection. The models were constructed from MRI scans of a healthy human subject and a turbulent flow model was used for the numerical simulation. The consequences of the three turbinate surgeries were compared with originally healthy nasal model as well as the one with severe nasal obstruction. In the normal nose, the bulk of streamlines traversed the common meatus adjacent to the inferior and middle turbinate in a relatively vortex free flow. When the inferior turbinate was enlarged, the streamlines were directed superiorly at higher velocity and increased wall shear stress in the nasopharynx. Of the three surgical techniques simulated, wall shear stress and intranasal pressures achieved near-normal levels after resection of the lower third. In addition, airflow streamlines and turbulence improved although it did not return to normal conditions. As expected, radical turbinate resection resulted in intra-nasal aerodynamics of atrophic rhinitis demonstrated in previous CFD studies. There is little evidence that inspired air is appropriately conditioned following radical turbinate surgery. Partial reduction of the hypertropic turbinate results in improved nasal aerodynamics, which was most evident following resection of the lower third. The results were based on a single individual and cannot be generalised without similar studies in other subjects.

Quantum Turbulence in a Propagating Superfluid Vortex Front

We present experimental, numerical, and theoretical studies of a vortex front propagating into a region of vortex-free flow of rotating superfluid 3He-B. We show that the nature of the front changes from laminar through quasiclassical turbulent to quantum turbulent with decreasing temperature. Our experiment provides the first direct measurement of the dissipation rate in turbulent vortex dynamics of 3He-B and demonstrates that the dissipation becomes mutual-friction independent with decreasing temperature, and it is strongly suppressed when the Kelvin-wave cascade on vortex lines is predicted to be involved in the turbulent energy transfer to smaller length scales.

Flow Field Characterization at the Onset of Gas Entrainment in a Single Downward Discharge Using Particle Image Velocimetry

The incipience of two-phase flow in discharging branches from a stratified gas-liquid region has major implications in industrial applications where safety is of concern. An experimental investigation of the liquid side flow field at the onset of gas entrainment, in a single downward oriented discharging branch, was presented. Particle image velocimetry was used to measure the liquid side flow field in horizontal and vertical planes. Averaged velocity profiles were presented and demonstrated a highly radial flow. The particle image velocimetry data were validated using continuity and showed that the mass flow rate to be in the range of 10–25% of the expected value. Further, the vortex-free flow field assumption, used previously in the development of analytical and empirical models, was found to be reasonable.

Transition to Superfluid Turbulence

Turbulence in superfluids depends crucially on the dissipative damping in vortex motion. This is observed in the B phase of superfluid 3He where the dynamics of quantized vortices changes radically in character as a function of temperature. An abrupt transition to turbulence is the most peculiar consequence. As distinct from viscous hydrodynamics, this transition to turbulence is not governed by the velocity-dependent Reynolds number, but by a velocity-independent dimensionless parameter 1/q which depends only on the temperature-dependent mutual friction -- the dissipation which sets in when vortices move with respect to the normal excitations of the liquid. At large friction and small values of 1/q < 1 the dynamics is vortex number conserving, while at low friction and large 1/q > 1 vortices are easily destabilized and proliferate in number. A new measuring technique was employed to identify this hydrodynamic transition: the injection of a tight bundle of many small vortex loops in applied vortex-free flow at relatively high velocities. These vortices are ejected from a vortex sheet covering the AB interface when a two-phase sample of 3He-A and 3He-B is set in rotation and the interface becomes unstable at a critical rotation velocity, triggered by the superfluid Kelvin-Helmholtz instability.

Measurement of Turbulence in Superfluid3He-B

The experimental investigation of superfluid turbulence in 3He-B is generally not possible with the techniques which have been developed for 4He-II. We describe a new method by which a transient burst of turbulent vortex expansion can be generated in 3He-B. It is based on the injection of a few vortex loops into rotating vortex-free flow. The time-dependent evolution of the quantized vorticity is then monitored with NMR spectroscopy. Using these techniques the transition between regular (i.e. vortex number conserving) and turbulent vortex dynamics can be recorded at T ~ 0.6 Tc and a number of other characteristics of turbulence can be followed down to a temperature of T ~ 0.4 Tc.

Optimization of a stagnation point flow reactor design for metalorganic chemical vapor deposition by flow visualization

Various design parameters of a stagnation point flow reactor such as mixing chamber, gas distributor and reactor shape are optimized by a technique of flow visualization. A dense smoke of TiO 2 particles generated in the mixing cup with the help of unidirectional tangential jets of TiCl 4, H 2O and helium is used to show the flow patterns. A sheet of laser (5 mW He-Ne) light formed with the help of a cylindrical lens is used to illuminate the trajectory of smoke particles. The flow patterns are recorded photographically. Rapid and uniform mixing of a number of gas streams is achieved by tangential jets. A “capillary plug” as an ideal gas distributor, incorporated in the inlet, removes the swirl due to tangential jets completely and develops an axially uniform gas velocity profile across the inlet. Various reactor shapes such as cylindrical, triangular, diffuser and modified diffuser (a diffuser with reduced height) are studied for their performance. The modified diffuser with capillary plug as a gas distributor in the inlet is the only appropriate metalorganic chemical vapor deposition (MOCVD) reactor configuration that can develop and sustain a smooth, laminar and vortex free flow at room temperature as well as at 773 K in absence of substrate rotation and /or application of vacuum.

Applying methods of numerical modeling to optimize a plasma burner of atmospheric pressure

The shape of a plasma burner is optimized by the methods of numerical modeling. Vortex-free flow is created in the burner merely at the expense of selecting the external tube profile rather than by introduction of additional protective flows into the burner.

The asymptotic solution of a problem in the theory of waves on the surface of a vortex flow

THE PROBLEM of the wave motion of a liquid flowing round a solid cylindrical nucleus with constant vortex velocity is considered. The chosen velocity distribution in the layer of the liquid is close to reality. Asymptotic formulas are obtained which enable the wave distribution pattern on the free surface of the liquid to be clearly represented, and the results are compared with the case of a vortex-free flow. In hydrodynamic problems arising in the study of wave motion in the oceans it is necessary to allow for the curvature of the earth and the occurrence of oceanic currents. In view of its complexity the mathematical problem arising from this has not been developed, not only for the hydrodynamic problem in the general formulation, but also for the simplest case where a liquid layer uniformly covering a solid sphere and subjecty to the simplest circulations is considered. However, this difficulty can be overcome in special problems for particular regions of the ocean. The problem of wave motion on the surface of a liquid layer flowing uniformly round a solid cylinder was solved in [1]. The case of a vortex-free flow was considered. In this paper, using the results obtained in [1], wave propagation on the surface of a liquid layer is investigated for the case of a flow with constant vortex velocity.

The solar temperature reversal and convective motions

Given an equation of State, the three equations of mass, momentum and energy conservation determine the vortex free flow fields in a star. The solar data processed by Athay (1966) is a measure of the dissipation of the fluid, while the use of an empirical temperature profile (BCA, 1968) permits values for the gradients in the equations of fluid flow rendering them algebraic, with solutions independent of boundary conditions. This approach serves as a consistency check on the methods with which data have been processed by inquiring to what degree the basic conservation laws have been satified, and by directly implying a velocity field which can be scrutinized for its observational consequences.