Numerical analyis of turbulent flow in a Coanda ejector

The task of this study is to investigate the influence of various geometric parameters and pressure ratios on the Coanda ejector performance. For numerically investigations we use an implicit formulation of the compressible Reynolds-average Navier-Stokes equations (RANS) for axisymmetric flow with a shear stress transport k − ω (SST model) turbulence model. The numerically results was obtained for a total pressure range 1-5 Bars, imposed at the reservoir inlet. The effect of various factors, such as, the pressure ratio, primary nozzle and ejector configurations on the system performance has been evaluated based on defined performance parameters. The numerical results have been compared with theoretical and experimental results for a given Coanda ejector configuration. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three-dimensional effects of an air curtain used to restrict cold room infiltration

The aim of this study was to compare the measured effectiveness of an air curtain device at different jet velocities against a three-dimensional (3-D) computational fluid dynamics (CFD) model. The air curtain device was not as wide as the entrance and had a geometry that encouraged 3-D flow. By carefully setting up the air curtain an effectiveness of 0.71 was achieved compared to the initial value of only 0.31 as set by the air curtain device installer. The 3-D CFD model predicted the infiltration through the entrance with no air curtain to an accuracy of within 20–32%. The predicted effectiveness, E, of the air curtain at different jet velocities was 0.10–0.15 lower than measured. The shape of the effectiveness curve against jet velocity was well predicted. CFD has shown that the flow from this air curtain cannot be considered as 2-D. The central part of the jet is deflected away from the cold store by the Coanda effect caused by the air curtain device’s fan body. The edges of the jet are deflected into the cold store by the stack pressures and turn into the void caused by the deflected central jet.     

The relationship between the vortical structure and the wall shear stress in a blind trough cavity subject to a jet impingement

In a blind trough cavity subject to a jet– impingement, the jet switching phenomenon has been known for decades. The large vortices, formed by the Kelvin– Helmholtz instability play a crucial role in this phenomenon– they are the main cause of the fluid entrainment phenomenon, which consequently evoke the Coanda effect and finally results in the jet switch. As the jet swings, the vortical structure inside the cavity changes together with the impinigement point. The aim of this article is to describe the relationship between the wall shear stress, i.e. the motion of the impingement point, and the vortical structure.The analysed data were obtained using the TR PIV system, the caity aspect ratios 16:24 and 18:24, jet hydraulic diameter based Reynolds numbers 3000, 11200 and 19600, and the impingement angles 0°, 5°, 10° and 15°. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Active Control of Separating Boundary Layer

Flow control refers to the ability to alter flows with the aim of achieving a desired effect: examples include drag reduction, noise attenuation, improved mixing or increased combustion efficiency among many other industrial applications. The reduction and control of the viscous drag force exerted on bodies moving in a fluid is of great technical interest. Several active and passive methods to achieve a delay of separation in the boundary layer have been developed and are being developed. In this paper we present a new concept for boundary layer separation control that is based on the synthetic jet concept which converts acoustic oscillations into mean fluid motions. We use synthetic jets as methods for Coanda effect's amplification. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Collision of incompressible inviscid fluids effluxing from two nozzles

This paper concerns the mathematical theory of the collision problem of two-dimensional incompressible inviscid fluids issuing from two given nozzles. The main result reads that for given two co-axis symmetric semi-infinitely long nozzles with arbitrary variable sections, imposing the incoming mass fluxes in two nozzles, there exists a smooth impinging outgoing jet, such that the two free boundaries of the impinging jet initiate smoothly at the endpoints of the nozzles and approach to some asymptotic direction in downstream, and the pressure on the free surface remains a constant. Furthermore, we show that there exists a unique smooth surface separating the two nonmiscible fluids and there exists a unique stagnation point in the fluid region and its closure. Moreover, some results on the uniqueness and the estimates of the location of the impinging outgoing jet are also established. Finally, the asymptotic behaviors, the precise estimate to the deflection angle and other properties to the impinging outgoing jet are also considered.     

The contact problem with the bulk application of intermolecular interaction forces (a refined formulation)

A refined formulation of the contact problem when there are intermolecular interaction forces between the contacting bodies is considered. Unlike the traditional formulation, it is assumed that these forces are applied to points within the body, rather than to the surface of the deformable body as a contact pressure, and that the body surface is load-free. Solutions of the contact problems for a thin elastic layer attached to an absolutely rigid substrate and for an elastic half-space are analysed. The refined and traditional formulations of the problem when there is intermolecular interaction are compared. ©2013     

The influence of electric fields and surface tension on Kelvin–Helmholtz instability in two-dimensional jets

We consider nonlinear aspects of the flow of an inviscid two-dimensional jet into a second immiscible fluid of different density and unbounded extent. Velocity jumps are supported at the interface, and the flow is susceptible to the Kelvin–Helmholtz instability. We investigate theoretically the effects of horizontal electric fields and surface tension on the nonlinear evolution of the jet. This is accomplished by developing a long-wave matched asymptotic analysis that incorporates the influence of the outer regions on the dynamics of the jet. The result is a coupled system of long-wave nonlinear, nonlocal evolution equations governing the interfacial amplitude and corresponding horizontal velocity, for symmetric interfacial deformations. The theory allows for amplitudes that scale with the undisturbed jet thickness and is therefore capable of predicting singular events such as jet pinching. In the absence of surface tension, a sufficiently strong electric field completely stabilizes (linearly) the Kelvin–Helmholtz instability at all wavelengths by the introduction of a dispersive regularization of a nonlocal origin. The dispersion relation has the same functional form as the destabilizing Kelvin–Helmholtz terms, but is of a different sign. If the electric field is weak or absent, then surface tension is included to regularize Kelvin–Helmholtz instability and to provide a well-posed nonlinear problem. We address the nonlinear problems numerically using spectral methods and establish two distinct dynamical behaviors. In cases where the linear theory predicts dispersive regularization (whether surface tension is present or not), then relatively large initial conditions induce a nonlinear flow that is oscillatory in time (in fact quasi-periodic) with a basic oscillation predicted well by linear theory and a second nonlinearly induced lower frequency that is responsible for quasi-periodic modulations of the spatio-temporal dynamics. If the parameters are chosen so that the linear theory predicts a band of long unstable waves (surface tension now ensures that short waves are dispersively regularized), then the flow generically evolves to a finite-time rupture singularity. This has been established numerically for rather general initial conditions.     

The limiting properties of piecewise-potential subcritical and critical jet streams of an ideal gas

The limiting properties of subcritical and critical (with Mach numbers M ⩽ 1) plane-parallel jet streams are investigated in the approximation of an ideal (inviscid and non-heat-conducting) gas. Chaplygin's equation is used with the pressure and the angle of inclination of the velocity as the independent variables, which are measured from the limiting values corresponding to the cross-section of the equalizing of the jet with respect to these variables. The stream function in the neighbourhood of the “equalizing cross-section” is represented in the form of an expansion in powers of the “distance to the origin of the coordinates” (in the plane of the independent variables) with coefficients which depend on a previously unknown combination of the independent variables. The limiting property of the flow, i.e. the position of the equalizing cross-section at a finite of infinite distance, is defined by the leading terms of the expansion. A symmetric potential jet and symmetric piecewise-potential jets flowing out into a submerged space in the case of subcritical and critical pressure drops are considered as examples. The critical pressures of the potential parts of the composite jet can be different or identical (including when the thermodynamic properties of the gases are different).     

Simulation of eye deformation in the measurement of intraocular pressure

The procedure of measuring the intraocular pressure by an optical analyzer is numerically simulated. The cornea and the sclera are considered as axisymmetrically deformable shells of revolution with fixed boundaries; the space between these shells is filled with incompressible fluid. Nonlinear shell theory is used to describe the stressed and strained state of the cornea and sclera. The optical system is calculated from the viewpoint of the geometrical optics. Dependences between the pressure in the air jet and the area of the surface reflecting the light into a photodetector are obtained. The shapes of the regions on the cornea surface are found from which the reflected light falls on the photodetector. First, the light is reflected from the center of the cornea, but then, as the cornea deforms, the light is reflected from its periphery. The numerical results make it possible to better interpret the measurement data.     

Experimental in-situ investigations on fluid flow during High Pressure Processing by means of LDA and HWA

In a tube injection system for High Pressure Processing (HPP) of foods and biomaterials, pressure transmitting medium is injected into the vessel to increase the pressure up to 1000 MPa generating a submerged liquid jet. The presence of a turbulent free jet during pressurizing and its positive influence on the homogeneity of the product treatment have already been examined by computational fluid dynamics investigations. However, up to now there is no experimental evidence, supporting the existence and properties of turbulence of a free jet during HPP due to difficulties in gaining in–situ insight into the high pressure vessel and the lack of high pressure withstanding probes. Hence, we developed two experimental setups: (1) HP–Laser Doppler Anemometry (HP–LDA), and (2) HP–Hot Wire Anemometry (HP–HWA). This paper presents first results of velocity profiles measured by LDA and HWA under high pressure conditions up to 300 MPa. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical and physical simulation of the interaction between a gas jet and a liquid free surface

In this work a two phase 3D mathematical model was developed using the volume of fluid (VOF) algorithm, which is able to accurately describe the cavity geometry and size as well as the liquid flow patterns created when a gas jet that impinges on a liquid free surface. These phenomena are commonly found in steelmaking operations such as in the Electric Arc Furnace (EAF) and the Basic Oxygen Furnace (BOF) where oxygen jets impinge on a steel bath and they control heat, momentum and mass transfer. The model was successfully validated with measurements made on a physical model through velocity fields obtained by Particle Image Velocimetry (PIV) and high speed camera images of the cavity. Agreement between model predictions and experimental measurements is excellent in both x-velocity component of the liquid and cavity sizes. The cavity formed in the liquid by the impinging jet depends on a force balance at the free surface where the inertial force of the jet governs this phenomena, while the liquid circulation depends on also the jet inertial force of the jet, but its angle plays an important role, being the lowest angle the best choice to shear the bath and promote stronger circulation and better mixing in the liquid.     

Size distribution of convective thermals in an unstable stratified turbulent surface layer

An ensemble of convective thermals is considered in the surface layer of penetrative turbulent convection over a homogeneous heated horizontal surface. An integral model of an unsteady spontaneous jet having an exact self-similar solution is proposed to describe the dynamics of an isolated convective element. A statistical model for an ensemble of convective elements using a hydrodynamic analogy of the isolated spontaneous jet equations is suggested. It is supposed that motion of the elements of an ensemble corresponds to a statistic invariant that combines the squared velocity and the diameter of the jet. Using the combination of the statistic invariant of an ensemble and the Boltzmann distributions on squares of velocities, the size distribution of spontaneous jets in a convective surface layer of the atmosphere is constructed, which agrees with available experimental data.      

Conservation laws and conserved quantities for laminar two-dimensional and radial jets

A systematic way to derive the conserved quantities for the liquid jet, free jet and wall jet using conservation laws is presented. Both two-dimensional and radial jets are considered. The jet flows are described by Prandtl’s momentum boundary layer equation and the continuity equation. The multiplier approach (also know as variational derivative approach) is first applied to construct a basis of conserved vectors for the system. The basis consists of two conserved vectors. By integrating the corresponding conservation laws across the jet and imposing the boundary conditions, conserved quantities are derived for the liquid jet and the free jet. The multiplier approach is then applied to construct a basis of conserved vectors for the third-order partial differential equation for the stream function. The basis consists of two local conserved vectors one of which is a non-local conserved vector for the system. The conserved quantities for the free jet and the wall jet are derived from the corresponding conservation laws and boundary conditions. The approach gives a unified treatment to the derivation of conserved quantities for jet flows and may lead to a new classification of jets through conserved vectors and their multipliers.     

The influence of electric fields and surface tension on Kelvin–Helmholtz instability in two-dimensional jets

We consider nonlinear aspects of the flow of an inviscid two-dimensional jet into a second immiscible fluid of different density and unbounded extent. Velocity jumps are supported at the interface, and the flow is susceptible to the Kelvin–Helmholtz instability. We investigate theoretically the effects of horizontal electric fields and surface tension on the nonlinear evolution of the jet. This is accomplished by developing a long-wave matched asymptotic analysis that incorporates the influence of the outer regions on the dynamics of the jet. The result is a coupled system of long-wave nonlinear, nonlocal evolution equations governing the interfacial amplitude and corresponding horizontal velocity, for symmetric interfacial deformations. The theory allows for amplitudes that scale with the undisturbed jet thickness and is therefore capable of predicting singular events such as jet pinching. In the absence of surface tension, a sufficiently strong electric field completely stabilizes (linearly) the Kelvin–Helmholtz instability at all wavelengths by the introduction of a dispersive regularization of a nonlocal origin. The dispersion relation has the same functional form as the destabilizing Kelvin–Helmholtz terms, but is of a different sign. If the electric field is weak or absent, then surface tension is included to regularize Kelvin–Helmholtz instability and to provide a well-posed nonlinear problem. We address the nonlinear problems numerically using spectral methods and establish two distinct dynamical behaviors. In cases where the linear theory predicts dispersive regularization (whether surface tension is present or not), then relatively large initial conditions induce a nonlinear flow that is oscillatory in time (in fact quasi-periodic) with a basic oscillation predicted well by linear theory and a second nonlinearly induced lower frequency that is responsible for quasi-periodic modulations of the spatio-temporal dynamics. If the parameters are chosen so that the linear theory predicts a band of long unstable waves (surface tension now ensures that short waves are dispersively regularized), then the flow generically evolves to a finite-time rupture singularity. This has been established numerically for rather general initial conditions.     

A fully meshless method for ‘gas – evaporating droplet’ flow modelling

A meshless method for modelling two-phase flows with phase transition is described. The method is based on consideration of three systems: viscous-vortex blobs, thermal-blobs and droplets; and can be applied for numerical simulation of 2D non-isothermal flows of ‘gas-evaporating droplets’ in the framework of the one-way coupled two-fluid approach. The carrier phase is viscous incompressible gas. The dispersed phase is presented by a cloud of identical spherical droplets, and, due to evaporation, the radius and mass of droplets are time dependent. The carrier phase parameters are calculated using the viscous-vortex and thermal-blob method; the dispersed phase parameters are calculated using the Lagrangian approach. Two applications have been considered: (i) a standard benchmark – Lamb vortex; (ii) a cold spray injected into a hot quiescent gas. In the latter problem three cases corresponding to three droplet sizes were investigated. The smallest droplets (of the three cases considered) are more readily entrained by the carrier phase and form ring-like structures; the flow shows better mixing. Larger droplets evaporate less intensively. The medium sized droplets collect into two narrow bands stretched along the jet axis. The largest droplets form a two-phase jet, which remains close to the jet axis. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bio-inspired propulsion: Downstream travelling wave motion of a surface with finite & infinite extension

The thrust force on a surface that performs a fish-like travelling wave motion downstream to an oncoming flow is discussed. Unsteady potential flow, with vortex shedding from the trailing edge, is known to explain the generation of thrust. Contrarily, fish swimming has been related to the flow over an infinitely extended surface. To interlink both problems, the potential flow over the surface of finite length is considered in the limit of high wave numbers. It turns out that the leading order, space-periodic pressure does not contribute to thrust. Thus, the perturbation pressure is essential for propulsion. Besides, laminar flow is considered in the space-periodic setting. The present results reveal – in contrast to literature – that the surface force is always drag. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Heat and mass transfer in annular liquid jets: I. Formulation

Heat and mass transfer phenomena in annular liquid jets are analyzed at high Reynolds numbers by means of a model derived from the governing equations that takes into account the effects of surface tension and boundary conditions at the gas–liquid interfaces and the large differences between the thermal and mass diffusivities, densities, dynamic viscosities, and thermal conductivities between gases and liquids. The model clearly illustrates the stiffness in both space and time associated with the concentration, linear momentum and energy boundary layers, and the initial cooling of the gases enclosed by the jet when, starting from a steady state where gases are injected into the volume enclosed by the jet at a rate equal to the heat and mass absorption rates by the liquid, gas injection is stopped. It is shown that, owing to the non-linear integrodifferential coupling between the fluid dynamics and heat and mass transfer processes, the pressure of the gases enclosed by the jet may vary in either a monotonic or an oscillatory manner depending on the large number of non-dimensional parameters that govern the heat and mass transfer phenomena. For the underpressurized jets considered here, it is shown that thermal equilibrium is achieved at a much faster rate than that associated with mass transfer, double diffusive phenomena in the liquid may occur, and the mass and volume of the gases enclosed by the jet may increase or decrease as functions of time until a steady equilibrium condition is reached.     

Steady and Unsteady Jet Wiping Processes

The jet wiping process is widely used in continuous coating applications to remove the excess amount of liquid entrained by a sheet moving out of a liquid bath. Typical fields of applications are hot dip galvanization of metal strips and coating of photographic films. The process is based on the impact of a gas jet onto the liquid film carried by the solid substrate. In the present study the process is investigated for the case of strictly two‐dimensional flow. It is assumed that inertia effects on the film flow can be neglected, whereas the effects of the pressure gradient and the shear stress distribution of the impinging jet and the surface tension of the liquid film are taken into account. As a result it is possible to derive a single kinematic wave equation which governs the distribution of the film thickness. Numerical results for representative steady and unsteady processes including the formation of shock discontinuities are presented.     

Heat and mass transfer in annular liquid jets: III. Combustion within the volume enclosed by the jet

The nonlinear dynamics of and heat and mass transfer processes in annular liquid jets are analyzed by means of a nonlinear system of integrodifferential equations which account for the liquid motion and the gases enclosed by the jet. Both linear and sinusoidal heat and mass addition sources are considered to take place homogeneously within the volume enclosed by the jet's inner interface in an attempt to simulate the combustion of hazardous wastes or materials within this volume. It is shown that the liquid's temperature at the jet's inner interface increases rapidly with linear heat addition, but drops also quickly to its initial value once heat addition is ended, whereas the pressure coefficient and the volume enclosed by the jet increase until they reach a maximum value and then decrease in an oscillatory manner towards their steady values. For the case of sinusoidal heat addition, it is shown that the pressure coefficient and interfacial concentration, temperature and heat and mass fluxes oscillate in a sinusoidal manner with the same frequency as that of the sinusoidal heat source. It is also shown that mass transfer phenomena are much slower than heat transfer ones. For the case of linear mass addition, it is shown that the temperature of the gases enclosed by the jet first decreases because of dilution and then it increases until it reaches a constant value that corresponds to the same temperature for the gases and the flowing liquid. The pressure of the gases enclosed by the jet first increases because of mass addition and then slowly decreases because of mass absorption by the jet.     

Simulation of free turbulent particle-laden jet using Reynolds-stress gas turbulence model

Free two-phase flows occur in many practical applications, such as sprays or particle drying and combustion. This paper deals with mathematical modelling of a free turbulent two-phase jet. A steady, axisymmetric, dilute, monodisperse, particle-laden, turbulent jet injected into a still environment, has been considered. The model treats the gas-phase from an Eulerian standpoint and the motion of particles from a Lagrangian one. Closure of the system of time averaged transport equations has been accomplished by using a Reynolds-stress turbulence model. The particles–fluid interaction has been considered by the PSI-Cell concept. Both the effect of interphase slip and the effect of particle dispersion have been taken into account.