Control of two-dimensional turbulent wall jet on a coanda surface

The Coanda effect that is the tendency of a fluid jet to stay attached to an adjacent curved surface that is very well shaped has been employed to improve the performance of various devices. The main objective of this paper is to investigate ways of keeping the flow attached to a larger length of a Coanda surface. There are considered two possibilities: one passive, which uses a slot that connects the low pressure and high pressure points on the Coanda surface and an active one, based on the principle of synthetic jet, created through an orifice located near the point of detachment of the jet. Reynolds averaged Navier-Stokes simulations (RANS) with shear stress transport k-ω (SST model) of Menter have been used to compute the two-dimensional turbulent wall jet. The numerical results are presented for the two methods considered. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The nonsimilar laminar wall jet along a moving wall,in a free stream and in a free stream/moving wall

The flow of a laminar wall jet along either a moving plate, or in a free stream, or in combined moving plate and free stream is considered. The plate is isothermal and its temperature is different from that of the ambient fluid. The governing boundary-layer equations are converted into non-dimensional form and are solved numerically. Velocity and temperature profiles as well as the variation of wall shear stress and wall heat transfer are presented for all cases considered. For the case of a moving plate new results have been found although this problem has been investigated in the past. For the case of the free stream and the combined moving plate/free stream all the results are new and are presented for the first time in the literature. The three cases have been tackled with a unified way.     

Study of a jet incident on a porous wall in a gravity field

The problem of an inviscid jet impacting on a porous wall ina gravity field is considered. By transforming this into a minimumproblem, existence and uniqueness results are proved. Propertiesof the flow region, of the stream function, and of the freeboundary are established. The monotonicity of the stream functionwith respect to the given velocities is also obtained. The mathematicalresults established allow one to obtain and to compare the numericalapproximations of the stream function and of the free boundaryfor the flows, with and without gravity, by using a finite-elementmethod.     

Temperature distribution in a laminar plane wall jet

In the present note the temperature distribution in a laminar plane wall jet has been studied. It is found that a similarity solution of the energy equation exists. The resulting ordinary differential equation is reduced to a hypergeometric equation by a suitable transformation of the similarity variable and the solution, for arbitrary values of the Prandtl number, is obtained. It is concluded that the heat transfer at the wall at a given section and the product of volume and heat-flux through any cross-section of the boundary layer increase with the increase in the value of Prandtl number respectively.     

Free-surface shapes of a jet injecting through a porous wall

For a jet incident on a porous wall at which the normal fluidspeed is specified, it is found that the problem of determiningthe free surface of the jet is governed by a system of nonlinearintegral equations relating the flow angles on the boundary,on the free surface, and on the porous wall. With a constantnormal speed at the porous wall, the system reduces to an integralequation for the flow angle, which is solved numerically; anda comparison with previous results is made. Numerical results,corresponding to different nonconstant normal jet speeds alongthe porous wall, are also presented. The extension of this formulationto include the effect of gravity is also given.     

Laminar jet impingement on an indented wall

Summary The Navier-Stokes equations are solved numerically to study the problems of laminar, axisymmetric jet impinging normally on an indented wall. The results obtained for three different wall geometries and Reynolds number range upto 25 are compared with those for the impingement on a plane wall to study the influence of indentation. The overall flow picture remains similar to the plane wall case qualitatively but the wall shear stress and pressure distribution get altered in the indented region.

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Zusammenfassung Es wird der Strömungsverlauf eines laminaren achsensymmetrischen Strahles nach dem Aufprall auf eine Wand mit Einbuchtung analysiert. Hierzu wird die numerische Lösung der Navier-Stokeschen Gleichungen benutzt. Die Ergebnisse für drei verschiedene Wandgeometrien, als auch für verschiedene Reynolds-Zahlen bis auf 25, sind mit dem Fall der ebenen Wand verglichen, um hieraus den Einfluß der Einbuchtung festzustellen. Das globale Strömungsbild bleibt in allen Fällen qualitativ ähnlich. Es wurde jedoch festgestellt, daß im Bereich der Einbuchtung die Wandschubspannung sowie die Druckverteilung gewisse Änderungen aufweisen.

     

Temperature distribution in a laminar plane wall jet due to variably heated wall

The heat transfer in a laminar incompressible plane wall jet due to a variably heated wall has been studied. It is assumed that the difference of temperatures between the wall and the issuing jet is inversely proportional to an arbitrary exponent of the distance from the slit. A similar solution of the energy equation is possible. The solutions, for arbitrary values of the Prandtl number and of the exponent are obtained. It is found that in some cases the heat transfer at the wall may become zero or negative.     

The wall jet flow of a conducting gas over a permeable surface in the presence of a variable transverse magnetic field

The effects of the magnetic field, Mach number and the permeability parameter on the wall jet flow (radial or plane) of an electrically conducting gas spreading over a permeable surface have been investigated. Taking the Prandtl number of the fluid as unity and assuming a linear relationship between viscosity and temperature, it is found that similar solutions for the velocity distribution exist for a specified distribution of the normal velocity along the wall and the corresponding distribution of the transverse magnetic field. Previous non-magnetic flow results have been improved by adopting a new and simple transformation of variables.     

Rheological effect on thermocapillary flow of a liquid film jet painted on a moving boundary

In the present paper, a liquid (or melt) film of relatively high temperature ejected from a vessel and painted on the moving solid film is analyzed by using the second-order fluid model of the non-Newtonian fluid. The thermocapillary flow driven by the temperature gradient on the free surface of a Newtonian liquid film was discussed before. The effect of rheological fluid on thermocapillary flow is considered in the present paper. The analysis is based on the approximations of lubrication theory and perturbation theory. The equation of liquid height and the process of thermal hydrodynamics of the non-Newtonian liquid film are obtained, and the case of weak effect of the rheological fluid is solved in detail.     

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)     

The mechanics of a powder-drive water jet

We consider the processes in a powder-drive pulse water jet in which the acceleration of the water shell occurs as the result of the energy from burning powder. The one-dimensional motion of the fluid is described in the nonstationary formulation, while the combustion of the powder is described in a quasistationary formulation. The barriers are assumed rigid. In a numerical solution that is presented we use the method of complete computation. For a specific structure of the cannon we give the results of numerical computations. We discuss a simplified approach for estimating the parameters of the apparatus. Four figures. Bibliography: 5 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 124–128.     

The axisymmetric free laminar jet of a power-law fluid

Summary The solution of the boundary-layer equations for an axisymmetric free laminar jet of a power-law fluid is investigated. It is shown that similar solutions are possible only forn1/2, wheren is the exponent in the power-law model. Forn>1/2, the axial velocity decay is proportional to the (–1/2n–1) power of the distance downstream and the jet spreads at a rate proportional to the (1/2n–1) power of the distance. Forn=1/2, the velocity decay and the rate of spread are exponential. Experimental data are presented which demonstrate that the predicted exponential decay occurs in real fluids.

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Zusammenfassung Ähnliche Lösungen der Grenzschichtgleichungen für einen achsensymmetrischen laminaren Strahl von Potenzgesetz-Flüssigkeiten werden gegeben. Diese Lösungen werden mit vorhandenen experimentellen Daten verglichen.

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Nomenclature d orifice diameter - D characteristic length - f preliminary dependent variable - F final dependent variable - J momentum inx-direction - K coefficient in power law model - n exponent in power law model - Re generalized Reynolds number - u x-component of velocity;u _o=characteristic velocity;u _p =initial velocity;=u/u _o;u _m =velocity on centerline of jet. - v y-component of velocity; - x coordinate in axial direction; ; = distance from orifice in experimental jet - y coordinate in radial direction; - function of - function of - parameter in final similarity transformation - preliminary independent variable - final independent variable - fluid density - shear stress - stream function     

The drag force on the grains in a permeable medium subjected to a water jet

Summary A theory for destruction of rock with a high speed water jet is derived on the basis of viscous flow through porous media. The theory yields that a grain in the rock exposed to a water jet is subjected to a hydraulic force proportional to the water pressure gradient in the rock and to the volume of the grain. If a semi-space of a presaturated rock is hit by a water jet of sufficient pressure the theory predicts the initial stage of the crater to be an annular crater the radius of which is twice the radius of the jet. In the case of a dry rock the theory predicts that the typical ring structure of the initial stage of the crater should not occur. The conclusion is that in destruction of rock with a high-pressure water jet the permeability is a very important parameter in contrast to the case of mechanical destruction.

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Zusammenfassung Eine Theorie über Gesteinsdestruktion mit Hochdruckwasserstrahl gründet sich auf die Theorie viskoser Strömung durch poröse Medien. Die Theorie besagt dass eine Partikel im Gestein durch einwirken eines Wasserstrahls einer hydraulischen Kraft ausgesetzt wird die proportional zum Gradienten des Wasserdruckes im eigentlichen Gestein und proportional zum Volumen der Partikel ist. Wenn ein Halbraum eines wassergesättigten Gesteins von einem Wasserstrahl mit ausreichend hohen Druck getroffen wird, sagt die Theorie, so soll das Anfangsstadium des sich bildenden Kraters ringförmig sein mit einem Radius doppelt so gross als der Radius des Wasserstrahls. Im Falle trockenen Gesteins, erklärt die Theorie, soll die typische Ringstruktur im Anfangsstadium des Kraters nich auftreten. Zusammenfassend kann man sagen die Permeabilität ist ein bedeutend wichtiges Parameter bei Gesteinsdestruktion mit Hochdruck wasserstrahl im Gegensatz zum Fall mechanischer Destruktion.

     

The boundary layer on a wall nearly parallel to a magnetic field

This paper calculates the structure of the boundary layer which occurs at the wall of a nonconducting duct in fully-developed laminar flow of a conducting fluid when the wall is inclined at a small angle to the uniform transverse magnetic field and when the Hartmann numberM is high. When is large compared withM ^–1/2 the layer splits into a Hartmann layer on the inclined wall and a weak shear layer emanating from the duct corner along field lines. These two layers cause equal reductions in the total flow rate.

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Zusammenfassung Diese Arbeit behandelt die Struktur der Grenzschicht, die an der Wand eines nicht leitfähigen Kanals entsteht die eine vollentwickelte Laminarströmung einer leitfähigen Flüssigkeit führt, wobei die Wand einen kleinen Winkel mit dem gleichförmigen transversalen Magnetfeld bildet und die Hartmannsche ZahlM groß ist. Für große Werte von im Vergleich zuM ^–1/2 teilt sich die Grenzschicht in einen Hartmannsche Schicht an der geneigten Wand und eine schwache Scherschicht, die von der Ecke des Kanals entlang der Feldlinien ausgeht. Die beiden Schichten verursachen die gleichen Verminderungen in der Durchflußmenge.

     

The onset of stochastic pulsations at the early non-linear stage of the development of perturbations in the jet of an incompressible fluid propagating along a wall

The Korteweg-De Vries equation, which describes the non-linear propagation of perturbations in a jet of incompressible fluid emanating from a slit in a planar screen and propagating along a wall is considered. When account is taken of the natural vibrations of the wall, the equation becomes inhomogeneous. If an external action is specified in the form of a running wave, the particular solution of the inhomogeneous equation may be sought in an analogous form. As a result, the simplest problem in the theory of dynamical systems in the Hamiltonian formulation arises. As usual, the existence of a homoclinic structure in the neighbourhood of the separatrices is deduced from an analysis of a Poincaré transformation. Among the trajectories belonging to the homoclinic structure in the secant plane, there are some with properties which are formulated in terms of determinate chaos. A fundamentally important conclusion concerning the dual role of solitons at the non-linear stage of the wave motion of the fluid follows: on the one hand, they serve as the nuclei of large-scale coherent structures and, on the other hand, they are responsible for the onset of stochastic pulsations.     

Experiments on the impingement of a supersonic jet on a flat plate

Zusammenfassung Es wird über Versuche berichtet, bei denen ein Strahl mit Überschallgeschwindigkeit auf eine ebene Platte auftrifft. Für verschiedene Machzahlen und Plattenneigungen wurden die Druckverteilungen gemessen. Zur Diskussion der Ergebnisse wird eine einfache Hodographenmethode herangezogen.

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Symbols C _p Pressure coefficient - h Thickness of jet sheet - M Mach number - P _a Ambient pressure - P _p Plate pressure - r Radial distance in plane of the jet sheet - R Radius of the jet - u, v Velocity components - V Velocity resultant - x, y Cartesian coordinates in plane of flow symmetry - Ratio of specific heats - Plate incidence angle - Azimuth angle of radius vectorr     

The dynamics of a meandering coastal jet in the lee of a cape

In a barotropic model of an oceanic channel, bounded to the north by a straight coast indented by a Gaussian cape, the evolution of a coastal jet is studied numerically. In the absence of the cape, the barotropic instability of the jet is determined. In the presence of the cape, a regular row of meanders develops downstream of this feature, and becomes stationary for a particular range of parameters. The relevant parameters are the velocity and width of the jet, size of the cape, and beta effect. The formation of meanders occurs first via the instability of the jet, then via the generation of vorticity anomalies at the cape, which are advected both downstream by the flow and offshore by the radiation of Rossby waves. Once the meanders are established, they remain stationary features if the propagation velocity of the meanders (due to the dipolar effect at the coast) opposes the jet velocity and the phase speed of the wave on the vorticity front. Finally, a steady state of a regular row of meanders is also obtained via a matrix method and is similar to that obtained in the time-dependent case.     

Orbital stability of solitary waves on a ferrofluid jet

We prove the orbital stability of small-amplitude axisymmetric solitary waves on the surface of an incompressible, inviscid ferrofluid jet. The ferrofluid surrounds a current-carrying rod and is subject to the azimuthal magnetic field generated by the rod. We show that under appropriate assumptions on the magnitude of the magnetic intensity in the ferrofluid, both the trivial flow and the solitary waves with strong surface tension are conditionally orbitally stable, while the conditional orbital stability of solitary waves with near-critical surface tension can be deduced from properties of the corresponding dispersive PDE model equation. The arguments are based on the recent orbital stability results for internal waves by Chen and Walsh (2022) and an improved version of the Grillakis–Shatah–Strauss method introduced by Varholm et al. (2020).