On a round jet of inviscid liquid

Summary An analysis is made of a round jet of inviscid liquid which ejects from a nozzle of slowly varying profile, under the influence of gravity. The matched asymptotic expansion technique is applied to deal with the singularity at the nozzle exit and numerical examples are presented for the details of the flow near the nozzle exit, using the composite expansion.

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Übersicht Es wird das Ausströmen eines runden Strahls einer reibungslosen Flüssigkeit aus einer Düse mit langsam veränderlichem Profil unter dem Einfluß der Schwere untersucht. Mit Hilfe einer gemischten asymptotischen Entwicklung wird der Einfluß der Singularität am Düsenausgang erfaßt. Es werden einige numerische Beispiele mitgeteilt, aus denen Einzelheiten der Strömung am Ausgang der Düse zu ersehen sind.

     

Extrudate swell for a round jet with large surface tension

The problem of extrudate swell of a viscoelastic fluid from a round pipe is studied by the method of domain perturbations. The perturbation problems are solved by a finite-element method through second-order in the flow rate parameter ∈ for small flow rates. The analysis extends the work of Sturges on swelling in two-dimensional channels to round capillary tubes. In perturbation studies for small ∈, the rheology of the fluid may be expressed by three parameters, the viscosity and the two constants α₁ and α₂ appearing at order two in the expansion of the extra stress around zero shear. Surface tension has an important influence on the shape of the jet at low speeds. The shape of the surface on a round jet depends on α₁ and α₂, in the plane jet only on α₁. The analysis predicts that no matter what the constitutive equation may be, the jet will first contract if the radius of the pipe is sufficiently small. The contraction takes place in a length less than $\text{1}\text{10}$ the diameter of the jet and is followed by a swell. The contraction is usually small and may be hard to observe. There are five different contributions to the jet shape at second-order but only the viscoelastic ones persist as the pipe radius goes to zero.     

Newtonian liquid jet impaction on a high-speed moving surface

In the railroad industry a friction modifying agent may be applied to the rail or wheel in the form of a liquid jet. In this mode of application the interaction between the high-speed liquid jet and a fast moving surface is important. Seven different Newtonian liquids with widely varying shear viscosities were tested to isolate the effect of viscosity from other fluid properties. Tests were also done on five surfaces of different roughness heights to investigate the effects of surface roughness. High-speed video imaging was employed to scrutinize the interaction between the impacting jet and the moving surface. For all surfaces, decreasing the Reynolds number reduced the incidence of splash and consequently enhanced the transfer efficiency. At the elevated Weber numbers of the testing, the Weber number had a much smaller impact on splash than the Reynolds number. The ratio of the surface velocity to the jet velocity has only a small effect on the splash, whereas increasing the roughness-height-to-jet-diameter ratio substantially decreased the splash threshold.     

Newtonian liquid jet impaction on a high-speed moving surface

In the railroad industry a friction modifying agent may be applied to the rail or wheel in the form of a liquid jet. In this mode of application the interaction between the high-speed liquid jet and a fast moving surface is important. Seven different Newtonian liquids with widely varying shear viscosities were tested to isolate the effect of viscosity from other fluid properties. Tests were also done on five surfaces of different roughness heights to investigate the effects of surface roughness. High-speed video imaging was employed to scrutinize the interaction between the impacting jet and the moving surface. For all surfaces, decreasing the Reynolds number reduced the incidence of splash and consequently enhanced the transfer efficiency. At the elevated Weber numbers of the testing, the Weber number had a much smaller impact on splash than the Reynolds number. The ratio of the surface velocity to the jet velocity has only a small effect on the splash, whereas increasing the roughness-height-to-jet-diameter ratio substantially decreased the splash threshold.     

Effects of jet velocity profiles on a round jet in cross-flow

This paper reports the results of an experimental investigation on the effects of jet velocity profiles on the flow field of a round jet in cross-flow (JICF) using laser-induced fluorescence and digital particle-image velocimetry techniques (DPIV). Tophat and parabolic jets were considered, with the momentum ratios (MRs) ranging from 2.3 to 5.8. Results show that the thicker shear layer associated with a parabolic JICF is able to delay the formation of leading-edge and lee-side vortices when compared to the tophat JICF at the corresponding MR. As a result, there is an increase in jet penetration and a reduction in the near-field entrainment of cross-flow fluid by a parabolic JICF. Also, the less coherent nature of the leading-edge and lee-side vortices in a parabolic JICF is more likely to break up sporadically into smaller-scaled vortices. In addition, DPIV results show that a parabolic JICF exhibits not only a faster velocity recovery of cross-flow fluid at the jet lee-side than the corresponding tophat JICF, it also consistently registers a higher magnitude of the peak average vorticity than the tophat JICF for all MR considered. Despite these differences, the time-averaged flow topology for both cases share many salient features.     

Short capillary waves on the surface of a stretching cylindrical jet of a viscous liquid

This paper presents asymptotic formulas describing the evolution of short–wave perturbations on the surface of a cylindrical viscous liquid jet with the radius decreasing in time. The effects of Reynolds and Weber numbers and the initial wavenumber on the decay of the perturbations are analyzed.     

Prediction of stagnation point heat transfer for a single round jet impinging on a concave hemispherical surface

This paper deals with a systematic procedure for assessment of fluid flow and heat transfer parameters for a single round jet impinging on a concave hemispherical surface. Based on Scholkemeier's modifications of the Karman-Pohlhausen integral method, expressions are derived for evaluation of the momentum thickness, boundary layer thickness and the displacement thickness at the stagnation point. This is followed by the estimation of thermal boundary layer thickness and local heat transfer coefficients. A correlation is presented for the Nusselt number at the stagnation point as a function of the Reynolds number for different non-dimensional distances from the exit plane of the jet to the impingement surface.

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Bestimmung des Staupunktes bei der Wärmeübertragung für einen einzelnen Strahl, der auf eine konkave halbkugelige Oberfläche trifft

Zusammenfassung Diese Arbeit beschäftigt sich mit dem systematischen Verfahren der Bewertung von Fluidströmungen und Wärmeübertragungsparametern für einen einzelnen runden Strahl, der auf eine konkave halbkugelförmige Oberfläche trifft. Das Verfahren beruht auf Scholkemeiers Modifikation des Karman-Pohlhausen Integrationsverfahrens. Ausdrücke sind für die Berechnung der Impuls-Dicke, der Grenzschichtdicke und der Verschiebungsdicke am Staupunkt hergeleitet worden. Dies ist aus der Berechnung der thermischen Grenzschichtdicke und des lokalen Wärmeübertragungskoeffizienten abgeleitet worden. Es wird eine Gleichung für die Nusselt-Zahl am Staupunkt als Funktion der Reynolds-Zahl für verschiedene dimensionslose Abstände vom Strahlaustrittspunkt bis zum Auftreffpunkt auf die Oberfläche vorgestellt.

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Nomenclature c _p specific heat at constant pressure - d diameter of single round nozzle - h ₀ heat transfer coefficient at the stagnation point - H distance from the exit plane of the jet to the impingement surface - k thermal conductivity - Nu _0.5 Nusselt number based on impinging jet quantities=h _0.50/k - Nu _{0.5, 0} stagnation point Nusselt number=h _{0 0,50}/k - p pressure - p _a ambient pressure - p ₀ maximum pressure or stagnation pressure - p(x) static pressure at a distancex from the stagnation point - R radius of curvature of the hemisphere - Re _J jet Reynolds number=U _Jd/ - Re _0.5 Reynolds number based on impinging jet quantities=u _{m0 0.50}/ - T temperature - T _a room temperature - T _J jet temperature - T _W wall temperature - u velocity component inx andx directions (Fig. 1) - u _m jet centerline (or maximum) free jet velocity: external (or maximum) boundary layer velocity aty= _m - u _m0 arrival velocity defined as the maximum velocity the free jet would have at the plane of impingement if the plane were not there - U _J jet exit velocity - x* non-dimensional coordinate starting at the stagnation point=x/2 _0.50 - x, y rectangular Cartesian coordinates - y coordinate normal to the wall starting at the wall - ratio of thermal to velocity boundary layer thickness= _T/_m - ₀ ratio of thermal to velocity boundary layer thickness at the stagnation point - * inner layer displacement thickness - _0.50 jet half width at the plane of impingement if the plate were not there - _m inner boundary layer thickness atu=u _m - Pohlhausen's form parameter - dynamic viscosity - kinematic viscosity=/ - fluid density - momentum thickness - ₀ momentum thickness at the stagnation point     

Reynolds number effects on the behavior of a non-buoyant round jet

The behavior of a non-buoyant circular water jet discharged from a contraction nozzle was experimentally investigated. In this experiment, the Reynolds number of the jet, based on the mean velocity results obtained by particle image velocimetry (PIV), ranged from 177 to 5,142. From the experimental results, we found that the cross-sectional profile of the axial velocity for a laminar flow near the nozzle did not show a top-hat distribution, whereas the profiles with Reynolds number higher than 437 were almost top-hat. The length of the zone of flow establishment (ZFE) was found to decrease with increasing Reynolds number. The measured centerline velocity decayed more rapidly and, consequently, approached the theoretical equation earlier near the nozzle as the Reynolds number increased. The decay constant for the centerline velocity of the turbulent cases was relatively lower than that discovered in theory. It is assumed that this probably resulted from the use of the contraction nozzle. Verifying the similarity of the lateral velocity profiles demonstrated that the Gaussian curve was properly approximated only for the turbulent jets and not for the laminar or transitional flows. The jet half width seldom grew for the laminar or transitional flows, whereas it grew with increasing axial distance for the turbulent flows. The spreading rates for the turbulent flows gradually decreased with increasing Reynolds number. The normalized turbulence intensity along the jet centerline increased more rapidly with the axial distance as the Reynolds number increased, and tended to the constant values proposed by previous investigators. The Reynolds shear stress levels were also found to increase as the Reynolds number increased for the turbulent jets.     

Symmetric shapes of contact of a jet with the surface of a heavy liquid

The plane linearized problem of oblique impingement of a weightless jet of an ideal incompressible fluid on the surface of a heavy fluid is considered. Flows are sought with symmetric forms of the contact region. Mathematically we arrive at the problem of the eigenvalues and eigenfunctions of an integral equation; solving this problem we obtain various contact forms. The fundamental result for the infinitesimally thin jet of finite intensity is derived by passing to the limit, yielding a result analagous with the forms of free vibrations of a string. Some results are presented for the problem under consideration in the nonlinear formulation.The two-dimensional problem on (vertical) impingement of a jet on a liquid was solved by Olmstead and Raynor [1]. Some results for oblique impingement of a sufficiently thin, slightly curved jet are presented by Frolov [2], Information on other studies, primarily experimental, is presented in [3].This problem is related to the model of a jet curtain of an air-cushion vehicle; in this regard we note the study of Stepanov [4] in which, in particular, a result is obtained for an infinitesimally thin jet curtain.     

The stick-slip problem for a round jet

Summary The stick-slip problem for a round jet studied in Part I gives a good approximation for the swell of a low speed jet when the surface tension is large but it fails when the surface tension is small. In this paper a new stick-slip problem (II) is defined and solved using matched eigenfunction expansions. The new problem reduces to that solved in Part I when the surface tension is large and gives good results in the case of zero and small surface tension.With 18 figures     

The stick-slip problem for a round jet

Summary The stick-slip problem for a round jet is solved in two ways: by a Wiener-Hopf method and by a direct method in which eigenfunction solutions in the pipe and jet are matched on their common boundary. The same solution is obtained by the two methods, but the eigenfunction method is more direct and converges more rapidly. Reliable graphs are presented for the distributions of the velocity components, stresses and pressures at different axial positions in the pipe and jet. The shape of the free surface for the low speed jet is computed by a perturbation method.

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Zusammenfassung Das Haft-Gleit-Problem wird für einen runden Strahl auf zwei verschiedene Weisen gelöst: durch die Wiener-Hopf-Methode und durch eine direkte Methode, bei der die Eigenfunktionslösungen für Rohr und Freistrahl an der gemeinsamen Grenze aneinander angeschlossen werden. Mit beiden Methoden erhält man die gleiche Lösung, aber die Eigenfunktionsmethode ist direkter und konvergiert schneller. Glaubwürdige graphische Darstellungen des Verlaufs der Geschwindigkeitskomponenten, der Spannungen und der Drücke für verschiedene axiale Lagen in Rohr und Freistrahl werden mitgeteilt. Die Gestalt der freien Oberfläche für einen mit langsamer Geschwindigkeit austretenden Strahl wird mit Hilfe einer Störungsmethode berechnet.

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With 12 figures and 3 tables     

Boiling heat transfer characteristics of nanofluids jet impingement on a plate surface

The jet boiling heat transfer of a bar water–CuO particle suspensions (nanofluids) jet impingement on a large flat surface was experimentally investigated. The experimental results were compared with those from water. The quantificational effects of the nanoparticles concentration and the flow conditions on the nucleate boiling heat transfer and the critical heat flux (CHF) were investigated. The experimental data showed that the jet boiling heat transfer for the water–CuO nanofluid is significantly different from those for water. The nanofluids have poor nucleate boiling heat transfer compared with the base fluid due to that a very thin nanoparticle sorption layer was formed on the heated surface. The CHF for the nanofluid increased compared with that of water. The reasons were that the solid–liquid contact angle decreased due to a very thin sorption layer on the heated surface and the jet and agitating effect of the nanoparticles on the subfilm layer enhance supply of liquid to the surface.     

Coaxial atomization of a round liquid jet in a high speed gas stream: A phenomenological study

Coaxial injectors have proven to be advantageous for the injection, atomization and mixing of propellants in cryogenic H₂/O₂ rocket engines. Thereby, a round liquid oxygen jet is atomized by a fast, coaxial gaseous hydrogen jet. This article summarizes phenomenological studies of coaxial spray generation under a broad variation of influencing parameters including injector design, inflow, and fluid conditions. The experimental investigations, performed using spark light photography and high speed cinematography in a shadow graph setup as main diagnostic means, illuminate the most important processes leading to atomization. These are identified as turbulence in the liquid jet, surface instability, surface wave growth and droplet detachment. Numerical simulations including free surface flow phenomena are a further diagnostic tool to elucidate some atomization particulars. The results of the study are of general importance in the field of liquid atomization.     

Parametric analysis of a round jet impingement on a heated plate

In this study, the flow and heat transfer characteristics of a round air jet have been experimentally investigated in details using two techniques: Particle Image Velocimetry (PIV) and the Laser Doppler Velocimetry (LDV). The measurement of the mean velocity components are compared, and agree well with the experimental data obtained by Baydar (1999). The distributions of the velocity, turbulence quantities and temperature profiles are analyzed in the main characteristic regions of the jet where the heat transfer occurs. Parametric variations were conducted to produce information about the influences of the Reynolds number (Re = 1000, 2000, 3000), the distance between the pipe exit and the flat impingement plate (h/d = 1 and h/d = 2) and the temperature of the plane (T_p = 22 °C, 54 °C, 96 °C) on the impinging jet flow field.     

Effect of initial conditions on the near-field development of a round jet

This paper examines the effects of using different grids, placed at the nozzle exit plane, on the subsequent development of a subsonic round air jet. Modifications to the initial development of the jet are achieved in a passive manner by placing different grids at the nozzle exit plane. Time-averaged statistics of the velocity, including spectra, are combined with a numerical linear instability investigation. The grids suppress the initial shear layer instability whereas they damp the jet column instability. As a result, the streamwise decay and radial spreading of the perturbed jets are reduced. The instability analysis yields realistic values for the fastest growing instability frequency but incorrect growth rates.     

狭缝射流撞击圆柱表面的湍流特性实验研究

实验研究了狭缝射流撞击圆柱表面后壁面射流区的平均流动和湍流特 性. 考察了雷诺数 Re (6000-20000), 喷口到受撞表面距 离 Y/W (5-13), 喷口宽度 W (6.25mm, 9.38mm), 受撞表 面曲率(半圆柱体直径 D = 150mm)对流动和湍流结构的影响. 通过分析 X 热线 在壁面射流区的测量结果发现，在近壁区域，表面曲率、 Re_{w} , Y/W 和 S/W 等 参数对 \sqrt {\overline{u^2}} / U_m 的影响比对 \sqrt {\overline{v^2}} / U_m 强，并且切 应力 \overline {uv} /U_m^2 对表面曲率变化最敏感. 当喷口与受撞击表面之间的距 离 Y/W 在一定范围内增加时， 沿圆柱表面流动的流向和横向的湍流强度增强. 用平板射流和圆柱体表面壁面射流的数据进行比较，从而得到表面曲率对壁面射流特 性的影响. 结果表明，曲率对壁面射流的影响较强， 并随着 S/W 的增大而增强. 随着雷诺数的增大，壁面曲率的影响也有强化的趋势.     

Destabilisation of a compressed vortex by a round jet

This paper presents data and analysis related to the compression and the breakdown of a tumbling motion after radial disruption in a simple geometry of the compression chamber of a model engine with large optical access. The disruption is a round jet injection perpendicular to the vorticity tube. Two configurations of injection are selected. They correspond respectively to a straight jet that competes with the tumble and an inclined jet that adds angular momentum to the large-scale rotating motion. The ratio between the angular momentum brought by the spray and the initial angular momentum of the tumble is of the order of 30% and is representative of the direct-injection engine situation at moderate rotation rate. The injection is performed at bottom dead centre (BDC) in a well-defined and well-known tumbling motion. The data are obtained in the symmetry plane of a square chamber by using particle image velocimetry (PIV) and planar laser induced fluorescence (PLIF). A calibration is made in order to take account of acetone fluorescence yield during compression. The analysis of the injection phase at BDC shows that the mean topology of the flow after both injections differs significantly and that the vorticity tube is significantly distorted only in the vicinity of the injection plane. Strong transverse mean flows are detected by analysing the divergence of the mean velocity field. Although a mean rotation is still observed after injection during the compression phase, the authors show that no strong vortex core is evident. An important consequence of this finding, confirmed by the evolution of the global in-plane mean and fluctuating kinetic energy in the symmetry plane is that no vortex breakdown occurs during the compression after the injection event. Therefore, the global fluctuating kinetic energy at the end of the compression is much lower after an injection. During the first half of the compression, an inhomogeneous distribution of the jet fluid in the chamber is detected by the PLIF measurements. The transport of the jet fluid clearly results from both in-plane and out-of-plane motions triggered by the injection jet. This spatial repartition depends strongly on the injection strategy and can be very difficult to control accurately from cycle to cycle. The mixture is more homogeneous at top dead centre (TDC) with a low value of the spatial variance of the mean concentration field.     

ATOMIZATION OF A LIQUID DROP BY PULSATION

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