Flow and breakup characteristics of elliptical liquid jets

This paper presents the results of an experimental study on liquid jets discharging from elliptical orifices into still ambient air. The experiments were conducted with a set of elliptical orifices of approximately same area of cross section but varying orifice aspect ratio using water and water–glycerol mixture as experimental fluids. The flow behavior of liquid jets was analyzed using their photographs captured by an imaging system. The measurements obtained for the elliptical liquid jets were compared with the circular liquid jets discharging from a circular orifice of the same area of cross section. Elliptical geometry of the orifice results in a flow process by which the emanating liquid jet periodically switches its major and minor axes as it flows downstream of the orifice. In this paper, we attempt to characterize the axis-switching process through its wavelength and amplitude. For a given elliptical orifice, the axis-switching process is dominantly seen in a particular range of flow conditions. The effects of the orifice aspect ratio and liquid viscosity on the axis-switching process are revealed through this study. The experimental results on jet breakup show that axis-switching process has a destabilizing effect on elliptical liquid jets within a particular range of flow conditions and it results in shorter breakup lengths compared to the circular jet. The extent to which axis-switching destabilizes the jet is dictated by the viscosity of liquid. An increase in orifice aspect ratio destabilizes elliptical liquid jets with low viscosity like water; however, this behavior seems to get obscured in water–glycerol mixture elliptical jets due to high viscosity.     

On the behavior of viscoelastic free jets with elliptical cross section

In [1,2] we develop a comprehensive theory of one space dimensional closure models (closed systems of 1-D equations for the unknown, or modal, variables) for free viscoelastic jets. These closure models are derived via asymptotics from the full 3-D boundary value problem under the conditions of a Von Kármán-like flow geometry, a Maxwell-Jeffreys constitutive model, elliptical free surface cross section, and a slender jet scaling. The focus of the present paper is to determine the consequences and predictions of the lowest order system of equations in this asymptotic analysis. For the special cases of elliptical inviscid and Newtonian free jets, subject to the effects of surface tension and gravity, our model predicts oscillation of the major axis of the free surface elliptical cross section between perpendicular directions with distance down the jet, and draw-down of the cross section, in agreement with observed behavior. In the absence of surface tension the transformation from a cross section with major axis in one direction to a cross section with major axis in the perpendicular direction occurs only once, in agreement with the observation of Taylor [4]. In viscoelastic regimes, our model predicts swell of the elliptical extrudate and distortion of the elliptical extrudate cross section from the dimensions of the die aperture.     

The influence of the twist of individual fibers in 2D fibered networks

In this work, we propose a model for surfaces made of inextensible fibers that generalizes the existing approach to fibered networks, by taking into account not only the bending resistance of individual fibers, but also their resistance to twist. Assuming that the total energy of the network depends on the shear between the fibers as well as their curvature and twist, we derive the equilibrium equations and discuss an application to a cylindrical shell made of inextensible helical fibers. We discuss the effect of twisting stiffness on the loading–extension curve of the cylinder.     

椭圆锥动效应对机械抖动激光陀螺振动特性的影响

对机械抖动激光陀螺的振动特性进行了理论分析,得到了水平振动下陀螺测量敏感轴存在椭圆锥动效应,并得出了该锥动效应引起的陀螺输入角速度表达式。利用有限元分析软件ANSYS,对机械抖动激光陀螺进行了随机振动分析,仿真证实了锥动效应的存在,并采用物理方法试验验证了椭圆圆锥运动的存在及其锥动幅角的大小。通过数值仿真与分析,指出了减小锥动效应,提高陀螺振动性能的有效措施是增大抖动偏频机构的横向抗弯刚度。改进设计的试验结果表明,采用大横向抗弯刚度的新型抖动偏频机构使陀螺的抗振性能提高了4倍多。     

Investigation of the length and wave structure of the gas-dynamic section in straight and spreading gas jets

The results are given of an experimental investigation of the wave structure of straight and spreading gas jets. Dependences are obtained for the calculation of the length of the gas-dynamic part of straight and spreading gas jets.     

The influence of walls on the motion of a sphere in non-Newtonian liquids

The influence of the contained wall on the drag of a sphere moving through a non-Newtonian fluid is analysed in this work separately for the low Reynolds number and the high Reynolds number regions. In the former, we make use of the two-concentric-sphere model. It is predicted that the wall effect will decrease with the increase of the shear-thinning anomaly and this is in a reasonable agreement with the available experimental data and correlations. The wall effect in the high Reynolds number region is analysed in this work using the cell model (used to study the motion of an assemblage of solid spheres) and the predictions are in satisfactory agreement with the available empirical correlation for non-Newtonian fluids. Presented at the First Conference of European Rheologists, Graz (Austria), April 14–16, 1982.     

Simulation of the motion of thin rotating jets of a viscous incompressible fluid

A regular procedure is proposed for deriving approximate equations of motion of straight thin rotating jets of a viscous incompressible fluid, and similarity parameters of such flows are established. The problem of the stability of free steady motion of a finite jet is considered in the framework of a model that takes into account in the zeroth approximation the effects of viscosity, the rotation of the jet, and capillarity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 51–59, March–April, 1984.     

The motion of viscous liquid column with finite length in a vertical straight capillary tube

This paper deals with the motion of viscous liquid column with finite length and two free surfaces in a vertical straight capillary tube. It is assumed that fluid is Newtonian. Linearizing the boundary conditions, analytic expressions in the form of infinite series have been obtained for velocity, piessure and free surface at low Reynolds number. The numerical calculation is carried out for a set of cylinder’s length of water and blood. It has been revealed that there are considerable circulating currents at the upper and lower meniscuses. Its maximum velocity is about 57% of the average velocity of the mainstream. Iner-tial effect is also studied in this paper. Using the time-dependent method in finite difference techniques, numerical solution of the corresponding nonlinear equation at Re<24.5 is computed. Comparing it with analytic exact solution at low Reynolds number shows that inertial effect is negligible provided Re<24.5.     

Analytical solution for motion of an elliptical inclusion in gradient stress field

We present a rigorous analytical solution for motion of an elliptical inclusion in isotropic matrix driven by gradient stress field. The interfacial diffusion is considered as the dominant mechanism for the motion. We demonstrate that normal stress gradient on the interface is the major driven force, while the strain energy density gradient is negligible. A key prediction of the solution is that for a given inclusion the motion velocity is proportional to stress gradient only, indicating that the solution is applicable for inclusion motion in nonuniform stress field of varying stress gradient, and that the inclusion tends to move towards the region of lower stress in nonuniform stressed materials.     

The effect of sidewalls on rectangular jets

An experimental study is presented regarding the influence of sidewalls on the turbulent free jet flow issuing from a smoothly contracting rectangular nozzle of aspect ratio 15. “Sidewalls” are two parallel plates, flush with each of the slots’ short sides, practically establishing bounding walls extending the nozzle sidewalls in the downstream direction. Measurements of the streamwise and lateral velocity mean and turbulent characteristics have been accomplished, with an x-sensor hot wire anemometer, up to an axial distance of 35 nozzle widths, for jets with identical inlet conditions with and without sidewalls. Centreline measurements for both configurations have been collected for three Reynolds numbers, Re_D = 10,000, 20,000 and 30,000. For Re_D = 20,000 measurements in the transverse direction were collected at 13 different downstream locations in the range, x = 0–35 nozzle widths, and in the spanwise direction at three different downstream locations, x = 2, 6 and 25 nozzle widths.Results indicate that, the two jet configurations (with and without sidewalls) produce statistically different flow fields. Sidewalls do not lead to the production of a 2D flow field as undulations in the spanwise mean velocity distribution indicate. They do increase the two-dimensionality of the jet increasing the longevity of 2D spanwise rollers structures formed in the initial stages of entrainment, which are responsible for the convection of longitudinal momentum towards the outer field, establishing larger streamwise mean velocities at the jet edges. In the near field, up to 25 nozzle widths, lower outward lateral velocities in the presence of the sidewalls are held responsible for the decrease of turbulent terms including rms of velocity fluctuations and Reynolds stresses. Skewness factors increase monotonically across the shear layers from negative values to positive forming sharp peaks at the outer edges of the jet, illustrative of the presence of well defined 2D roller structures in the jet with sidewalls.     

LBE simulation of coherent vortex motion and heat transfer in jets of cross flow

Lattice Boltzmann equation method is used to simulate the coherent vortex motions and interactions and the heat transfer characteristics of jets in cross flow (JICFs) via TD2G9 model. After validation, the characteristics of cross flow under different Reynolds numbers are illustrated, including the mean profiles, the Reynolds stress tensor, the vortex and temperature fields, the temperature gradients near the walls, and the coherent correlation of vortex motions. The results show that the velocity profiles in JICF can be characterized by three basic regions, which are mainly caused by the mergence of JICF with the main flow. The temperature gradient near the walls can also be categorized by four basic regions, which are caused mainly by the impulse of JICFs too. Coherent vortex motions are found in JICF for Re = 3000, which are proved by strong periodic correlation of flow variables over a fixed area.     

The annular twist mapping of the restricted three-body problem

This paper presents a new derivation of the twist mapping in the planar restricted problem. It differs from other treatments in the use of a novel canonical transformation which allows for the utilization of symplectic reduction techniques.     

Gas jets in fluidized beds: The influence of particle size,shape and density on gas and solids entrainment

Gas has been injected in two-dimensional fluidized beds of solids different in size, density and shape. The ranges of solids sizes and bed heights were such as to produce relatively steady permanent jets.The mechanics of dispersion of these jets has been studied measuring jet angles, jet gas and solids velocity profiles, and particle entrainment velocities. The proportions of total mass and momentum flowrates pertaining to gas and solids have been calculated from these data.     

The nonlinear evolution of swirling jets

We investigate the mechanisms of vorticity concentration, reorientation and stretching in a swirling jet, whose dynamics is dominated by the competition of a Kelvin-Helmholtz-type vortex sheet instability and a centrifugal Rayleigh instability. To this end, we employ an inviscid Lagrangian vortex filament technique. It is found that the axial jet velocity profile breaks the symmetry of the pure swirling flow. Conversely, the swirl is seen to modify the case dominated by a Kelvin-Helmholtz instability in that it results in the formation of counterrotating vortex rings. A pinch-off mechanism is observed which leads to a dramatic decrease in the local jet diameter. Furthermore, the vortex ring circulation is seen to be time dependent.

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Sommario In questo lavoro si analizza la dinamica della vorticità in un setto rotante in cui siano presenti, ed in competizione reciproca, fenomeni di instabilità di Kelvin-Helmholtz e di Rayleigh. A tale scopo si adotta una metodologia di soluzione non viscosa, Lagrangiana a filamenti vorticosi. Viene mostrato come il profilo di velocità assiale del getto altera la simmetria del moto di pura rotazione. Viceversa, la presenza della rotazione modifica il flusso dominato dall'instabilità di Kelvin-Helmholtz attraverso la formazione di anelli vorticosi controrotanti. L'interazione di questi due campi di velocità porta sia ad una considerevole riduzione del diametro locale del getto, sia ad una variazione temporale della circolazione degli anelli vorticosi.

     

On the influence of initial conditions on the motion of water confined within a tank

The aim of this paper is to investigate the influence of initial values on the motion of waves in shallow water confined between two vertical walls of a tank with a polygonal bottom. A method introduced by G.S.S. Ludford to study a Riemann problem in gas dynamics is modified and used to obtain an estimate of the time of breakdown of an initially smooth but arbitrary wave motion on the surface of the water.     

The effects of fluctuating body forces on annular liquid jets

Summary The nonlinear dynamics of axisymmetric, inviscid, incompressible, thin, annular liquid jets subjected to fluctuating body forces is studied numerically by means of an adaptive finite difference method which maps the time-dependent, curvilinear geometry of the jet into a unit square. The fluctuating body forces may arise from fluctuations in the gravitational acceleration in inertial frames or from the acceleration of a non-inertial frame of reference which translates parallelly to an inertial one. It is shown that both the pressure coefficient and the axial location at which the annular jet becomes a solid one are periodic functions of time with a period equal to that of the imposed body force fluctuations, and that their magnitude increases as the amplitude of the body force fluctuations is increased. It has also been shown that, for both intermittent, sinusoidal or rectangular excitations, increases in the frequency of the excitation result in the creation of superharmonics, broad, albeit peaked, spectra, and closed phase planes with many loops.The research reported in this paper was supported by Project PB91-0767 from the D.G.I.C.Y.T. of Spain.     

The region of possible motion of the planar circular restricted three-body problem under the influence of a ring

This paper discusses the region of possible motion of planar cir-cular restricted three-body problem that one primarg in them has aring and it gives the equation of motion of the third body.Some re-sults are as follows:(1)The location of equilibrium points depends on the parameter μof the system;inner radius a and outer radius b of the ring;the dis-tance l between two primaries;and the ratio θ of the mass of the ringwith the sum of masses of the primary which has the ring and the ringitself.when α,b,l,θare constant.the number of the equilibriumpoints varies with μ,it is five at most and three at least.Besideseach triangular point and two primaries form an isosceles triangle.(2)When α.b.l.θ are constant,we give a range of μ.If μ isin this range.the structure of the region of possible motion of thethird body is the same as that of general planar circular restrictedthree-body problem.     

The trajectories of large fire fighting jets

This article describes a computer simulation of the trajectories of large water jets which allow the effects of changes in initial velocity, elevation, nozzle diameter, and head and tail winds to be examined. The rather limited information on aerodynamic drag of large jets obtained by other workers is used. The predicted trajectories compare well with the limited data available in the literature.The results also show that for a given flow rate an optimum pressure, and hence an optimum nozzle diameter, exists for maximum throw distance which has important implications for the design of the whole system including the pumps. The optimum elevation in still air lies in the range 30–40°. Wind effects are shown to be very important.