Large Eddy Simulations of Swirling Nozzle-Jet Flow Undergoing Vortex Breakdown

We developed a numerical setup to simulate swirling jet flow undergoing vortex breakdown. Our simulation code CONCYL solves the compressible Navier-Stokes equations in cylindrical coordinates using high-order numerical schemes. A nozzle is included in the computational domain to account for more realistic inflow boundary conditions. Preliminary results of a Re = 5000 compressible swirling jet at Mach number M a = 0.6 with an azimuthal velocity as high as the maximum axial velocity (swirl number S = 1.0 ) capture the fundamental characteristics of this flow type: At a certain point in time the jet spreads and develops into a conical vortex breakdown. A stagnation point-flow in the vicinity of the jet axis is clearly visible with the stagnation point located close to the nozzle exit. The stagnation point precesses in time around the jet axis, moving up- and downstream. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Formation of a jet in case of non-stationary flow of a perfect fluid from a slit

The problem of flow of a perfect fluid from a slit separating two parallel planes is given a mathematical formulation for the case of a submerged jet, as well as for the case of a flow with a free boundary. Various types of flow are classified. The results of numerical solutions are compared with experimental data. The phenomenon of reversal of the vortex sheet which occurs when the flow rate through the slit is reduced, is discussed. The self-modelling problem is solving using the method of matching the asymptotic expansions. A cumulative effect is discovered, namely that the rate of penetration of a narrow central part of the self-modelling jet exceeds the rate of flow of the main part of the jet by one order of magnitude.     

Modeling the disintegration of modulated liquid jets using volume-of-fluid (VOF) methodology

In this study, we present the numerical investigations on the effect of finite velocity modulations imposed on an otherwise unperturbed cylindrical liquid jet issuing into stagnant gas. Sinusoidal velocity fluctuations of finite frequency and amplitude are imposed at the liquid jet inlet and the resulting liquid jet surface deformation is captured using a volume of fluid (VOF) methodology, utilizing compressive interface capturing scheme for arbitrary meshes (CICSAM) scheme. Variation of the simulation parameters, comprising of the mean liquid jet velocity, modulation amplitude and frequency grouped together using a set of non-dimensional parameters, leads to the formation of a wide gamut of reproducible liquid structures such as waves, upstream/downstream directed bells, chains of droplets similar to those observed in experiments. Elaborate tests on the effect of injection velocity and inlet jet diameter are investigated to characterize the breakup process. The computations efficiently capture the diverse flow structures generated by the evolving modulated liquid jet inclusive of several non-linear dynamics such as growth of surface waves, ligament interaction with shear vortices and its subsequent thinning process. The simulations identify the deterministic behavior of modulated liquid jets to predict liquid disintegration modes under given set of non-dimensional parameters.     

Multiphase Jet Flow in Abrasive Water Jet Cutting

A numerical model for ultra-high velocity abrasive water jets (AWJ) is developed and jet dynamic characteristics are calculated under steady-state, turbulent, compressible, multi-phase flow conditions. The model is tested by comparison with analytical solutions for related theoretical problems, generally with very good agreement. Simulations of more realistic flows produce the expected values and behavior. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

高压水射流作用下岩石破碎机理及过程的数值模拟研究

根据连续介质力学和有限元理论,给出了高压水射流破岩系统中流体和岩石的控制方程,并建立了相应的有限元列式．运用连续损伤力学和细观损伤力学理论,建立了适用于水射流破岩全过程分析的岩石损伤模型以及宏细观损伤的耦合模式．数值计算的结果较真实地反映了水射流破岩过程中,岩石的动态响应以及水射流动力学特性的演化过程,普通连续水射流破碎岩石主体所用的时间为毫秒量级,破岩的主要形式是卸载及射流冲击所产生的拉伸破坏,并呈“阶跃式”发展．数值计算与相关试验结果基本吻合,表明该分析方法是可行的,可用来指导高压水射流破岩理论的进一步研究及应用．     

Numerical study of flow asymmetry and self-sustained jet oscillations in geometrically symmetric cavities

In this paper we present the results of numerical investigation of self-sustained oscillations of a jet confined in a symmetric cavity. This work represents an attempt to reproduce empirical observations of asymmetric flows in geometrically symmetric systems and to extend the jet flow investigations to more complex possible scenarios. A well-known example of such two-dimensional flow has been reported experimentally and reproduced numerically for simple flow [E. Schreck, M. Schaefer, Numerical study or bifurcation in three-dimensional sudden channel expansions, Comput. Fluids 29 (2000) 583–593]. It has been found that for some particular control parameter, above its critical value (bifurcation point), the jet can be deflected to either of the two sides of the cavity. In this paper we report a similar behaviour which is, however, characterized by a more complicated flow pattern. While simple flow appears only within small cavity lengths the complex flows develops with increased cavity lengths. Unlike stationary asymmetric solutions accompanied by cavity jet oscillations, as experimentally reported in e.g., [A. Maurel, P. Ern, B.J.A. Zielinska, J.E. Wesfreid, Experimental study of self-sustained oscillations in a confined jet, Phys Rev. E 54 (1996) 3643–3651], in our investigations of both simple and complex asymmetric flow we observed the slow periodical drift of the jet from one to another side of the cavity. The essential control parameters were Reynolds number Re and the ratio length to inlet width L/d. According to experiments of Maurel et al. (1996), the jet is stable and symmetric, when both L/d and Re are below certain critical values, otherwise jet oscillations appear in both experiment and our simulation (cavity oscillations regime). However, further increase of either (or both) L/d and Re leads of so called free jet type oscillations regime. This paper describes complex jet behaviour within the later oscillations regime. We believe that both simple “classical” and “our” complex stationary asymmetric solutions (as well as superimposed cavity-type and free-jet oscillations) can be explained based on physical arguments as already done in previous works. However, the origin of slow drift motion remains still to be resolved. This might be of high importance for clear distinguishing between relevant physical and numerical features in future codes developments.     

Numerical solution of turbulent jet flows

The work deals with numerical modelling of several turbulent 3D jet flows: steady impinging jet, steady free jet in cross–flow, synthetic free jet (unsteady) and synthetic impinging jet (unsteady). The numerical method is based on artificial compressibility method with dual time extension for unsteady cases. Space discretization uses cell–centered finite volume method with third order accurate upwind approximation for convection, the time discretisations are implicit. Turbulence is modelled using two–equation eddy viscosity models and by explicit algebraic Reynolds stress model (EARSM by Wallin and Hellsten). The results of first three cases are compared with measurements. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparison and correction of the drop breakup models for stochastic dilute spray flow

Spray–gas interaction is common in many industrial applications that use a liquid jet injection system. Numerous liquid drops interact with the surrounding gas as they travel through the air. During such a travel, aerodynamic interaction between a drop and the surrounding gas flattens the drop and ultimately, breaks up the drop. The TAB (Taylor Analogy Breakup) model was proposed by O’Rourke and Amsden (1987) [6] for the KIVA spray code, but the use of this model has been controversial because the original paper that proposed this model has typographical errors. Another well-known drop breakup model, such as the DDB (Drop Deformation Breakup) model of Ibrahim et al. (1993) [8], has been widely used. However, although numerical solutions of the DDB model ostensibly make it appear superior to those of other previous breakup models, they contain errors that need to be amended. This paper aims to clarify the error controversies of both models; the typographical errors and the erroneous numerical solutions. The complete mathematical derivation of the TAB model is presented, and its correct numerical solutions are compared against the experimental data. We found that the TAB model was superior to other breakup models, such as Clark (1988) [7] and DDB.     

Transcritical Flow Over a Hole

Transcritical flow over a localized obstacle generates upstream and downstream nonlinear wavetrains. In the weakly nonlinear long-wave regime, this flow has been modeled with the forced Korteweg-de Vries (fKdV) equation, where numerical simulations and asymptotic solutions have demonstrated that the upstream and downstream nonlinear wavetrains have the structure of unsteady undular bores, connected by a locally steady solution over the obstacle. Further, it has been shown that when the obstacle is replaced by a step of semi-infinite length, it is found that a positive step generates only an upstream-propagating undular bore, and a negative step generates only a downstream-propagating undular bore. This result suggests that for flow over a hole, that is a step down followed by a step up, the two wavetrains generated will interact over the hole. In this paper, this situation is explored by numerical simulations of the fKdV equation.     

PARALLEL ADAPTIVE SIMULATION OF A PLUNGING LIQUID JET

This paper is concerned with three-dimensional numerical simulation of a plunging liquid jet. The transient processes of forming an air cavity around the jet, capturing an initially large air bubble, and the break-up of this large toroidal-shaped bubble into smaller bubbles were analyzed. A stabilized finite element method （FEM） was employed under parallel numerical simulations based on adaptive, unstructured grid and coupled with a level-set method to track the interface between air and liquid. These simulations show that the inertia of the liquid jet initially depresses the pool＇s surface, forming an annular air cavity which surrounds the liquid jet. A toroidal liquid eddy which is subse- quently formed in the liquid pool results in air cavity collapse, and in turn entrains air into the liquid pool from the unstable annular air gap region around the liquid jet.     

Annular Water Jets

An analysis is provided of a slender stream of water whose cross-sectionis the region lying between concentric circular free streamlines.In the absence of gravity, explicit integral expressions arederived for the radii as a function of distance along the jet.In particular, for intially-contracting jets, the collapse distance,at which the inner radius vanishes, is determined. In the presenceof gravity, the problem for both vertically upward and verticallydownward annular jets can be reduced to that of solving a non-linearordinary differential equation, and numerical solutions areobtained. An outline is given of the procedures required tomatch these free jets to exit flows from slender nozzles.     

Exact solution for an optimal impermeable parachute problem

In the paper there are solved direct and inverse boundary problems and analytical solutions are obtained for optimization problems in the case of some nonlinear integral operators. It is modeled the plane potential flow of an inviscid, incompressible and nonlimited fluid jet, witch encounters a symmetrical, curvilinear obstacle—the deflector of maximal drag. There are derived integral singular equations, for direct and inverse problems and the movement in the auxiliary canonical half-plane is obtained. Next, the optimization problem is solved in an analytical manner. The design of the optimal airfoil is performed and finally, numerical computations concerning the drag coefficient and other geometrical and aerodynamical parameters are carried out. This model corresponds to the Helmholtz impermeable parachute problem.     

含高浓度悬浮固粒运动射流稳定性研究

首先用连续介质耦合模型推导出含高浓度悬浮固粒运动射流的空间稳定性方程,然后借助渐进分析法和欧拉守恒差分格式,用有限差分数值解法得到不同流向位置、流场雷诺数、固粒属性和喷射装置运动速度时流场的稳定性特征曲线,说明喷射装置的反向运动使不稳定扰动频率范围扩大,正向运动则相反。固粒抑制流场的不稳定性,随着固粒等效斯托克斯数的减小,这种效应增强。这些结论,对于两相运动射流发展的认识有重要意义。     

Invariant solution for an axisymmetric turbulent free jet using a conserved vector

An axisymmetric turbulent free jet described by an effective viscosity, which is the sum of the kinematic viscosity and the kinematic eddy viscosity, is investigated. The conservation laws of the jet are derived using the multiplier method. A second conserved vector, in addition to the elementary conserved vector, exists provided the effective viscosity has a special form. The Lie point symmetry associated with the elementary conserved vector is obtained and used to generate the invariant solution. The analytical solution is derived when the effective viscosity depends only on the distance along the jet. The numerical solution is obtained when the effective viscosity depends also on the distance across the jet. The eddy viscosity causes an apparent increase in the viscosity of the mean flow which produces an increase in the width of the jet due to an increase in diffusion and also a decrease in the maximum mean velocity along the axis of the jet.     

Laminar jet of a compressible pseudo-plastic fluid

Similarity solutions of the boundary layer equations for compressible pseudo-plastic fluids for plane symmetrical jet are obtained in a closed form. Behaviour of velocity component perpendicular to the axis of the jet is discussed in detail.     

Finite element simulation of shaped charges

This paper analyzes by numerical simulation the formation, the fragmentation, and the penetration in a plate of a copper jet that develops in a shaped charge. A finite element Lagrangian code has been used to gain insight into this problem. The study is conducted in two dimensions, axisymmetric. An explicit contact/friction algorithm is used to treat multi-body dynamics. A remeshing algorithm is needed to follow the high deformation pattern of the copper jet. The calculations account for rate-dependent plasticity, heat conduction and thermal coupling. A criterion is introduced to model the jet break-up. The simulations reveal in particular a gradient of shear deformation across the jet.     

Computation of the Free-Surface Shape of an Inviscid Jet Incident on a Porous Wall

We consider the problem of determining the steady free-surfaceshape of an incompressible, inviscid, irrotational jet incidentupon a porous wall. A fixeddomain method based on the Baiocchitransformation is used to determine accurate numerical approximationsto the free surfaces. Results are presented for cases in whichthe jet is incident either perpendicularly or obliquely to thewall. We also consider the effect of gravity on the above cases,and examine the pressure field in the jet.     

Annular liquid jets in zero gravity

The equations describing the steady-state behavior of long annular liquid jets and liquid membranes in zero gravity are solved analytically as a function of the pressure difference across the jet or membrane, Weber number, and nozzle exit angle. The ranges of the parameters for which the analytical solutions are valid are determined, and analytical solutions of the mass absorption rate are obtained as a function of the Peclet and Weber numbers, nozzle exit angle, pressure difference, and thickness of the annular liquid jet. It is shown that the convergence length of annular liquid jets and liquid membranes increases as the Weber number, nozzle exit angle, and pressure coefficient are increased. It is also shown that the mass absoption rate increases as the nozzle exit angle, pressure coefficient, and Weber number are increased; however, the mass absorption rate decreases as the Peclet number and annular jet initial thickness-to-radius ratio are increased.