CFD prediction of the trajectory of a liquid jet in a non-uniform air crossflow

This paper describes a predictive numerical modelling methodology for calculation of deflection and deformation of liquid jets in air crossflows. The methodology combines Jet Embedding (JE) with Volume-of-Fluid (VOF) in a computational fluid dynamics (CFD) based approach. The combined JE/VOF methodology applies the JE concept of modelling the air and liquid phases in separate but linked models, with a representation of the liquid column embedded in the crossflow model. The crossflow is modelled in a CFD calculation using CFX4.2 and the separate jet model is written in FORTRAN 77. A multi-fluid implementation of the VOF technique, in CFX4.2, is used to model deformation of the liquid column cross-section in a series of two-dimensional models along the column trajectory. The crossflow, jet and deformation calculations are linked by an iterative procedure which advances from the nozzle exit in a series of time-steps. The JE/VOF methodology is used to make a prediction of a time-average trajectory of a deflected liquid column, with a progressively deformed cross-section, in an air crossflow. The prediction demonstrates that the JE/VOF methodology is capable of producing a physically realistic result.     

Numerical simulation of impact of a jet on a wall

A computing technique for simulating the impact of a high-speed liquid jet on a wet wall is implemented. Such an impact generates shock waves in the jet, in the liquid layer on the wall, and in the gas surrounding the liquid. Also, the interphase boundary is strongly deformed by such an impact. The technique is based on the Constrained Interpolation Profile-Combined Unified Procedure (CIP-CUP) method combined with the dynamically adaptive Soroban grids. The gas-dynamic equations describing the liquid and gas flow are integrated without an explicit separation of the liquid-gas boundary. Such an approach is shown to be efficient for the considered problems. It allows us to obtain solutions without oscillations near the interfaces (including the case where they interact with the shock waves). For illustrative purposes, we provide the computational results for several one-dimensional and twodimensional problems with the typical features of the impact of a high-speed liquid jet on a wall, as well as a comparison with the known analytical and numerical solutions. The computational results for the problem of the impact of a high-speed liquid jet on a wall covered by a thin liquid layer are also presented.     

Numerical solution of a Newtonian jet emanating from a converging channel

A theoretical analysis has been carried out to find the shape and final thickness of a Newtonian jet emanating from a converging channel. The gravitational force is neglected but the surface tension effect is included in the present analysis. There are four variables, i.e. the contraction ratio L, the converging angle θ, the Reynolds number Re and the capillary number Ca, that completely determine the flow field. The effects of these four variables on the motion of the jet are examined. The mathematical problem of the jet is formulated with stream function and vorticity as dependent variables. The boundary-fitted coordinate transformation method developed by Thompson et al. is adopted to map the flow geometry into a regular domain for numerical integration, and the finite difference method is applied to solve the flow equations in the transformed plane. We have found that the final thickness of the jet will reach its frozen value as L > 15. As Re > 50, the jet contraction coefficient is very close to that of a potential Helmholtz jet. Surface tension is only important if Re is small. The jet contraction coefficients as functions of Re and θ are presented. We have also found that a vortex may exist in the converging channel if the converging angle θ > 75°.     

Computational study of effect of tabs on a jet in a cross flow

A three-dimensional viscous flow analysis is performed using a time-marching Reynolds-averaged Navier-Stokes code for the case of a jet in a cross flow with a delta tab placed on the windward side of the jet to inhibit mixing for film cooling applications. The flow configuration which was previously studied experimentally, involved a jet discharging normally from the floor of the wind tunnel test section into the cross flow with a momentum ratio (jet/cross-flow) of 36. The computed results are compared with the experimental data which include streamwise velocity and vorticity distributions at various axial locations downstream of the jet. The computational results show reasonably good agreement with the experimental data.     

应用于喷水推进器的流量传感器数值仿真

针对于推进器出口的流量为10-2m3/h数量级的小型喷水推进器,采用了能够测量小流量的切向式涡轮流量传感器测量推进器的流量。在对传感器详细分析的基础上,应用流体力学软件对其进行了数值仿真,并将仿真结果和实验结果比较,仪表系数相对误差最大值为5.70%,结果表明:提出的模型能反映传感器内部流体的流动状态,为应用于小流量喷水推进器的分析提供可靠的仿真模型。     

Numerical solution of the Riemann-Hilbert problem for a vertical jet under gravity

We consider steady, plane, irrotational and incompressible flow in an infinite channel between two horizontal planes. The flow is formed by two equal but opposite uniform streams approaching from infinity and meeting over a horizontal slot, whence they emerge as a vertical jet under gravity. Conformal mapping is used, and the Riemann-Hilbert solution is obtained for a mixed boundary value problem in the upper half-plane. Numerical methods are introduced, and the problem programmed and run on a digital computer; results are obtained and some difficulties of the computing are discussed.     

Numerical simulation of electrohydrodynamic jet and printing micro-structures on flexible substrate

Microsystem Technologies - This paper aims to present the simulation work and obtain optimized parameters for the development of drop-on-demand electrohydrodynamic jet (DoD E-Jet) to print control...     

Numerical simulation of the interaction of a circular synthetic jet with a boundary layer

In this work, a 3D numerical simulation of circular synthetic jets issued into a laminar boundary layer developing over a flat plate was undertaken in a complementary manner alongside with an experimental study with the aim of achieving an improved understanding of the fluid mechanics underlying the interaction process between the synthetic jets and the boundary layer. The simulation was carried out in FLUENT at two diaphragm operating conditions, which produced two distinctly different vortical structures and shear stress footprints on the wall. The simulation results were validated using experimental data and a good agreement was achieved. The temporal evolution of coherent structures formed as the result of this interaction was examined using the Q-criterion. The hierarchy of the coherent structures was established which provided a credible explanation of the wall shear stress pattern observed in both the experiment and the simulation. The high spatial resolution in the near-wall region and 3D nature of the simulation results provide the information about the flow field which is not only consistent with but also additional to that from the experiment, leading to an improved understanding of the interaction process between the synthetic jets and the boundary layer and its resultant structures.     

Numerical fluid loading coefficients for the modal velocities of a cylindrical shell

The generalized fluid loading coefficients for the modal velocities of a simply-supported shell section are defined and formulated. The simplified nature of infinite cylindrical coordinates is employed in the geometry of interaction by assuming the predominance radial effects in a baffled extension of the finite shell. An efficient numerical procedure for the computational evaluation of the integrals which define the direct and cross mode components of the fluid impedance is presented and applied. The approach and illustrated results are directly applicable in the combined solution of shell and fluid interaction problems.     

A way to estimate the discharge of the melt jet flowing out of a melting furnace

A way to estimate the discharge of melt jet flowing out of a melting furnace is examined. We analyze the efficiency of algorithms for image matching in order to estimate the jet velocity. To decrease the time needed for estimating the 2D motion of melt flow, it is suggested to calculate the shift of 2D images according to two independent 1D projections. This approach makes it possible to estimate on-line the flow rate and to do it in television standard.     

缩合反应喷射混合器的数值模拟与验证

采用Fluent软件数值模拟缩合反应制多胺系统的喷射混合器,根据不同几何尺寸喷射器内的速度、压力、组分浓度分布情况,提出优化的喷射器设计并中试装置验证,表明物料的混合效果良好,喷射器压力变化的实验值与模拟值几乎相符,本文所建模型可为工业规模的喷射混合器设计、放大提供依据和参考.     

Numerical simulations of the flow and sound fields of a heated axisymmetric pulsating jet

The flow and sound fields of a heated axisymmetric pulsating jet have been investigated by direct numerical solution of the compressible Navier-Stokes equations in cylindrical coordinates using highly accurate numerical methods. Effects of pulsating frequency and amplitude on the flow structure and sound generation have been examined. The results show that the organized unsteadiness associated with the periodic pulsation leads to a variety of vortical structures in the pulsating flow field. The pulsating frequency and amplitude strongly affect the vortical flow structures and the radiated sound fields. At the higher pulsating frequency, the vortices in the pulsating jet become smaller and the radiated sound field has smaller wavelength. The pressure fluctuation amplitude of the sound field is inversely proportional to the distance from the sound source. Both the larger pulsating frequency and larger pulsating amplitude lead to stronger sound emissions from the pulsating jet. It has been found that the pressure fluctuation amplitude of the sound field is approximately proportional to the pulsating amplitude and frequency.     

Numerical simulation of turbulent combustion of subsonic gas jet flows

A physical and mathematical model of turbulent combustion of subsonic gas fuel jet flows flowing into an air space is proposed. The processes are described by averaged equations of the boundary layer with a turbulent viscosity model and a combustion diffusion model. As turbulent viscosity models, the well-known two-parameter k-? standard and k-?? models are taken. The results of the averaged and pulsating flow characteristics?? comparison of numerical calculations with the experimental data are presented.     

Numerical study of a steel sub-frame in fire

Steel-framed buildings are generally designed with “simple” shear-resisting connections, and lateral forces are resisted by vertical bracing and shear walls. When a beam is considered then the effects of the longitudinal restraints by the adjacent structure and the rotational restraint by the connections has to be taken into account. Because of structural interaction, the beam behaviour at elevated temperature is rather complex.This paper presents a numerical parametric study of a structural system consisting of an exposed steel beam restrained between a pair of fire protected steel columns. The structural sub-frame is modelled using 3D shell elements, thereby taking into account the effect of the local failure modes, and the realistic behaviour of the sub-frame exposed to natural fire. The numerical model accounts for the initial geometrical imperfections, nonlinear temperature gradient over the cross-section, geometrical and material nonlinearity and temperature dependent material properties.Results obtained using a general Finite Element software – LUSAS and a fire dedicated software – SAFIR, are compared. The influence of following variables: beam span/depth ratio, lateral restraint, gradient temperature within the cross-section and mechanical load level is presented in the paper. The failure modes, the development of the internal forces and displacements throughout the analysis are considered to exemplify the effects of the variables considered.     

Numerical research on mixing characteristics of different injection schemes for supersonic transverse jet

A numerical method using AUSMDV scheme and k-ω SST turbulence model with an explicit compressibility correction was developed,and a 3-D numerical simulation of a supersonic flow field with a vertical sonic jet of hydrogen was performed.Good agreement between numerical results and experimental data validated the reliability of the numerical method.Whereafter,two parameters,mass-weighted average total pressure and mixing efficiency,were defined to evaluate the mixing performance of different injection schemes...     

Numerical procedure for the determination of an unknown coefficients in parabolic equations

A numerical procedure for an inverse problem of determination of unknown coefficients in a class of parabolic differential equations is presented. The approach of the proposed method is to approximate unknown coefficients by a piecewise linear function whose coefficients are determined from the solution of minimization problem based on the overspecified data. Some numerical examples are presented.     

喷射反应器内液-液湍流微观混合的研究

通过定义局部分离度,来定量表征喷射器内液-液湍流微观混合规律。其定义式为:(实验所得H~+浓度-模拟所得H~+浓度)/模拟所得H~+浓度。选用酸碱反应体系,利用PLIF技术得到沿喷射器轴线的H~+浓度;采用Fluent软件,利用Standard k-ε模型,模拟获得相同操作条件下的H~+浓度变化趋势。得到不同操作条件下,分离度沿喷射器轴线的变化,结果表明:(1)引流速度不变,喷嘴速度越大,两流体越容易达到微观尺度的均匀混合;(2)喷嘴速度不变,引流速度越大,两流体反而不容易达到微观尺度上的均匀混合;(3)速度比一定的情况下,喷嘴速度越大,越有利于流体的微观混合。     

Numerical investigation of air suction through the louvers of a funnel due to high velocity air jet

The present investigation predicts the suction flow rate from the atmosphere through the louvers of a funnel (used in naval and merchant ships) when the high velocity exhaust comes out from a nozzle or a set of nozzles placed inside the funnel. Conservation equations of mass and momentum have been solved for the funnel with a surrounding computational domain so that the suction can take place at the louvers entry. The resulting equations have been solved numerically using finite volume technique in an unstructured grid employing eddy viscosity based two equation k-ε turbulence model. It has been found from the computation that the air suction rate into the funnel increases with the increase in louvers opening area, nozzle flow rate and height of the funnel. There exists optimum protrusion of the nozzle into the funnel for which maximum suction of air can be achieved with a prescribed nozzle flow rate and all other parameters of the funnel remaining fixed. Similarly there also exists optimum funnel diameter where the suction rate of air becomes the highest with all other parameters remaining fixed. There also exists optimum louver opening area on the funnel where the suction rate becomes the maximum as a function of the funnel diameter. The inclination of the funnel with respect to the vertical has no effect on mass ingress of air into it. An optimum nozzle diameter could be decided for a particular funnel diameter by considering the funnel suction rate and the back pressure developed by the nozzle per meter length of the pipe containing the nozzle (intersection of the two curves gives the optimum point of operation).     

A simplified model for the viscous crossflow in a slotted test section

A simplified physical model is constructed which simulates the viscous crossflow in a fluid layer near the slots at a fixed streamwise location in a slotted wind tunnel. For low to moderate Reynolds numbers, numerical solutions of the two-dimensional, incompressible Navier-Stokes equation in stream function and vorticity, which govern the model flow, are obtained. Fairly general slot geometry is incorporated by means of the Thompson-Thames-Mastin transformation. An approximate factorization scheme with cyclic acceleration parameters is employed to solve a finite difference analog of the stream function equation. The vorticity equation is numerically solved with a modified version of the classical alternating direction implicit (ADI) scheme. Although no quantitative assessment of solution accuracy can be made, numerical results for variation in incremental wall pressure around the slot are at least qualitatively similar to some experimental results of Berndt and Sorenson[21].     

Numerical approximation of stochastic differential delay equation with coefficients of polynomial growth

Although numerical methods of nonlinear stochastic differential delay equations (SDDEs) have been discussed by several authors, there is so far little work on the numerical approximation of SDDE with coefficients of polynomial growth. The main aim of the paper is to investigate convergence in probability of the Euler-Maruyama (EM) approximate solution for SDDE with one-sided polynomial growing drift coefficient and polynomial growing diffusion coefficient. Moreover, we prove the existence-and-uniqueness of almost surely exponentially stable global solution for this nonlinear stochastic delay system. Finally, a computer simulation confirms the efficiency of our numerical method.