Non-Boussinesq turbulent buoyant jet of a low-density gas leaks into high-density ambient

In this article, we study the problem of low-density gas jet injected into high-density ambient numerically which is important in applications such as fuel injection and leaks. It is assumed that the local rate of entrainment is consisted of two components; one is the component of entrainment due to jet momentum while the other is the component of entrainment due to buoyancy. The integral models of the mass, momentum and concentration fluxes are obtained and transformed to a set of ordinary differential equations using some similarity transformations. The resulting system is solved to determine the centerline quantities which are used to get the mean axial velocity, mean concentration and mean density of the jet. Therefore, the centerline and mean quantities are used together with the governing equation to determine some important turbulent quantities such as, cross-stream velocity, Reynolds stress, velocity-concentration correlation, turbulent eddy viscosity and turbulent eddy diffusivity. Throughout this paper the developed model is verified by comparing the present results with experimental results and jet/plume theory from the literature.     

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)     

Assessment of an Eulerian CFD model for prediction of dilute droplet dispersion in a turbulent jet

The turbulent dispersion of non-evaporating droplets in an axisymmetric round jet issuing from a nozzle is investigated both experimentally and theoretically. The experimental data set has a well-defined inlet boundary with low turbulence intensity at the nozzle exit, so that droplet dispersion is not affected by the transport of nozzle-generated fluctuating motion into the jet, and is influenced solely by turbulence in the gas phase produced in the shear layer of the jet. This data set is thus ideal for testing algebraic models of droplet fluctuating motion that assume local equilibrium with the turbulence in the gas phase. Moreover, the droplet flux measurements are sufficiently accurate that conservation of the total volume flow of the droplet phase has been demonstrated. A two-fluid turbulence modelling approach is adopted, which uses the k–ε turbulence model and a simple algebraic model that assumes local equilibrium to predict the fluid and droplet turbulent correlations, respectively. We have shown that the k–ε turbulence model lacks generality for predicting the spread of momentum in jets with and without a potential core. However, in general, the model predicts the radial dispersion of droplets in the considered turbulent jet with reasonable accuracy over a broad range of droplet sizes, once deficiencies in the k–ε turbulence model are taken into account.     

Numerical simulation of unsteady flows with transient regimes

Self-oscillatory flows in aerodynamics and astrophysics are studied. The two-dimensional compressible gas equations are solved using the implicit Runge-Kutta scheme of the third order with respect to the inviscid terms and of the second order with respect to the viscous terms. An algebraic Cebeci-Smith turbulence model is used. Weakly unsteady and strongly unsteady flow regimes are observed. The former occur in a supersonic flow past a cylinder with a front projection and in the heliosphere. Such flows became stable when the turbulent diffusion is taken into account. The latter flows occur when a supersonic jet meets an obstacle and when such a jet penetrates a cavity. In these flows, the amplitude of oscillations slightly decreases when the turbulent diffusion is taken into account.     

Investigation of a mixing length and a two-equation turbulence model utilizing the finite element method

The finite element method is used to analyse turbulent coaxial jet flow using the mixing length viscosity model. The predictions from the model are shown to compare favourably with the results of experiment and of a finite difference based method. The implementation of a two-equation turbulence model in the finite element context is also discussed and the feasibility of such an approach is demonstrated by an analysis of fully developed turbulent flow in smooth walled pipes and channels.     

泄爆诱导的湍流、旋涡和外部爆炸

基于k-ε湍流模型和Eddy-dissipation燃烧模型,采用同位网格SIMPLE算法,对充满甲烷-氧气预混气的带导管柱形泄爆容器向空气中泄爆的情形进行了数值模拟．根据计算结果,分析了泄爆后外流场中可燃云团、火焰和压力的变化过程．结果表明,外部爆炸是因射流火焰点燃高压区中的可燃云团,从而引起的剧烈湍流燃烧所致．同时还讨论了外流场湍流和涡量的分布特征．射流火焰进入外部可燃云团后,湍流主要分布在平均动能梯度较大的区域,而不在火焰阵面上．涡量分布主要受斜压效应的影响,在压力和密度梯度斜交区域,其值较大．     

Numerical modeling of turbulence-induced interfacial instability in two-phase flow with moving interface

The present paper introduces a new interfacial marker-level set method (IMLS) which is coupled with the Reynolds averaged Navier–Stokes (RANS) equations to predict the turbulence-induced interfacial instability of two-phase flow with moving interface. The governing RANS equations for time-dependent, axisymmetric and incompressible two-phase flow are described in both phases and solved separately using the control volume approach on structured cell-centered collocated grids. The transition from one phase to another is performed through a consistent balance of kinematic and dynamic conditions on the interface separating the two phases. The topological changes of the interface are predicted by applying the level set approach. By fitting a number of interfacial markers on the intersection points of the computational grids with the interface, the interfacial stresses and consequently, the interfacial driving forces are easily estimated. Moreover, the normal interface velocity, calculated at the interfacial markers positions, can be extended to the higher dimensional level set function and used for the interface advection process. The performance of linear and non-linear two-equation k–ε turbulence models is investigated in the context of the considered two-phase flow impinging problem, where a turbulent gas jet impinging on a free liquid surface. The numerical results obtained are evaluated through the comparison with the available experimental and analytical data. The nonlinear turbulence model showed superiority in predicting the interface deformation resulting from turbulent normal stresses. However, both linear and nonlinear turbulence models showed a similar behavior in predicting the interface deformation due to turbulent tangential stresses. In general, the developed IMLS numerical method showed a remarkable capability in predicting the dynamics of the considered two-phase immiscible flow problems and therefore it can be applied to quite a number of interface stability problems.     

Size distribution of convective thermals in an unstable stratified turbulent surface layer

An ensemble of convective thermals is considered in the surface layer of penetrative turbulent convection over a homogeneous heated horizontal surface. An integral model of an unsteady spontaneous jet having an exact self-similar solution is proposed to describe the dynamics of an isolated convective element. A statistical model for an ensemble of convective elements using a hydrodynamic analogy of the isolated spontaneous jet equations is suggested. It is supposed that motion of the elements of an ensemble corresponds to a statistic invariant that combines the squared velocity and the diameter of the jet. Using the combination of the statistic invariant of an ensemble and the Boltzmann distributions on squares of velocities, the size distribution of spontaneous jets in a convective surface layer of the atmosphere is constructed, which agrees with available experimental data.      

Computed oscillations of a confined submerged liquid jet

The jet oscillation observed in thin slab continuous casting is studied numerically by modelling the flow of liquid injected through a submerged entry nozzle and into a cavity. The oscillation relies on the exchange of fluid between recirculation cells on each side of the jet via a cross-flow through the gap between the nozzle shaft and the broad face of the cavity wall. Features of the oscillating jet are investigated by varying the resistance to cross-flow. This resistance occurs naturally since the nozzle obstructs cross-flow. The predicted oscillation can be manipulated by altering the cross-flow (through the use of an effective resistance force in the model) or stopped altogether to form a static asymmetrical flow pattern. Flow calculations are performed using a transient, two-dimensional, turbulent, fluid flow model.     

Re.ned Modeling of the pressure redistribution/scrambling under consistent consideration of scalar turbulence effects in turbulent combustion

In practical turbulent flow problems of engineering importance the coupling between velocity and scalar turbulence along with the variable density plays a non negligible role. For computations using second moment closure approach, the pressure redistribution/scrambling is the most critical term to be modeled as well known. Almost all existing models consist in rescating models derived on a constant density basis in a density weighted form. With regard to turbulent premixed combustion in fact, the application of such models to a range of transient one‐dimensional and two‐dimensional premixed flames in the flamelet regime has been found to yield unsatisfactory results, see [1]. As pointed out by Sadiki [2], the use of the Favre method must be consistently considered as far as open thermodynamic systems are concerned. Furthermore, the need for maintaining certain invariance properties, physical and mathematical realizability conditions in formulating turbulence models is well accepted. Because turbulent processes are irreversible, these efforts demand a carefull consideration of thermodynamic concepts. Based on the results in [1] and following [2], this work aims to derive a physically consistent formulation of the pressure redistribution/scrambling term under consideration of the variable density. Considering the case of premixed flames, the thermochemistry is included by means of a single reactive scalar ‐ the reaction progress variable. The accuracy of the model extensions proposed is demonstrated by comparing the numerical results with experimental data in opposed jet premixed flame configuration.     

An assessment of streamline curvature effects on the mixing region of a turbulent plane jet in crossflow

The flow field of a turbulent plane jet in a weak or moderate crossflow, which is characterised by mild streamline curvature, has been investigated computationally. The values of the jet-to-crossflow velocity ratios chosen are 6, 9 and 10. The time-averaged Navier–Stokes equations are solved on a staggered Cartesian grid using the standard k–ϵ model and the k–ϵ model with streamline curvature modification. The predictions using both the models are compared with available experimental data. It has been shown that by accounting for the effect of streamline curvature in the k–ϵ model results in good prediction of this flow configuration.     

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.     

A Conservative Formulation and a Numerical Algorithm for the Double-Gyre Nonlinear Shallow-Water Model

We present a conservative formulation and a numerical algorithm for the reduced-gravity shallow-water equations on a beta plane, subjected to a constant wind forcing that leads to the formation of double-gyre circulation in a closed ocean basin. The novelty of the paper is that we reformulate the governing equations into a nonlinear hyperbolic conservation law plus source terms. A second-order fractional-step algorithm is used to solve the reformulated equations. In the first step of the fractional-step algorithm, we solve the homogeneous hyperbolic shallow-water equations by the wave-propagation finite volume method. The resulting intermediate solution is then used as the initial condition for the initial-boundary value problem in the second step. As a result, the proposed method is not sensitive to the choice of viscosity and gives high-resolution results for coarse grids, as long as the Rossby deformation radius is resolved. We discuss the boundary conditions in each step, when no-slip boundary conditions are imposed to the problem. We validate the algorithm by a periodic flow on an $f$-plane with exact solutions. The order-of-accuracy for the proposed algorithm is tested numerically. We illustrate a quasi-steady-state solution of the double-gyre model via the height anomaly and the contour of stream function for the formation of double-gyre circulation in a closed basin. Our calculations are highly consistent with the results reported in the literature. Finally, we present an application, in which the double-gyre model is coupled with the advection equation for modeling transport of a pollutant in a closed ocean basin.     

Large Eddy Simulation of turbulent confined coaxial swirling jets

Large eddy simulations of swirling flow in a coaxial-jet combustor are reported. Two experimental test cases have been chosen from the literature. In both cases the configuration consists of two coaxial jets which enter into an expansion duct with the annular jet being swirled, the inner jet unswirled. The main features of the flow are well predicted in the simulations. The mean velocities and the turbulent fluctuations are compared with the experimental data and show good agreement. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Assessment of turbulence modeling for gas flow in two-dimensional convergent–divergent rocket nozzle

In the present study, the turbulent gas flow dynamics in a two-dimensional convergent–divergent rocket nozzle is numerically predicted and the associated physical phenomena are investigated for various operating conditions. The nozzle is assumed to have impermeable and adiabatic walls with a flow straightener in the upstream side and is connected to a plenum surrounding the nozzle geometry and extended in the downstream direction. In this integrated component model, the inlet flow is assumed a two-dimensional, steady, compressible, turbulent and subsonic. The physics based mathematical model of the considered flow consists of conservation of mass, momentum and energy equations subject to appropriate boundary conditions as defined by the physical problem stated above. The system of the governing equations with turbulent effects is solved numerically using different turbulence models to demonstrate their numerical accuracy in predicting the characteristics of turbulent gas flow in such complex geometry. The performance of the different turbulence models adopted has been assessed by comparing the obtained results of the static wall pressure and the shock position with the available experimental and numerical data. The dimensionless shear stress at the nozzle wall and the separation point are also computed and the flow field is illustrated. The various implemented turbulence models have shown different behavior of the turbulent characteristics. However, the shear-stress transport (SST) k–ω model exhibits the best overall agreement with the experimental measurements. In general, the proposed numerical procedure applied in the present paper shows good capability in predicting the physical phenomena and the flow characteristics encountered in such kinds of complex turbulent flow.     

An assessment of turbulence models applied to the simulation of a two-dimensional submerged jet

This paper is concerned with the investigation of the performance of different turbulence models in the numerical prediction of transient flow caused by a confined submerged jet. Several widely used models, i.e., the standard k–ε, RNG k–ε, low Reynolds number k–ε models and the differential Reynolds stress model, as included in CFD codes, were compared with each other for a two-dimensional, incompressible, turbulent jet flow and with reported experimental data. A flapping oscillation was predicted regardless of the model used. A chosen Strouhal (St) number definition brought the fundamental frequencies from both the experiments and computations into close proximity. However, different turbulence models have exhibited quite different behaviours in terms of the frequency and regularity of the oscillation and in terms of the scale and duration of the vortices generated. All versions of the k–ε model yielded regular oscillations, which agree with experimental observations. On the other hand, the Reynolds stress (RS) model produced a complex pattern but a slower dissipation of vortices. In addition, some aspects of gridding and inflow representation are also discussed.     

CFD-半解析模型混合的管束结构流弹失稳预测方法

横向流作用下管束结构传统流弹失稳模型的建立或多或少需要获取实验流体力参数作为输入条件.因此非常需要开发一种不依赖实验数据的管束结构流弹失稳模型.该文提出了一种改进的CFD仿真与半解析方法混合的管束结构流弹失稳预测方法.采用CFD仿真方法获取半解析模型中关键的相位延迟函数,并根据速度将其表示为简单的分段函数.最终预测了横向流作用下间距比为1.375的平行三角形与正三角形管束结构的流弹失稳阈值,预测结果与文献中的实验结果吻合良好.该文提出的CFD-半解析模型混合方法同样适用于其他管束结构的流弹失稳预测,为蒸汽发生器传热管流弹失稳现象的研究提供了一种时间成本较低的预测方法.     

反映强流动曲率效应的非线性湍流模型

首先定性地分析了流线曲率效应对流场湍流结构的影响,然后以U型槽道流为典型算例,对多种湍流模型进行了评估．评估的模型包括:线性涡粘性模型,二阶和三阶非线性涡粘性模型,二阶显式代数应力模型和Reynolds应力模型．评估结果表明,性能良好的三阶非线性涡粘性模型,如黄于宁等人发展的HM模型以及CLS模型,可以较好地描述流线的曲率效应对湍流结构的影响,如凸曲率作用下内壁附近湍流强度的衰减和凹曲率作用下外壁附近湍流的增强,并且较好地确定了管道下游的分离点位置和分离泡长度,其预测的结果和实验符合较好,与Reynolds力模型的结果十分接近,因此可以较好地应用于具有曲率效应的工程湍流的计算．