A coupled CFD-DEM analysis of granular flow impacting on a water reservoir

Massive debris flows or rock avalanches falling into a water reservoir may cause devastating hazards such as overtopping or dam breakage. This paper presents a coupled Computational Fluid Dynamics and Discrete Element Method (CFD-DEM) analysis on the impacting behaviour of a granular flow falling from an inclined slope into a water reservoir. The coupling between CFD and DEM considers such important fluid–particle interaction forces as the buoyancy force, the drag force and the virtual mass force. It is found that the presence of water in the reservoir can generally help to reduce direct impact of granular flow on the check dam behind the reservoir, minimizes the intense collisions and bouncing among particles and helps form a more homogeneous final deposited heap as compared to the dry case. While the interparticle/particle–wall frictions and collisions dominate the energy dissipation in the dry granular flow, the majority of kinetic energy of the granular system in the wet case is first transferred to the water body, which leaves the granular flow itself to become a contact-shearing dominant one and causes impulse wave travelling between the check dam and the slope surface for a rather sustained period before settling down. A power law distribution is found for the velocity profile of the granular flow travelling on both the slope and the reservoir ground surfaces, and it may change temporarily to a linear distribution at the transition point of the slope toe where the Savage number depicts a peak. The consideration of rolling friction among particles may homogeneously reduce the travelling velocity of the granular flow and alleviate the overall impact on the check dam. The impact on the check dam depends on both the initial debris releasing height and the reservoir water level. Medium water levels in the reservoir have been found to be generally safer when the initial debris height is relatively high.     

Analysis of peristaltic two-phase flow with application to ureteral biomechanics

Fluid flow in the ureter is sometimes accompanied by solid particles that are produced in the kidneys or result from the breakup of larger kidney stones; ureteral peristalsis is affected by the presence of these solids. Peristaltic flow is analyzed for a solitary traveling wave in an axisymmetric tube with an incompressible, Newtonian fluid in which identical, solid spherical particles are distributed. A two-phase flow model is used in conjunction with a perturbation method based on a small radius to length ratio of the wave to obtain a closed-form solution of the flow and particle velocities. The phenomenon of trapping in which closed fluid recirculation streamlines in a moving coordinate frame occurs is discussed. Peristaltic pumping is affected as particle volume fraction is increased. The pressure drop diminishes as the amplitude ratio (wave amplitude/wave radius) decreases. The pressure in the contracted part of the ureter increases as the particle volume fraction is increased. It is suggested that certain pathological and physiological manifestations on the ureter can be related to these findings. The results may also be relevant to the transport of other physiological fluids and industrial applications in which peristaltic pumping is used.     

Investigation of Waves Interaction in Annular Gas–Liquid Flow Using High-Speed Fluorescent Visualization Technique

High-speed fluorescent visualization complex has been developed for quantitative investigation of the process of interaction of waves on liquid film in annular two-phase flow. Evolution of ripples on disturbance waves surface and disturbance waves coalescence are investigated. It is shown that all the ripples in presence of disturbance waves appear at the base of the back front of disturbance waves and then either decelerate, travel on substrate and are overtaken by the following disturbance wave or accelerate, grow and then disappear at the front of disturbance wave. The disappearance happens due to entrainment of liquid into the core of gas stream. Several scenarios of coalescence of disturbance waves were identified. For disturbance waves with close velocities different types of remote interaction were observed.     

The free surface fluid flow over a step of an arbitrary shape in a channel

A boundary integral technique has been developed for the two-dimensional, free surface fluid flow in an arbitrary shaped channel. For steady, ideal, irrotational fluid flow a system of boundary integral equations are derived which are based on the Riemann-Hilbert technique for mixed boundary value problems of an analytical function. The boundary integral equations are solved for the fluid speed on both the solid boundary and the free surface, the shape of the free surface and for the critical Froude number for which waves first occur.     

Unsteady pressure waves and shock waves in elastic tubes containing bubbly air-water mixtures

Summary The flow of a two-phase fluid through elastic tubes is more complex than that of a single phase fluid. The mathematical model is based on an one-dimensional approach to the flow of a liquid-gas mixture. The one-dimensional equations for transient two-phase flow through elastic tubes are a system of nonlinear hyperbolic partial differential equations if the bubbles and the liquid particles move with the same velocity. Included in the model are the effects of wall elasticity, compressibility of the gas and the liquid, the surface tension and the variable area change. The propagation of finite pressure waves and shock waves in a liquid containing gas bubbles has been investigated. The results show a differently strong influence of the parameters on the wave propagation speed and on the shock wave relations.

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Zur Ausbreitung von Druck- und Stoßwellen in instationären Blasen-Flüssigkeitsströmungen durch elastische Leitungen

Zusammenfassung Es ist bekannt, daß bei der mathematischen Beschreibung einer Zweiphasenströmung insofern Schwierigkeiten auftreten können, als unter bestimmten Voraussetzungen sowohl reelle als auch komplexe charakteristische Richtungen auftreten können. Für den Fall gleicher Geschwindigkeiten von Blasen und Flüssigkeit erhält man aus den instationären Gleichungen ein nichtlineares hyperbolisches Differentialgleichungssystem. Berücksichtigt werden die Elastizität der Wandungen, die Kompressibilität des Gases und der Flüssigkeit sowie die Oberflächenspannung. Wellenausbreitungsgeschwindigkeiten und Stoßrelationen werden angegeben. Die Resultate zeigen einen unterschiedlich starken Einfluß der verschiedenen Parameter auf die Wellenaus-breitungsgeschwindigkeit und die Stoßrelationen.

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With 13 Figures     

Analysis and computation of non-equilibrium two-phase flows

Non-equilibrium fluid mechanics and thermodynamics of two-phase vapour-droplet and gas-particle flow are considered. Formation of the droplets as well as their subsequent interaction with the vapour are discussed. A new theory of nucleation in steam turbines is developed that reproduces many aspects of measured droplet size spectra which cannot be explained by any available steady-flow theories. (Steam turbines are responsible for 80% of global electricity production and the presence of moisture significantly reduces turbine efficiency costing 50 million pounds per annum in UK alone.) Fluid dynamic interactions discussed include flow instabilities induced by condensation, condensation wave theory, relaxation gas dynamics for vapour-droplet flow, thermal choking due to non-equilibrium condensation, the structure of shock waves and their development through unsteady processes, and jump conditions and the interpretation of total pressure in two-phase flows.     

Propagation and decay of acceleration waves in thermoconsolidating media

Summary The propagation of acceleration waves in a fluid-saturated porous medium is considered. The two-phase medium is the system consisting of a porous elastic solid skeleton, filled with a viscous compressible fluid. Two types of the media are taken into account: the medium composed of definite conductors and the medium composed of non-conductors. The method of singular surfaces has been used in these considerations. The acceleration waves in the medium consisting of non-conductors are not homentropic, in general. In this paper the conditions are determined which must be fulfilled to satisfy the acceleration waves to be homentropic.The propagation conditions of the waves are formulated and analysed. As usual in such a two-phase medium two longitudinal waves and one transverse wave are propagated. The growth equations of homothermal and homentropic waves are derived, and their solutions are analysed.     

An algorithm for modelling the interaction of a flexible rod with a two‐dimensional high‐speed flow

We present an algorithm for modelling coupled dynamic interactions of a very thin flexible structure immersed in a high‐speed flow. The modelling approach is based on combining an Eulerian finite volume formulation for the fluid flow and a Lagrangian large‐deformation formulation for the dynamic response of the structure. The coupling between the fluid and the solid response is achieved via an approach based on extrapolation and velocity reconstruction inspired in the Ghost Fluid Method. The algorithm presented does not assume the existence of a region exterior to the fluid domain as it was previously proposed and, thus, enables the consideration of very thin open boundaries and structures where the flow may be relevant on both sides of the interface. We demonstrate the accuracy of the method and its ability to describe disparate flow conditions across a fixed thin rigid interface without pollution of the flow field across the solid interface by comparing with analytical solutions of compressible flows. We also demonstrate the versatility and robustness of the method in a complex fluid–structure interaction problem corresponding to the transient supersonic flow past a highly flexible structure. Copyright © 2005 John Wiley & Sons, Ltd.     

Flexural- and capillary-gravity waves due to fundamental singularities in an inviscid fluid of finite depth

Wave motion due to line, point and ring sources submerged in an inviscid fluid are analytically investigated. The initially quiescent fluid of finite depth, covered by a thin elastic plate or by an inertial surface with the capillary effect, is assumed to be incompressible and homogenous. The strengths of the sources are time-dependent. The linearized initial-boundary-value problem is formulated within the framework of potential flow. The perturbed flow is decomposed into the regular and the singular components. An image system is introduced for the singular part to meet the boundary condition at the flat bottom. The solutions in integral form for the velocity potentials and the surface deflexions due to various singularities are obtained by means of a joint Laplace-Fourier transform. To analyze the dynamic characteristics of the flexural- and capillary-gravity waves due to unsteady disturbances, the asymptotic representations of the wave motion are explicitly derived for large time with a fixed distance-to-time ratio by virtue of the Stokes and Scorer methods of stationary phase. It is found that the generated waves consist of three wave systems, namely the steady-state gravity waves, the transient gravity waves and the transient flexural/capillary waves. The transient wave system observed depends on the moving speed of the observer in relation to the minimal and maximal group velocities. There exists a minimal depth of fluid for the possibility of the propagation of capillary-gravity waves on an inertial surface. Furthermore, the results for the pure gravity and capillary-gravity waves in a clean surface can also be recovered as the flexural and inertial parameters tend to zero.     

Interfacial capillary–gravity waves due to a fundamental singularity in a system of two semi-infinite fluids

The interfacial capillary–gravity waves due to a transient fundamental singularity immersed in a system of two semi-infinite immiscible fluids of different densities are investigated analytically for two- and three- dimensional cases. The two-fluid system, which consists of an inviscid fluid overlying a viscous fluid, is assumed to be incompressible and initially quiescent. The two fluids are each homogeneous, and separated by a sharp and stable interface. The Laplace equation is taken as the governing equation for the inviscid flow, while the linearized unsteady Navier–Stokes equations are used for the viscous flow. With surface tension taken into consideration, the kinematic and dynamic conditions on the interface are linearized for small-amplitude waves. The singularity is modeled as a simple mass source when immersed in the inviscid fluid above the interface, or as a vertical point force when immersed in the viscous fluid beneath the interface. Based on the integral solutions for the interfacial waves, the asymptotic wave profiles are derived for large times with a fixed distance-to-time ratio by means of the generalized method of stationary phase. It is found that there exists a minimum group velocity, and the wave system observed will depend on the moving speed of the observer. Two schemes of expansion of the phase function are proposed for the two cases when the moving speed of an observer is larger than, or close to the minimum group velocity. Explicit analytical solutions are presented for the long gravity-dominant and the short capillary-dominant wave systems, incorporating the effects of density ratio, surface tension, viscosity and immersion depth of the singularity.     

地震波斜入射条件下重力坝动力响应分析

为建立反映设计地震动的斜入射波场,将地表地震动时程分量分解为斜入射的平面SV波和平面P波,使其共同作用下在地表产生与设计地震动分量相同的响应,而其他方向响应为0,根据固体介质中波的传播理论,推导了斜入射波入射角度之间的关系,以及幅值与设计地震动分量的联系,通过采用平面波和远场散射波混合透射的应力人工边界条件,得到了反映设计地震动的地震波斜入射条件下的解析方式,以此为基础建立了时域计算分析模型。将该方法应用于某重力坝―地基动力相互作用分析,在不同地基刚度下与垂直入射的情况进行了比较,计算结果表明：地震波斜入射时对重力坝结构有明显的影响,尤其是坝－基交界面上,结构的动力响应要大于地震波垂直入射时结构的动力响应。该方法在均匀地基假设下构造了反映地表设计地震动特征的斜入射波系,斜入射波系在地表的响应具有非一致特征,同时该方法考虑了地基的辐射阻尼,可用于重大工程在地震动非一致输入下的动力响应分析。     

Role of interphase interactions during gas detonation in inert porous medium

A mathematical model of detonation in a two-phase mixture consisting of a gaseous monofuel and closely packed noninflammable solid particles is proposed. The structure of detonation waves in a pure gas is compared to that in monodisperse mixtures with various diameters of particles. Two special regimes of detonation are separated, in which (i) gas is immediately inflamed due to shock compression and (ii) ignition starts at the surface of particles, upon reflection of the chock wave front. It is shown that inertial effects during the flow past particles can both increase and decrease the detonation velocities. The calculated detonation velocities well agree with experimental data.     

Discrete-element modelling and smoothed particle hydrodynamics: potential in the environmental sciences

Particle-based simulation methods, such as the discrete-element method and smoothed particle hydrodynamics, have specific advantages in modelling complex three-dimensional (3D) environmental fluid and particulate flows. The theory of both these methods and their relative advantages compared with traditional methods will be discussed. Examples of 3D flows on realistic topography illustrate the environmental application of these methods. These include the flooding of a river valley as a result of a dam collapse, coastal inundation by a tsunami, volcanic lava flow and landslides. Issues related to validation and quality data availability are also discussed.     

旋流沉砂池除砂废水流场与结构参数优化模拟

在旋流沉砂池砂石废水处理中,具有复杂流态的高浓度固液两相流问题一直是难以攻克的难题,给工程设计与运行带来很大困难。该文采用分子动理学方法从固液两相流相互作用的微观特性出发,得出合理描述旋流沉砂池内高浓度下颗粒间碰撞项的Eulerian-Eulerian 两相流模型。采用滑移网格技术实现了旋流沉砂池桨叶转动区域的模拟。结合西南某水电工程砂石废水处理中的旋流沉砂池流场进行了模拟,并讨论了搅拌桨转速、桨叶位置、叶片数量和叶片角度对旋流沉砂池内水相、颗粒相的影响。结果表明:该水电站砂石处理系统旋流沉砂池的最佳桨叶结构和运行工况为:桨叶转速r=105rap/min,桨叶位置z=592mm,叶片数量为4 片,叶片角度为45°。     

Finite element simulation and visualization of leaky Rayleigh wavesfor ultrasonic NDE

The generation and propagation properties of transient leaky Rayleigh waves are characterized by a two-dimensional finite element model. The displacement vector is used as the primary variable for the solid medium and a potential scalar, which is a replacement for the pressure, is taken as the fundamental variable for the fluid medium. The coupled system of finite element equations are solved in the time domain by direct integration through the central difference scheme. Three configurations are considered: the conversion of a Rayleigh surface wave into a leaky Rayleigh wave, a focused beam probing a fluid/solid interface at the Rayleigh angle, and the interaction of a defocused wave with the interface. The wave velocity in the fluid (water) is lower than the Rayleigh wave velocity in the solid (aluminum). The wave propagation profile in each case is predicted by the model. The finite element model proves to be an effective tool for surface acoustic device design and ultrasonic NDE     

Influence of irregular canyon shape on location of truncation surface

Fluid–structure interaction phenomenon, by its nature, is three-dimensional and consequently dependant on the shape of a dam and canyon that in-fact defines the spatial domain where the generated acoustic waves are spread. The complex topography of the terrain in general requires sufficiently large extent of reservoir to be included in the model, which is undoubtedly feasible if BEM technique is used. This paper shows that the irregular canyon shape dictates “the most adequate” location of the truncation surface that gives the smallest negative impact on calculation accuracy. The derived conclusions are based on various 3D analyses of a rigid dam–reservoir system with different shapes and lengths of the fluid domain, where the fluid is treated as incompressible and inviscid. The presented work contributes towards disclosure of the topographic site effects and towards promotion of simple and effective procedure for generation of BE mesh, which is quite accurate in following the topology of the terrain.     

Powder discharge from a hopper-standpipe system modelled with CPFD

In this paper, computational particle fluid dynamic (CPFD) modelling approach was used to describe the discharge of a fine glass beads powder from different hopper-standpipe geometries. The comparison between the CPFD predictions and the experimental results in terms of solid discharge rates, surface cone shape during discharge and pressure drops in the standpipe. The comparison allowed to assess on the possibility to use the CPFD modelling approach to simulate the powder flow in the hopper-standpipe system even accounting for the rather complex interactions between the interstitial gas and the particles occurring in the presence of a standpipe. Furthermore, the effect of hopper geometry on powder discharge was investigated with the CPFD model and verified experimentally in some purposely built hoppers. Finally, the relationships between the hopper geometry parameters (hopper outlet diameter and hopper half angle) and the flow parameters (solid discharge rate, height of characteristic surface, particle volume fraction, particle velocity, gas pressure and flow pattern) were obtained.     

模型试验及数值模拟下尾矿库溃坝尾砂流演变预测

尾矿库溃坝所产生的尾砂流类似于地质灾害中的泥石流,具有发展迅速、破坏性强、影响范围广和预警时间不足等特点,研究溃坝尾砂流的演变规律及其影响范围对防灾减灾具有重要的意义。该研究利用RAMMS碎屑流软件建立了数值三维模型进行数值仿真溃坝模拟,通过物理模型(1∶150)试验研究了溃坝的尾砂流对下游的演变进程和影响范围,并将其试验数据与数值计算结果对比分析,验证了数值模拟在溃坝仿真上的可靠性和有效性。结果表明:以漫顶水流到达拦砂坝底开始计时,尾矿坝溃坝9 min尾砂流开始冲击距尾矿坝0.7 km处的下游村庄;随着溃坝的持续,溃坝泥砂淤积逐步加深,水位继续升高,并在18 min对下游造成全面淹没,影响范围达0.558 km ²,库内尾砂的溃泄总量可达1.3×10⁷ m ³。建议在尾矿库的设计、管理和风险评估过程中,结合潜在的危险范围,合理的增加防灾减灾的措施。     

Nonstationary Rayleigh waves on the thermally-insulated surfaces of some thermoelastic bodies of revolution

Summary The influence of heat conduction and thermal relaxation on the propagation of the surface waves polarized in the sagittal plane along the heat-insulated surfaces of the following thermoelastic bodies of revolution: a cylinder, a sphere, a torus, and a cone is investigated. The modified Maxwell law is used as the law of heat conduction, which allows one to take a finite speed of heat propagation into account. The nonstationary surface waves are interpreted as lines (a straight line or a diverging or converging circumference) on which the temperature and the components of the stress and strain tensors experience a discontinuity. Each of the discontinuity lines propagates with a constant normal velocity across the free from stresses and thermally-insulated surface of the body of revolution along the corresponding lines of curvature and is obtained by coming onto the body's surface of the three strong discontinuity complex wave surfaces which intersect along this line: quasi-thermal, quasi-longitudinal and quasi-transverse volume waves. By applying the theory of discontinuities, the velocities and the intensities of the surface waves have been found. It has been shown that the attenuation of the surface wave intensity is determined by the two factors: the coupling between the related strain and temperature fields and the change in curvature of the surface wave with time if the wave is a curvilinear one.     

模型试验及数值模拟下尾矿库溃坝尾砂流演变预测

尾矿库溃坝所产生的尾砂流类似于地质灾害中的泥石流,具有发展迅速、破坏性强、影响范围广和预警时间不足等特点,研究溃坝尾砂流的演变规律及其影响范围对防灾减灾具有重要的意义。该研究利用RAMMS碎屑流软件建立了数值三维模型进行数值仿真溃坝模拟,通过物理模型(1∶150)试验研究了溃坝的尾砂流对下游的演变进程和影响范围,并将其试验数据与数值计算结果对比分析,验证了数值模拟在溃坝仿真上的可靠性和有效性。结果表明:以漫顶水流到达拦砂坝底开始计时,尾矿坝溃坝9 min尾砂流开始冲击距尾矿坝0.7 km处的下游村庄;随着溃坝的持续,溃坝泥砂淤积逐步加深,水位继续升高,并在18 min对下游造成全面淹没,影响范围达0.558 km ²,库内尾砂的溃泄总量可达1.3×10⁷ m ³。建议在尾矿库的设计、管理和风险评估过程中,结合潜在的危险范围,合理的增加防灾减灾的措施。