Influence of large eddies on the suspension of solid particles

The phenomena of solid particles suspensions, in a turbulent flow, can more conveniently be described by stochastic models than by diffusion models, particularly in the case of relatively coarse particles.

The fundamental difficulties of using such models are principally due to the difficulty of performing direct measurements of probabilities, because the number of observations (or tests) necessary to obtain physically representative values is important (theoretically infinite).

We have used such a model to describe the movement of spheres in an inclinable pipe.

To do so, we have identified the movement through a Markov process which permits us to show that we can characterize it by the limit distribution for passage probabilities in a cross section. We have used a special system of close-circuit television to measure it, doing a sufficiently large number of observations for the measurements to be significant.

In the case of a vertical pipe, the phenomena is one-dimensional. By using the model stochastic displacement, we obtain a differential equation which it is possible to integrate by assuming an obviously constant radial dispersion. The interpretation of limit distributions for passage probabilities and visual observations of particles movement in the pipe have caused us to conclude that the mean displacment is due, on one hand, to a radial acceleration bounded to a stochastic rotation of the flow and, on the other hand, to the effect of the mean velocity gradient. The experimental results show that the radial dispersion is a function of the relative dimension of particles with respect to the macroscale of the turbulence.

In the case of an inclined pipe, a two-dimensional stochastic model of the displacement is possible, but the integration of the equation is quite complicated and may be done numerically. We have prefered a two-dimensional simulation model. The results of the simulations permit us to obtain a limit repartition of passage probabilities, the moments of which we have compared with those that we have measured. These comparisons show that the model obviously represents the phenomena when the pipe is horizontal or very slightly inclined but differs in the near vertical case. This is due to the simplicity of the model in which we neglect the radial acceleration we have considered previously and the effect of which is negligible in comparison with gravity when the pipe is inclined.

The interpretation of the measurements by comparison of moments with the two-dimensional model shows that the angular dispersion of solid particles is essentially due to big eddies and that the particle diameters are not essential parameters in this case.

By associating this conclusion with that obtained previously concerning the radial dispersion, it seems that the eddies bigger than the macroscale of turbulence may be of capital importance in the dispersion of solid particles and that it will be of practical interest to characterize them as a function of a mean parameter of the flow.

The study of the movement of sufficiently large particles seems to be a method which is able to give this result.     

On the Electric Potential Induced by a Homogeneous Magnetic Field in a Turbulent Pipe Flow

In this paper we study a turbulent pipe flow of a weakly electrical conducting fluid subjected to a homogeneous magnetic field which is applied perpendicular to the flow. This configuration forms the basis of a so-called electromagnetic induction flow meter. When the Hartmann number is small so that modification of flow by the Lorenz force can be neglected, the influence of the magnetic field results only in a spatially and temporally varying electric potential. The magnitude of the potential difference across the pipe is then proportional to the flow rate and this constitutes the principle of the flow meter. In this study the flow and electric potential are computed with help of a numerical flow simulation called Large-Eddy Simulation (LES) to which we have added an equation for the electrical potential. The results of the LES have been compared with experiments in which the electric potential is measured as a function of time at several positions on the circumference of the pipe. Both the experimental and numerical results for the mean potential at the pipe wall agree very well with an exact solution that can be obtained in this particular case of a homogeneous magnetic field. Furthermore, it is found that fluctuations in the electric potential due to the turbulence, are small compared to the velocity fluctuations. Based on the results we conclude that electrical-magnetic effects in pipe flow can be accurately computed with LES.     

Analysis of pipe flow transition. Part II. Energy transfer

The present article describes the results from a study of nonlinear mechanisms at work during the process of transition to turbulence in pipe flows. Using an accurate hybrid finite-difference code for the simulation of unsteady incompressible pipe flow, we have performed a direct numerical simulation designed to model experiments performed by Han, Tumin and Wygnanski [12]. Based on these numerical data, we have conducted a meticulous investigation of the dynamic interactions of the structures and flow modes that can be observed during this process. Based on this study, we can paint a detailed picture of the dynamical interactions of flow structures during both the linear and nonlinear stages of pipe flow transition. While this picture does have some similarities to earlier proposed mechanisms, we find that even for the simple cases considered here the structure of the pertinent interactions is much richer than suggested by these earlier models.     

Slope effect on core-annular flow

To facilitate the flow of heavy viscous oils in a pipe, a water-lubricated transport is generally used. The water migrates into the regions of high shear at the pipe wall where it lubricates the flow. The pumping pressures are balanced by wall shear stresses in the water, the process therefore requires pressures comparable to pumping water alone, with no dependence on the viscosity of the oil. This means that significant savings in pumping power can be derived from this process, provided that it is well monitored. Indeed, the flow of a water/oil mixture in a pipe has two main characteristics. First, the fluids can adopt different spatial arrangements called flow regimes, and second, the presence of a water layer at the channel wall significantly reduces the global pressure drop. In this paper, an experimental investigation was performed on the effect of pipe slope and fluids flow rates on flow regimes, pressure drop and interfacial instability.     

Stability analysis of fluid-fluid interfaces

Two problems in pipe flow are discussed in which the stability of fluid-fluid interfaces plays an important role. A stability analysis for a simplified 2-D geometry is presented. In gas-liquid pipe flow different flow regimes occur. This is known to be related to the stability properties of the flow. We shall present a linear stability analysis of plane two-phase Poiseuille flow. Two different unstable modes can occur, corresponding to experimental findings for pipe flow. The first is a finite wavelength mode related to the transition to wavy flow via a Hopf bifurcation. The second unstable mode is an infinite wavelength mode, which may be related to the transition to slug flow. Core-annular flow can be used to transport very viscous crude oils. The crude oil is surrounded by a thin water film, which prevents the core from touching the wall. In the hydrodynamic force balance, waves on the interface play an important role. A linear stability analysis of plane Poiseuille-Couette flow can predict the wavelength in agreement with experimental results even far beyond the critical point. No non-linear analysis is available as yet.     

Effect of the pattern of initial perturbations on the steady pipe flow regime

The influence of the inlet flow formation mode on the steady flow regime in a circular pipe has been investigated experimentally. For a given inlet flow formation mode the Reynolds number Re* at which the transition from laminar to turbulent steady flow occurred was determined. With decrease in the Reynolds number the difference between the resistance coefficients for laminar and turbulent flows decreases. At a Reynolds number approximately equal to 1000 the resistance coefficients calculated from the Hagen-Poiseuille formula for laminar steady flow and from the Prandtl formula for turbulent steady flow are equal. Therefore, we may assume that at Re > 1000 steady pipe flow can only be laminar and in this case it is meaningless to speak of a transition from one steady pipe flow regime to the other. The previously published results [1–9] show that the Reynolds number at which laminar goes over into turbulent steady flow decreases with increase in the intensity of the inlet pulsations. However, at the highest inlet pulsation intensities realized experimentally, turbulent flow was observed only at Reynolds numbers higher than a certain value, which in different experiments varied over the range 1900–2320 [10]. In spite of this scatter, it has been assumed that in the experiments a so-called lower critical Reynolds number was determined, such that at higher Reynolds numbers turbulent flow can be observed and at lower Reynolds numbers for any inlet perturbations only steady laminar flow can be realized. In contrast to the lower critical Reynolds number, the Re* values obtained in the present study, were determined for given (not arbitrary) inlet flow formation modes. In this study, it is experimentally shown that the Re* values depend not only on the pipe inlet pulsation intensity but also on the pulsation flow pattern. This result suggests that in the previous experiments the Re* values were determined and that their scatter is related with the different pulsation flow patterns at the pipe inlet. The experimental data so far obtained are insufficient either to determine the lower critical Reynolds number or even to assert that this number exists for a pipe at all.     

A theoretical model for core-annular flow of a very viscous oil core and a water annulus through a horizontal pipe

A theoretical model has been developed for core-annular flow of a very viscous oil core and a water annulus through a horizontal pipe. Special attention was paid to understanding how the buoyancy force on the core, resulting from any density difference between the oil and water, is counterbalanced. This problem was simplified by assuming the oil viscosity to be so high that any flow inside the core may be neglected and hence that there is no variation of the profile of the oil-water interface with time. In the model the core is assumed to be solid and the interface to be a solid/liquid interface.By means of the hydrodynamic lubrication theory it has been shown that the ripples on the interface moving with respect to the pipe wall can generate pressure variations in the annular layer. These result in a force acting perpendicularly on the core, which can counterbalance the buoyancy effect.To check the validity of the model, oil-water core-annular flow experiments have been carried out in a 5.08 cm and an 20.32-cm pipeline. Pressure drops measured have been compared with those calculated with the aid of the model. The agreement is satisfactory.     

Transport modeling of sedimenting particles in a turbulent pipe flow using Euler–Lagrange large eddy simulation

A volume-filtered Euler–Lagrange large eddy simulation methodology is used to predict the physics of turbulent liquid–solid slurry flow through a horizontal periodic pipe. A dynamic Smagorinsky model based on Lagrangian averaging is employed to account for the sub-filter scale effects in the liquid phase. A fully conservative immersed boundary method is used to account for the pipe geometry on a uniform cartesian grid. The liquid and solid phases are coupled through volume fraction and momentum exchange terms. Particle–particle and particle–wall collisions are modeled using a soft-sphere approach. Three simulations are performed by varying the superficial liquid velocity to be consistent with the experimental data by Dahl et al. (2003). Depending on the liquid flow rate, a particle bed can form and develop different patterns, which are discussed in light of regime diagrams proposed in the literature. The fluctuation in the height of the liquid-bed interface is characterized to understand the space and time evolution of these patterns. Statistics of engineering interest such as mean velocity, mean concentration, and mean streamwise pressure gradient driving the flow are extracted from the numerical simulations and presented. Sand hold-up calculated from the simulation results suggest that this computational strategy is capable of predicting critical deposition velocity.     

Extremely large-amplitude oscillation of soft pipes conveying fluid under gravity

In this work, the nonlinear behaviors of soft cantilevered pipes containing internal fluid flow are studied based on a geometrically exact model, with particular focus on the mechanism of large-amplitude oscillations of the pipe under gravity. Four key parameters, including the flow velocity, the mass ratio, the gravity parameter, and the inclination angle between the pipe length and the gravity direction, are considered to affect the static and dynamic behaviors of the soft pipe. The stability analyses show that, provided that the inclination angle is not equal to π, the soft pipe is stable at a low flow velocity and becomes unstable via flutter once the flow velocity is beyond a critical value. As the inclination angle is equal to π, the pipe experiences, in turn,buckling instability, regaining stability, and flutter instability with the increase in the flow velocity. Interestingly, the stability of the pipe can be either enhanced or weakened by varying the gravity parameter, mainly dependent on the value of the inclination angle.In the nonlinear dynamic analysis, it is demonstrated that the post-flutter amplitude of the soft pipe can be extremely large in the form of limit-cycle oscillations. Besides,the oscillating shapes for various inclination angles are provided to display interesting dynamical behaviors of the inclined soft pipe conveying fluid.     

Transient effects of orthogonal pipe oscillations on laminar developing incompressible flow

This paper presents a numerical study of the transient developing laminar flow of a Newtonian incompressible fluid in a straight horizontal pipe oscillating around the vertical diameter at its entrance. The flow field is influenced by the tangential and Coriolis forces, which depend on the through‐flow Reynolds number, the oscillation Reynolds number and the angular amplitude of the pipe oscillation. The impulsive start of the latter generates a transient pulsating flow, whose duration increases with axial distance. In any cross‐section, this flow consists of a pair of symmetrical counter‐rotating vortices, which are alternatively clockwise and anti‐clockwise. The circumferentially averaged friction factor and the axial pressure gradient fluctuate with time and are always larger than the corresponding values for a stationary pipe. On the other hand, local axial velocities and local wall shear stress can be smaller than the corresponding stationary pipe values during some part of the pipe oscillation. The fluctuation amplitude of these local variables increases with axial distance and can be as high as 50% of the corresponding stationary pipe value, even at short distances from the pipe entrance. Eventually, the flow field reaches a periodic regime that depends only on the axial position. The results show that the transient flow field depends on the pipe oscillation pattern (initial position and/or direction of initial movement). Copyright © 2000 John Wiley & Sons, Ltd.     

Secondary flows and particle centrifugation in slightly tilted rotating pipes

A theoretical analysis is presented of viscous incompressible laminar flow in a pipe which rotates around an axis held at small angle with respect to its symmetry-axis. Analogous to the results of Barua and Benton [1, 2], solutions in closed-form are given for circulatory flows in the cross-sectional plane of the pipe due to Coriolis forces in combination with Hagen-Poiseuille flow through the pipe. The solutions are used to derive analytical expressions for trajectories of solid or liquid particles entrained in the gas and being subject to centrifugation and the said secondary flows. It is shown that despite centrifugation, particles can be locked into circulatory trajectories thus remaining suspended in the gas flowing through the pipe.     

Three-Dimensional Laser-Doppler Velocimeter Measurements in Swirling Turbulent Pipe Flow

The present work is an experimental study of the evolutioncharacteristics of swirl in the flow in a pipe at a moderately highReynolds number and over a wide range of swirl numbers characterisingthe swirl strength. The measurements are done by 3D LDV in a speciallydesigned facility that works on the principle of refractive-indexmatching. Swirl with the well-defined distribution of a constant angularvelocity is introduced into the test section of this facility by a swirlgenerating device in which a tube bundle in the pipe rotates about thepipe axis. The measurements have been processed to yield themean-velocity vector and the Reynolds stress tensor in this flow. Ananalysis of the measured evolution characteristics brings out a dominanteffect of swirl with a solid body rotation as the annihilation ofReynolds shear streses.     

Dynamical stability analysis of a hose to the sky

The Stratospheric Shield was proposed as a geoengineering concept to control the Earth's climate and reverse global warming. This approach seeks to release sulphur dioxide (SO₂) aerosols in the stratosphere to decrease the amount of sunlight that reaches the surface of the Earth. It was proposed that this can be done by pumping liquefied SO₂ from the ground to the stratosphere in a 30 km long hose supported by aerostats.In this paper we evaluate the dynamic stability of a hose to the sky considering distributed supportive aerostats and an atomiser nozzle that forces a radial discharge of the fluid at the free end of the pipe. We modelled the pipe as a taut string conveying fluid using the finite element method.With a nozzle that discharges the flow straight through, we found that the pipe loses stability by buckling when the tension becomes null at least at one location along its length. This instability can be avoided by having a sufficient minimum tension T₀ throughout the whole length of the pipe. The distribution of aerostats does not influence this instability but it modifies the mode shapes and affects the complex frequencies. The atomiser discharging the flow radially at the tip of the pipe has for effect to remove the possibility of an instability; its use is thus recommended. Moreover, we showed that the Coriolis damping can be significant and that by appropriately selecting the number of aerostats as well as the dimensionless flow velocity, stability can be increased. With this in mind, a functional hose to the sky could be designed to maximise Coriolis damping and thus passively damp the motion of the pipe due to forcing from the wind.     

The Effective Permeability of Cracks and Interfaces in Porous Media

The presence of interfaces in fluid/solid biphasic media is known to strongly influence their behavior both in terms of solid deformation and fluids flow. Mathematical models have traditionally represented these interfaces as lines of no-thickness and whose behavior is given in terms of effective permeabilities whose physical meaning is often disconnected to the microscopic nature of the interface. This article aims to reconcile macroscopic and microscopic interface representations by investigating how the nature of microscopic flows and pressures in the interface can be used to explain its macroscopic behavior. By invoking a proper thickness average operation, we derive an closed form expression that relates the effective interfaces permeabilities to its microscopic properties. In particular, we find that the effective interface permeabilities are strongly influenced by three factors: the ratio of bulk and interface permeabilities, the fluid viscosity, and the physical thickness of the interface.

     

WATER HAMMER PRESSURE OF HYDRAULIC LIFTING PIPELINE IN DEEP-SEA MINING PILOT SYSTEM

深海采矿系统可能由于突然停泵、断电或机械故障等引起提升管道中流体速度瞬间变化, 导致管道内压力剧烈变化, 这种水击现象对管道破坏极大. 基于固液两相流体连续性原理和动量定理, 推导出含粗颗粒的固液两相流体管道水击压力的计算公式. 采用深海采矿中试系统参数, 模拟计算不同水体流速、不同流体浓度以及不同管径条件下的水击压力. 分析结果表明, 流速、体积浓度和管径是影响水击压力的重要因素, 其中, 流速影响最大. 研究结果可为深海采矿系统工程设计提供依据.     

Non-planar responses of cantilevered pipes conveying fluid with intermediate motion constraints

In this paper, the nonlinear responses of a loosely constrained cantilevered pipe conveying fluid in the context of three-dimensional (3-D) dynamics are investigated. The pipe is allowed to oscillate in two perpendicular principal planes, and hence its 3-D motions are possible. Two types of motion constraints are considered. One type of constraints is the tube support plate (TSP) which comprises a plate with drilled holes for the pipe to pass through. A second type of constraints consists of two parallel bars (TPBs). The restraining force between the pipe and motion constraints is modeled by a smoothened-trilinear spring. In the theoretical analysis, the 3-D version of nonlinear equations is discretized via Galerkin’s method, and the resulting set of equations is solved using a fourth-order Runge–Kutta integration algorithm. The dynamical behaviors of the pipe system for varying flow velocities are presented in the form of bifurcation diagrams, time traces, power spectra diagrams and phase plots. Results show that both types of motion constraints have a significant influence on the dynamic responses of the cantilevered pipe. Compared to previous work dealing with the loosely constrained pipe with motions restricted to a plane, both planar and non-planar oscillations are explored in this 3-D version of pipe system. With increasing flow velocity, it is shown that both periodic and quasi-periodic motions can occur in the system of a cantilever with TPBs constraints. For a cantilevered pipe with TSP constraints, periodic, chaotic, quasi-periodic and sticking behaviors are detected. Of particular interest of this work is that quasi-periodic motions may be induced in the pipe system with either TPBs or TSP constraints, which have not been observed in the 2-D version of the same system. The results obtained in this work highlight the importance of consideration of the non-planar oscillations in cantilevered pipes subjected to loose constraints.     

Turbulent Flow and Dispersion of Inertial Particles in a Confined Jet Issued by a Long Cylindrical Pipe

In this work we examine first the flow field of a confined jet produced by a turbulent flow in a long cylindrical pipe issuing in an abrupt angle diffuser. Second, we examine the dispersion of inertial micro-particles entrained by the turbulent flow. Specifically, we examine how the particle dispersion field evolves in the multiscale flow generated by the interactions between the large-scale structures, which are geometry dependent, with the smaller turbulent scales issued by the pipe which are advected downstream. We use Large-Eddy-Simulation (LES) for the flow field and Lagrangian tracking for particle dispersion. The complex shape of the domain is modelled using the immersed-boundaries method. Fully developed turbulence inlet conditions are derived from an independent LES of a spatially periodic cylindrical pipe flow. The flow field is analyzed in terms of local velocity signals to determine spatial coherence and decay rate of the coherent K–H vortices and to make quantitative comparisons with experimental data on free jets. Particle dispersion is analyzed in terms of statistical quantities and also with reference to the dynamics of the coherent structures. Results show that the particle dynamics is initially dominated by the Kelvin–Helmholtz (K–H) rolls which form at the expansion and only eventually by the advected smaller turbulence scales.     

Debris flow modeling: A review

A debris flow represents a mixture of sediment particles of various sizes and water flowing down a confined, channel-shaped region (e.g., gully, ravine or valley) down to its end, at which point it becomes unconfined and spreads out into a fan-shaped mass. This review begins with a survey of the literature on the physical-mathematical modeling of debris flows. Next, we discuss the basic aspects of their phenomenology, such as dilatancy, internal friction, fluidization, and particle segregation. The basic characterization of a debris flow as a mixture motivates the application of the continuum thermodynamical theory of mixtures to formulate a model for a debris flow as a viscous fluid-granular solid mixture. A major advantage of such a formulation, which goes beyond the most general models in the literature, e.g., Takahashi (1991), is that it can be used to expose and better understand the assumptions underlying existing models, as well as to derive new, more sophisticated models. Finally, we delve into the issue of how such models have been or can be implemented numerically, as well as general boundary conditions for debris flows.Dedicated to Professor Reint de Boer upon the occasion of his 60^th birthday     

非牛顿流体固粒悬浮流的若干问题

非牛顿流体固粒悬浮流具有广泛的应用背景,其特殊的流动属性使其成为一些新兴技术领域的核心突破点.同时,该流动又比较复杂,即便是在低固粒浓度的情况下,非牛顿流体特性也会对整个系统的微结构产生重要的影响,从而进一步影响固粒的运动.本文给出了非牛顿流体方程、固粒运动方程和非牛顿流体固粒悬浮流的特征参数,分析了这些参数的作用;阐述了单个固粒在管道中的径向移动、多固粒的相互作用和聚集、多固粒形成的链状结构以及非圆球固粒运动等方面的研究成果、结果分析以及尚未解决的问题,并对以上问题进行了总结和展望,给出了需要深入研究的具体问题和内容,旨在为进一步的研究提供参考和依据.