Numerical modeling of downslope flows of different rheology

Naturally occurring flow along a long homogeneous slope is numerically simulated. It is taken into account that the flow is able to capture the slope material and to entrain it into motion. The flow depth and velocity increase with time at the expense of the capture. The medium in motion is simulated using different rheological models including those of Herschel & Bulkley and Cross, as well as the power-law fluid model. For all the models the time dependences of the total depth and the mean flow velocity are obtained. The slope inclination effect on the dynamic flow parameters is studied. For the Herschel–Bulkley model the yield strength effect is also investigated. On the basis of the numerical calculations some assumptions are made and then used to derive asymptotic formulas for the bottom material entrainment rate at large times from the entrainment onset for all the above-listed rheological models.     

On unsteady unidirectional flows of a second grade fluid

Some properties of unsteady unidirectional flows of a fluid of second grade are considered for flows produced by the sudden application of a constant pressure gradient or by the impulsive motion of one or two boundaries. Exact analytical solutions for these flows are obtained and the results are compared with those of a Newtonian fluid. It is found that the stress at the initial time on the stationary boundary for flows generated by the impulsive motion of a boundary is infinite for a Newtonian fluid and is finite for a second grade fluid. Furthermore, it is shown that initially the stress on the stationary boundary, for flows started from rest by sudden application of a constant pressure gradient is zero for a Newtonian fluid and is not zero for a fluid of second grade. The required time to attain the asymptotic value of a second grade fluid is longer than that for a Newtonian fluid. It should be mentioned that the expressions for the flow properties, such as velocity, obtained by the Laplace transform method are exactly the same as the ones obtained for the Couette and Poiseuille flows and those which are constructed by the Fourier method. The solution of the governing equation for flows such as the flow over a plane wall and the Couette flow is in a series form which is slowly convergent for small values of time. To overcome the difficulty in the calculation of the value of the velocity for small values of time, a practical method is given. The other property of unsteady flows of a second grade fluid is that the no-slip boundary condition is sufficient for unsteady flows, but it is not sufficient for steady flows so that an additional condition is needed. In order to discuss the properties of unsteady unidirectional flows of a second grade fluid, some illustrative examples are given.     

Investigation Of Turbulence at the Molecular Level

The influence of the molecular structure of gas flows on the characteristics of turbulent flows and the influence of the properties of molecules on turbulent processes have been studied. A review of the results of studies of turbulent processes is presented. Data on flows at the boundary of a supersonic jet and in a pipe with a divergent inlet section, and Hagen–Poiseuille flow are given. Experimental study of Hagen–Poiseuille flow has shown that the molecular properties of the medium have an effect on the critical Reynolds number. It is shown that in comparing the critical Reynolds numbers for flows of different gases at different pressures, the common determining parameter is the second virial coefficient.     

Rheology of a dilute suspension of axisymmetric Brownian particles

Explicit results are presented for the complete rheological properties of dilute suspensions of rigid, axisymmetric Brownian particles possessing fore-aft symmetry, when suspended in a Newtonian liquid subjected to a general three-dimensional shearing flow, either steady or unsteady. It is demonstrated that these rheological properties can be expressed in terms of five fundamental material constants (exclusive of the solvent viscosity), which depend only upon the sizes and shapes of the suspended particles. Expressions are presented for these scalar constants for a number of solids of revolution, including spheroids, dumbbells of arbitrary aspect ratio and long slender bodies. These are employed to calculate rheological properties for a variety of different shear flows, including uniaxial and biaxial extensional flows, simple shear flows, and general two-dimensional shear flows. It is demonstrated that the rheological properties appropriate to a general two-dimensional shear flow can be deduced immediately from those for a simple shear flow. This observation greatly extends the utility of much of the prior Couette flow literature, especially the extensive numerical calculations of Scheraga et al. (1951, 1955).The commonality of many disparate results dispersed and diffused in earlier publications is emphasized, and presented from a unified hydrodynamic viewpoint.     

Migration of a solid particle in the vicinity of a plane fluid–fluid interface

The slow migration of a small and solid particle in the vicinity of a gas–liquid, fluid–fluid or solid–fluid plane boundary when subject to a gravity or an external flow field is addressed. By contrast with previous works, the advocated approach holds for arbitrarily shaped particles and arbitrary external Stokes flow fields complying with the conditions on the boundary. It appeals to a few theoretically established and numerically solved boundary-integral equations on the particle’s surface. This integral formulation of the problem allows us to provide asymptotic approximations for a distant boundary and also, implementing a boundary element technique, accurate numerical results for arbitrary locations of the boundary. The results obtained for spheroids, both settling or immersed in external pure shear and straining flows, reveal that the rigid-body motion experienced by a particle deeply depends upon its shape and also upon the boundary location and properties.     

Motion of a spherical particle under the influence of osmotic forces

One of the basic mechanisms through which biological cells preserve the consistency of their structure is the regulation of material exchange between cell and surrounding medium. The regulation is performed by a thin semipermeable membrane surrounding the cell; it passes some materials freely, while allowing only slight transmission of others, or completely blocking passage. Water shows the maximum penetrating power. If there exists on both sides of the membrane an aqueous solution of some material which does not penetrate the membrane, then under the influence of osmotic pressure water flows into that region where the material concentration is higher, as long as the difference in hydrostatic pressure does not suppress the motion [1, 2]. The viscous flow which develops may lead to displacement of a particle.     

One class of self-similar flows of a radiating gas

This article discusses self-similar statements of the problem of the motion of a completely radiating and absorbing gas. The field of radiation is assumed to be quasi-steady-state, and the contribution of the radiation to the internal energy, as well as the pressure and the viscosity of the medium, are not taken into account. The presence of local thermodynamic equilibrium is assumed. The absorption coefficient is approximated by a power function of the pressure and the density. Scattering of the radiation is not taken into account. Under these assumptions, there exist self-similar statements of the problem for one-dimensional unsteady-state flows (a strong detonation, the problem of plug-flow, motion under the effect of a radiation source, and others) and two-dimensional steady-state flows (flow in a diffuser, supersonic flow around a wedge or a cone). It is shown that there exists a non steady-state spherically symmetrical flow depending on four parameters; this flow is adiabatic in spite of the presence of radiation. This article is made up of seven sections. It is shown in the first section that the presence of radiation leads to the appearance of new dimensional constants, entering into the equations of the problem. The second section is devoted to self-similar nonsteady-state one-dimensional flows. The third section contains a detailed study of one class of such flows. In a partial case, adiabatic flows of a radiating gas are obtained. In the fourth and fifth sections, a detailed analysis is made of the initial and boundary conditions from the point of view of dimensionality. The sixth section describes self-similar two-dimensional steady-state flows of a radiating-absorbing gas. The seventh section consists of remarks with respect to approximations of the transfer equation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 8–22, July–August, 1970.     

Numerical simulations of non-stationary flows of non-Newtonian fluids between concentric and eccentric cylinders by stream-tube method and domain decomposition

This study involves a theoretical formulation of the stream-tube method in non-stationary flows. Initially, this approach allowed flow computations by determining an unknown transformation between the physical domain and a mapped domain where the streamlines are rectilinear and parallel. To take into account vortex zones, we define local transformations of subregions of the physical domain that are mapped into rectangular domains where the transformed streamlines are still parallel and straight. The local functions must be determined numerically from the governing equations and boundary conditions put together with compatibility equations. The method enables to compute streamlines and flow data at every time, using distinguishing properties, as verification of mass conservation and definition of rectangular meshes allowing to adopt finite-difference schemes. The numerical simulations concern different non-Newtonian fluids under various geometrical and kinematic specifications related to flows between concentric and eccentric cylinders, leading to comparisons with literature data. The results also highlight the influence of the rheological properties on the flow characteristics in unsteady conditions.     

Stable Propagation of Saturation Overshoots for Two-Phase Flow in Porous Media

Propagation of saturation overshoots for two-phase flow of immiscible and incompressible fluids in porous media is analyzed using different computational methods. In particular, it is investigated under which conditions a given saturation overshoot remains stable while moving through a porous medium. Two standard formulations are employed in this investigation, a fractional flow formulation and a pressure–saturation formulation. Neumann boundary conditions for pressure are shown to emulate flux boundary conditions in homogeneous media. Gravity driven flows with Dirichlet boundary conditions for pressure that model infiltration into heterogeneous media with position-dependent permeability are found to exhibit pronounced saturation overshoots very similar to those seen in experiment.     

The Permeability of a Representative Carbonate Volume with a Large Vug

There are fundamental challenges in characterizing transport properties of a porous medium with large cavities, or vugs, when the characteristic size of the cavity is larger than or equal to 1 cm. Neither existing flow models nor common laboratory measurements are well suited to deal with such challenges. The present study determines the effective permeability of a representative carbonate volume with an arbitrary connected-through large vug. It also determines the minimum matrix permeability that impacts the flow in vuggy carbonates. The Stokes and Darcy models are used to capture the flows in the vug and in the matrix, respectively. At the interface, the flow models interact through slippage based on the Beavers–Joseph–Saffman model. The developed model is tested with analytical solutions available in the literature and using independent laboratory measurements. The results have major implications for characterizing the effective transport properties of carbonates, which constitute more than half of the world’s hydrocarbon reserves.     

Behavior of viscoelastic glass bead suspensions under superposed flows

Parallel superposed flows may be useful in order to explain the rheological behavior of viscoelastic suspensions. It has been shown that relaxation times of molecules are affected by a combined flow, and the rheological behavior of glass bead suspensions in a viscoelastic medium is explaned in terms of such variations.     

非对称槽道中涡旋波的特性研究

利用PIV流场显示技术，对振荡流体在非对称槽道中涡旋波的产生、发展和消失的规律进 行了实验研究和分析，测得了涡旋波流场的速度矢量图，阐明了涡旋波流场周期性变化的特 点. 结合涡动力学方程，深入分析并揭示了做周期性运动的流体能在槽道中产生波的特性这 一规律，从中发现：流体周期变化的非定常性和不对称的槽道结构是形成涡旋波流动的主要 因素. 本文对涡旋波流场中各个旋涡的速度分布和涡量进行了测量和计算，分析了涡旋波 强化传质的机理，并研究了Re数对涡旋波流动的影响     

Some uses of Green's theorem in solving the Navier–Stokes equations

This paper gives a review of methods where Green's theorem may be employed in solving numerically the Navier–Stokes equations for incompressible fluid motion. They are based on the concept of using the theorem to transform local boundary conditions given on the boundary of a closed region in the solution domain into global, or integral, conditions taken over it. Two formulations of the Navier–Stokes equations are considered: that in terms of the streamfunction and vorticity for two-dimensional motion and that in terms of the primitive variables of the velocity components and the pressure. In the first formulation overspecification of conditions for the streamfunction is utilized to obtain conditions of integral type for the vorticity and in the second formulation integral conditions for the pressure are found. Some illustrations of the principle of the method are given in one space dimension, including some derived from two-dimensional flows using the series truncation method. In particular, an illustration is given of the calculation of surface vorticity for two-dimensional flow normal to a flat plate. An account is also given of the implementation of these methods for general two-dimensional flows in both of the mentioned formulations and a numerical illustration is given.     

Flow and blockage of highly concentrated granular suspensions in non-Newtonian fluid

Studying the flow of highly concentrated granular suspensions represents a great challenge since they are characterized by a rather complex rheological behavior. In addition, macroscopic heterogeneities may be induced by the flow during rheological measurements due to the eventual relative motion between the liquid and the granular phases that may take place under certain conditions. Solid–liquid separation may ultimately lead to flow blockage. In the present investigation we consider experimentally the influence of the rheological properties of the suspending fluid on the transition between the flow and blockage of a concentrated suspension in a squeeze set-up geometry. The suspending fluid consists of an aqueous Xanthan solution for which rheological properties can be tuned by changing the polymer concentration. For each polymer concentration, it is shown that there exist flow parameters (squeeze velocity and gap thickness) for which one has a transition between homogeneous flow of the suspension and its blockage. Blockage diagrams, delimiting flowability and blockage zones, are then determined. Physical arguments are given to relate the evolution of the blockage diagrams to the flow parameters and rheological properties of suspending fluid.     

非等温黏弹性复杂流动的改进SPH方法模拟

非等温黏弹性流体广泛存在于自然界和工业生产中,准确预测黏弹性流体的非等温流动机理和复杂流变特性有着重要的应用价值.文章提出一种改进的光滑粒子流体动力学(smoothed particle hydrodynamics,SPH)方法对非等温黏弹性复杂流动进行了数值模拟,其中流体的黏弹特性通过eXtended Pom-Pom本构模型来表征.为了提高模拟结果的精度,采用了一种核函数梯度的修正算法;为了灵活地施加边界条件,发展了边界粒子和虚拟粒子相联合的边界处理方法;为了消除流动过程中的拉伸不稳定性,施加了粒子迁移技术.运用改进SPH方法数值模拟了液滴撞击固壁和F型腔注塑成型问题,通过与Basilisk软件得到的结果进行比较验证了改进SPH方法求解非等温黏弹性流体的有效性.通过利用不同粒子初始间距进行计算,评价了改进SPH方法的数值收敛性.研究了非等温流动相较于等温流动的不同流动特征,深入分析了不同热流变参数对流动过程的影响.数值结果表明,文章提出的改进SPH方法可稳定、准确地描述非等温黏弹性复杂流动的传热机理、复杂流变特性和自由面变化特性.     

Heat transfer in channels in the laminar flow of a non-newtonian liquid with slip

We consider the case of quasi-isothermal heat transfer in the laminar flow of a non-Newtonian medium with slip in circular and plane channels. The calculation is based on the simultaneous solution of the equations of energy, motion, and a rheological relation with the specific boundary conditions which takes into account discontinuity in the velocity and temperature on the heat-transfer surface.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 146–151, September–October, 1971.     

An SPH model for free surface flows with moving rigid objects

This paper presents a computational model for free surface flows interacting with moving rigid bodies. The model is based on the SPH method, which is a popular meshfree, Lagrangian particle method and can naturally treat large flow deformation and moving features without any interface/surface capture or tracking algorithm. Fluid particles are used to model the free surface flows which are governed by Navier–Stokes equations, and solid particles are used to model the dynamic movement (translation and rotation) of moving rigid objects. The interaction of the neighboring fluid and solid particles renders the fluid–solid interaction and the non‐slip solid boundary conditions. The SPH method is improved with corrections on the SPH kernel and kernel gradients, enhancement of solid boundary condition, and implementation of Reynolds‐averaged Navier–Stokes turbulence model. Three numerical examples including the water exit of a cylinder, the sinking of a submerged cylinder and the complicated motion of an elliptical cylinder near free surface are provided. The obtained numerical results show good agreement with results from other sources and clearly demonstrate the effectiveness of the presented meshfree particle model in modeling free surface flows with moving objects. Copyright © 2013 John Wiley & Sons, Ltd.     

Hydrodynamic formation of stable anisotropic structures in Couette flow of dilute suspensionFormation hydrodynamique pour structures anisotropiques stables dans un flux de Couette d'une suspension diluée

The problem of rotary motion of rigid axially symmetric elongated particles in the Couette flow of dilute suspension with anisotropic carrier fluid is solved. It is shown that the stable stationary solutions of the dynamical set of ordinary differential equations describing the particles rotary motion are possible in the case of forming the stationary anisotropy in the carrier fluid of the suspension. It allows us to detect the stationary orientation of suspended particles and formation of stable anisotropic liquid-crystalline structures in the considered suspension under the action of hydrodynamic forces. The study of rheological properties of such a structured suspension shows that it behaves as a viscoelastic quasi-Newtonian anisotropic liquid medium. To cite this article: E.Yu. Taran et al., C. R. Mecanique 332 (2004).