Statistics of contact force network in dense granular matter

We investigate the distribution of contact forces in a static granular system and in annular shear granular flow, using the discrete element method, and considering the influences of both packing fraction and friction coefficient. We find the existence of a critical packing fraction. If the packing fraction is lower than this critical value, all contact forces in granular system vanish. For shear granular flow, the critical packing fraction is significantly smaller than that for static granular system. The ...     

Automatic extraction method of force chain information and its application in the flow photoelastic experiment of granular matter

The force chain is the core of the multi-scale analysis of granular matter. Accurately extracting the force chain information among particles is of great significance to the study of particle mechanics and geological hazards caused by particle flow. However, in the photoelastic experiment, the precise identification of the branching points of force chains has not been effectively realized. Therefore, this study proposes an automatic extraction method of force chain key information. First, based on the Hough transform and the Euclidean distance, a particle geometric information identification model is established and geometric information such as particle circle center coordinates, radius, contact point location, and contact angle is extracted. Then, a particle contact force information identification model is established following the color gradient mean square method. The model realizes the rapid calibration and extraction of a large number of particle media contact force information. Next, combined with the force chain composition criterion and its quasilinear feature, an automatic extraction method of force chain information is established, which solves the problem of the accurate identification of the force chain branch points. Finally, in the photoelastic experiment of ore drawing from a single drawpoint, the automatic extraction method of force chain information is verified. The results show that the macroscopic distribution of force chains during ore drawing from a single drawpoint is left–right symmetrical. Strong force chains are mostly located on the two sides of the model but in small numbers and they mainly develop vertically. Additionally, the ends are mostly in a combination of Y and inverted Y shapes, while the middle is mostly quasilinear. Weak force chains are abundant and mostly distributed in the middle of the model, and develop in different directions. The proposed extraction method accurately extracts the force chain network from the photoelastic experiment images and dynamically characterizes the force chains of granular matter, which has significant advantages in particle geometry information extraction, force chain branch point discrimination, force chain retrieval, and force chain distribution and its azimuthal characterization. The results provide a scientific basis for studying the macroscopic and microscopic mechanical parameters of granular matter.     

Lagrangian velocity and acceleration statistics of fluid and inertial particles measured in pipe flow with 3D particle tracking velocimetry

Three-dimensional particle tracking velocimetry (3D-PTV) has been applied to particle-laden pipe flow at Reynolds number 10,300, based on the bulk velocity and the pipe diameter. The volume fraction of the inertial particles was equal to 1.4 × 10⁻⁵. Lagrangian velocity and acceleration statistics were determined both for tracers and for inertial particles with Stokes number equal to 2.3, based on the particle relaxation time and the viscous time scale. The decay of Lagrangian velocity and acceleration correlation functions was measured both for the fluid and for the dispersed phase at various radial positions. The decay of Lagrangian velocity correlations is faster for inertial particles than for flow tracers, whereas the decay of Lagrangian acceleration correlations is about 25% slower for inertial particles than for flow tracers. Further differences between inertial and tracer particles are found in velocity fluctuations evaluated for both positive and negative time lags. The asymmetry in time of velocity cross-correlations is more pronounced for inertial particles. Quadrant analysis revealed another difference still near the wall: ejection and sweep events are less frequent for inertial particles than for tracers.     

Flow of a mixture of a viscous fluid and a granular solid in an orthogonal rheometer

In this paper, we study the flow of a linearly viscous fluid and a granular solid, consisting of many particles, situated between two parallel plates rotating about different axes. Flow in orthogonal rheometers has been studied for many viscoelastic fluids so that their rheological properties can be measured. The mixture is modeled using the theory of interacting continua, and constitutive relations for the fluid phase, the granular phase, and the interaction forces are provided. For a very special case, an analytical solution to the equations of motion is also provided.     

Mean flow characteristics of a 3D turbulent wall jet over an isothermal and an insulating flat surface

An experimental study was carried out on the mean aerodynamic and heat-exchange characteristics of a weaklyheated air jet flowing over an isothermal and an insulating flat surface. The jet issued from a contracting profiled rectangular nozzle (39×22 m² outlet) at 30 m/sec velocity (Re _d =~5.5×10⁴) and incidence angle α₀, π/12, π/6, π/4. It was established that as α₀ increases, so do the decay rates of the axial velocity and temperature along the jet axis as well as the jet width, while the jet thickness decreases. Parallel examination of an in sulating and an isothermal surface permitted separation of the heat-exchange process between the jet and the surrounding medium, from that between the jet and the wall surface-with the conclusion tha tin the isothermal case, the exchange with the surface intensifies as α₀ increases.     

3D full-loop simulation and experimental verification of gas-solid flow hydrodynamics in a dense circulating fluidized bed

Because of their advantages of high efficiency and low cost, numerical research methods for large-scale circulating fluidized bed （CFB） apparatus are gaining ever more importance. This article presents a numer- ical study of gas-solid flow dynamics using the Eulerian granular multiphase model with a drag coefficient correction based on the energy-minimization multi-scale （EMMS） model. A three-dimensional, full-loop, time-dependent simulation of the hydrodynamics of a dense CFB apparatus is performed. The process parameters （e.g., operating and initial conditions） are provided in accordance with the real experiment to enhance the accuracy of the simulation. The axial profiles of the averaged solid volume fractions and the solids flux at the outlet of the cyclone are in reasonable agreement with experimental data, thereby verifying the applicability of the mathematical and physical models. As a result, the streamline in the riser and standpipe as well as the solids distribution contours at the cross sections is analyzed. Computational fluid dynamics （CFD） serves as a basis for CFB modeling to help resolve certain issues long in dispute but difficult to address experimentally. The results of this study provide the basis of a general approach to describing dynamic simulations of gas-solid flows.     

Driving forces and kinking of an oblique crack in bonded nonhomogeneous materials

Summary  Plane elasticity solutions are presented for the problem of an oblique crack in two bonded media. The material model under consideration consists of a homogeneous half-plane with an arbitrarily oriented crack and a nonhomogeneous half-plane. The Fourier integral transform method is employed in conjunction with the coordinate transformations of field variables in the basic elasticity equations. Formulation of the crack problem results in having to solve a system of singular integral equations for arbitrary crack surface tractions. A crack perpendicular to or along the bonded interface between the homogeneous and nonhomogeneous constituents arises as a limiting case. In the numerical results, the values of mixed-mode stress intensity factors are provided for various combinations of relevant geometric and material parameters of the bonded media. Subsequently, the infinitesimal kinks from the tips of a main crack are presumed, with the corresponding local driving forces being evaluated in terms of the stress intensities of the main crack. The criterion of maximum energy release rate is applied with the aim of making some conjectures concerning the likelihood of kinking and the probable kink direction based on the approximation of local homogeneity and brittleness of the crack-tip behavior. Received 25 September 2001; accepted for publication 13 February 2002     

Numerical simulation of cavitating flow in 2D and 3D inducer geometries

A computational method is proposed to simulate 3D unsteady cavitating flows in spatial turbopump inducers. It is based on the code FineTurbo, adapted to take into account two‐phase flow phenomena. The initial model is a time‐marching algorithm devoted to compressible flow, associated with a low‐speed preconditioner to treat low Mach number flows. The presented work covers the 3D implementation of a physical model developed in LEGI for several years to simulate 2D unsteady cavitating flows. It is based on a barotropic state law that relates the fluid density to the pressure variations. A modification of the preconditioner is proposed to treat efficiently as well highly compressible two‐phase flow areas as weakly compressible single‐phase flow conditions. The numerical model is applied to time‐accurate simulations of cavitating flow in spatial turbopump inducers. The first geometry is a 2D Venturi type section designed to simulate an inducer blade suction side. Results obtained with this simple test case, including the study of its general cavitating behaviour, numerical tests, and precise comparisons with previous experimental measurements inside the cavity, lead to a satisfactory validation of the model. A complete three‐dimensional rotating inducer geometry is then considered, and its quasi‐static behaviour in cavitating conditions is investigated. Numerical results are compared to experimental measurements and visualizations, and a promising agreement is obtained. Copyright © 2004 John Wiley & Sons, Ltd.     

A numerical study of an unsteady laminar flow in a doubly constricted 3D vessel

Unsteady flow dynamics in doubly constricted 3D vessels have been investigated under pulsatile flow conditions for a full cycle of period T. The coupled non‐linear partial differential equations governing the mass and momentum of a viscous incompressible fluid has been numerically analyzed by a time accurate Finite Volume Scheme in an implicit Euler time marching setting. Roe's flux difference splitting of non‐linear terms and the pseudo‐compressibility technique employed in the current numerical scheme makes it robust both in space and time. Computational experiments are carried out to assess the influence of Reynolds' number and the spacing between two mild constrictions on the pressure drop across the constrictions. The study reveals that the pressure drop across a series of mild constrictions can get physiologically critical and is also found to be sensitive both to the spacing between the constrictions and the oscillatory nature of the inflow profile. The flow separation zone on the downstream constriction is seen to detach from the diverging wall of the constriction leading to vortex shedding with 3D features earlier than that on the wall in the spacing between the two constrictions. Copyright © 2002 John Wiley & Sons, Ltd.     

Experiments and simulations of gas-solid flow in an airlift loop reactor

The hydrodynamics in a gas-solid airlift loop reactor was investigated systematically using experimental measurements and CFD simulation.In the experiments,the time averaged parameters,such as solid fraction and particle velocity,were measured by optical fiber probe.In the simulation,the modified Gidaspow drag model accounting for the interparticles clustering was incorporated into the Eulerian-Eulerian CFD model with particulate-phase kinetic theory.Predicted values of solid fraction and particle velocity ...     

Bubble and liquid turbulence characteristics of bubbly flow in a large diameter vertical pipe

The bubble and liquid turbulence characteristics of air–water bubbly flow in a 200 mm diameter vertical pipe was experimentally investigated. The bubble characteristics were measured using a dual optical probe, while the liquid-phase turbulence was measured using hot-film anemometry. Measurements were performed at six liquid superficial velocities in the range of 0.2–0.68 m/s and gas superficial velocity from 0.005 to 0.18 m/s, corresponding to an area average void fraction from 1.2% to 15.4%. At low void fraction flow, the radial void fraction distribution showed a wall peak which changed to a core peak profile as the void fraction was increased. The liquid average velocity and the turbulence intensities were less uniform in the core region of the pipe as the void fraction profile changed from a wall to a core peak. In general, there is an increase in the turbulence intensities when the bubbles are introduced into the flow. However, a turbulence suppression was observed close to the wall at high liquid superficial velocities for low void fractions up to about 1.6%. The net radial interfacial force on the bubbles was estimated from the momentum equations using the measured profiles. The radial migration of the bubbles in the core region of the pipe, which determines the shape of the void profile, was related to the balance between the turbulent dispersion and the lift forces. The ratio between these forces was characterized by a dimensionless group that includes the area averaged Eötvös number, slip ratio, and the ratio between the apparent added kinetic energy to the actual kinetic energy of the liquid. A non-dimensional map based on this dimensionless group and the force ratio is proposed to distinguish the conditions under which a wall or core peak void profile occurs in bubbly flows.     

Analytic calculation of the stresses in an ensiled granular mediumCalcul analytique des contraintes dans un matériau granulaire ensilé

We present in this Note a new analytic approach, of continuous medium type, which improves the Janssen theory and enables us to calculate the stresses in an ensiled granular medium. This approach is based on the two dimensional equilibrium equations, coupled with the Mohr–Coulomb criterion and a slip condition at the walls of the silo. An analytic resolution is developed to compute the stresses for cohesive and non cohesive materials in the whole silo. To cite this article: O. Millet et al., C. R. Mecanique 334 (2006).     

Numerical observations of turbulence structure modification in channel flow over 2D and 3D rough walls

The effects of wall roughness on turbulence structure modifications were explored by numerical experiments, carried out using Large Eddy Simulation techniques. The wall geometry was made using an archetypal artificial method, thus to achieve irregular two- and three-dimensional shapes. The proposed roughness shapes are highly irregular and are characterised by high and small peaks, thus it can be considered a practical realistic roughness. Their effects are analysed comparing the turbulence quantities over smooth, 2D and 3D rough walls of fully developed channel flow at relatively low friction Reynolds number ${\mathit{Re}}_{\tau }=395$. Both transitional and fully rough regimes have been investigated. The two rough surfaces were built in such a way that the same mean roughness height and averaged mean deviation is obtained. Despite of this, very different quantitative and qualitative results are generated. The analysis of the mean quantitative statistics and turbulence fluctuations shows that deviations are mainly concentrated in the inner layer. These results support the Townsend’s similarity hypothesis. Among the geometrical parameters, which characterise the wall geometries, roughness slope correlates well with the roughness function $\mathrm{\Delta }{U}^{+}$. Specifically, a logarithmic law is proposed to predict the downward shift of the velocity profile for the transitional regime. Instantaneous view of turbulent organised structures display differences in small-scale structures. The flow field over rough surfaces is populated with coherent structures shorter than those observed over flat planes. The comparative analysis of both streaks and wall-normal vortical structures shows that 2D and 3D irregularities have quite different effects. The results highlight that 3D rough wall are representative of a more realistic surface compared to idealised 2D roughness.     

Shape optimisation of an oscillating body in fluid flow by adjoint equation and ALE finite element methods

The purpose of this paper is to determine the shape of an oscillating body by minimising drag and lift forces, located in a transient incompressible viscous fluid flow by means of the Arbitrary Lagrangian Eulerian finite element method and an optimal control theory. A performance function is expressed by the drag and lift forces. The performance function should be minimised satisfying the state equation and the constant volume condition. Therefore, this problem can be transformed into a minimisation problem without constraint by the Lagrange multiplier method. The adjoint equation and the gradient of the performance function are used to update the shape of the body. In this study, as a minimisation technique, the weighted gradient method is applied. The final shape is obtained of which drag and lift forces are reduced by 66.2% and 92.8%, respectively. The final shape obtained by this study is compared with the final shape of the non-oscillating body. The obtained final shape of the oscillating body is significantly different from the non-oscillating body.     

A numerical solution of 3D inviscid rotational flow in turbines and ducts

The numerical solutions of inviscid rotational (Euler) flows were obtained using an explicit hexahedral unstructured cell vertex finite volume method. A second-order-accurate, one-step Lax–Wendroff scheme was used to solve the unsteady governing equations discretized in conservative form. The transonic circular bump, in which the location and the strength of the captured shock are well predicted, was used as the first test case. The nozzle guide vanes of the VKI low-speed turbine facility were used to validate the Euler code in highly 3D environment. Despite the high turning and the secondary flows which develop, close agreements have been obtained with experimental and numerical results associated with these test cases. © 1998 John Wiley & Sons, Ltd.     

Elastic fields of 2D and 3D misfit particles in an infinite medium

In micromechanics, accurate quantification of the elastic field (stress, strain, and displacement) caused by the presence of an inclusion in an infinite body is desired for both the particle and matrix materials. Ideally, the solution should be applicable to any particle geometry or shape and for any distribution of misfit along the interface (i.e. misfit profile). This work presents a dislocation-based numerical method, that is an extension to earlier work in this journal [Lerma, J.D., Khraishi, T., Shen, Y.L., Wirth, B.D., 2003. The elastic fields of misfit cylindrical particles: a dislocation-based numerical approach. Mech. Res. Commun. 30, 325–334], for determining the elastic fields of volume misfit particles with arbitrary misfit distribution or particle shape.     

An experimental study of drag on a single tube and on a tube in an array under two-phase cross flow

In this work, the drag coefficient and the void fraction around a tube subjected to two-phase cross flow were studied for a single tube and for a tube placed in an array. The drag coefficients were determined by measuring the pressure distribution around the perimeter of the tube. Single tube drag data were taken when the tube was held both rigidly and flexibly. The test tube was made of acrylic and was 2.2 cm in diameter and 20 cm in length. In the experiments, liquid Reynolds number ranged from 430 to 21,900 for the single tube and liquid gap Reynolds number ranged from 32,900 and 61,600 for the tube placed in a triangular array. Free stream void fraction was varied from 0 to 0.4. At low Reynolds numbers, the ratio of two-phase to single-phase drag coefficient is found to be a strong function of εGr/Re2. However, at high Reynolds numbers only void fraction is the important parameter. Empirical correlations have been developed for the ratio of two-phase drag on a single tube and on a tube placed in an array.     

Simulation and measurement of 3D shear-driven thin liquid film flow in a duct

Three-dimensional flow behavior of thin liquid film that is shear-driven by turbulent air flow in a duct is measured and simulated. Its film thickness and width are reported as a function of air velocity, liquid flow rate, surface tension coefficient, and wall contact angle. The numerical component of this study is aimed at exploring and assessing the suitability of utilizing the FLUENT-CFD code and its existing components, i.e. Volume of Fluid model (VOF) along with selected turbulence model, for simulating the behavior of 3D shear-driven liquid film flow, through a comparison with measured results. The thickness and width of the shear-driven liquid film are measured using an interferometric technique that makes use of the phase shift between the reflections of incident light from the top and bottom surfaces of the thin liquid film. Such measurements are quite challenging due to the dynamic interfacial instabilities that develop in this flow. The results reveal that higher air flow velocity decreases the liquid film thickness but increases its width, while higher liquid flow rate increases both its thickness and width. Simulated results provide good estimates of the measured values, and reveal the need for considering a dynamic rather than a static wall contact angle in the model for improving the comparison with measured values.