Smoothed particle hydrodynamics for coarse-grained modeling of rapid granular flow

We simulated rapid flow in transient plane Couette flows of granular particles using the smoothed particle hydrodynamics(SPH) solutions of a set of continuum equations.This simulation was performed to test the viability of SPH in solving the equations for the solid phase of the two-fluid model associated with fluidization.We found that SPH requires the handling of fewer particles in simulating the collective behavior of rapid granular flow,thereby bolstering expectations of solving the equations for the solid phase in the two-fluid modeling of fluidization.Further work is needed to investigate the effect of terms describing pressure and viscous stress of solids on stability in simulations.     

Smoothed particle hydrodynamics formulation for penetrating impacts on ballistic gelatine

A particle method is applied to the investigation of impact biomechanics in the case of penetrating ballistic. A three dimensional model is proposed using the Smoothed Particle Hydrodynamics (SPH) method combined with Finite Elements (FE) method. The problem consists in the violent impact of a steel sphere on soft tissues, simulated by 20% ballistic gelatine (BG) material which is considered as a very interesting human tissue surrogate. Comparisons with experimental data are established to validate the proposed model. The results, in terms of penetrating curves, show very promising results. The use of particle methods appears to be an interesting way to model high speed loading, especially penetrating ballistic impact whose classical FE modelling can bring some important limitations in terms of mesh and element distortions.     

Incompressible smoothed particle hydrodynamics simulation of multifluid flows

This paper presents an incompressible SPH (ISPH) technique to simulate multifluid flows. The SPH method is a mesh‐free particle modeling approach that can treat free surfaces and multi‐interfaces in a simple and efficient manner. The ISPH method employs an incompressible hydrodynamic formulation to solve the fluid pressure that ensures a stable pressure field. Two multifluid ISPH models are proposed following different interface treatments: the coupled ISPH model does not distinguish the different fluid phases and applies the standard ISPH technique across the interface, whereas the decoupled ISPH model first treats each fluid phase separately and then couples the different phases by applying pressure and shear stress continuities across the interface. The two proposed models were used to investigate a gravity underflow with a low density ratio in a Generalized Reservoir Hydrodynamics (GRH) flume and a horizontal lock exchange flow with a high density ratio. Comparisons with data and relevant numerical error analysis indicated that the decoupled model performed well in cases of both low and high density ratios because of the accurate treatment of interface boundaries. Copyright © 2011 John Wiley & Sons, Ltd.     

Transient non-Newtonian flow of a suspension with a compressible particle phase

Equations governing transient two-phase fluid-particle laminar flow over an infinite porous flat plate are developed. Both phases are assumed to behave as non-Newtonian power-law fluids. The mathematical model accounts for particle-phase viscous and diffusive effects. The particles are assumed spherical in shape and having a non-uniform density distribution. The resulting governing equations are nondimensionalized and solved numerically subject to appropriate initial and boundary conditions using an iterative, implicit, tri-diagonal finite-difference method. Graphical results for the displacement thicknesses and the skin-friction coefficients for both the fluid and particle phases are presented and discussed to illustrate special trends of the solutions.     

Numerical simulation of landslide impulsive waves by incompressible smoothed particle hydrodynamics

An incompressible‐smoothed particle hydrodynamics (I‐SPH) formulation is presented to simulate impulsive waves generated by landslides. The governing equations, Navier–Stokes equations, are solved in a Lagrangian form using a two‐step fractional method. Landslides in this paper are simulated by a submerged mass sliding along an inclined plane. During sliding, both rigid and deformable landslides mass are considered. The present numerical method is examined for a rigid wedge sliding into water along an inclined plane. In addition solitary wave generated by a heavy box falling inside water, known as Scott Russell wave generator, which is an example for simulating falling rock avalanche into artificial and natural reservoirs, is simulated and compared with experimental results. The numerical model is also validated for gravel mass sliding along an inclined plane. The sliding mass approximately behaves like a non‐Newtonian fluid. A rheological model, implemented as a combination of the Bingham and the general Cross models, is utilized for simulation of the landslide behaviour. In order to match the experimental data with the computed wave profiles generated by deformable landslides, parameters of the rheological model are adjusted and the numerical model results effectively match the experimental results. The results prove the efficiency and applicability of the I‐SPH method for simulation of these kinds of complex free surface problems. Copyright © 2007 John Wiley & Sons, Ltd.     

Variational principles in hydrodynamics of a non-Newtonian fluid

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Numerical simulation of fluid–particle hydrodynamics in a rectangular spouted vessel

A three-dimensional, Eulerian simulation was developed to describe isothermal, two-phase flow of the continuous (water) and dispersed (solid particles) phases in a rectangular spouted vessel. The mass and momentum conservation equations for each phase were solved using the finite volume technique, which treats each phase separately, while coupling them through drag, turbulence, and energy dissipation due to particle fluctuations. Particle–particle interactions via friction were also included.     

Smoothed particle hydrodynamics techniques for the solution of kinetic theory problems: Part 2. The effect of flow perturbations on the simple shear behavior of LCPs

The effect of slight perturbations to simple shear flow of liquid-crystalline polymers (LCPs) is explored by using the SPH technique to solve the unapproximated orientation distribution function equation arising from the Doi Theory. First, the case of simple shear flow is outlined, and it is shown that skewed distributions play an important role in the transition from periodic to steady behavior as the shear rate is increased. Next, we consider perturbations to flows that are slightly more extensional than simple shear, parametrized by the flow type parameter α. They are shown to eliminate all periodic director behavior (tumbling and wagging), even when the relative increment in flow type is small. At lower shear rates (or more properly, lower Peclet number Pe based upon the rotational diffusivity), the elimination occurs through a homoclinic bifurcation, the transition being rather abrupt as the flow type is changed. At higher Pe, periodic behavior is suppressed more gradually through a Hopf bifurcation, with tumbling being replaced by wagging and negative θ flow-aligning, where θ is the angle of the director in the shear plane. The effect of these perturbations on rheological behavior is also explored. As the flow is made slightly more extensional, the zero-shear rate limiting value of the generalized viscosity η decreases dramatically, due to the slowing down of tumbling as the system approaches a homoclinic orbit; as Pe is increased, the viscosity rises again before falling, due to the induction of wagging behavior where tumbling would normally prevail in simple shear. Finally, it is found when the flow type is changed sufficiently, the interesting, non-monotonic behavior of rheological functions seen in simple shear of LCPs is replaced by monotonic behavior, even though the flow is still relatively close to simple shear.     

Numerical simulation of pulsatile non-Newtonian flow in the carotid artery bifurcation

Both clinical and post mortem studies indicate that, in humans, the carotid sinus of the carotid artery bifurcation is one of the favored sites for the genesis and development of atherosclerotic lesions. Hemodynamic factors have been suggested to be important in atherogenesis. To understand the correlation between atherogenesis and fluid dynamics in the carotid sinus, the blood flow in artery was simulated numerically. In those studies, the property of blood was treated as an incompressible, Newtonian fluid. In fact, however, the blood is a complicated non-Newtonian fluid with shear thinning and viscoelastic properties, especially when the shear rate is low. A variety of non-Newtonian models have been applied in the numerical studies. Among them, the Casson equation was widely used. However, the Casson equation agrees well only when the shear rate is less than 10 s-1. The flow field of the carotid bifurcation usually covers a wide range of shear rate. We therefore believe that it may not be sufficient to describe the property of blood only using the Casson equation in the whole flow field of the carotid bifurcation. In the present study, three different blood constitutive models, namely, the Newtonian, the Casson and the hybrid fluid constitutive models were used in the flow simulation of the human carotid bifurcation. The results were compared among the three models. The results showed that the Newtonian model and the hybrid model had verysimilar distributions of the axial velocity, secondary flow and wall shear stress, but the Casson model resulted in significant differences in these distributions from the other two models. This study suggests that it is not appropriate to only use the Casson equation to simulate the whole flow field of the carotid bifurcation, and on the other hand, Newtonian fluid is a good approximation to blood for flow simulations in the carotid artery bifurcation.     

Numerical simulation of the non-Newtonian blood flow through a mechanical aortic valve

This work focuses on the comparison between Newtonian and non-Newtonian blood flows through a bileaflet mechanical heart valve in the aortic root. The blood, in fact, is a concentrated suspension of cells, mainly red blood cells, in a Newtonian matrix, the plasma, and consequently its overall behavior is that of a non-Newtonian fluid owing to the action of the cells’ membrane on the fluid part. The common practice, however, assumes the blood in large vessels as a Newtonian fluid since the shear rate is generally high and the effective viscosity becomes independent of the former. In this paper, we show that this is not always the case even in the aorta, the largest artery of the systemic circulation, owing to the pulsatile and transitional nature of the flow. Unexpectedly, for most of the pulsating cycle and in a large part of the fluid volume, the shear rate is smaller than the threshold level for the blood to display a constant effective viscosity and its shear thinning character might affect the system dynamics. A direct inspection of the various flow features has shown that the valve dynamics, the transvalvular pressure drop and the large-scale features of the flow are very similar for the Newtonian and non-Newtonian fluid models. On the other hand, the mechanical damage of the red blood cells (hemolysis), induced by the altered stress values in the flow, is larger for the non-Newtonian fluid model than for the Newtonian one.     

Turbulent flow of non-Newtonian substances

Summary A unique shear stress-shear rate relationship exists for laminar flow of any time independent substance in a tube, whereas this is not the case for turbulent flow. In order to obtain a unique relationship for turbulent flow, a new approach based on the elementary theoretical interpretation of experimental data is adopted in the present paper. In particular, wall shear stress is found to be a unique function of a new turbulent pseudo shear rate term. In this relationship therè are two parameters which characterize a given substance — the limiting viscosity at high shear rateµ _m and a factor _m which takes into account modification of turbulent structure by the non-Newtonian properties. Both of these parameters must be determined experimentally. Methods of predicting pressure gradients and of scaling up are outlined. In applying the approach to suspensions in which the solid phase has a density greater than that of the liquid medium, it may be important to determine the increment in shear stress equivalent to the energy required to maintain the solid particles in suspension.The validity of this approach is confirmed by data for the flow of a variety of substances including kaolin suspensions and Carbopol solutions in tubes ranging in diameter from 1.5 to 20 mm. Nomenclature C volume fraction solid in suspension - D tube diameter - f Darcy-Weisbach friction factor - g gravitational acceleration - K _s proportionality constant defined by eq. [10] - L length of tube - P pressure - Re Reynolds number - t exponent defined by eq. [1] - V mean velocity - V ^* volume of particles in pipe lengthL - W settling velocity of particles - _m factor defined by eq. [1] - shear rate - turbulent pseudo shear rate defined by eqs. [8] and [9] - _w wall shear stress - ( _w) _s increment in wall shear stress due to presence of settling particles - µ _m limiting viscosity at high rate of shear - ₁ density of carrier liquid - _m density of mixture - _s density of solid Professor of Chemical Engineering, University of Toronto and scientific advisor to Worthington (Canada) Ltd.With 8 figures     

Three-dimensional simulation of two viscoelastic droplets impacting onto a rigid plate using smoothed particle hydrodynamics

In this article, a smoothed particle hydrodynamics method is developed to simulate the dynamic process of the impact of two viscoelastic droplets onto a rigid plate. The Oldroyd-B fluid is considered as the rheological model to describe the viscoelastic characteristics. An artificial stress is added into the momentum equation to remove the tensile instability. The solution of the problem of two successive impacts of droplets are demonstrated to be in good agreement with the literature data. The problem of two droplets impacting simultaneously onto a rigid plate is investigated.     

Neighbour lists in smoothed particle hydrodynamics

Since smoothed particle hydrodynamics (SPH) is based on interactions with the closer neighbouring particles, implementing the neighbour list is a key point in terms of the high performance of the code. The efficiency of the method depends directly on how to build and use the neighbour list. In the present work, the available searching algorithms for SPH codes are analyzed. Different gridding algorithms are evaluated, the gains in efficiency obtained from reordering of particles is investigated and the cell‐linked list and Verlet list methods are studied to create the neighbour list. Furthermore, an innovative searching procedure based on a dynamic updating of the Verlet list is proposed. The efficiency of the algorithms is analyzed in terms of computational time and memory requirements. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive smoothed particle hydrodynamics for high strain hydrodynamics with material strength

This paper presents the implementation of an adaptive smoothed particle hydrodynamics (ASPH) method for high strain Lagrangian hydrodynamics with material strength. In ASPH, the isotropic kernel in the standard SPH is replaced with an anisotropic kernel whose axes evolve automatically to follow the mean particle spacing as it varies in time, space, and direction around each particle. Except for the features inherited from the standard SPH, ASPH can capture dimension-dependent features such as anisotropic deformations with a more generalized elliptical or ellipsoidal influence domain. Two numerical examples, the impact of a plate against a rigid surface and the penetration of a cylinder through a plate, are investigated using both SPH and ASPH. The comparative studies show that ASPH has better accuracy than the standard SPH when being used for high strain hydrodynamic problems with inherent anisotropic deformations. PACS 46.15.-x, 83.10.Rs, 83.50.-v     

Numerical simulation of soil–water interaction using smoothed particle hydrodynamics (SPH) method

An application of smoothed particle hydrodynamics (SPH) to simulation of soil–water interaction is presented. In this calculation, water is modeled as a viscous fluid with week compressibility and soil is modeled as an elastic–perfectly plastic material. The Mohr–Coulomb failure criterion is applied to describe the stress states of soil in the plastic flow regime. Dry soil is modeled by one-phase flow while saturated soil is modeled by separate water and soil phases. Interaction between soil and water is taken into account by means of pore water pressure and seepage force. Simulation tests of soil excavation by a water jet are calculated as a challenging example to verify the broad applicability of the SPH method. The excavations are carried out in two different soil models, one is dry soil and the other is fully saturated soil. Numerical results obtained in this paper have shown that the gross discontinuities of soil failure can be simulated without any difficulties. This supports the feasibility and attractiveness of this a new approach in geomechanics applications. Advantages of the method are robustness, conceptual simplicity and relative ease of incorporating new physics.     

DEM simulation of particle mixing in a sheared granular flow

Mixing behaviors of particles are simulated in a sheared granular flow using differently colored but otherwise identical glass spheres, with five different bottom wall velocities. By DEM simulation, the solid fractions, velocities, velocity fluctuations and granular temperatures are measured. The mixing layer thicknesses are compared with the calculations from a simple diffusion equation using the data of apparent self-diffusion coefficients obtained from the current simulation measurements. The calculations and simulation results showed good agreements, demonstrating that the mixing process of granular materials occurred through the diffusion mechanism.     

DEM simulation of particle mixing in a sheared granular flow

Mixing behaviors of particles are simulated in a sheared granular flow using differently colored but otherwise identical glass spheres, with five different bottom wall velocities. By DEM simulation, the solid fractions, velocities, velocity fluctuations and granular temperatures are measured.The mixing layer thicknesses are compared with the calculations from a simple diffusion equation using the data of apparent self-diffusion coefficients obtained from the current simulation measurements. The calculations and simulation results showed good agreements, demonstrating that the mixing process of granular materials occurred through the diffusion mechanism.     

Helical flow of some non-Newtonian liquids

Rheologica Acta - The equations of Cross and Cassou describing two types of shear-thinning liquids are extended to flow in two dimensions. The resulting equations are then applied to helical flow...