•Direct numerical simulation of bi-disperse particle-laden gravity currents.•2D and 3D simulations in the lock-exchange configuration.•Full computation of kinetic, potential and dissipative terms of ...the energy balance.•Influence of the different initial proportion of fine and coarse particles.•Computation of important quantities of interest for geophysics.
We present a numerical investigation of bi-disperse particle-laden gravity currents in the lock-exchange configuration. Previous results, based on numerical simulation and laboratory experiments, are used to establish comparisons. Our discussion focuses on explaining how the presence of more than one particle diameter influences the main features of the flow, such as deposit profile, the evolution of the front location and suspended mass. We develop the complete energy budget equation for bi-disperse flows. A set of two and three-dimensional direct numerical simulations (DNS), with different initial compositions of coarse and fine particles, are carried out for Reynolds number equal to 4000. Such simulations show that the energy terms are strongly affected by varying the initial particle fractions. The addition of a small amount of fine particles into a current predominantly composed of coarse particles increases its run-out distance. In particular, it is shown that higher amounts of coarse particles have a dumping effect on the current development. Comparisons show that the two-dimensional simulation does not reproduce the intense turbulence generated in 3D cases accurately, which results in a significant difference in the suspended mass, front position as well as the dissipation term due to the advective motion.
Modeling dispersed solid phases in fluids still represents a computational challenge when considering a small-scale coupling in wide systems, such as the atmosphere or industrial processes at high ...Reynolds numbers. A numerical method is here introduced for simulating the dynamics of diffusive heavy inertial particles in turbulent flows. The approach is based on the position/velocity phase–space particle distribution. The discretization of velocities is inspired from lattice Boltzmann methods and is chosen to match discrete displacements between two time steps. For each spatial position, the time evolution of particles momentum is approximated by a finite-volume approach. The proposed method is tested for particles experiencing a Stokes viscous drag with a prescribed fluid velocity field in one dimension using a random flow, and in two dimensions with the solution to the forced incompressible Navier–Stokes equations. Results show good agreements between Lagrangian and Eulerian dynamics for both spatial clustering and the dispersion in particle velocities. In particular, the proposed method, in contrast to hydrodynamical Eulerian descriptions of the dispersed phase, is able to reproduce fine particle kinetic phenomena, such as caustic formation or trajectory crossings. This indicates the suitability of this approach at large Stokes numbers for situations where details of collision processes are important.
La modélisation de particules solides dispersées dans un fluide reste actuellement un défi numérique, surtout lorsqu'il y a une grande séparation d'échelles entre le couplage et l'écoulement, comme par exemple dans l'atmosphère ou les écoulements industriels à grand nombre de Reynolds. Une méthode numérique est ici présentée dans le but de simuler la dynamique de particules lourdes diffusives dans des écoulements turbulents. L'approche est basée sur la distribution des particules dans l'espace des phases positions–vitesses. La discrétisation en vitesses s'inspire de la méthode de Boltzmann sur réseau et est choisie de telle manière à ce qu'elle corresponde à des déplacements discrets entre deux pas de temps. Pour chaque position spatiale, l'évolution temporelle de la quantité de mouvement est résolue par une approche de volumes finis. La méthode proposée est testée pour des particules soumises à un frottement visqueux de Stokes, avec des écoulements aléatoires en une dimension, et avec des solutions de l'équation de Navier–Stokes incompressible forcée en deux dimensions. Les résultats montrent un bon accord entre les simulations lagrangiennes et eulériennes pour reproduire les concentrations préférentielles et la dispersion des vitesses des particules. De plus, la méthode proposée, contrairement à des descriptions hydrodynamiques des suspensions, permet de résoudre le croisement de trajectoires et la formation de caustiques, ce qui montre sa pertinence aux grands nombres de Stokes pour les situations où les détails des processus de collision sont importants.
The averaged momentum and energy equations for disperse two phase flows are derived by extending a recently developed ensemble averaging method. The resulting equations have a ‘two-fluid’ form and ...the closure problem is phrased in terms of quantities that are amenable to direct numerical simulation. An application of the general theory is given in the dilute limit (first-order in the particle volume fraction), and at low particle Reynolds number. In this case, an analytical closure of the equations free of ad hoc approximations is explicitly given. New effects due to non-uniform particle distribution are identified.
Appendix 2: Report of study group on disperse flow Sundaresan, Sankaran; Eaton, John; Koch, Donald L. ...
International journal of multiphase flow,
07/2003, Letnik:
29, Številka:
7
Journal Article, Conference Proceeding
Recenzirano
In this report, we have outlined a number of scientific challenges which represent building blocks for the comprehensive understanding of disperse flows encountered in a variety of technologies and ...in nature. In dilute particle-laden turbulent flows, we see a need for more realistic descriptions of particle–fluid and particle–particle interactions that would ultimately be suitable for incorporation in large eddy simulations. Experiments are needed to clarify the mechanisms by which particles modulate turbulence. Progress in computer simulation methods and kinetic-theory analyses are leading to new opportunities to obtain the equations of motion for more concentrated multiphase flows which are strongly influenced by or dominated by the disperse phase. However, instabilities inherent to the multiphase nature of these flows lead to the very complex behavior of industrial scale multiphase flows. We require a better understanding of these instabilities as well as coarse-grained models for the average multiphase flows at larger scales. A major issue in dense granular flows is to elucidate the manner in which particle–particle frictional interactions can lead either to mixing or segregation of different particle species.
The first part of the paper addresses some questions concerning the interpretation of averaged-equations descriptions of multiphase flows. A general result on the connection between hyperbolicity and ...stability is presented and its implications discussed. Exact expressions for the momentum equations applicable to dilute suspensions of spheres in potential flow and in Stokes flow are then presented. These results are only accurate to first order in the disperse-phase volume fraction, but they are nevertheless valuable due to the paucity of exact relations in disperse flows. Finally, the issue of the mixture pressure in a disperse flow is addressed, and some non-dilute results obtained by means of numerical simulations are described. The Appendix contains a summary of a recently developed ensemble-averaging formulation.
Discrete element method (DEM) is widely used in industrial and environmental applications for numerical modelling of mixing and transport of lumpy materials. However, it is computationally expensive ...for a large number of particles. To reduce this cost, we have implemented a revision approach for traditional coarse graining as proposed by Bierwisch et al. J. Mech. Phys. and Solids, 57, 31, 2009. We introduce the use of variable coarse grain ratio instead of the uniform one to provide faster computation compare to the traditional coarse graining giving more flexibility to reduce the number of particles. To overcome the problem of violation of geometrical similarity derived from this method, we implement a correction parameter to measure overlap distance between parcels containing small and large particles. The results show fairly good agreement between the revision model, reference DEM simulations and the experimental data of W. Sui et al. Nature Sci. Reports, 7, 8, 2017.
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•Introducing a faster alternative tool for poly disperse granular flow simulation.•The simulation results are validated with respect to experimental data.•Better accuracy in particle distribution compare to traditional coarse graining.•Providing a prediction method for the revision parameter.
AbstractIn water distribution systems, premature decay of disinfectants inside water storage tanks can increase the costs of disinfectant input, depending on the mixing type that takes place in the ...tank. In this paper, the influence of the flow regime of a water storage tank upon the disinfection cost was assessed. Equations relating disinfectant cost to the disinfectant’s decay rate and the mean residence time are presented and compared for three flow regimes: ideal mixed flow, ideal plug flow, and disperse flow. As the decay rate or the mean residence time increased, the cost went to the order of 100 times for plug flow, when compared to mixed flow. The dispersive flow regime presented disinfection costs that were up to 10 times the cost for the mixed flow regime. Given these differences, some general guidelines concerning baffling, inlet characteristics, and water depth-to-diameter ratio were presented in order to obtain a flow closer to the plug regime and, consequently, diminish the chlorination costs. Finally, a case study was presented, based upon the guidelines, showing that a change in the inlet diameter or inlet orientation of a water storage tank can reduce the chlorination cost.
Simulation of polydisperse flows must include the effects of particle–particle interaction, as breakage and aggregation, coupling the population balance equation (PBE) with the multiphase modelling. ...In fact, the implementation of efficient and accurate new numerical techniques to solve the PBE is necessary. The direct quadrature method of moments, known as DQMOM, is a moment-based method that uses an optimal adaptive quadrature closure and came into view as a promising choice for this implementation. In the present work, DQMOM was implemented in two CFD packages: the commercial ANSYS CFX, through FORTRAN subroutines, and the open-source OpenFOAM, by directly coding the PBE solution. Transient zero-dimensional and steady one-dimensional simulations were performed in order to explore the PBE solution accuracy using several interpolation schemes. Simulation cases with dominant breakage, dominant aggregation and invariant solution (equivalent breakage and aggregation) were simulated and validated against an analytical solution. The solution of the population balance equation was then coupled to the two-fluid model, considering that all particles classes share the same velocity field. Momentum exchange terms were evaluated using the local instantaneous Sauter mean diameter of the size distribution function. The two-dimensional tests were performed in a backward facing step geometry where the vortex zones traps the particles and provides high rates of breakage and aggregation.
The problem of establishing the temperature profile in a radiatively cooling-down disperse flow in the presence of external thermal radiation is considered. A comparison of the obtained analytical ...estimates of the speed of establishment of an equilibrium profile with the results of numerical solution is made. The amplitude of the wave phenomena accompanying the establishment of temperature has been calculated.
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