Finite element simulation of compressible particle-laden gas flows

AbstractA macroscopic two-fluid model of compressible particle-laden gas flows is considered. The governing equations are discretized by a high-resolution finite element method based on algebraic flux correction. A multidimensional limiter of TVD type is employed to constrain the local characteristic variables for the continuous gas phase and conservative fluxes for a suspension of solid particles. Special emphasis is laid on the efficient computation of steady state solutions at arbitrary Mach numbers. To avoid stability restrictions and convergence problems, the characteristic boundary conditions are imposed weakly and treated in a fully implicit manner. A two-way coupling via the interphase drag force is implemented using operator splitting. The Douglas–Rachford scheme is found to provide a robust treatment of the interphase exchange terms within the framework of a fractional-step solution strategy. Two-dimensional simulation results are presented for a moving shock wave and for a steady nozzle flow

Efficient simulation of chromatographic separation processes

This work presents the development and testing of an efficient, high resolution algorithm developed for the solution of equilibrium and non-equilibrium chromatographic problems as a means of simultaneously producing high fidelity predictions with a minimal increase in computational cost. The method involves the coupling of a high-order WENO scheme, adapted for use on non-uniform grids, with a piecewise adaptive grid (PAG) method to reduce runtime while accurately resolving the sharp gradients observed in the processes under investigation. Application of the method to a series of benchmark chromatographic test cases, within which an increasing number of components are included over short and long spatial domains and containing shocks, shows that the method is able to accurately resolve the discontinuities and that the use of the PAG method results in a reduction in the CPU runtime of up to 90%, without degradation of the solution, relative to an equivalent uniform grid

ASHEE: a compressible, equilibrium-Eulerian model for volcanic ash plumes

A new fluid-dynamic model is developed to numerically simulate the non-equilibrium dynamics of polydisperse gas-particle mixtures forming volcanic plumes. Starting from the three-dimensional N-phase Eulerian transport equations for a mixture of gases and solid particles, we adopt an asymptotic expansion strategy to derive a compressible version of the first-order non-equilibrium model, valid for low concentration regimes and small particles Stokes $St<0.2$. When $St < 0.001$ the model reduces to the dusty-gas one. The new model is significantly faster than the Eulerian model while retaining the capability to describe gas-particle non-equilibrium. Direct numerical simulation accurately reproduce the dynamics of isotropic turbulence in subsonic regime. For gas-particle mixtures, it describes the main features of density fluctuations and the preferential concentration of particles by turbulence, verifying the model reliability and suitability for the simulation of high-Reynolds number and high-temperature regimes. On the other hand, Large-Eddy Numerical Simulations of forced plumes are able to reproduce their observed averaged and instantaneous properties. The self-similar radial profile and the development of large-scale structures are reproduced, including the rate of entrainment of atmospheric air. Application to the Large-Eddy Simulation of the injection of the eruptive mixture in a stratified atmosphere describes some of important features of turbulent volcanic plumes, including air entrainment, buoyancy reversal, and maximum plume height. Coarse particles partially decouple from the gas within eddies, modifying the turbulent structure, and preferentially concentrate at the eddy periphery, eventually being lost from the plume margins due to the gravity. By these mechanisms, gas-particle non-equilibrium is able to influence the large-scale behavior of volcanic plumes.Comment: 29 pages, 22 figure

Algorithmes efficaces pour la simulation de gouttes entraînées

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

High-resolution finite volume methods for dusty gas jets and plumes

We consider a model for dusty gas flow that consists of the compressible Euler equations for the gas coupled to a similar (but pressureless) system of equations for the mass, momentum, and energy of the dust. These sets of equations are coupled via drag terms and heat transfer. A high-resolution wave-propagation algorithm is used to solve the equations numerically. The one-dimensional algorithm is shown to give agreement with a shock tube test problem in the literature. The two-dimensional algorithm has been applied to model explosive volcanic eruptions in which an axisymmetric jet of hot dusty gas is injected into the atmospher and the expected behavior is observed at two different vent velocities. The methodology described here, with extensions to three dimensions and adaptive mesh refinement, is being used for more detailed studies of volcanic jet processes