A virtual boundary method with improved computational efficiency using a multi-grid method

The flow around spherical, solid objects is considered. The boundary conditions on the solid boundaries have been applied by replacing the boundary with a surface force distribution on the surface, such that the required boundary conditions are satisfied. The velocity on the boundary is determined by extrapolation from the flow field. The source terms are determined iteratively, as part of the solution. They are then averaged and are smoothed out to nearby computational grid points. A multi-grid scheme has been used to enhance the computational efficiency of the solution of the force equations. The method has been evaluated for flow around both moving and stationary spherical objects at very low and intermediate Reynolds numbers. The results shows a second order accuracy of the method both at creeping flow and at Re = 100. The multi-grid scheme is shown to enhance the convergence rate up to a factor 10 as compared to single grid approach. Copyright (C) 2004 John Wiley Sons, Ltd

Interaction between an incompressible flow and elastic cantilevers of circular cross-section

The purpose of this work is to study the deformation of elastic cantilevers due to hydrodynamic forces by coupled fluid-structure interaction simulations. The cantilever is placed in a rectangular duct and the Reynolds number based on bulk velocity and cantilever diameter is 400. Reduced velocities in the range pi/4 to 2 pi are studied, which covers both un-synchronised motion and the initial branch of synchronisation. The cantilever surface is represented by a virtual boundary method which replaces a solid object in flow by additional force distribution to satisfy local boundary condition. The flow field is solved using a Cartesian finite difference code and the deformation of the cylinder a finite element approach using one-dimensional beam elements is used. (C) 2013 Elsevier Inc. All rights reserved

On the modelling of turbulent flow and mixing in stirred reactors

This thesis concerns the numerical simulations and modelling of the flow structure and scalar transport in stirred reactors. For this Large Eddy Simulations (LES) have been used. The flow situation in a stirred reactor includes several flow phenomena that are not well predicted by "standard" two-equation models, e.g. swirl, stagnation points and anisotropic turbulence. Also, using LES one can obtain data unavailable when using a Reynolds Averaged Navier-Stokes (RANS) approach, such as the spectral content of the solution. However, LES requires a high degree of resolution in time and space which, combined with long sampling times to obtain converged statistics, put higher demands on the computer hardware. One major difficulty when simulating flow in stirred reactors is how to incorporate the effects of the moving boundaries, i.e. the turbine blades. Several approaches have been proposed in the past spanning from deforming and/or sliding grids to stationary boundary conditions based on LDA measurements and the use of moving momentum source terms in the equations of motion. The numerical aspects of representing complex moving boundaries have been investigated and a model based on local velocity differences is presented. The results show that complex moving boundaries can be represented on a Cartesian grid in this way with reasonable numerical accuracy and efficiency. The influence of several Sub-Grid Scale (SGS) models, both for turbulence and mixing, on the flow and the transport of inert additives has been studied. However, for this the geometrically simpler case of a circular jet impinging on a flat plate is considered. The main reasons being that simulating the complex flow structure of stirred reactors is quite time consuming, in terms of CPU time. Also, the additional geometrical complexity may mask some physical factors/problems. The study of SGS model effects suggests that the choice of SGS model has a significant effect on the results and that a eddy viscosity based dynamic model could be the best choice