An HMM--ELLAM scheme on generic polygonal meshes for miscible incompressible flows in porous media

We design a numerical approximation of a system of partial differential equations modelling the miscible displacement of a fluid by another in a porous medium. The advective part of the system is discretised using a characteristic method, and the diffusive parts by a finite volume method. The scheme is applicable on generic (possibly non-conforming) meshes as encountered in applications. The main features of our work are the reconstruction of a Darcy velocity, from the discrete pressure fluxes, that enjoys a local consistency property, an analysis of implementation issues faced when tracking, via the characteristic method, distorted cells, and a new treatment of cells near the injection well that accounts better for the conservativity of the injected fluid

A numerical investigation of the interactions between adjacent cooling tower plumes

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Cooling tower plume rise, dilution and dispersion is investigated using a numerical model. Both single and double sources are considered. The main aim of the investigation is concerned with comparison of the computational results to existing wind tunnel experimental data as well as simple empirical rise height formula. Analysis of the interaction of adjacent sources, and subsequent rise augmentation compared to that of a single source, is a central theme of the work. A full-scale hybrid mechanical cooling tower is modelled as a surface mounted cuboid block 20 m high with an internal development duct of 10 m diameter. Both jet and moderately buoyant plume type sources are studied. Two exit velocity ratios are also considered. An oncoming atmospheric boundary is modelled with an associated logarithmic velocity profile and profiles of turbulence kinetic energy and length scale. Two double source orientations, tandem and side-by-side with respect to the oncoming cross wind, are studied. Physical symmetry is utilised and so only half of the domain is modelled. Both the small-scale (wind tunnel) and full-scale were modelled. The small-scale work used combinations of a low Reynolds number k-e turbulence model and both hybrid and QUICK discretisation schemes. The high Reynolds numbers encountered in the fullscale allowed the use of a number of different turbulence models, namely the standard k-e model, the RNG k-e model and a differential flux model, combined again with the hybrid and QUICK discretisation schemes. The results of a number of sensitivity tests showed that plume rise in this case was not sensitive to the turbulence model constant C3 or to source turbulence levels. A decrease in the turbulent Prandtl number led to a marked increase in the turbulent diffusion of the thermal plume. Horizontal plume spreading was underpredicted in both small and full-scales compared to the experimental data. Plume rise and dilution was, in the majority of cases, predicted accurately compared to both the experimental data and also to rise heights given by simple empirical relationships. Generally, the choice of discretisation scheme was a more important factor than choice of turbulence model. Interaction of side-by-side plumes was dominated by the interaction of the rotating vortex pairs within the plumes. A tandem source arrangement led to early merging and efficient rise enhancement. Merging into a single type plume occurred sooner with an decrease in exit velocity ratio, R.This study was partly funded by the National Power PLC, the Science and Engineering Research Council, and Brunel University

A hybrid numerical flux for supersonic flows with application to rocket nozzles

The numerical simulation of shock waves in supersonic flows is challenging because of several instabilities which can affect the solution. Among them, the carbuncle phenomenon can introduce nonphysical perturbations in captured shock waves. In the present work, a hybrid numerical flux is proposed for the evaluation of the convective fluxes that avoids carbuncle and keeps high-accuracy on shocks and boundary layers. In particular, the proposed flux is a combination between an upwind approximate Riemann problem solver and the Local Lax-Friedrichs scheme. A simple strategy to mix the two fluxes is proposed and tested in the framework of a discontinuous Galerkin discretisation. The approach is investigated on the subsonic flow in a channel, on the supersonic flow around a cylinder, on the supersonic flow on a flat plate and on the flow in a overexpanded rocket nozzle

CFD simulation using FLUENT and RANS3D - A validation exercise

The present work involves two-dimensional numerical simulation of three benchmark problems like (i) Laminar flow in a lid driven cavity (ii) Turbulent flow past a backward facing step and (iii) turbulent flow past NACA0012 aerofoil, using in-house flow solution code RANS3D and the commercially available FLUENT code. The results obtained using these codes are compared with the available measurement data and/or other computations