The development of a generalised finite element scheme for heat transfer and fluid flow analysis

Shemirani, F, 1991. The development of a generalised finite element scheme for heat transfer and fluid flow analysis. PhD, Nottingham Trent University.

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Abstract

A generalised finite element scheme to analyse two-dimensional fluid flow with heat transfer under the steady state condition has been developed. The Analysis of both laminar and turbulent flow regimes in complicated geometries is facilitated. Imposition of various types of flow boundary conditions is achieved with minimal effort.

Throughout its development, the emphasis has been on making the scheme efficient in terms of computer storage and run-time. In order to achieve this goal, a number of innovations have been introduced both at the finite element discretisation and the solution stages. Advantages have been taken from the recent developments in the Finite Element Method (FEM), as well as adopting some of the established techniques used by the Finite Volume Method (FVM). As a result the scheme is shown to have a computational efficiency comparable with those employing the FVM.

A simple streamline upwind technique is devised in representing the advection terms in the governing transport equations. Verification tests are carried out which demonstrate the accuracy of the streamline technique in treating advection. The upwinding is shown to produce significantly smaller numerical diffusion errors than those arising from previous upwind approximations. The results also show that the technique is unconditionally stable and produces no spurious spatial oscillations. The technique is straightforward and can be added to conventional Galerkin type finite element codes quite readily.

For the solution of the coupled transport equations, an equal order interpolation is used for all variables including pressure. Pressure and velocities are segregated and are obtained separately. A SIMPLER-like algorithm is used to sequentially solve and update velocity components and pressure. The solution is carried out in an iterative fashion. At each iteration, systems of equations are solved by a technique similar to that used in the FVM. A line-by-line Tri-diagonal matrix solution algorithm is developed for the completely unstructured grids that are generated by the FEM. The technique is particularly efficient in terms of storage requirements and computational speed. It also takes advantage of the nature of the system of equations to be solved.

Several laminar benchmark exercises with and without heat transfer are performed. These include developing and fully developed isothermal duct flow, backward facing step flow, natural convection in square cavity and Jet impingement with heat transfer. Results show that the adopted equal order velocity-pressure method can predict the benchmark solutions efficiently and accurately. Spurious pressure modes are also shown to be completely absent.

In modelling turbulent flows, the k-ϵ two equation eddy viscosity model is employed. The advection part of the k and ϵ equations are discretised by the upwind technique developed in this research. Special treatment of the source terms eliminate the possibility of producing negative values of k or ϵ during the iterative solution sequence, which can cause convergence difficulties. By combining the Law of the Wall and the Log Law of the Wall to determine shear stresses near solid regions, the need for an excessively fine mesh in these regions is avoided.

Item Type:	Thesis
Creators:	Shemirani, F.
Date:	1991
ISBN:	9781369312829
Identifiers:	Number Type PQ10182984 Other
Rights:	This copy of the thesis has been supplied under the condition that anyone who consults it is understood to recognise that its copyright rests with its author and that no quotations from the thesis and no information derived from it may be published without the author's prior consent.
Divisions:	Schools > School of Science and Technology
Record created by:	Linda Sullivan
Date Added:	28 Aug 2020 09:25
Last Modified:	15 Jun 2023 09:34
URI:	https://irep.ntu.ac.uk/id/eprint/40555

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