Throughout the past decade, interest has grown in the use of boundary-fitted coordinate systems in many areas of computational fluid dynamics. The boundary-fitted technique provides an exact method of implementing finite-difference numerical schemes in curved flow geometries and offers an alternative solution procedure to the finite-element method. The unavoidable large bandwidth of the global stiffness matrix, employed in finite-element algorithms, means that they are computationally less efficient than corresponding finite-difference schemes. As a consequence, the boundary-fitted method offers a more efficient process for solving partial differential flow equations in awkwardly shaped regions. This thesis describes a versatile finite-difference numerical scheme for the solution of the shallow water equations on arbitrary boundary-fitted non-orthogonal curvilinear grids. The model is capable of simulating flows in irregular geometries typically encountered in river basin management. Validation tests have been conducted against the severe condition of jet-forced flow in a circular reservoir with vertical side walls, where initial reflections of free surface waves pose major problems in achieving a stable solution. Furthermore, the validation exercises have been designed to test the computer model for artificial diffusion which may be a consequence of the numerical scheme adopted to stabilise the shallow water equations. The thesis also describes two subsidiary numerical studies of jet-forced recirculating flow in circular cylinders. The first of these implements a Biot-Savart discrete vortex method for simulating the vorticity in the shear layers of the inflow jet, whereas the second employs a stream function/vorticity-transport finite-difference procedure for solving the two-dimensional Navier-Stokes equations on a distorted orthogonal polar mesh. Although the predictions from the stream function/vorticity-transport model are confined to low Reynolds number flows, they provide a valuable set of benchmark velocity fields which are used to confirm the validity of the boundary-fitted shallow water equation solver.

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published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

This work focuses on the simulation of turbulent swirling flows within the framework of second-moment closure. The main objectives are to assess the performance of currently available turbulence models in predicting such flows, and to develop new closure models which would further enhance current predictive ability, and hence, to provide a reliable turbulence model for engineering applications that would help the design process and reduce the development costs of industrial combustion systems. Attention is confined to isothermal flows, and predictions have been carried out for three major swirling cases: a weakly and a strongly swirling free jet and a confined strongly swirling flow in which an annular swirling stream is discharged together with a non-swirling central jet into a suddenly enlarging circular chamber. In the last case, mass transfer has also been examined by predicting the behaviour of an inert scalar tracer with which the central jet has been laced. The existing turbulence models examined are the standard versions of the k — e Boussinesq-viscosity model, the algebraic stress closure and the differential stress closure (BVM, ASM and DSM, respectively), as well as modified ASM and DSM variants. One outcome of this study is that neither the standard versions of the BVM, ASM and DSM nor their previously modified forms examined here predict adequately swirling-flow behaviour. An important conclusion emerging from preliminary efforts has been that the algebraic approximation of stress transport in terms of the transport of turbulence energy—which is a widely used practice—is fundamentally flawed in the presence of swirl. Specifically, the method returns a physically unrealistic behaviour of the normal stresses. It is this conclusion which eventually led to the ASM methodology being discarded and to the exclusive use of the differential methodology. Within the framework of differential closures, two new pressure-strain models have been proposed, namely the Isotropization of Production and Convection Model (IPCM) and the Cubic Quasi-Isotropic Model (CQIM). The former emerged as an extension of the standard DSM approach with the inclusion of the convection tensor into the turbulence isotropization mechanism, whereas the latter follows from a more rational and fundamental approach in which non-linear anisotropy effects have been incorporated, with the resulting model made to satisfy the limit of two-dimensional turbulence. Comparisons between predicted solutions and measurements for swirling flow show that the IPCM produces a marked improvement over all the other models considered, while it does not significantly alter the behaviour of the standard stress closure in non-swirling conditions. Only very limited improvement is achieved by the CQIM, however, despite its success in predicting nearly homogeneous shear flows. The merits and weaknesses of all the models examined are discussed in detail, and the IPCM is recommended as the best approach for predictions of swirling flows. Within the study of the confined case, considerations were extended to the modelling of scalar transport by a second-moment flux closure, and comparisons are made between eddy-diffusivity and flux-closure calculations and experimental data. Computational results show that the distribution of the scalar field is primarily governed by aero-dynamic features. There are indications, however, that the flux model is superior to the eddy-diffusivity model.

The computational analysis of vortex shedding flow is presented, using the commercially available computational fluid dynamics(CFD) software package PHOENICS. In this analysis it is shown how the use of the conventional PHOENICS default first-order hybrid-upwind convective differencing scheme provides an excellent example of the effects of multidimensional false diffusion. These effects are substantially reduced with the introduction of an alternative scheme, SUCCA ( Skew Upwind Corner Convection Algorithm), for the modelling of convective transport in 2D and 3D analyses; resulting in the promotion of continuous vortex shedding for the 2D model. The mechanism of pulsating flow influence on the vortex shedding process has also been simulated. The results show that a complex transient phenomenon such as vortex shedding can be analysed using the PHOENICS code but only with the implementation of an alternative convection algorithm. The results also demonstrate the SUCCA scheme's ability to accurately represent convective transport and hence substantially reduce the effects of multidimensional false diffusion in numerical flow analyses.

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<p> A new experimental setup for studies on wake flow instability and its control, which has been designed and manufactured, is introduced and described. The main body is a dual-sided flat plate with an elliptic leading edge and a blunt trailing edge. Permeable surfaces enable boundary layer suction and/or blowing that introduce the feature of adjusting the inlet condition of the wake created behind the plate. This, in combination with a trailing edge that is easily modified, makes it an ideal experiment for studies of different control methods for the wake flow instability. Additionally, a vortex detection program have been developed in order to detect, analyse and compare small-scale vortical structures in the wake behind the plate for different inlet conditions and control methods applied to the wake flow. Instantaneous velocity fields behind a cylinder subjected to suction or blowing through the entire cylinder surface have been analysed with this program. The results of the analysis show that the major change for different levels of blowing or suction is the location of vortices while the most common vortex size and strength are essentially unchanged.</p>