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This work is concerned with the modelling of fluid flows on moving domains. The physical problems considered are free surface flows, possibly in the presence of the surface tension phenomena, fluid-rigid body and fluid-structure interaction. The fluid flow considered is governed by the incompressible Navier-Stokes equations. It is modelled by stabilised low order velocity-pressure finite elements. A detailed analysis of time integration strategies is performed leading to the choice of the discrete implicit generalised-α method for the temporal discretisation. The motion of the fluid domain is accounted for by an arbitrary Eulerian-Lagrangian (ALE) strategy. Different mesh update methods are considered. The free surface and the fluid-solid interfaces are modelled carefully, satisfying the necessary conservation properties. These computational ingredients result in fully implicit and strongly coupled sets of nonlinear equations, which are rephrased in a common general framework by decomposing the problems into the fluid, the interface and possibly the solid domains. In order to obtain the exact solution variables, a partitioned Newton-Raphson procedure, based on the exact linearization of the residuals, is developed. Thus, the strong coupling is resolved and optimal convergence can be expected. Finally, a number of two dimensional or axisymmetric numerical examples is presented which demonstrate the robustness and the efficiency of the overall algorithm. The strategy is verified against various reference solutions. The numerical examples include the simulation of the filling of drops, the stretching of liquid bridges, the vortex induced oscillations and the galloping of solid bodies.

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In this study, an existing compressible Navier-Stokes scheme is adapted for the simulation of incompressible flow by using artificial compressibility proposed by Chorin (1967). A cell vertex finite volume algorithm is presented for the simulation of 3D steady and unsteady incompressible fluid flow on unsaturated meshes. The algorithm uses an efficient edge-based data structure. For viscous flow, the application of unsaturated hybrid meshes is introduced. The time-marching algorithms are presented which applied into the scheme for steady solution by using an explicit multi-stage Runge-Kutta time stepping. To accelerate convergence, a multigrid scheme with the automatic creation of coarse mesh is used. In order to improve the convergence, the Turkel’s preconditioning is employed. Dual time approach is used in order to obtain unsteady solution. Here, the explicit multi-stage Runge Kutta pseudo time is employed to find the solution every physical time step. The implicit backward time step is used for physical time step. Several cases with various geometric complexity are presented to evaluate the accuracy of the proposed scheme and to use it as prediction tools for practical problem. From those cases, it can be concluded that the scheme with multigrid acceleration technique can be used for the simulation of incompressible flow from simple geometry until complex geometry by using unstructured meshes accurately and efficiently.

Mould filling is an important part of the casting process and cannot be neglected if an accurate analysis of casting solidification is desired. A numerical technique has been developed to model heat transfer and solidification of metal during and after the filling of a mould. The simulation incorporates a macroscopic fluid flow and heat transfer analysis from the initial stages of filling until filling is completed. Solidification is accounted for as is the temperature dependence of the fluid velocity as solid forms at the mould walls. The computing technique is based on the SOLA-VOF finite difference method for two dimensional mould geometries. Heat conduction and energy transport are modelled using coupled heat conduction-heat convection equations. Limitations of the computing technique are demonstrated.

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This study presents the results of an investigation of liquid flow and dispersion in the bulk and wall region as well as liquid dispersion in the whole cross-section in a packed column with and without counter-current gas flow. In the study a column of 30 cm in diameter packed with 2.54 cm Rashig rings was used. Water was uniformly distributed at the top while air was introduced and distributed uniformly at the bottom of the packed column. Using a point injector, an input pulse of sodium choride solution was introduced at the axis of the column through a small diameter injection tube at a bed height of 25 cm. The responses were measured at four radial positions, using conductivity cells attached to the supporting plate, and were recorded simultaneously with the input pulse, which was recorded as a pressure signal using a pressure transducer. The dispersion equation was solved analytically, and the axial and radial dispersion coefficients in the bulk region were estimated by a non-linear optimization technique. The values of interstitial liquid velocity in the bulk region were estimated from the first moment of the input and output pulses. A plane tracer injector was used to introduce an input pulse of sodium chloride solution to the whole cross section area of the column at bed height of 15 cm. The responses were measured at four radial positions, simultaneously using the four conductivity cells. The input pulse was recorded as a pressure signal. A dispersion equation was solved analytically and total dispersion coefficients were estimated by a non-linear optimization technique. The values of the interstitial liquid velocity in the bulk and wall region were estimated from the first moment on the input and output pulses. The responses in the bulk and wall region were used separately in a dispersion equation which was solved analytically to estimate the axial dispersion coefficients in the bulk and wall region respectively. The operation was repeated at eight different heights up to 150 cm, and the total dispersion coefficients were estimated at each height for different liquid and gas flow rates. The above results were used to study the validity of Gunn's (1980) theoretical analysis, which was based on the assumption that the total dispersion coefficients in a packed column has two important contributions, local dispersion in the packing and axial dispersion due to the differences in liquid flow conditions between the wall and bulk regions of packing. By this treatment, a two-dimensional formulation of dispersion may be reduced to a one-dimensional axisymmetric formulation of dispersion for the limit of long dispersion times. Good agreement between experiment and theory was found.

In recent years continuing development of the axial flow compressor for use in the aero-engine has increased its susceptibility to unsteady flow phenomena which can cause severe blade vibration. A source which has emerged and become of considerable importance is excitation by acoustic resonances. An experimental investigation in a single stage axial flow compressor rig has been performed to ascertain whether acoustic resonances can be excited by vortex shedding from loaded aerofoil section blades. A further experimental programme, to study further the effect of inter-row spacing, was peformed in both an open jet facility and a wind tunnel facility with a tandem plate arrangement. Results showed that acoustic resonances could be excited in a compressor stage in which there was severe blade loading. The speed range over which the resonances were excited was demonstrated to be not only a function of the degree of loading but also the inter-row spacing. Vortex shedding will drive a resonance when the shedding is correlated by the resonant acoustic field and interaction between the vortices and the acoustic field in the vicinity of the blades may result in a net positive input of acoustic energy. As a result the phase of the acoustic field as vortices pass over the trailing edge of the shedding blades and the leading and trailing edges of the downstream blades, control the energy generation. The inter-row spacing controls the phase of the downstream blade interaction and therefore is a major factor influencing the resonant acoustic amplitude. As well as the fundamental acoustic mode, a resonance can also drive significant blade vibration in two other consequential frequency bands which are: a) Sum and Difference frequency bands due to acoustic non-linearity and b) Sidebands of the fundamental modes due to spatial modulation effects caused by flow distortions.