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The Air Inlet Method of Characteristics Analysis Tool (AIMCAT), a tool based in Python 3, is developed to model supersonic air inlet geometries during the early phases of design. The method of characteristics (MOC) is used to solve the governing equations for an inviscid, irrotational, isentropic, steady, supersonic flowfield. A comparison is made between modeling shock waves implicitly using Mach wave coalescence and modeling them explicitly using oblique shock relations. Multiple test cases are used to assess the accuracy of the tool by comparing to experimental wind tunnel data. Good general agreement was achieved over the majority of the supersonic portion of the flowfield for all test cases. The implicit shock mesh achieved better accuracy for shock wave positions compared to the explicit shock mesh. However, the explicit shock mesh captured total pressure losses across the shocks which is of value when assessing the efficiency of the inlet. Both approaches show their respective values and their suitability depends on the conditions being studied. AIMCAT has shown initial promise, however further development is need to improve its utility and robustness.

Elastic effects on the hydrodynamic instability of inviscid parallel shear flows are investigated through a linear stability analysis. We focus on the upper convected Maxwell model in the limit of infinite Weissenberg and Reynolds numbers. Specifically, we study the effects of elasticity on the instability of a few classes of simple parallel flows, specifically plane Poiseuille and Couette flows, the hyperbolic-tangent shear layer and the Bickley jet. The equation for stability is derived and solved numerically using the Chebyshev collocation spectral method. This algorithm is computationally efficient and accurate in reproducing the eigenvalues. We consider flows bounded by walls as well as flows bounded by free surfaces. In the inviscid, nonelastic case all the flows we study are unstable for free surfaces. In the case of wall bounded flow, there are instabilities in the shear layer and Bickley jet flows. In all cases, the effect of elasticity is to reduce and ultimately suppress the inviscid instability. The numerical solutions are compared with the analysis of the long wave limit and excellent agreement is shown between the analytical and the numerical solutions. We found flows which are long wave stable, but nevertheless unstable to wave numbers in a certain finite range. While elasticity is ultimately stabilizing, this effect is not monotone; there are instances where a small amount of elasticity actually destabilizes the flow. The linear stability in the short wave limit of shear flows bounded by two parallel free surfaces is investigated. Unlike the plane Couette flow which has no short wave instability, we show that plane Poiseuille flow has two unstable eigenmodes localized near the free surfaces which can be combined into an even and an odd eigenfunctions. The derivation of the asymptotics of these modes shows that our numerical eigenvalues are in agreement with the analytic formula and that the difference between the two eigenvalues tends to zero exponentially with the wavenumber. / Ph. D.

Tsunami are a very dangerous natural hazard, as highlighted in recent years by the Indian Ocean Tsunami of 2004 and the Japan Tsunami of 2011. In the last decade, tsunami have claimed hundreds of thousands of lives, and caused billions of dollars in damage around the world. The hazard posed to coastal communities by tsunami is expected to increase in the future, due to population growth, intensification of coastal development and sea level rise due to climate change. Tsunami may be generated by a number of different source mechanisms. One such source mechanism is a submarine landslide, which can occur in a number of marine environments containing significant sediment accumulation on a sloping seafloor. The high amplitudes and rapid celerities of landslide-generated tsunami make them very dangerous to communities in the vicinity of the landslide, although these waves do not possess the potential for transoceanic devastation. The objectives of this research project are to carry out a series of two-dimensional physical experiments investigating the waves generated by a rigid block landslide moving along a horizontal boundary. The use of a horizontal boundary has the advantage that waves propagating in the offshore and onshore directions may be measured (unlike previous studies using sloping boundaries). The landslide motion is provided by a mechanical system, allowing testing of a broad range of motion, and isolation of the wavemaking properties of different phases of landslide motion. Experiments are carried out in a 14.66 m long flume, with width 0.25 m and working depth 0.50 m. A false floor installed in the flume provides the sliding surface for the landslide motion, and houses the mechanical system. A series of preliminary particle tracking velocimetry experiments confirm the ability of the mechanical system to achieve its velocity targets to within 5% or better, depending on the parameters of the landslide motion. Full spatial and temporal resolution of the wave field is achieved using a laser-induced fluorescence technique to identify the air-water interface to sub-pixel accuracy. The measurements obtained using laser-induced fluorescence are validated against measurements from a resistance wave gauge, with sub-millimetre agreement. In an additional experiment, the particle tracking velocimetry technique provides measurements of the subsurface velocity field. The landslide motion during all experiments consists of an initial period of constant acceleration, followed by a period of constant velocity, followed by a deceleration to rest (at the same rate as the initial acceleration). The landslide acceleration generates two dispersive packets of waves, travelling in the offshore and onshore directions. The offshore-propagating wave packet contains a leading crest and the onshore-propagating wave packet contains a leading trough, with both waves approaching the shallow water limit. A free surface depression forms above the landslide during its constant-velocity motion, and its amplitude may be predicted to within approximately 20% using standard hydraulic theory (considering a frame of reference moving with the landslide). The offshore-propagating waves passing over the landslide cause the amplitude of this depression to fluctuate over time. The deceleration of the landslide generates two additional packets of waves with the opposite polarity to the waves generated by the landslide acceleration. The full spatial and temporal resolution of the generated wave field allows the calculation of the potential energy within the wave field. Additionally, the energy (and mass) within the onshore- and offshore-propagating wave packets may be estimated by calculating these quantities within the onshore and offshore regions of the experimental domain. The wave packets generated by the initial landslide acceleration transport positive mass in the offshore direction, and negative mass in the onshore direction. This mass transport is balanced by the waves generated during the deceleration of the landslide. The nondimensional landslide acceleration, landslide Froude number and submergence depth are varied during the physical experiments. The landslide Froude number has the greatest effect on the behaviour of the generated wave field. At low Froude numbers, the wave field is dominated by the waves generated by the acceleration and deceleration of the landslide. As the Froude number increases, the onshore-propagating waves become negligible in amplitude compared to the offshore-propagating waves. Additionally, the free surface depression increases in amplitude and a group of short-wavelength waves become trapped behind the landslide. These waves exhibit highly nonlinear behaviour at landslide Froude numbers greater than 0.5. The simple experimental geometry allows comparison between the measured wave fields with the predictions of three mathematical models. Two inviscid-irrotational models, differing in their treatment of the bottom boundary condition, provide comparisons over the entire parameter space. These models under-predict the amplitudes of the generated waves, and fail to correctly predict the ongoing interaction between the landslide and the offshore-propagating waves. The inclusion of bottom boundary nonlinearity improves the predictions of the amplitude of the leading waves, and the potential energy within the wave field. However, both of the inviscid models do not predict the extent of wave trapping behaviour behind the landslide observed in the experiments. A viscous model, formulated in the DNS solver Gerris, improves the predictions of wave trapping (and amplitude in general) in one experiment. Although the model still under-predicts the amplitudes of the generated waves, it correctly predicts the amplification of the waves behind the landslide during its constant-velocity motion. The failure of the inviscid models to predict the amplitudes of these waves can be mostly attributed to the linearised free surface condition used by both models. The presence of the turbulent wake may also have a secondary effect on these predictions. An extension of the linear inviscid-irrotational model to three dimensions allows the effect of the landslide width on the amplitudes of the generated waves to be determined. As the width increases, the behaviour of the waves approaches the two-dimensional limiting case.

This report describes the governing equation and boundary conditions for a marine propeller operating in a uniform flow field of inviscid and irrotational fluid. A method is presented by which the velocity and pressure on the blade surface of the propeller can be numerically simulated, using hyperboloidal, constant strength source and doublet panels. Accuracy of the numerical method is verified through comparison with analytically known results and the ability of the numerical simulation to predict the thrust and torque on a propeller in open water is assessed through comparison with published experimental results. The thrust and torque results for the propeller are near the experimental measurements but do not converge to a common value as the panel size decreases.

Two extensions to the proper orthogonal decomposition (POD) technique are considered for steady transonic aerodynamic applications. The first is to couple the POD approach with a cubic spline interpolation procedure in order to develop fast, low-order models that accurately capture the variation in parameters, such as the angle of attack or inflow Mach number. The second extension is a POD technique for the reconstruction of incomplete or inaccurate aerodynamic data. First, missing flow field data is constructed with an existing POD basis constructed from complete aerodynamic data. Second, a technique is used to develop a complete snapshots from an incomplete set of aerodynamic snapshots. / Singapore-MIT Alliance (SMA)

The field of Computational Fluid Dynamics (CFD) is in a continual state of advancement due to new numerical techniques, optimization of existing codes, and the increase in memory and processing speeds of computers. In this thesis, the solution technique for a pre-existing Navier-Stokes flow solver is adapted from an explicit Runge Kutta method to a Lower-Upper Symmetric Gauss-Seidel (LU-SGS) implicit time integration method. Explicit time integration methods were originally used in CFD codes because these methods require less memory. Information needed to advance the flow in time is localized to each grid point. These explicit methods are, however, restricted by time step sizes due to stability criteria. In contrast, implicit methods are unaffected by a large time step sizes but are restricted by memory requirements due to the complexities of unstructured grids. The implementation of LU-SGS performs grid re-ordering for unstructured meshes because of the coupling of grid points in the integration method's solution. The explicit and implicit flow solvers were tested for inviscid flows in incompressible, compressible, and transoinc flow regimes. The results found by comparing the implicit and explicit algorithms revealed a significant speed up in convergence to steady state by the LU-SGS method in terms of iteration number and CPU time per iteration.

A viscous/inviscid interaction method for predicting the effect of viscosity on the performance of wetted and cavitating propulsors is presented. The emphasis is placed on steady wetted and cavitating propulsor flows. A three-dimensional low order potential based boundary element method is strongly coupled with a two dimensional integral boundary layer analysis method based on the strip theory assumption. The influence of viscosity on the outer inviscid flow is modeled through the wall transpiration model by distributing “blowing” sources on the propulsor blade and trailing wake surfaces. The boundary layer edge velocities are expressed as the sum of the inviscid edge velocity and a correction which depends only on the boundary layer variables. The influence of outer potential flow on the inner boundary layer flow is considered through the edge velocities. In the case of sheet cavitation, a “thin” cavity approach is employed and the viscous/inviscid interaction method is applied on the blade surface underneath the cavity. On the cavity surface, the friction force coefficient is forced to be zero. Numerical predictions by the present viscous/inviscid interaction method are presented for open, ducted, and water-jet propulsors. For water-jet propulsors, the flow is solved in an iterative manner by solving the rotor and stator problems separately and by considering the time-averaged effects of one component on the other. Predicted forces, pressure distributions, and boundary layer variables are compared with those predicted by other numerical methods and experimental measurements. / text

Over the last forty or so years interest in the study of wing-tip vortices has increased, primarily due to the introduction of larger passenger aircraft and their subsequent interaction with smaller aircraft. The vortices generated by these larger aircraft present a problem in two main areas; the wake hazard problem, where other aircraft can be subjected to the large tangential velocities of the vortex, and the interaction with ground based features of vortices created during landing and take-off. The first of these is particularly dangerous close to the ground when aircraft are in a high lift configuration at take-off and landing. As the vortices effectively scale with aircraft wing span, significant encounters between large vortices and smaller aircraft have been documented over the years. An example of one such documented wake vortex interaction incident can be found in Ogawa. In this study, the system of vortices are described as classical Batchelor vortices (or linear superpositions thereof) which are then subjected to small perturbations. By discretising the domain and solving for the eigenvalues of the system it is possible to ascertain the stability characteristics of the flow as a function of the system parameters which include the axial wave-number, the spacing of the vortices, their cross-flow decay rate and their axial strength. We first consider the inviscid instability of multiple tip vortices, an approximation which is valid in the limit of large Reynolds numbers. In this limit the stability of the flow is dominated by the axial component of the basic vortex flow. The governing equations of continuity and momentum are reduced to a second order partial differential equation (PDE). This equation is solved numerically to determine which vortex configurations produce the greatest instability growth rate. These results are extended to consider the effect of compressibility on the inviscid instability. Finally we consider the effects of viscosity on the stability of the full Batchelor similarity solution which results in a second order PDE in four dependent variables. The stability equations are solved both globally (for the entire eigenspectra) and locally (for a single eigenvalue in a pre-determined region) using codes that run in both serial and parallel form. The numerical methods are based on pseudospectral discretisation (Chebyshev polynomials for Cartesian and radial directions and Fourier for azimuthal) in the global scheme, the eigenvalues being recovered either with a QZ algorithm or a shift-and-invert Arnoldi algorithm. For the local scheme, fourth order centred finite-diffences are used in conjunction with an iterative eigenvalue recovery method. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1383207 / Thesis (Ph.D.) - University of Adelaide, School of Mathematical Sciences, 2010

Over the last forty or so years interest in the study of wing-tip vortices has increased, primarily due to the introduction of larger passenger aircraft and their subsequent interaction with smaller aircraft. The vortices generated by these larger aircraft present a problem in two main areas; the wake hazard problem, where other aircraft can be subjected to the large tangential velocities of the vortex, and the interaction with ground based features of vortices created during landing and take-off. The first of these is particularly dangerous close to the ground when aircraft are in a high lift configuration at take-off and landing. As the vortices effectively scale with aircraft wing span, significant encounters between large vortices and smaller aircraft have been documented over the years. An example of one such documented wake vortex interaction incident can be found in Ogawa. In this study, the system of vortices are described as classical Batchelor vortices (or linear superpositions thereof) which are then subjected to small perturbations. By discretising the domain and solving for the eigenvalues of the system it is possible to ascertain the stability characteristics of the flow as a function of the system parameters which include the axial wave-number, the spacing of the vortices, their cross-flow decay rate and their axial strength. We first consider the inviscid instability of multiple tip vortices, an approximation which is valid in the limit of large Reynolds numbers. In this limit the stability of the flow is dominated by the axial component of the basic vortex flow. The governing equations of continuity and momentum are reduced to a second order partial differential equation (PDE). This equation is solved numerically to determine which vortex configurations produce the greatest instability growth rate. These results are extended to consider the effect of compressibility on the inviscid instability. Finally we consider the effects of viscosity on the stability of the full Batchelor similarity solution which results in a second order PDE in four dependent variables. The stability equations are solved both globally (for the entire eigenspectra) and locally (for a single eigenvalue in a pre-determined region) using codes that run in both serial and parallel form. The numerical methods are based on pseudospectral discretisation (Chebyshev polynomials for Cartesian and radial directions and Fourier for azimuthal) in the global scheme, the eigenvalues being recovered either with a QZ algorithm or a shift-and-invert Arnoldi algorithm. For the local scheme, fourth order centred finite-diffences are used in conjunction with an iterative eigenvalue recovery method. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1383207 / Thesis (Ph.D.) - University of Adelaide, School of Mathematical Sciences, 2010