No description available.

No description available.

The support of an EPSRC research studentship grant is acknowledged. I also would like to thank the IMechE for the receipt of a Thomas Andrew common grant.

No description available.

This thesis aims to resolve some open questions about sonic boom, and particularly secondary sonic boom, which arises from long-range propagation in a non-uniform atmosphere. We begin with an introduction to sonic boom modelling and outline the current state of research. We then proceed to review standard results of gas dynamics and we prove a new theorem, similar to Kelvin's circulation theorem, but valid in the presence of shocks. We then present the definitions used in sonic boom theory, in the framework of linear acoustics for stationary and for moving non-uniform media. We present the wavefront patterns and ray patterns for a series of analytical examples for propagation from steadily moving supersonic point sources in stratified media. These examples elucidate many aspects of the long-range propagation of sound and in particular of secondary sonic boom. The formation of `fold caustics' of boomrays is a key feature. The focusing of linear waves and weak shock waves is compared. Next, in order to address the consistent approximation of sonic boom amplitudes, we consider steady motion of supersonic thin aerofoils and slender axisymmetric bodies in a uniform medium, and we use the method of matched asymptotic expansions (MAE) to give a consistent derivation of Whitham's model for nonlinear effects in primary boom analysis. Since for secondary boom, as for primary, the inclusion of nonlinearities is essential for a correct estimation of the amplitudes, we then study the paradigm problem of a thin aerofoil moving steadily in a weakly stratified medium with a horizontal wind. We again use MAE to calculate approximations of the Euler equations; this results in an inhomogeneous kinematic wave equation. Returning to the linear acoustics framework, for a point source that accelerates and decelerates through the sound speed in a uniform medium we calculate the wavefield in the `time-domain'. Certain other motions of interest are also illustrated. In the accelerating and in the manoeuvring motions fold caustics that are essentially the same as those from steady motions in stratified atmospheres again arise. We also manage to pinpoint a scenario where a `cusp caustic' of boomrays forms instead. For the accelerating motions the asymptotic analysis of the wavefield reveals the formation of singularities which are incompatible with linear theory; this suggests the re-introduction of nonlinear effects. However, it is a formidable task to solve such a nonlinear problem in two or three dimensions, so we solve a related one-dimensional problem instead. Its solution possesses an unexpectedly rich structure that changes as the strength of nonlinearity varies. In all cases however we find that the singularities of the linear problem are regularised by the nonlinearity.

This thesis presents the study of transonic cavity flows using CFD. The main focus of the thesis is on the turbulence modelling and simulation of cavity flows. The thesis aims to show the range of applicability of turbulence modelling for cavity flows. Aspects of cavity flow control are also addressed. The cavity models a weapons bay with a length-to-depth (L/D) ratio of 5 and length-to-width (L/W) ratio of 1. The flow is set to transonic speeds (M=0.85) and the Reynolds number based on the cavity length is in the turbulent regime (Re=6.783 million). At these flow conditions, very high noise levels are encountered inside the cavity combined with intense acoustic and turbulent interactions. Unsteady Reynolds-Averaged Navier-Stokes (URANS) was initially applied and the effectiveness of various two-equation turbulence models such as the Wilcox k - ω and the Menter's Baseline k - ω and SST turbulence models was assessed. Computations were first performed with the 2D clean cavity to minimise the computational cost, where the 2D cavity was a reasonable representation of the full 3D cavity with doors-on. Results demonstrated that linear statistical turbulence models generally gave reasonable qualitative predictions of the cavity flow-field but on coarse grids only. The amplitudes of the noise levels and frequencies were however less well predicted and the level of agreement deteriorated with grid refinement for the L/D=5 cavity. Nonetheless, out of the models employed, the SST model proved to be the most robust and provided the best agreement with experimental pressure and PIV measurements. The velocity distributions and the turbulent and acoustic spectra at the cavity floor were also analysed and compared with experiments (where possible) and in doing so the influence of turbulent processes in the cavity highlighted. With the higher acoustic frequencies and the broadband noise less well predicted with linear statistical two-equation turbulence models, attention was diverted towards simulation methods such as Large-Eddy Simulation (LES) and Detached-Eddy Simulation (DES). Numerical results for the 3D L/D=5 cavity with a width-to-depth ratio (W/D) of 1 in both doors-on and doors-off configurations were compared with experiments. Even for coarse grid simulations, better agreement was found between the LES/DES results and experimental pressure and PIV measurements for various grid levels and time-steps than URANS.