No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

The subject of fluid flows over axisymmetric bodies has increased in recent times, as they can be used to model flows over a swept wing, spinning projectiles and aeroengines amongst other things. A better mathematical understanding of the transition from laminar to turbulent flow within the boundary layer could lead to an improvement in the design of such applications. We consider a compressible fluid flow over a rotating cone, defined by half-angle ψ. The mean flow boundary-layer equations are derived and we conduct a high Reynolds number asymptotic linear stability analysis. The flow is susceptible to instabilities caused by inviscid crossflow modes (type I ) and modes caused by a viscous-Coriolis balance force (type II ). Both are considered, along with the effects of changes in the cone half-angle, the magnitude of the local Mach number and the temperature at the cone wall. A surface suction along the cone wall is also analysed.

The stability characteristics of an incompressible viscous pressure-driven flow of an electrically conducting fluid between two parallel boundaries in the presence of a transverse magnetic field are compared and contrasted with those of Plane Poiseuille flow (PPF). Assuming that the outer regions adjacent to the fluid layer are perfectly electrically insulating, the appropriate boundary conditions are applied. The eigenvalue problems are then solved numerically to obtain the critical Reynolds number Rec and the critical wave number ac in the limit of small Hartmann number (M) range to produce the curves of marginal stability. The non-linear two-dimensional travelling waves that bifurcate by way of a Hopf bifurcation from the neutral curves are approximated by a truncated Fourier series in the streamwise direction. Two and three dimensional secondary disturbances are applied to both the constant pressure and constant flux equilibrium solutions using Floquet theory as this is believed to be the generic mechanism of instability in shear flows. The change in shape of the undisturbed velocity profile caused by the magnetic field is found to be the dominant factor. Consequently the critical Reynolds number is found to increase rapidly with increasing M so the transverse magnetic field has a powerful stabilising effect on this type of flow.

The primary aim of this study is to develop and validate a hydrodynamic model for the design of pleated cartridge filters. This software package is intended to develop into a cost effective, robust and reliable design tool to enable engineers to appraise the operation of a filter. Mathematical theories are still being developed in order to build sound software for coupled flows in geometrically complicated domains. This is mainly due to the little understanding of the mathematical theories in addressing interfacial constraints in coupled flows. A 2-D computer code has been developed to simulate both Newtonian and non-Newtonian flows in the filter. The model is based on a flow model described by the Stokes, Continuity and Darcy equations. These equations are solved by the weighted residuals finite element method. Two U-V-P schemes based on the Lagrange and Taylor-Hood elements are developed and tested on various coupled flow physical problems with the latter scheme proving to be capable of coping with complex geometries. The limitations of the Lagrange scheme are described.

The current research focuses on the use of synthetic jets with a rectangular orifice of high aspect ratio as means of separation suppression. Large Eddy Simulations of a synthetic jet in a quiescent domain and a the flow over a two-dimensional hill with a synthetic jet in the vicinity of separation were undertaken. Experimental results presented during the NASA workshop titledI "CFD Validation a of Synthetic Jets and Turbulent Separation Control" were used for validation purposes. In the case of the flow of a synthetic jet in a quiescent domain, agreement between LES and experimental results is only qualitative. The The jet spread is under-predicted and the centre-line velocity is over-predicted downstream of the jet orifice. Also the primary vortex pair is shown to travel slower than that in the experiment. In the case of the flow over a two-dimensional hill, the flow without any kind of separation control as well as the tlow with a synthetic jet in the vicinity of separation were simulated. The agreement in long-time-averaged velocity and Reynolds stresses between LES and experimental resuhs was good in both baseline and synthetic-jet cases.