Vortex sheet technique for the computation of unsteady flows

this thesis is concerned with the study of vortex sheet technique for the computation of unsteady flows. Development has been made on the discretization of the vortex sheet by replacing the constant distribution of vorticity in each element with a linear distribution. This refinement increases accuracy and reduces the strength of the singularities at the boundaries of the discretized sheet elements, which is brought about by the process of discretization. numerical method is used in the study of the following unsteady flow phenomena: (i) the roll-up of a vortex sheet and the analyses of a spiral core; (ii) the shedding of vorticity from a semi-infinite plate; and (iii) the transient heat transfer around a heated plate with flow separation. The following are the findings of this study. (1) The circumferential average of spiral core structure is stable as seen from the result in which the geometrical centre of the core coincides with the centroid of the core. (2) During the time interval following the initial shedding of vorticity, the growth rate of the separation bubble near the leading edge of a semi-infinite plate, is a constant, and is independent of the Strouhal number. (3) Unlike many well known vortex sheets which have a strong tendency to roll up, the vortex sheet generated from the leading edge of a semi-infinite plate shows the structure of the small-scale spirals, which are suspected of being caused by Kelvin- Helmholtz\u27s instability. These small-scale spirals become very prominent in the present results w h e n the flow is perturbed under resonance frequency. These results are in good agreement with the results from a well known experiment done by Pierce (1961). (4) The rolling up of the vortex sheet has strong influences on the heat transfer coefficient and the temperature distribution near the point of flow separation. (5) The maximum value of instantaneous Nusselt numbers decreases with time while the location of the maximum value of instantaneous Nusselt numbers moves downstream. Contrary to the expectation of many works, the points of flow reattachment and the maximum Nusselt numbers do not coincide evident that the applications of the vortex sheet technique are very suitable for the computation of unsteady flow. The free shear layer is represented by a vortex sheet and the evolution of the vortex sheet is traced and used to study the properties, such as velocity, stream function and velocity potential, in the flow field. These also allow further investigation into the other characteristics of the flow field, such as forces, temperature, and energy