الفهرس | Only 14 pages are availabe for public view |
Abstract Vortex breakdown In swirling flows IS characterized by an abrupt change in the structure of the nominally axisymmetric core. The main objective of the present thesis is to give the results of theoretical investigations of axisymmetric vortex breakdown, therefore, been solved partial differential equations, which describe the phenomenon. For this purpose, the finite difference scheme is proposed and investigated theoretically as well as numerically by solving the equations describing the axisymmetric vortex breakdown which called Navier-Stokes equations. Steady solutions of the Navier-Stokes equations, in terms of velocity and pressure, for breakdown are obtained numerically using the ”Artificial Compressibility” technique combined with an ”Alternating Direction Implicit” finite-difference scheme. Axisymmetry is assumed and boundary conditions are carefully applied at the boundaries of a large finite region in an axial plane while resolution near the axis is maintained by a coordinate transformation. Comparing the theoretical results, which are obtained for the same Reynolds numbers based on the free-stream axial velocity and a characteristic core radius, with [Hafez et al 1986] show that a slight difference of 4% and this should be considered within the descent agreement in the comparisons of theory. Significantly, on one hand, this work shows that the axial velocity near the axis (w axis) decreases with axial length (z) and then back again to increase. Also, it is found that with increasing the value of specified circumferential velocity (V) increasing in the rate of decrease In aXIS velocity is happened near the axis as a result of the phenomenon. On the other hand, the swirl velocity (tz) decreases with increasing in (2). Moreover, it’s noticed that the rate of decrease is small at the small circumferential velocity (V). The results agreed with the practical results of others have been offering some curves to clarify this. |