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The liquid flowfield in a full or partially-filled right circular cylinder in rapid axial rotation is investigated numerically. The governing equations ar the axisymmetric, unsteady, viscous, incompressible Navier-Stokes equations. These equations are written in stream function-vorticity form for a cylindrical coordinate system in a nonrotating reference frame. The governing equations are discretized using second-order finite-differences for time and space on a nonuniform grid employing logarithmic stretching in regions where high flow gradients are anticipated. Time dependent solutions for Reynolds numbers between 1,000 and 100,000 have been obtained using a Gauss-Seidel relaxation procedure. For partially filled cases the free surface is assumed to be cylindrical and located at a constant radius from the axis of spin. Numerical solutions for full cylinders are consistent with previous solutions and experimental data. Numerical solutions for a partially-filled cylinder are consistent with experimental data for a liquid centrifuge except at the free surface. Computations of the roll moment exerted on the cylinder by the contained liquid shows a smaller moment for the partially-filled compared with the full cylinder results. Keywords: Finite difference, Incompressible flow, Liquid filled projectile, Liquid moment, Unsteady flow, Rotating liquids. (MJM).
Unsteady algorithms Fully Implicit and Crank Nicholson were developed for body fitted curvilinear coordinate system to study the incompressible flow over two-dimensional ellipses. In addition, explicit cyclic boundary condition was implemented to facilitate analysis of vortex shedding. Unsteady flow over circular cylinders was simulated for different Reynolds numbers and compared with experimental data. Flow over ellipses was simulated to study the effect of aspect ratio on drag coefficient. It was observed that the drag coefficient increased as the aspect ratio increased reaching an asymptotic value as the ellipse approached a flat plate.
This Volume is the Proceedings of the IUTAM Symposium on Unsteady Separated Flows and Their Control held in Corfu, Greece, 18–22 June 2007. This was the second IUTAM Symposium on this subject, following the symposium in Toulouse, in April 2002. The Symposium consisted of single plenary sessions with invited lectures, - lected oral presentations, discussions on special topics and posters. The complete set of papers was provided to all participants at the meeting. The thematic sessions of this Symposium are presented in the following: Experimental techniques for the unsteady ow separation Theoretical aspects and analytical approaches of ow separation Instability and transition Compressibility effects related to unsteady separation Statistical and hybrid turbulence modelling for unsteady separated ows Direct and Large-Eddy Simulation of unsteady separated ows Theoretical/industrial aspects of unsteady separated ow control This IUTAM Symposium concerned an important domain of Theoretical and Applied Mechanics nowadays. It focused on the problem of ow separation and of its control. It achieved a uni ed approach regrouping the knowledge provided from theoretical, experimental, numerical simulation and modelling aspects for unsteady separated ows (incompressible and compressible regimes) and included ef cient control devices to achieve attenuation or suppression of separation. The subject - eas covered important themes in the domain of fundamental research as well as in the domain of applications.
This book consists of 37 articles dealing with simulation of incompressible flows and applications in many areas. It covers numerical methods and algorithm developments as well as applications in aeronautics and other areas. It represents the state of the art in the field.
Flow over elliptic cylinders can be considered prototypical of flow over a range of bluff bodies since the geometry allows one to study the effect of both thickness and angle-of-attack on the flow field. Therefore a careful study of this flow should provide valuable insight into the phenomenon of unsteady separation and the structure of bluff body wakes. With this in mind, a spectral collocation technique has been developed to simulate the three-dimensional incompressible flow over elliptic cylinders and unlike spectral element and spectral multi-domain techniques, here the flow is solved in a single domain. The equations are discretized on a body fitted elliptic cylindrical grid and properties of the metric associated with this coordinate system are used to solve the governing equations in an efficient manner. Other key issues including the inflow and outflow boundary conditions and time-discretization are discussed in detail with the hope that this will facilitate future simulations of simdar flows.