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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.
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.
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.
This book discusses the subject of wave/current flow around a cylinder, the forces induced on the cylinder by the flow, and the vibration pattern of slender structures in a marine environment.The primary aim of the book is to describe the flow pattern and the resulting load which develops when waves or current meet a cylinder. Attention is paid to the special case of a circular cylinder. The development in the forces is related to the various flow patterns and is discussed in detail. Regular as well as irregular waves are considered, and special cases like wall proximities (pipelines) are also investigated.The book is intended for MSc students with some experience in basic fluid mechanics and for PhD students.
The fundamental equations for compressible flow are solved using a velocity - pressure - vorticity formulation producing a solution that satisfies continuity and vorticity definitions up to machine accuracy. Chapter 1 reviews many algorithms used to solve this problem. Unlike those methods, no pressure - velocity relation or artificial compressibility is assumed in the present formulation, so the equations for kinematics, pressure and momentum are decoupled independent building blocks in the iterative process. As a consequence, the resulting modular algorithm can be used directly for compressible or incompressible flows, contrasting with other current techniques. Moreover the present formulation also applies to two-dimensional and three-dimensional, structured and unstructured grids without any changes, even though only the two-dimensional version was implemented. In Chapter 2, the original formulation is described. A functional minimization technique is used to discretize the kinematics equations, mimicking continuous methods used in the field of functional analysis and providing a common framework to understand, model and implement the solution algorithm. Suitable preconditioning and radial interpolation techniques are employed to balance precision and computational speed. The Poisson equation for pressure is solved similarly by minimizing a suitable functional. The momentum equations are then solved using a finite volume approach adding a controlled amount of artificial viscosity according to mesh size and Reynolds number, resulting in a stable calculation. The vorticity is then obtained as the curl of the velocity. Temperature is similarly computed from the energy equation in an outer loop. Suitable adjustments to pressure and temperature enable the ideal gas equation to fit both the compressible and incompressible paradigmsSubsequent chapters deal with validation, applying the computer efficient implementation of the algorithm to a variety of well documented aerodynamic benchmark problems. Examples include compressible and incompressible flow, steady and unsteady problems and flow over cylinders and airfoils over a variety of Reynolds and subsonic Mach numbers.