CFD OF CYCLOIDAL PROPULSION SYSTEM

CFD OF CYCLOIDAL PROPULSION SYSTEM

ABSTRACT

Computational Fluid Dynamics, or simply CFD is concerned with obtaining numerical solution to fluid flow problems by using computers. The advent of high-speed and large-memory computers has enabled CFD to obtain solutions to many flow problems including those that are compressible or incompressible, laminar or turbulent, chemically reacting or non-reacting.
The equations governing the fluid flow problem are the continuity (conservation of mass), the Navier-Stokes (conservation of momentum), and the energy equations. These equations form a system of coupled non-linear partial differential equations (PDEs). Because of the non-linear terms in these PDEs, analytical methods can yield very few solutions. In general, closed form analytical solutions are possible only if these PDEs can be made linear, either because non-linear terms naturally drop out (eg., fully developed flows in ducts and flows that are in viscid and irrotational everywhere) or because nonlinear terms are small compared to other terms so that they can be neglected (eg., creeping flows, small amplitude sloshing of liquid etc.). If the non-linearity in the governing PDEs cannot be neglected, which is the situation for most engineering flows, then numerical methods are needed to obtain solutions.
CFD is the art of replacing the differential equation governing the Fluid Flow, with a set of algebraic equations (the process is called discretization), which in turn can be solved with the aid of a digital computer to get an approximate solution. The well-known discretization methods used in CFD are Finite Difference Method (FDM), Finite Volume Method (FVM), Finite Element Method (FEM), and Boundary Element Method (BEM).
FDM is the most commonly used method in CFD applications. Here the domain including the boundary of the physical problem is covered by a grid or mesh. At each of the interior grid point the original Differential Equations are replaced by equivalent finite difference approximations. In making this replacement, we introduce an error, which is proportional to the size of the grid. Making the grid size smaller to get an accurate solution within some specified tolerance can reduce this error