| The analysis of many fluid flows of practical interest such as liquid films and jets are complicated by the presence of free surface boundaries. Exact solutions are scare and increasingly, numerical methods are being applied to predict local flow properties and hydrodynamic structure. Like the unknown pressure and velocities, the shape and the position of the boundary must be determined as part of the solution. This information is needed for the design of cooling schemes in high-temperature applications, to optimize heat treatment of metals, and to improve material production processes. The objective of this research is to develop an accurate and efficient numerical method that can be applied to the simulation of free surface flow problems, i.e. horizontal jets, impinging jets and films with and without rotation.;The governing equations are written in terms of primitive variables and solved by the non-staggered grid fractional step method when hydraulic jumps are absent in the flow. The physical domain is transformed to a rectangle for two-dimensional problems or a parallelepiped for three-dimensional problems by means of a numerical mapping technique. The pressure Poisson equation is formulated in the same manner as on a staggered grid and solved with a SOR method. The location of the phase boundary is accomplished by applying both, the normal-stress condition or the kinematic boundary condition depending on the physical force that regulates the behavior of the flow.;The method was applied to solve plane Newtonian jet flows. The numerical predictions are in good agreement with the results based on the finite and spectral element methods as well as the finite difference streamfunction vorticity formulation. The boundary conditions at the free surface are more accurately satisfied when compared with available data.;In the presence of hydraulic jumps, the problem is modeled using the shallow-water approximation and the governing equations are solved using shock capturing schemes. The governing equations were discretized using both the l and flux vector splitting methods. The finite difference technique incorporates a numerical mapping so that the flow regime is transformed to a regular domain for numerical integration. These methods were applied for the simulation of a thin film flowing radially outward on a stationary disk. In this formulation, a first-order forward difference approximation for the time derivative was used. The results showed the location of the hydraulic jump could be predicted.;Among the advantages of the non-staggered grid fractional step method are: the accuracy is second order in space and time, it can handle three-dimensional problems in complex geometries such as flows that turn 90°, it is possible to perform large eddy simulations and to implement turbulent models, and because of local orthogonality at the surface, melting problems can be studied with this method. The flux vector splitting technique can be used to analyze thin films with singularities present in the flow field. |
