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Abstract
A control volume based finite element method has been developed for the prediction of three-dimensional flows through ducts of arbitrary cross section.
The formulation has been carried out using the partially parabolic assumption to approximate the Navier Stokes equatons. Though axial diffusion is neglected, downstream effects are assumed to have a significant effect on the flow upstream, these effects being transmitted through the agency of pressure. This is incorporated into the solution scheme by retaining the local axial pressure gradient term in the streamwise momentum equation instead of approximating it by the gradient of the mean pressure. The resulting scheme is capable of handling a number of complex duct flow situations.
The domain is discretized into three dimensional prism shaped elements of triangular cross section. These elements are used for the construction for three-dimensional control volumes of polygonal cross section. Integral conservation equations are written for each control volume, resulting in a set of nominally linear algebraic equations, which are then solved sequentially and iteratively. In contrast to prevailing practice, an equal order formulation is employed, i.e., pressure and velocity are stored at an equal number of nodes in the calculation domain.
Since the equations of fluid flow are not parabolic, a true marching procedure is not possible. The domain is swept plane by plane, updating quantities as the plane is visited. To hasten convergence of the overall iterative procedure, a block correction procedure for pressure is employed at the end of each sweep of the domain. Essentially, a coarse grid solution of the three-dimensional Poisson equation is effected to augment the quasi two-dimensional solution obtained during the sweep through the domain. The proposed method is applied to a number of test problems. Where possible, comparisons between exact and computed solutions are made.
The main contribution of the thesis is an efficient calculation procedure that is applicable to duct flows with significant pressure variations in the cross section.
