Three Dimensional Flow Within Conduits of Arbitrary Geometrical Configurations

Abstract

A general fully elliptic calculation scheme has been developed along with a three dimensional transformation procedure for arbitrary non-orthogonal coordinate systems, for the purpose of the predictions of the three dimensional turbulent flows within ducts of arbitrary geometrical configurations.

After the completion of the calculations on the various test flow cases which include; the laminar developing flows in square and triangular ducts, the laminar separated flow in a constricted circular tube as well as the fully developed turbulent flow in a square, rectangular and trapezoidal ducts, this elliptic scheme has been employed for the calculations of the three dimensional developing turbulent flows in square duct with two equation (k and (epsilon)) model coupled to the algebraic stress model. The predicted results have been extensively compared with two sets of experimental data as well as the calculations by the parabolic marching procedure, with strong emphasis on the local structure of turbulence.

The confidence gained through a series of these calculations, has eventually led to an attempt on the predictions of the three dimensional separated flows, namely, the laminar flow in a converging-diverging rectangular duct and the turbulent flow in a rectangular diffuser. The predicted results, especially those of the latter flow case, have revealed extremely complex natures of the three dimensional fully elliptic flow.