Paper presented at the 5th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 1-4 July, 2007.
The focus of this paper is on mathematical formulation and
computation of uniform flow solutions in horizontal or nearly
horizontal pipes. Continuity and momentum equations are
derived considering an arbitrary number of fluids. Closure
relationships are introduced and complete definitions of
hydraulic diameters are given for co-current and countercurrent
flows. A numerical procedure to compute phase holdups
and pressure gradients is outlined. The iterative and direct
method is shown to be robust and not limited by the choice of
the friction factor correlations needed to define shear stresses.
Uniform flow equations are linearized so that Newton’s
methods can be applied in the search for solutions. It is given
evidence that the Jacobian matrix of the shear stress functions
can be used as a measure of the flow stability.