A general hydraulic loss coefficient correlation for perpendicular, cylindrical, finite length dividing pipe junctions is developed and implemented in a discrete dividing-flow manifold model. Dividing-flow manifolds are used in several technical appliances, e.g., in water and wastewater treatment, swimming pool technology, air engineering, and polymer processing. Ensuring uniform flow distribution is a major goal of a flow manifold system design, whose accuracy is usually determined by the accuracies of applied flow coefficients. Coefficient of turning losses is calculated by a computational fluid dynamics (CFD)-based approach applying a nonlinear fit. In the case of a single-phase flow, the loss coefficient depends on four dimensionless parameters: the Reynolds number, the ratio of port and header flow velocities, the diameter ratio, and the ratio of the port length and the diameter of the pipe. Instead of experimentally covering this four-dimensional parameter space, more than 1000 judiciously chosen three-dimensional simulations were run to determine the loss coefficient for the parameter range most used in engineering practice. Validated results of our novel resistance formula show that the velocity and port length to header diameter ratios have a significant effect on the turning loss coefficient, while the diameter ratio and Reynolds number dependency are weaker in the investigated parameter ranges.

Two hydraulic losses take effect at the junction point of three cylindrical conduits. These two quantities are considered to be functions of the three signed flow rates and two geometrical parameters: the cross-sectional area ratio and the angle between the main conduit and branch tube. A new design of experiment is developed for exploring the parameter space with continuous response surfaces, which cover both dividing and combining flow regimes with a general trigonometric formula. The loss coefficients are determined by using a steady-state, single-phase, three-dimensional (3D) computational fluid dynamics (CFD) model. To help the analytical treatment, a new reference velocity formulation is introduced. The new loss coefficient formula is validated against known empirical correlations for different junction types and flow directions. The obtained continuous solution promotes the applicability of the resistance model in hydraulic network models.

Abstract