Computer Simulations Using Pattern Specific Loss Coefficients for Cross Junctions

Detailed $K$-factors measured for a symmetrical nonreducing steel cross junction were published in this journal in 2010. This article describes a variable $K$-factor model for cross junctions that can take advantage of the published data and be incorporated into most existing hydraulic simulation software. The raw data are transformed and represented with bicubic spline surfaces. Newton’s method is used to solve the system of equations resulting from linearization of the equations. Despite the variable junction $K$-factors, solutions converge quadratically or nearly so. For each iteration step, flow patterns must be detected, cross legs identified, and $K$-factors updated. Inherent complexity of flow through cross junctions creates challenges: $K$-factor surfaces have steep gradients and the values are often negative, branches with laminar flow occur alongside branches with turbulent flow, and flow stoppage is recurrent. In addition to comparing solutions based on constant and variable $K$-factors, intriguing flow phenomena are highlighted and suggested as research topics. An important application of the methods presented in this article is validation of hydraulic simulation software.