Junction Losses for Arbitrary Flow Directions

Abstract

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.

Parameter Study of a Loss Reducing Passive Flow Control Method in a Square-to-square Sudden Expansion

“…As former measurements have demonstrated that the flow is fairly symmetrical [9,14], only a quarter channel is used for the present parameter study in order to reduce the size of the numerical mesh, thus the time needed for the simulations. The upstream duct length ( l 1 = 5d h1 ) has been set to be long enough to avoid any possible upstream effect of the sudden expansion [16], while the downstream length ( l 2 = 10d h2 ) is chosen to be long enough to allow for sufficient flow relaxation, thus determining the loss coefficient with low uncertainty. The adequacy of the utilized downstream length has been confirmed by additional CFD studies for l 2 = 46d h2 .…”

“…1. the extrapolation method [12,13,16]; 2. maximum pressure method [9, 10, 14]; 3. semi-empirical method [8,9]. These three approaches are briefly described below.…”

Numerical investigation of fluid flow in fracture junctions with consideration to effect of fracture morphology

“…The k ‐ ɛ model is typically used to simulate a fully developed turbulent flow away from the wall, while the k ‐ ω model is more widely used in boundary layer problems. In this study, a shear‐stress transport k ‐ ω model ( k ‐ ω SST), 25,26 which combines the advantages of both models, was used owing to its excellent suitability to simulations of fluid flow in junctions 24 …”

“…Earlier studies on the fluid split ratio have mostly focused on the fluid flow in pipe junctions 10‐24 . However, few studies have calculated the fracturing fluid flow at the fracture junction.…”