The Application of the Integral Momentum Balance on the Pressure Drop of a Sudden Contraction

Abstract

A new approach based on the momentum balance to calculate the pressure drop in turbulent flow through sharp-edged axisymmetric sudden contractions is presented. The momentum balance needs the velocity as well as the pressure distributions on the boundaries of the control volume. These distributions are obtained by a series of numerical simulations with different settings for the discharge, as well as the contraction ratio. The numerical model itself is validated by the comparison of the simulated and measured pressure drops in a laboratory experiment at different positions. To get easily applicable hydraulic formulations for the pressure drop depending on the discharge and the contraction ratio, the missing momentum and pressure coefficients are determined from the simulated velocity and pressure distributions. Only the pressure coefficient shows a dependency on the contraction ratio. After fitting the dependency by a simple analytical expression, a new formulation for the hydraulics of a sharp-edged sudden contraction based solely on momentum balance was obtained. The comparison with own experimental results as well as the classical parameterization of Idelchik show in both cases very good agreement.