Discharge Coefficients for Thin Restriction Orifices Based on the Homogeneous Direct Integration Method

Abstract

The discharge coefficient (C d ) of restriction orifices (ROs) operating in critical flow is an empirical parameter required to reconcile actual and theoretical flow values. A literature review shows a wide range of proposed C d values. This paper investigates the fundamental origin of this dispersion and develops a rigorous methodology to estimate C d values for thin ROs based on the homogeneous direct integration (HDI) method and available experimental data. The application of this methodology shows that C d values depend on the thermodynamic phase of the inlet fluid and allows for estimation of differentiated C d values for vapor and two-phase flow. These differentiated C d values lead to more accurate flow calculations in situations where the thermodynamic phase of the depressurized fluid can change due to evaporation, condensation, or entrainment. The deviations between actual and predicted flowrates with C d values calculated with the proposed methodology vary between less than 4 and 10% depending on the state of the inlet fluid. More accurate C d values are expected to contribute to increasing the accuracy of depressurization simulations usually performed to design, troubleshoot, and analyze process safety systems such as flare networks.