Numerical investigation of leakage behaviour in long radius elbows

This paper focuses on the relationship between leakage opening areas and pressure heads for 90 degrees long radius elbows under elastic limits using finite element analysis (SAP 2000). The results indicate that leakage opening areas grow linearly as the system pressure increases and the relation is described by the pressure-area slope (M). A sensitivity study was performed to show the effect of various parameters on M. as well as the leakage exponent (N). It was found that elbow internal diameter has the largest influence on the pressure-area slope, followed by the modulus of elasticity and finally elbow wall thickness. The longitudinal stress and Poisson's ratio have a negligible effect on M. Furthermore, leak quantity is related to the pressure raised to a power ranging from 0.495 to 0.592. Regression, analysis was used to derive an empirical equation to predict the pressure-area slope of round holes within elbows with different properties.