Mathematical Model for Viscoplastic Fluid Hammer

Abstract

The current work presents a mathematical model to simulate “viscoplastic fluid hammer”-overpressure caused by sudden viscoplastic fluid deceleration in pipelines. The flow is considered one-dimensional, isothermal, laminar, and weakly compressible and the fluid is assumed to behave as a Bingham plastic. The model is based on the mass and momentum balance equations and solved by the method of characteristics (MOC). The results show that the overpressures taking place in viscoplastic fluids are smaller than those occurring in Newtonian fluids and also that two pressure gradients-one negative and one positive-are possibly noted after pressure stabilization. The pressure stabilizes nonuniformly on the pipeline because viscoplastic fluids present yield stresses. Overpressure magnitudes depend not only on the ratio of pressure wave inertia to viscous effect but also on the Bingham number. The pipeline designer should take into account the viscoplastic fluid behavior reported in this paper when engineering a new pipeline system.