Flow Variation of Duckbill Valve Jet in Relation to Large Elastic Deformation

Abstract

Duckbill-shaped elastomer valves are often installed on wastewater effluent diffusers, stormwater outfalls, and industrial flow systems to prevent backflow and sediment/salt water intrusion. Unlike fixed diameter nozzles, the flow from a duckbill valve (DBV) depends both on the driving pressure and the size of the valve opening. A nonlinear large deformation finite element analysis of a prototype DBV is reported herein. The elastomer is modeled as a hyperelastic incompressible solid, and the flow inside the DBV, shaped like a converging nozzle, is treated as energy conserving. The deformed valve is computed iteratively from sequential standard large deformation analysis of the internal flow and pressure loading. The calculations show that the valve opening is lip shaped, and the maximum stress occurs around the two sides of the saddle of the DBV; maximum strains are on the order of 5%. In contrast to the traditional square-root head–discharge dependence, a linear pressure–discharge relation is predicted for a range of elastomer thickness; the jet velocity/valve opening area varies nonlinearly with discharge. The normalized predictions of valve discharge flow and opening area as a function of the driving pressure are in excellent agreement with experimental data.