Modeling Fluid Inertia Effects in External Gear Machines Through Lumped Parameter Approach

Abstract Lumped parameter modeling is a consolidated technique for analyzing the fluid dynamic behavior of positive displacement machines, owing to their computational swiftness and the ease to integrate other physical domains affecting the operation of the machine. With some very limited exceptions, this modeling technique typically neglects fluid inertia and momentum effects. This paper proposes an approach to study the effects of fluid inertia affecting the pressurization and depressurization of the tooth space volumes of an external gear pump. The approach is based on considering the fluid inertia in the pressurization grooves and, inside the control volumes with a peculiar sub-division. Further, frequency dependent friction is also modeled to provide realistic damping of the fluid inside these channels. Validation of the model has been performed by comparing the lumped parameter model with a full three-dimensional Navier Stokes solver. The quantities compared such as tooth space volume pressures and outlet volumetric flowrate show a good match between the two approaches for varying operating speeds. The paper lastly, also discusses what operating conditions and geometries play a significant role that governs the necessity to model such fluid inertia effects in the first place.