A generalized lumped-parameter model for analyzing external gear machines with shear-thinning operating fluids

External gear machines are frequently used to transport non-Newtonian fluids in high pressure applications. However, a coexistence of low viscosity and significant shear thinning can present pumping challenges for off-the-shelf EGM designs. These difficulties arise in part due to the effects of viscoelasticity on the displacing action of the pump and the internal flow leakages. Previous studies have focused on three-dimensional CFD, but limited work has been done on a simulation tool for these effects which considers the radial micromotions of the gears. In this work, a fast lumped-parameter model for the simulation of external gear machines with non-Newtonian operating fluids is developed by dividing the pump into several control volumes and flow paths between them. A method of estimating flow for non-Newtonian fluid models is proposed as well as a novel Reynolds-type equation, and both are implemented within the model. The article then proceeds to compare the mean flow and pressure ripple predicted by this model with experiments to validate the methodology. The mean relative error of the model for the steady-state flowrate prediction is found to be 1.5 % and that of the amplitude prediction for the transient pressure ripple response is found to be 7.4 %. Finally, the results of the model are discussed and conclusions are drawn.