The calculation of fluid leaks in the peristaltic hydraulic machine

Background: In the peristaltic pumps, a significant gap can remain in the compressed working body, and therefore, unlike other positive-displacement hydraulic machines, volumetric losses may significantly affect the actual flow rate of the pump. The gap’s shape is determined by approximate dependencies or by numerical methods, but both of these approaches have their own drawbacks. Objecive: Determination of the parameters of the gap in the compressed pump’s hose and calculation of fluid leaks in the pump using both theoretical dependencies and numerical methods. Methods: The object of this study is a peristaltic pump that uses a hose compressed by two rollers. The theoretical flow rate was determined according to the existing theory of positive-displacement hydraulic machines, with the rotor velocity and the volume of the working chambers. It was assumed that the hose in the pump body has the shape of a torus, and the SolidWorks Simulation software product was used to determine the shape of the gap in the compression region and the amount by which the volume inside the hose decreases due to compression by the roller. The resulting geometry of the deformed hose was transferred to the STAR-CCM+ computational fluid dynamics software, where the velocity field in the gap and the dependence of the gap resistance coefficient on the Reynolds number were obtained. For the final determination of leaks in the gap, the Weisbach formula for local losses in the gap and the Darcy-Weisbach formula for friction losses along the length of the pump hose were used. The Darcy coefficient was calculated assuming that the flow in the pump hose is laminar. Results: Comparison of the calculation results with the experimental dependencies showed that the proposed leaks calculation method in the pump can be used at laminar flow and rotation velocities of the pump rotor not less than 100 rpm. Conclusions: The usage of theoretical dependencies and numerical methods to determine the gap’s parameters and to calculate leaks in the pump has shown its effectiveness, but for more accurate results, it is necessary to take into account additional factors, as the flow in the pump is non-stationary.