Theoretical analysis of hydrodynamics of the cream churning process in a batch butter churn equipped with a Möbius strip working body

The study investigates the hydrodynamic processes occurring during the whipping of cream in a device with a working element shaped like a double Möbius strip. The relevance of the work stems from the need to improve the efficiency of butter production, particularly for small-scale farms, where traditional churning methods are often energy-intensive and insufficiently productive. The aim of the research is to analyze the flow characteristics generated by the working element and their impact on the cream-whipping process. The object of the study was a butter churn with a double Möbius strip working element, located at the «Agromechanics» Research Institute (Ganja, Azerbaijan). Methods included mathematical modeling to analyze centrifugal and vortex flows, as well as the determination of key parameters such as rotational speed (n=700→900 rpm) and strip width (b=0.03→0.05 m). Formulas for calculating centrifugal velocity, force, and turbulent flows were applied. The results showed that increasing the rotational speed to (n=900 rpm) and the strip width to (b=0.05 m) leads to maximum values of centrifugal velocity (v=12.5 m/s) and force (F=1408.5 N), significantly intensifying the churning process. The turbulent flows generated by the Möbius strip promote uniform mixing and the disruption of fat globule membranes. The theoretical investigations show that the highest hydrodynamic activity is formed in the peripheral zone of the working chamber, where according to the calculated data, the most favorable conditions are created for coalescence of fat globules and formation of butter grains. The results obtained make it possible to predict that realization of the indicated hydrodynamic regimes can facilitate reduction of the duration of the churning process and specific energy consumption. The experimental assessment of these effects requires additional studies and is the subject of the further work.