By using Prandtl’s mixing length theory to model two-dimensional Reynolds stress equations, the pumping performance of a labyrinth screw pump (LSP) is studied and several key parameters are empirically determined. As a result, two innovative concepts, a cell head coefficient Kf and a pump total head coefficient Kb, are proposed. A simple empirical equation quantifying the effects of the main geometric parameters of the threads on the pump performance is obtained and compared with Golubiev’s experimental results (1965, “Studies on Seal for Rotating Shafts of High-Pressure Pumps,” Wear, 8, pp. 270–288; 1981, Labyrinth-Screw Pumps and Seals for Corrosive Media, 2nd ed., Mashinostroenie, Moscow, pp. 34–49). Both theoretical study and Golubiev’s results indicate that with an increase in screw lead, Kf increases while Kb decreases. Kf is inversely proportional to power of screw-sleeve relative diametrical clearance, and the power exponent varies with different shapes of thread. Finally, Kf decreases with an increase in the relative depth of the thread groove over a wide range. Furthermore, some empirical relations between Kf and screw lead, the screw-sleeve relative diametrical clearance and the relative depth of thread groove are fitted, respectively, based on the derived relation between Kf and thread geometric parameters and Golubiev’s experimental data, which would provide a theoretical basis for LSP design.

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