Calculation of temperature distributions in the rotors of oil-injected screw compressors

A mathematical model and a calculation procedure are proposed in this study to efficiently calculate the temperature distributions in the male and female rotors of the oil-injected screw compressors. The solution of the transient heat conduction problem of the rotors, which is subject to a periodic convective boundary condition and five steady boundary conditions, is obtained by solving the set of Helmholtz equations derived from the partial differential equations for transient heat conduction without internal heat. During the solving process, the periodic convective and the five steady boundary conditions are calculated using the six empirical constants together with the ideal convective heat-transfer coefficient and the ideal steady heat fluxes. The six empirical constants are determined by minimizing the difference between the calculated and measured temperatures of the rotors. The average errors of calculated temperatures at three locations of each of the male and female rotors are 5.45% and 4.85%, respectively. Results indicate that the heat is mainly transferred from the bearings installed on the outlet shaft of the rotors into the screws. Then, the heat is transferred from the screws to the compressed air and the bearings installed on the inlet shaft of the rotors. The temperature gradient in the axial direction is different at different positions along the screw. The results of the sensitivity analysis show that the three empirical constants that are used to calculate the heat convection between the screw and the compressed air, the heat transfer between the rotor and the bearing at the inlet shaft of the rotor and the heat transfer between the rotor and the bearing at the outlet shaft of the rotor, have a stronger impact on the outputs of the mathematical model than the other three empirical constants. The reduced mathematical model, using only the three empirical constants with the strongest impact, can be used in the studies of the temperature distribution in the rotor. The calculated temperature distributions in the screws can be used to estimate the approximate thermal deformation of the screws and thereby improve the screw profiles and the design of the oil-injected screw compressor. (C) 2011 Elsevier Masson SAS. All rights reserved.