Analytical Modeling of Helical Screw Machine for Analysis and Performance Prediction

Abstract

In this paper a numerical method for prediction and analysis of oil-free and oil-flooded screw compressor performance is presented. The model includes inlet and discharge dynamics, leakage throughout the machine, and the thermodynamics within the thread volumes and leakage paths. Calculation results are presented and compared to results from laboratory tests. INTRODUCTION In order to get a powerful tool for analysis and development of screw compressors and expanders a computer simulation method has been developed at Svenska Rotor Maskiner AB, Stockholm, Sweden. This development work has been made possible by the calculating capabilities of the digital computer and the great amount of laboratory tests and experience that Svenska Rotor Maskiner AB has gathered during all the years since the screw compressor was invented by Alf Lysholm. The advantages of using a simulation method in the development work are: -Gives the possibilities for detailed analysis and better understanding of the screw compressor performance. Reduction of experimental costs. Better control of parameters than in laboratory tests. It is almost impossible to hold a parameter completely constant in laboratory tests. To obtain a tool which can serve the above mentioned purposes, certain demands must be fulfilled. The computer program must be able to calculate the effects of the variations of the following parameters: 135 Clearances. Design of inlets and outlets. Rotor profile. Wrap angle. Length/diameter ratio. Lobe-combination. Rotor speed. Working medium. Cooling. Oil-injection rate. Oil viscosity. Solubility of refrigerant in injected oil. Viscous losses. THEORY The following processes have been considered in the physical model: (1) Expansion through the inlet during filling phase and adjustment for enthalpy flow through inlet and leakage paths. Flow losses and inlet pipe dynamics are considered. (2) Compression in the thread volume by using equations for polytropic process adjusted for mass and enthalpy leakage flows into or out from the thread as well as heat transfer losses. (3) Expansion through discharge with adjustment for enthalpy flow. Flow losses and outlet pipe dynamics are considered. (4) Mass and enthalpy flows in leakage paths by using isentropic flow equations for dry compressors or 2-phase viscous flow equations for oil-injected compressors. For oil-injected compressors, heat exchange between oil and gas in leakage paths is considered. (5) Mass and enthalpy flows caused by solubility of working fluid in the injected oil. (6) Friction losses due to oil in the leakage paths by using equations for flow friction combined with path geometry. A short description of the physical modelling is presented in table 1. The physical formulas describing these processes are arranged to a set of interrelated differential equations coupled by mass and enthalpy flows between control volumes. These equations are of the form dx ctf ' _f (~, ~· t) where x is a vector of state variables, u is the system-inputs, and f is a vector of nonlTnear state functions. The equations are computer coded and solved numerically on a digital computer.