Modeling complex vacuum systems from fundamental concepts

Abstract

The study of vacuum systems is especially relevant for their physical dimensioning. However, many cases present high complexity due to the number of components considered and the parameters that depend on the pressure. This work presents the development of the fundamental vacuum pumping equation applied to complex systems considering the gas behaving ideally. As a reference case, the equation was applied to a real vacuum system composed of two vacuum chambers interconnected by a conductance, which is of great interest to the refrigeration industry. As a result, a system of coupled and nonlinear differential equations was obtained. Based on the equation, a model was developed using Maple™ mathematical software, applying the equations and the vacuum pump parameters, as well as the characteristic dimensions of the system. The gas being pumped in the laminar flow regime within the rough vacuum range was also considered for model validation. The results obtained present the pressure drop curves as a function of time for each vacuum chamber under various conditions, showing consistency with the simulated cases.