Abstract
Many complex vacuum systems include edge-welded bellows. Their simulation in the molecular flow regime with a Test Particle Monte Carlo (TPMC) code, such as MolFlow+, can take considerable amounts of computing power and time. Therefore we investigated the change of the transmission probability of a bellow compared to a cylindrical tube in TPMC simulations. The results were used to develop an empirical model to simplify the geometry of a bellow in a TPMC model by replacing it with a cylindrical tube of extended length, consequently compensating the reduced conductance of the bellow. The simulated transmission probabilities of a variety of different bellow lengths have been used to fit the parameters of the model. Each bellow geometry simulated with MolFlow + comprised two cylindrical tubes, one at each end, and the central bellow section. The geometry of each bellow is described by two quantities. The first one is the total length of the geometry model normalized to the inner diameter of the bellow. The second one is the fraction of the bellow section with regard to the total length. Simulating a tube instead of a long bellow reduced the simulation time by a factor of up to 1000, while the error introduced through the replacement of the bellow with a cylindrical tube of modified length was in most cases negligible.
Highlights
Edge-welded bellows are important and common components of vacuum systems
Empirical formulae for the transmission probabilities of edge-welded bellows have not been presented in the literature so far, while for the case of cylindrical tubes, empirical formulae for arbitrary tube lengths exist
The aim of this paper is to provide an empirical formula for the transmission probability of edge-welded bellows of arbitrary length
Summary
Edge-welded bellows are important and common components of vacuum systems. Due to multiple scattering of gas particles inside the bellow elements, the transmission probability of gas particles through a bellow can be significantly reduced in comparison to a cylindrical tube of the same length. Empirical formulae for the transmission probabilities of edge-welded bellows have not been presented in the literature so far, while for the case of cylindrical tubes, empirical formulae for arbitrary tube lengths exist. The aim of this paper is to provide an empirical formula for the transmission probability of edge-welded bellows of arbitrary length. By using this formula, we propose a method. Collisions of rays with a facet correspond to the gas particle hitting the respective wall of the vacuum setup. The simulation ends when the gas particle is absorbed with a probability of α by the corresponding facet Otherwise, it is emitted again as another ray, usually following a cosine law.
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