Solution methods for gas flow in ducts through the whole pressure regime

Abstract

In vacuum technology it is frequently necessary to calculate gas flows over a wide range of pressures and flow conditions. Ideally, it is desirable to be able to conduct calculations for long and short ducts and for large and small pressure differences and flow rates. The basic requirement for a general purpose flow calculation method is a combined continuum/molecular model that provides a smooth transition between the flow regimes. Since gases are compressible a generally applicable model requires the application of thermodynamic flow relations. The thermodynamic flow equations are introduced and, in particular, a form applicable to laminar flow conditions together with equations that relate flow velocities to the applied boundary conditions (not generally covered in the fluid dynamics literature). In addition to circular cross-section ducts it is desirable to be able to include other common cross-section shapes so the equations discussed are generalised to include annular and rectangular cross-sections. Continuum flow formulas for these shapes are well known but there appear to be no published formulas for molecular flow in rectangular or annular cross-section ducts of arbitrary length. Empirical formulas which have been developed by the author for annular and rectangular ducts are presented.