Calculation of Conductivity of Profile Slotted Channels in Viscous Regime of Gas Flow

A semi-empiric formula for calculating the conductivity of the channel formed by the convex and concave cylindrical walls of the pump flow path is derived as applied to the calculation of the profile channels of contactless oil-free vacuum pumps, in particular, spiral, helical, two-rotor (ofRoots type), and plunger pumps. The proposed simple equation makes it possible to obtain the conductivity and mass rate values for complex profile channels with minimum computing time. Mathematical dependences are presented for calculating geometrical parameters of different-profile channels. The values calculated from the formula were verified by the numerical calculation using the FLUENT software package based on the Navier-Stokes equations for the viscous regime of gas flow. The calculation is performed for the entire range of geometrical parameters of channels for the known spiral vacuum pumps. The calculation results are presented graphically form and in the form of tables. The results obtained from the proposed formula are compared with the results ofsolving numerically the Navier-Stokes equations. The average discrepancy ofthe calculations is merely 2.5 %.

References

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