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

Authors: Salikeev S.I., Raykov A.A., Burmistrov A.V. Published: 20.11.2013
Published in issue: #4(93)/2013  


Category: Power-generating and Transport Machine Building  
Keywords: conductivity, slotted channels, viscous regime, spiral, geometric parameters

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 %.


[1] Vasil’eva T.S., Vasil’ev Y.K., Nesterov S.B. Analysis of the current state of the equipment market for creating and maintaining vacuum. Mater. 12 Naucho-Tekhn. Konf "Vakuumnaya nauka i tekhnika" [Proc. 12 Sci. Tech. Conf. "Vacuum science and technology"], Moscow, 2005, pp. 79-86 (in Russ.).

[2] Anufrieva I.V., Vasil’ev Y.K., Kemenov V.N., Nesterov S.B. Current state of the market of fore-vacuum oil-free pumping equipment. Vak. Tekh. Tekhnol. [Vac. Tech. Technol.], 2003, vol. 13, no. 2, pp. 93-99 (in Russ.).

[3] Ibragimov E.R. Povyshenie effektivnosti spiral’nogo kompressora sukhogo szhatiya. Diss. kand. tekhn. nauk [Improving the efficiency of a dry running scroll compressor. Cand. tehn. sci. diss.]. Kazan, 2009.

[4] Bird G.A. Molecular gas dynamics. Oxford, Clarendon Press, 1976. (Russ. ed.: Berd G.A. Molekulyarnaya gazovaya dinamika. Moscow, Mir Publ., 1981. 320 p.).

[5] Sharipov F., Bertoldo G. Rarefied gas flow through a long tube of variable radius. J. Vac. Sci. Technol., 2005, vol. A, no. 23, pp. 531-533.

[6] Sharipov F., Fahrenbach P., Zipp A. Numerical modeling of Holweck pump. J. Vac. Sci. Technol., 2005, vol. A, no. 23, pp. 1331-1339.

[7] Paranin Yu.A. Sovershenstvovanie metoda rascheta rabochego protsessa spiral’nogo kompressora sukhogo szhatiya s ispol’zovaniem rezul’tatov eksperimental’nykh issledovaniy Avtoreferat diss. kand. tekhn. nauk [Improvement of the method of calculation of dry running scroll compressor using the results of experimental studies. Cand. tehn. sci. diss. abstr.]. Kazan, 2011.

[8] Ibraev A.M. Povyshenie effektivnosti raboty rotornykh nagnetateley vneshnego szhatiya na osnove analiza vliyaniya geometricheskikh parametrov na ikh kharakteristiki. Diss. kand. tekhn. nauk [Improving the efficiency of rotary blowers with external compression by analyzing the influence of geometrical parameters on their performance. Cand. tehn. sci. diss.]. Kazan, 1987.

[9] Burmistrov A.V., Sharafeev L.Z., Salikeev S.I., Karablinov D.G., Bronshteyn M.D. A method for the rapid calculation of conductivity of slot channels formed by curvilinear walls of arbitrary geometry. Mater. 12 Naucho-Tekhn. Konf "Vakuumnaya nauka i tekhnika" [Proc. 12 Sci. Tech. Conf. "Vacuum science and technology"], Moscow, 2005, pp. 37-41 (in Russ.).

[10] Burmistrov A.V., Sharafeev L.Z., Bronshteyn M.D., Salikeev S.I., Karablinov D.G. Calculation of the conductivity of profile channels of non-contacting rotary vacuum pumps. Vak. Tekh. Tekhnol. [Vac. Eng. Technol.], 2006, vol. 16, no. 1, pp. 45-54 (in Russ.).

[11] Salikeev S.I., Burmistrov A.V., Bronshteyn M.D. Investigation of gas leakage through slot channels. Kompressornaya Tekh. Pnevm. [Compressor Tech. Pneumatics], 2005, no. 7, pp. 19-23 (in Russ.).

[12] Raykov A.A., Salikeev S.I., Burmistrov A.V. Experimental and theoretical study of indicator diagrams of a claw vacuum pump. Vestn. Kazan Tekhnol. Univ. [Herald of the Kazan Technol. Univ.], 2011, no. 15, pp. 210-214 (in Russ.).

[13] Burmistrov A.V. Sozdanie i issledovanie beskontaktnykh vakuumnykh nasosov. Avtoreferat diss. doct. tekhn. nauk [Development and study of non-contacting vacuum pumps. Dr. tehn. sci. diss. abstr.]. Moscow, 2006.