Abstract
We analyse the known approximate analytic solution of the problem of gas flow induced by the disc rotation inside a closed casing. It is shown that this solution is inapplicable because of the negative thickness of the boundary layer in the shaft neighborhood. Several new analytic solutions are obtained for the flow parameters inside the boundary layer of the casing motionless base. To reduce further the discrepancy between the analytic solution and the direct difference solution of three-dimensional Navier–Stokes equations it is proposed to account for the viscous friction force moment on the lateral casing wall. The consideration of this moment has improved considerably the accuracy of the approximate analytic solution.
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References
Baev, V.K., Bazhaikin, A.N., Frolov, A.D., Takeda, K., Hirano, Y.: Air cleaning from ammonia in agricultural-purpose rooms. Ecology and Industry of Russia 11, 13–16 (2005) (in Russian)
Draper, N.R., Smith, H.: Applied Regression Analysis. John Wiley & Sons, New York (1998)
Fadlun, E.A., Verzicco, R., Orlandi, P., Mohd-Yusof, J.: Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J. Comput. Phys. 161, 35–60 (2000)
Fomichev, V.P.: Device for Gas Cleaning. Patent RU No. 2229658 C2, Moscow (2004) (in Russian)
Khaidarov, S.V.: Experimental Investigation of Heat and Mass Exchange in Diametral Disc Fans. Ph.D. Thesis, ITAM SB RAS, Novosibirsk (2000) (in Russian)
Kim, J., Moin, P.: Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comp. Phys. 59, 308–323 (1985)
Kiselev, S.P., Vorozhtsov, E.V., Fomin, V.M.: Foundations of Fluid Mechanics with Applications: Problem Solving Using Mathematica. Birkhäuser, Basel (1999)
Lai, M.C., Lin, W.-W., Wang, W.: A fast spectral/difference method without pole conditions for Poisson-type equations in cylindrical and spherical geometries. IMA J. Numer. Anal. 22, 537–548 (2002)
Loitsyanskii, L.G.: Boundary Layer Aerodynamics. Gos. izdatelstvo tekhniko-teoreticheskoi literatury, Leningrad, Moscow (1941) (in Russian)
Loitsyanskii, L.G.: Laminar Boundary Layer. In: GIFML, Moscow (1962) (in Russian)
Morozov, V.A., Kirsanova, N.N., Sysoev, A.F.: A complex of algorithms for fast Fourier transform of discrete series. In: Numerical Analysis in FORTRAN, issue 15, pp. 30–51. The Moscow State Univ., Moscow (1976) (in Russian)
Prikhodko, Yu.M.: Investigation of Flow and Heat Exchange in Diametral Disc Fans at Low Reynolds Numbers. Ph.D. Thesis, ITAM SB RAS, Novosibirsk (2008) (in Russian)
Samarskii, A.A., Gulin, A.V.: Numerical Methods. Nauka, Moscow (1989) (in Russian)
Schacht, W., Vorozhtsov, E.V.: Implementation of Roe’s method for numerical solution of three-dimensional fluid flow problems with the aid of computer algebra systems. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds.) Computer Algebra in Scientific Computing/CASC 2004, pp. 409–422. Techn. Univ. Munich, Munich (2004)
Schultz-Grunow, F.: Der Reibungswiderstand rotierender Scheiben in Gehäusen. Zeitschr. für angew. Math. und Mech. 15, 191–204 (1935)
Solomakhova, T.S. (ed.): Centrifugal Ventilators. Mashinostroenie, Moscow (1975) (in Russian)
Tesla, N.: Turbine. US Patent No. 1061206, May 6 (1913)
Verzicco, R., Orlandi, P.: A finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates. J. Comput. Phys. 123, 402–414 (1996)
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Vorozhtsov, E.V. (2009). New Analytic Solutions of the Problem of Gas Flow in a Casing with Rotating Disc. In: Gerdt, V.P., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2009. Lecture Notes in Computer Science, vol 5743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04103-7_30
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DOI: https://doi.org/10.1007/978-3-642-04103-7_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04102-0
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