Applicability tests for empirical formulas: Analysis of turbulent flows and general comments
Tóm tắt
Direct and differential-invariant methods for processing experimental data are used to analyze Nikuradse’s results for a turbulent flow of a viscous liquid in round smooth tubes for various Reynolds numbers. It is found that direct testing ratios do not make it possible to draw a correct inference about the applicability of the Prandtl logarithmic profile. The explanation of this paradoxical result is given. It is shown that although direct applicability tests for empirical formulas do not generally ensure the necessary conditions of their applicability, they make it possible to draw subtle qualitative inferences that cannot be reached using the least-squares method.
Tài liệu tham khảo
Semendyaev, K.A., Empiricheskie formuly (Empirical Formulas), Moscow: Gosteortekhizdat, 1933.
Demidovich, B.P., Maron, I.A., and Shuvalova, E.Z., Chislennye metody analiza (Numerical Methods for Analysis), Moscow: Fizmatgiz, 1963.
Polyanin, A.D., Vyaz’mina, E.A., and Dil’man, V.V., New Methods for Processing Experimental Data: Applicability Tests for Empirical Formulas, Teor. Osn. Khim. Tekhnol., 2008, vol. 42, no. 4, p. 368 [Theor. Found. Chem. Eng. (Engl. Transl.), vol. 42, no. 4, p. 354].
Nikuradse, J., Gesetzma Ssigkeiten Der Turbulenten Stromung in Glatten Rohren, VDI-Forschungsheft, 1933, no. 356, p. 3.
Problemy turbulentnosti (Problems of Turbulence), Velikanov M.A. and Shveikovskii N.T., Eds., Moscow: Ob’ed. nauchno-tekhnicheskoe izdat. NKTP SSSR, 1936.
Miller, B., The Laminar-Film Hypothesis, Trans. ASME, 1949, vol. 71, no. 4, p. 357.
Prandtl, L., U Ber Den Reibungswiderstand Stro Mender, Luft. Erg. Aero. Vers.-Anst. Gottingen, 1927, vol. 3, p. 1.
Karman, T., Mechanische A Nnlichkeit Und Turbulenz, Proc. 3rd Int. Congress of Applied Mechanics, Stockholm, 1930, p. 611.
Prandtl, L., Neuere Ergebnisse Der Turbulenzforschung, VDI-Ztschr., 1933, vol. 77, no. 5, p. 105.
Schlichting, H., Boundary Layer Theory, New York: McGraw-Hill, 1974.
Loitsyanskii, L.G., Mekhanika zhidkosti i gaza (Fluid Mechanics), Moscow: Nauka, 1987.
Polyanin, A.D., Kutepov, A.M., Vyazmin, A.V., and Kazenin, D.A., Hydrodynamics, Mass and Heat Transfer in Chemical Engineering, London: Taylor & Francis, 2002.
Barenblatt, G.I., Podobie, avtomodel’nost’, promezhutochnaya asimptotika (Similarity, Self-Similarity, and Intermediate Asymptotics), Leningrad: Gidrometoizdat, 1982.
Al’tshul’, A.D., Gidravlicheskie poteri na trenie v truboprovodakh (Hydraulic Friction Losses in Pipelines), Moscow: GEI, 1963.
Al’tshul’, A.D., Gidravlicheskie soprotivleniya (Flow Resistance), Moscow: Nedra, 1982.