On the thixotropic effect of turbulence
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摘要
As a follow-up research of the work on the natural viscosity of turbulence of Huang et al. [Journal of Turbulence(2003)], here we investigate the thixotropic effect of a turbulent Newtonian fluid on the basis of the ensemble-averaged Navier–Stokes equation. In view of the natural viscosity, we show that in homogeneous isotropic turbulence the turbulent Newtonian fluid behaves like a thixotropic fluid, exhibiting the thixotropic effect with its natural viscosity decreasing with time.
As a follow-up research of the work on the natural viscosity of turbulence of Huang et al. [Journal of Turbulence(2003)], here we investigate the thixotropic effect of a turbulent Newtonian fluid on the basis of the ensemble-averaged Navier–Stokes equation. In view of the natural viscosity, we show that in homogeneous isotropic turbulence the turbulent Newtonian fluid behaves like a thixotropic fluid, exhibiting the thixotropic effect with its natural viscosity decreasing with time.
As a follow-up research of the work on the natural viscosity of turbulence of Huang et al. [Journal of Turbulence(2003)], here we investigate the thixotropic effect of a turbulent Newtonian fluid on the basis of the ensemble-averaged Navier–Stokes equation. In view of the natural viscosity, we show that in homogeneous isotropic turbulence the turbulent Newtonian fluid behaves like a thixotropic fluid, exhibiting the thixotropic effect with its natural viscosity decreasing with time.
引文
[1]R. S. Rivlin,The relation between the flow of non-Newtonian fluids and turbulent Newtonian fluids, Quarterly of Applied Mathematics 15(1957)212–214.
[2]S. C. Crow, Viscoelastic properties of fine-grained incompressible turbulence, Journal of Fluid Mechanics 33(1968)1–20.
[3]H. W. Liepmann, Free turbulent flows. in:A. Favré(Ed.),Mécanique de la Turbulence, pp. 211–226, Paris:CNRS, 1962.(in French)
[4]J. L. Lumley, Toward a turbulent constitutive equation, Journal of Fluid Mechanics 41(1970)413–434.
[5]P. J. H. Builtjes, Memory effects in turbulent flows,[Ph. D. thesis], Lab Aero-Hydrodynamics, Delft University of Technology,Netherlands, 1977.
[6]Y.-N. Huang, On modelling the Reynolds stress in the context of continuum mechanics, Communications in Nonlinear Science and Numerical Simulation 9(2004)543–559.
[7]J. Mewis, Thixotropy—a general review, Journal of Non-Newtonian Fluid Mechanics 6(1979)1–20.
[8]H. A. Barnes, Thixotropy—a review, Journal of Non-Newtonian Fluid Mechanics 70(1997)1–33.
[9]K. Weissenberg,A continuum theory of rheologicalphenomena, Nature 159(1947)310–311.
[10]A. Groisman, V. Steinberg, Elastic turbulence in a polymer solution flow, Nature 405(2000)53–55.
[11]C. Truesdell, The natural time of a viscoelastic fluid:its significance and measurement, Physics of Fluids 7(1964)1134–1142.
[12]C. Truesdell,The meaning of viscometry in fluid mechanics,Annual Review of Fluid Mechanics 6(1974)111–146.
[13]J. L. Lumley,Drag reduction by additives, Annual Review of Fluid Mechanics 1(1969)367–384.
[14]B. E. Launder, G. J. Reece, W. Rodi,Progress in thedevelopment of a Reynolds-stress turbulence closure, Journal of Fluid Mechanics 68(1975)537–566.
[15]J. C. Rotta,Statistische theorie nichthomogener turbulenz,Zeitschrift für Physik 129(1951)547–572.
[16]D. Naot, A. Shavit, M. Wolfshtein,Interactions betweencomponents of the turbulent velocity correlation tensor, Israel Journal of Technology 8(1970)259–269.
[17]P.-Y. Chou, On an extension of Reynolds’ method of finding apparent stress and the nature of turbulence, Chinese Journal of Physics 4(1940)1–33.
[18]J. L. Lumley, A. M. Yaglom, A century of turbulence, Flow, Turbulence and Combustion 66(2001)241–286.
[19]P.-Y. Chou,On velocity correlations and the solutions of the equations of turbulent fluctuation, Quarterly of Applied Mathematics 3(1945)38–54.
[20]B. E. Launder, An introduction to single-point closure methodology. in:T. B. Gatski, M. Y. Hussaini and J. L. Lumley(Eds.),Simulation and Modelling of Turbulent Flows, Chapter 6, pp.243–310. New York:Oxford University Press, 1996.
[21]S. Girimaji,A new perspective on realizability of turbulence models, Journal of Fluid Mechanics 512(2004)191–210.
[22]B. J. Daly, F. H. Harlow,Transport equations in turbulence,Physics of Fluids 13(1970)2634–2649.
[23]C. duP. Donaldson, Calculation of turbulent shear flows for atmospheric vortex motions, AIAA Journal 10(1972)4–12.
[24]P.-Y. Chou, R.-L. Chou,50 years of turbulence research in China, Annual Review of Fluid Mechanics 27(1995)1–15.
[25]Y.-N. Huang, F. Durst, K. R. Rajagopal, The natural viscosity of turbulence, Journal of Turbulence 4(2003)033.
[26]G. Comte-Bellot, S. Corrsin,The use of a contraction toimprove the isotropy of grid-generated turbulence, Journal of Fluid Mechanics 25(1966)657–682.
[27]M. S. Mohamed, J. C. LaRue, The decay power law in grid-generated turbulence, Journal of Fluid Mechanics 219(1990)195–214.
[28]J. Mewis, N. J. Wagner, Thixotropy, Advances in Colloid and Interface Science 147-148(2009)214–227.
[29]D. F. James, Boger fluids, Annual Review of Fluid Mechanics 41(2009)129–142.
[30]C. Truesdell, W. Noll, The Non-Linear Field Theories of Mechanics, Handbuch der Physik, Vol. III/3, Springer-Verlag, 1965.
[31]B. D. Coleman, H. Markovitz, W. Noll, Viscometric Flows of Non-Newtonian Fluids, Springer, 1966.
[32]C.-C. Wang, A new representation theorem for isotropic functions. Parts I and II, Archive for Rational Mechanics and Analysis 36(1970)166–223.
[33]P. Moin, K. Mahesh, Direct numerical simulation:A tool in turbulence research, Annual Review of Fluid Mechanics 30(1998)539–578.
[2]S. C. Crow, Viscoelastic properties of fine-grained incompressible turbulence, Journal of Fluid Mechanics 33(1968)1–20.
[3]H. W. Liepmann, Free turbulent flows. in:A. Favré(Ed.),Mécanique de la Turbulence, pp. 211–226, Paris:CNRS, 1962.(in French)
[4]J. L. Lumley, Toward a turbulent constitutive equation, Journal of Fluid Mechanics 41(1970)413–434.
[5]P. J. H. Builtjes, Memory effects in turbulent flows,[Ph. D. thesis], Lab Aero-Hydrodynamics, Delft University of Technology,Netherlands, 1977.
[6]Y.-N. Huang, On modelling the Reynolds stress in the context of continuum mechanics, Communications in Nonlinear Science and Numerical Simulation 9(2004)543–559.
[7]J. Mewis, Thixotropy—a general review, Journal of Non-Newtonian Fluid Mechanics 6(1979)1–20.
[8]H. A. Barnes, Thixotropy—a review, Journal of Non-Newtonian Fluid Mechanics 70(1997)1–33.
[9]K. Weissenberg,A continuum theory of rheologicalphenomena, Nature 159(1947)310–311.
[10]A. Groisman, V. Steinberg, Elastic turbulence in a polymer solution flow, Nature 405(2000)53–55.
[11]C. Truesdell, The natural time of a viscoelastic fluid:its significance and measurement, Physics of Fluids 7(1964)1134–1142.
[12]C. Truesdell,The meaning of viscometry in fluid mechanics,Annual Review of Fluid Mechanics 6(1974)111–146.
[13]J. L. Lumley,Drag reduction by additives, Annual Review of Fluid Mechanics 1(1969)367–384.
[14]B. E. Launder, G. J. Reece, W. Rodi,Progress in thedevelopment of a Reynolds-stress turbulence closure, Journal of Fluid Mechanics 68(1975)537–566.
[15]J. C. Rotta,Statistische theorie nichthomogener turbulenz,Zeitschrift für Physik 129(1951)547–572.
[16]D. Naot, A. Shavit, M. Wolfshtein,Interactions betweencomponents of the turbulent velocity correlation tensor, Israel Journal of Technology 8(1970)259–269.
[17]P.-Y. Chou, On an extension of Reynolds’ method of finding apparent stress and the nature of turbulence, Chinese Journal of Physics 4(1940)1–33.
[18]J. L. Lumley, A. M. Yaglom, A century of turbulence, Flow, Turbulence and Combustion 66(2001)241–286.
[19]P.-Y. Chou,On velocity correlations and the solutions of the equations of turbulent fluctuation, Quarterly of Applied Mathematics 3(1945)38–54.
[20]B. E. Launder, An introduction to single-point closure methodology. in:T. B. Gatski, M. Y. Hussaini and J. L. Lumley(Eds.),Simulation and Modelling of Turbulent Flows, Chapter 6, pp.243–310. New York:Oxford University Press, 1996.
[21]S. Girimaji,A new perspective on realizability of turbulence models, Journal of Fluid Mechanics 512(2004)191–210.
[22]B. J. Daly, F. H. Harlow,Transport equations in turbulence,Physics of Fluids 13(1970)2634–2649.
[23]C. duP. Donaldson, Calculation of turbulent shear flows for atmospheric vortex motions, AIAA Journal 10(1972)4–12.
[24]P.-Y. Chou, R.-L. Chou,50 years of turbulence research in China, Annual Review of Fluid Mechanics 27(1995)1–15.
[25]Y.-N. Huang, F. Durst, K. R. Rajagopal, The natural viscosity of turbulence, Journal of Turbulence 4(2003)033.
[26]G. Comte-Bellot, S. Corrsin,The use of a contraction toimprove the isotropy of grid-generated turbulence, Journal of Fluid Mechanics 25(1966)657–682.
[27]M. S. Mohamed, J. C. LaRue, The decay power law in grid-generated turbulence, Journal of Fluid Mechanics 219(1990)195–214.
[28]J. Mewis, N. J. Wagner, Thixotropy, Advances in Colloid and Interface Science 147-148(2009)214–227.
[29]D. F. James, Boger fluids, Annual Review of Fluid Mechanics 41(2009)129–142.
[30]C. Truesdell, W. Noll, The Non-Linear Field Theories of Mechanics, Handbuch der Physik, Vol. III/3, Springer-Verlag, 1965.
[31]B. D. Coleman, H. Markovitz, W. Noll, Viscometric Flows of Non-Newtonian Fluids, Springer, 1966.
[32]C.-C. Wang, A new representation theorem for isotropic functions. Parts I and II, Archive for Rational Mechanics and Analysis 36(1970)166–223.
[33]P. Moin, K. Mahesh, Direct numerical simulation:A tool in turbulence research, Annual Review of Fluid Mechanics 30(1998)539–578.