Abstract
The characteristic scales, dispersions, and dissipation rates of isotropic, degenerate, turbulent velocity and scalar fields as well as several third‐order moments for these fields have been determined and compared to those obtained by direct numerical simulation. These quantities determined as a time function were used to close the equation for the joint probability density of a scalar and its gradient, obtained by the authors earlier. The coefficients of this equation calculated using two models developed by the authors are in good agreement with those determined by direct numerical simulation.
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REFERENCES
C. Dopazo, Recent development in PDF methods, in: P. A. Libby and F. A. Williams (eds.), Turbulent Reacting Flows, Academic Press, New York (1994), pp. 375–474.
S. B. Pope, PDF methods for turbulent reactive flows, Progr. Energy Combust. Sci., 11, 119–192 (1985).
S. B. Pope, Recent Advances in Computational Fluid Dynamics, Lecture Notes in Engineering, Springer-Verlag (1989).
R. E. Meyers and E. E. O'Brien, The joint PDF of a scalar and its gradient at a point in turbulent flow, Combust. Sci. Technol., 26, 123–134 (1981).
L. Valino and C. Dopazo, Joint statistics of scalars and their gradients in nearly homogeneous turbulence, Adv. Turbulence, No. 3, 312–323 (1991).
V. A. Sosinovich, V. A. Babenko, and Yu. V. Zhukova, A closed equation for the joint probability density of the fluctuations of the turbulent reacting field of a scalar and its gradient, Inzh.-Fiz. Zh., 71,No. 5, 827–849 (1998).
A. S. Monin and A. M. Yaglom, Statistical Hydromechanics [in Russian], Pt. 2, Nauka, Moscow (1967).
J. R. Herring, Comparison of direct numerical simulations with predictions of two-point closures or isotropic turbulence convecting a passive scalar, J. Fluid Mech., 118, 205–219 (1982).
Yu. V. Zhukova, V. A. Babenko, and V. A. Sosinovich, Calculation of one-point statistical moments on the basis of the solution of equations for spectral distributions, in: Heat and Mass Transfer-98/99 [in Russian], Collection of Sci. Papers, ITMO NAN Belarusi, Minsk (1999), pp. 106–110.
V. A. Sosinovich, B. A. Kolovandin, V. A. Tsyganov, and C. Meola, A statistical turbulent reacting flow model, Int. J. Heat Mass Transfer, 30,No. 3, 517–526 (1987).
G. K. Batchelor, I. D. Howels, and A. A. Townsend, Small scale variation of convected quantities like temperature in a turbulent fluid, J. Fluid Mech., 5, 134–139 (1959).
R. M. Kerr, Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence, J. Fluid Mech., 153, 31–58 (1985).
D. Bogucki, J. A. Domaradzki, and P. K. Yeung, Direct numerical simulations of passive scalars with Pr>1 advected by turbulent flow, J. Fluid Mech., 343, 111–130 (1997).
G. Brethouwer, Mixing of Passive and Reactive Scalars in Turbulent Flows. A Numerical Study, Ph.D. Thesis, Delft (2000).
A. A. Townsend, The measurement of double and triple correlation derivatives in isotropic turbulence, Proc. Cambridge Phil. Soc., 43,No. 4, 560–570 (1947).
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Babenko, V.A., Zhukova, Y.V., Sosinovich, V.A. et al. Statistical Coefficients in the Equation for the Joint Probability Density of a Scalar and Its Gradient. Journal of Engineering Physics and Thermophysics 77, 324–337 (2004). https://doi.org/10.1023/B:JOEP.0000028511.25146.0c
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DOI: https://doi.org/10.1023/B:JOEP.0000028511.25146.0c