Numerical modeling of turbulent-transfer processes in a mixing zone
- 16 Downloads
Abstract
The series of moments of the velocity field in a two-dimensional zone of mixing is calculated in this article by numerically solving a system of turbulent-transfer differential equations derived from an equation for a single-point distribution function of the velocity pulsation field [1] and simplified to an approximation of the boundary layer. The closed form of the transfer equation is obtained at the level of the third moments using the Millionshchikov hypothesis [2]. The differential operator of the system under this closure turns out to be weakly hyperbolic [3], and not parabolic. A difference scheme is proposed that realizes the method of matrix fitting [4]. A comparison is carried out with an experiment [5, 6].
Keywords
Differential Equation Boundary Layer Distribution Function Mechanical Engineer Numerical ModelingPreview
Unable to display preview. Download preview PDF.
Literature cited
- 1.A. T. Onufriev, “Equations in the semiempirical theory of turbulent transfer,” Zh. Prikl. Mekh. Tekh. Fiz., No. 2, 62–71 (1970).Google Scholar
- 2.M. D. Millionshchikov, “Theory of homogeneous isotropic turbulence,” Dokl. Akad. Nauk SSSR,32, No. 9, 611–617 (1941).Google Scholar
- 3.G. Flaschke and G. Streng, “Correctness of boundary-value problem,” in: Matematika [Periodic collection of translations of foreign articles], No. 72/2, pp. 74–97 (1973).Google Scholar
- 4.I. M. Gel'fand and O. V. Lokutsievskii, “Fitting method for solving difference equations,” in: S. K. Godunov and V. S. Ryaben'kii, Introduction to the Theory of Difference Schemes [in Russian], Fizmatgiz, Moscow (1972), Appendix II.Google Scholar
- 5.H. W. Liepmann and J. Laufer, “Investigations of free turbulent mixing,” NASA Report No. 1257 (1947).Google Scholar
- 6.I. Wygnanski and H. E. Fiedler, “The two-dimensional mixing region,” J. Fluid Mech.,41, Part. 2, 327–361 (1970).Google Scholar
- 7.K. Rotta, “Statistiche theorie nichttogener turbulenz,” Z. Phys.129, No. 5, 547–572 (1951);131, No. 1, 51–77 (1951).Google Scholar
- 8.W. Rodi and D. B. Spalding, “Two-parameter model of turbulence and its application to free jets,” in: Warme und Stoffubertragung, Vol. 3, Springer-Verlag, Berlin (1970), pp. 85–95.Google Scholar
- 9.K. Hanjalic and B. E. Launder, “A Reynold's stress model of turbulence and its application to thin shear flows,” J. Fluid Mech.,52, Part. 4, 609–638 (1972).Google Scholar
- 10.R. Courant, Partial Differential Equations [Russian translation], Mir, Moscow (1964).Google Scholar
- 11.P. Bradshaw, D. H. Ferris, and P. N. Atwell, “Calculation of boundary layer development using turbulent energy equations,” J. Fluid Mech.,28, Part. 3, 593–616 (1967).Google Scholar
- 12.S. K. Godunov, “Difference method for numerically calculating discontinuous solutions of hydrodynamics equations,” Mat. Sb.,47, No. 3, 271 (1959).Google Scholar
- 13.G. B. Alalykin, S. K. Godunov, I. L. Kireeva, and L. A. Pliner, Solution of One-dimensional Gasdynamics Problems in Stationary Networks [in Russian], Nauka, Moscow (1970).Google Scholar
- 14.R. G. Batt, T. Kubota, and J. Laufer, “Experimental investigation of effective shear-flow turbulence on a chemical reaction,” in: AIAA Reacting turbulent flows conference, San Diego, California, June 17–18 (1970), Paper 70-721.Google Scholar
- 15.A. A. Townsend, Structure of Turbulent Shear Flow, Cambridge University Press.Google Scholar