Analytical Estimation of Velocity and Temperature Fields in a Circular Pipe on the Basis of Stochastic Equations and Equivalence of Measures
- 38 Downloads
A stream of nonisothermal Newtonian liquid in a circular smooth pipe is considered on the basis of systems of stochastic equations and of the physical law of equivalence of measures between laminar and turbulent motions. Analytical expressions were previously obtained for isothermal flows for the first and second critical Reynolds numbers, critical point, indices of velocity profiles, second-order correlation moments, correlation functions, and spectral functions depending on the parameters of initial turbulence. Analytical expressions, obtained with the use of the earlier derived formulas for the critical Reynolds numbers and the critical points, are presented for the indices of velocity and temperature profiles as functions of the initial turbulence parameters as well as of the Eckert and Prandtl numbers.
Keywordsequivalence of measures stochastic equations turbulence
Unable to display preview. Download preview PDF.
- 1.L. D. Landau, Toward the problem of turbulence, Dokl. Akad. Nauk SSSR, 44, 339−342 (1944).Google Scholar
- 4.A. N. Kolmogorov, Mathematical models of turbulent motion of an incompressible viscous fluid, Usp. Mat. Nauk, 59, Issue 1(355), 5–10 (2004).Google Scholar
- 6.D. Ruelle and F. Takens, On the nature of turbulence, Commun. Math. Phys., 20, 167−192 (1971), also 23, 343−344; http://dx.doi.org/ 10.1007/bf01646553.
- 9.A. S. Monin, On the nature of turbulence, Usp. Fiz.Nauk, 125, 97−122 (1978).Google Scholar
- 10.M. I. Rabinovich and M. M. Sushchik, Coherent structures in turbulent flows, in: A. V. Gaponov and M. I. Rabinovich (Eds.), Nonlinear Waves. Self-Organization [in Russian], Nauka, Moscow (1983), pp. 58–84.Google Scholar
- 11.G. M. Zaslavskii, Stochasticity of Dynamic Systems [in Russian], Nauka, Moscow (1984).Google Scholar
- 12.V. V. Struminskii, Origination of turbulence, Dokl. Akad. Nauk SSSR, 307, No. 3, 564–567 (1989).Google Scholar
- 16.S. A. Orzag and L. C. Kells, Transition to turbulence in plane Poiseuille and plane Couette flow, J. Fluid Mech., 96, No. 1, 159−205 (1980); doi.org/ 10.1017/s0022112080002066/.
- 17.A. V. Dmitrenko, Equivalence of measures and stochastic equations for turbulent fl ows, Dokl. Akad. Nauk, 450, No. 6, 651–658 (2013); doi.org/ 10.1134/s1028335813060098.
- 18.A. V. Dmitrenko, Equivalent measures and stochastic equations for determination of the turbulent velocity fields and correlation moments of the second order, Abstr. Int. Conf. "Turbulence and Wave Processes,"Lomonosov Moscow State University, November 26−28, 2013, Moscow(2013),pp. 39–40; http://www.dubrovinlab.msu.ru/turbulencemdm100ru.
- 19.A. V. Dmitrenko, Theory of Equivalent Measures and Sets with Repeating Denumerable Fractal Elements. Stochastic Thermodynamics and Turbulence. Determinacy–Randomness Correlator [in Russian], Galleya-Print, Moscow (2013); http://search.rsl.ru/ru/catalog/record/6633402.
- 20.A. V. Dmitrenko, Regular Coupling between Deterministic (Laminar) and Random (Turbulent) Motions — Equivalence of Measures, Scientifi c Discovery Diploma No. 458, registration No. 583 of December 2, 2013.Google Scholar
- 21.A. V. Dmitrenko, Some analytical results of the theory of equivalence measures and stochastic theory of turbulence for non-isothermal flows, Adv. Stud. Theor. Phys., 8, No. 25, 1101−1111 (2014); http://dx.doi.org/10.12988/astp.2014.49131.
- 22.A. V. Dmitrenko, The theory of equivalence measures and stochastic theory of turbulence for non-isothermal flow on the flat plate, First Thermal and Fluids Engineering Summer Conference, August 9−12, 2015, New York, NY, USA, "Thermal Fluids Engineering Addressing Grand Challenges"; http://www.astfe.org/tfesc/conference_program/.
- 23.A. V. Dmitrenko, Determination of critical Reynolds numbers for non-isothermal flows using stochastic theories of turbulence and equivalent measures, Heat Transf. Res., 46, Issue 12, 1102−1112 (2015); DOI: 10.1615/HeatTransRes.2015014191; http://dl.begellhouse.com/journals/46784ef93dddff27,forthcoming.html.
- 24.A. V. Dmitrenko, Fundamentals of Heat and Mass Transfer and Hydrodynamics of Single-Phase and Two-Phase Media. Criteria, Integral and Statistical Methods, and Direct Numerical Simulation [in Russian], Galleya-Print, Moscow(2008).Google Scholar
- 25.J. O. Hinze, Turbulence, 2nd edn., McGraw-Hill Book Company, New York (1975).Google Scholar
- 26.A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics, Vols. 1 and 2, MIT Press, Cambridge, Massachusetts, USA(1971).Google Scholar
- 27.H. Schlichting, Boundary-Layer Theory, 6th edn., McGraw-Hill Book Company, New York (1968).Google Scholar
- 28.S. B. Pope, Turbulent Flows, Cambridge University Press, Cambridge, UK (2000); http://dx.doi.org/ 10.1017/cbo9780511840531.
- 30.A. V. Dmitrenko, Calculation of the pulsations of pressure of heterogeneous turbulent flows, Dokl. Akad. Nauk, 415, No. 1, 44–47 (2007); http://dx.doi.org/ 10.1134/s1028335807120166.
- 31.A. V. Dmitrenko, Calculation of the boundary layer of atwo-phase medium, High Temp., 40, Issue 5, 706–715 (2002); http://dx.doi.org/ 10.1023/A:1020436720213.
- 33.A. V. Fursikov, Moment theory for Navier–Stokes equations with a random right-hand side, Izv. Ross. Akad. Nauk, 56, No. 6, 1273–1315 (1992).Google Scholar
- 34.A. V. Dmitrenko, Heat and mass transfer and friction in injection to a supersonic region of the Laval nozzle, Heat Transf. Res., 31, Issues 6–8, 338−399 (2000); http://dx.doi.org/: 10.1615/HeatTrasRes.v31.i6-8.30.
- 35.A. V. Dmitrenko, Film cooling in nozzles with large geometric expansion using method of integral relation and second moment closure model for turbulence, 33th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit AIAA Paper 97-2911 (1997); doi: 10.2514/6.1997-2911. http://arc.aiaa.org/doi/abs/ 10.2514/6.1997-2911.
- 36.A. V. Dmitrenko, Heat and mass transfer in combustion chamber using a second-moment turbulence closure including an influence coefficient of the density fluctuation in film cooling conditions, 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, AIAA Paper 98-3444 (1998); doi: 10.2514/6.1998-3444; http://arc.aiaa.org/doi/abs/ 10.2514/6.1998-3444.
- 37.A. V. Dmitrenko, Nonselfsimilarity of a boundary-layer flow of a high-temperature gas in a Laval nozzle, Aviats. Tekh., No. 1, 39–42 (1993).Google Scholar
- 38.A. V. Dmitrenko, Computational investigations of a turbulent thermal boundary layer in the presence of external flow pulsations, in: Proc. 11th Conf. Young Scientists, Moscow Physicotechnical Institute, Part 2, Moscow (1986), pp. 48–52. Deposited at VINITI 08.08.86, No. 5698-В86.Google Scholar