A Residual Thermodynamic Analysis of Turbulence – Part 1: Theory

Abstract

A new theoretical groundwork for the analysis of wall-bounded turbulent flows is offered, the application of which is presented in a parallel paper. First, it is proposed that the turbulence phenomenon is connected to the onset of an irreversible process – specifically the action of a slip flow – by which a new fundamental model can be derived. Fluid cells with specific dimensions – of length connected with the local slip length and thickness connected with the distance between two parallel slipping flows – can be hypothetically constructed, in which a specific kinetic energy dissipation can be considered to occur. Second, via a maximum entropy production process a self-organized grouping of cells occurs – which results in the distinct zones viscous sublayer, buffer layer, and the log-law region to be built up. It appears that the underlying web structure may take the form of either representing a perfect web structure without any visible swirls, or a partially defect web structure where unbalanced forces may result in the generation of apparent swirls – which in turn might grow into larger turbulent eddies. Third, on the transition from laminar to turbulent flows, a nominal connection between the onset of a turbulent wall boundary layer (in a pipe flow), the Reynolds number as well as the wall surface roughness can be derived.

Keywords

• Discrete slip flow
• Maximum Entropy Production
• turbulent eddy
• fracture structure

References

1. F.M. White, Fluid Mechanics, 2nd Ed., McGraw-Hill Book Company, 1986.
2. R.L. Panton, Incompressible Flow, John Wiley & Sons, New York, USA, 1984.
3. H. Tennekes, J.L. Lumley, A First Course in Turbulence, MIT Press, 1972.
4. P.A. Davidson, Turbulence: An Introduction for Scientists and Engineers, Oxford University Press, 2004.
5. K. Sreenivasan, P.A. Davidson, Y. Kaneda, K. Moffatt, A Voyage Through Turbulence, Cambridge University Press, 2011.
6. B. Herrmann, P. Oswald, R. Semaan and S. L. Bunton, "Modeling synchronization in forced turbulent oscillator flows", Commun Phys 3:195, 2020. DOI: 10.1038/s42005-020-00466-3.
7. P. Moin, K. Mahesh, “DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research”, Annual Review of Fluid Mechanics 30, 539-578, 1998.
8. L.F. Richardson, Weather Prediction by Numerical Process, Cambridge University Press, 1922.

9. A.N. Kolmogorov, “The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Numbers”, Proceedings of the USSR Academy of Sciences (in Russian), 30, 299-303, 1941. Translated into English by L. Levin: A.N. Kolmogorov, “The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Numbers”, Proceedings of the Royal Society A, 434, 9–13, 1991.
10. C. Liu, P. Lu, L. Chen, Y. Yan, "New Theories on Boundary Layer Transition and Turbulence Formation", Modelling and Simulation in Engineering, Article ID 619419, 2012.
11. R. Bose, P.A. Durbin, “Transition to Turbulence by Interaction of Free-Stream and Discrete Mode Perturbations”, Physics of Fluids 28:114105, 2016.
12. F. Ducros, P. Comte, M. Lesieur, “Large-Eddy Simulation of Transition to Turbulence in A Boundary Layer Developing Spatially Over a Flat Plate”, Journal of Fluid Mechanics, 326, 1–36, 1996.
13. B.E. Launder, D.B. Spalding, "The Numerical Computation of Turbulent Flows", Computer Methods in Applied Mechanics and Engineering 3, 269–289, 1974.
14. Y. Demirel, Nonequilibrium Thermodynamics: Transport and Rate Processes in Physical, Chemical and Biological Systems, 3rd Ed., Elsevier, 2014.
15. D. Kondepudi, I. Prigogine, Modern Thermodynamics: From Heat Engines to Dissipative Structures, Wiley, 1998.
16. M. Gustavsson, ‘‘Residual Thermodynamics: A Framework for Analysis of Non-Linear Irreversible Processes’’, Int. J. Thermodynamics, 15, 69–82, 2012.
17. M. Gustavsson, “A Residual Thermodynamic Analysis of Turbulence – Part 2: Pipe Flow Computations and Further Development of Theory”, submitted for publication.
18. I. Finnie, Y.H. Kabil, ”On The Formation of Surface Ripples During Erosion”, Wear 8, 60-69, 1965.
19. M. Gustavsson, “Fluid Dynamic Mechanisms of Particle Flow Causing Ductile and Brittle Erosion”, Wear 252, 845-858, 2002.
20. H. Enwald, E. Peirano, GEMINI: A Cartesian Multiblock Finite Difference Code for Simulation of Gas-Particle Flows, Publikation Nr 97/4, Department of Thermo and Fluid Dynamics, Chalmers University of Technology, Sweden, 1997.
21. M. Gustavsson, A.E. Almstedt, “Numerical Simulation of Fluid Dynamics in Fluidized Beds with Horizontal Heat Exchanger Tubes”, Chemical Engineering Science 55, 857–866, 2000.
22. M. Gustavsson, A.E. Almstedt, “Two-Fluid Modelling of Cooling-Tube Erosion in A Fluidized Bed”, Chemical Engineering Science 55, 867–879, 2000.
23. M. Gustavsson, "A Residual Thermodynamic Analysis of Inert Wear and Attrition, Part 1: Theory", International Journal of Thermodynamics 18, 26-37, 2015.
24. M. Gustavsson, "A Residual Thermodynamic Analysis of Inert Wear and Attrition, Part 2: Applications", International Journal of Thermodynamics 18, 39-52, 2015.
25. A. Kleidon, Y. Malhi, P.M. Cox, “Maximum Entropy Production in Environmental and Ecological Systems”, Phil. Trans. R. Soc. B 365, 1297-1302, 2010.