International Scientific Journal

Thermal Science - Online First

Authors of this Paper

External Links

online first only

Does shear viscosity play a key role in the flow across a normal shock wave?

Once there is a velocity gradient in a viscous fluid flow, such as that across a shock wave, a viscous force and viscous energy loss exist inside the flow according to the Navier-Stokes equation (NSE), which may confuse the relative contribution of compressibility and viscosity. In this paper, a viscous shear vector is defined as the component of gradient vector of local velocity magnitude perpendicular to the velocity vector. Then, a local viscous energy flux vector is defined from the viscous shear vector after being multiplied by the viscosity and the velocity magnitude. The divergence of the viscous energy flux vector results in new expressions for viscous force and loss of viscous energy, in which all the square terms of derivative of velocity components correspond to irreversible energy loss. The rest part can be taken as a kind of mechanical energy transfer done by the viscous force, from which the viscous force components can be got based on the assumption that the viscous force vector is parallel to the velocity vector. The new equations are different from and more complex than those in the traditional NSE. By the new theory, it is shown that there is no shear viscous force and shear viscous energy loss in the flow across a normal shock wave without velocity gradient perpendicular to the flow direction.
PAPER REVISED: 2023-04-21
PAPER ACCEPTED: 2023-12-13
  1. Saini, G. L., Some Basic Results on Relativistic Fluid Mechanics and Shock Waves, Journal of Mathematical Analysis and Applications, 56(1976), 3, pp.711-717
  2. Falkovich, G., et al., Particles and Fields in Fluid Turbulence, Reviews of Modern Physics, 73(2001), 4, pp.913-75
  3. McKeown, R., et al., Turbulence Generation through an Iterative Cascade of the Elliptical Instability, Science Advances, 6(2020) , 9, Article ID eaaz2717
  4. Xia, H., et al., Upscale Energy Transfer in Thick Turbulent Fluid Layers, Nature Physics, 7(2011), pp.321-4
  5. Bailly, C., and Comtme-Bellot, G., Turbulence, Springer, 2015
  6. Batchelor, G. K., An Introduction to Fluid Dynamics, Cambridge University Press, 2000
  7. Prandtl, L., Oswatitsch, K., and Wieghardt, K., Introduction to Hydrodynamics, Science Press, Bejing, 1981(in Chinese)
  8. Toth, A., and Bobok, E., Chapter 2. Basic Equations of Fluid Mechanics and Thermodynamics. In: Flow and Heat Transfer in Geothermal Systems, Elsevier, 2017. p. 21-55
  9. Spurk, J. H., and Aksel, N., Fluid Mechanics, 3 ed, Springer, 2020
  10. Rieutord, M., Fluid Dynamics: An Introduction, Springer, New York, 2015
  11. Masui, T., and Inoue, M., Viscous Fluid Mechanics, Beijing, Ocean Press, China, 1984(in Chinese)
  12. Nakayama, Y., Chapter 6. Flow of Viscous Fluid. In: Introduction to Fluid Mechanics, Elsevier Ltd., 2018, pp. 99-133
  13. Xie , M. L., Lin, J. Z., Zhou, H. C., Temporal Stability of a Particle-laden Blasius Boundary Layer, Modern Physics Letters B, 23(2009), 2, pp.203-216
  14. Li, Y. Q., Cao, H. L., Zhou, H. C., Zhou, J. -J., Liao, X. -Y., Research on Dynamics of a Laminar Diffusion Flame with Bulk Flow Forcing, Energy, 141 (2017), pp.1300-1312
  15. Zhou, H. C., Chen, D. L., Cheng, Q., A New Way to Calculate Radiative Intensity and Solve Radiative Transfer Equation through Using the Monte Carlo Method, Journal of Quantitative Spectroscopy and Radiative Transfer, (83)(2004), 3-4, pp.459-481
  16. Wang, D. D., Zhou, H. C., Quantitative Evaluation of the Computational Accuracy for the Monte Carlo Calculation of Radiative Heat Transfer, Journal of Quantitative Spectroscopy & Radiative Transfer, 226 (2019), pp. 100-114
  17. Zhou, H. C., Yu, B., Chen, Z. S., et al., A New Theory on Transfer and Dissipation of Viscous Energy in Compressible, Viscous Fluid Flow,, Dec. 22, 2022
  18. Tsien, H-S., Notes on Aerodynamics of Compressible Fluids, Shanghai, Shanghai Jiaotong University Press, China, 2022 (in Chinese)
  19. Dou, H. -S., Origin of Turbulence-Energy Gradient Theory, Springer, 2022
  20. John, D., and Anderson, J., Computational Fluid Dynamics: the Basics with Applications, McGraw-Hill, Education, 1995
  21. Rao, S. S., Basic Equations of Fluid Mechanics. In: The Finite Element Method in Engineering, Elsevier, 2018, pp. 589-610
  22. Yang, X. J., The Scaling-Law Flows: An Attempt at Scaling-Law Vector Calculus, Fractals, 2023, 3, doi:10.1142/S0218348X23401266
  23. Yang, X. J.,. An Insight on the Fractal Power Law Flow: from a Hausdorff Vector Calculus Perspective, Fractals, 30(2022), 3, Article ID 2250054