World Academy of Science, Engineering and Technology
Published March 24, 2009 | Version 6484
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Toward a New Simple Analytical Formulation of Navier-Stokes Equations

Description

Incompressible Navier-Stokes equations are reviewed in this work. Three-dimensional Navier-Stokes equations are solved analytically. The Mathematical derivation shows that the solutions for the zero and constant pressure gradients are similar. Descriptions of the proposed formulation and validation against two laminar experiments and three different turbulent flow cases are reported in this paper. Even though, the analytical solution is derived for nonreacting flows, it could reproduce trends for cases including combustion.

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References

  • J.C. Kalita, A.K. Dass, and N. Nidhi, "An Efficient Transient Navier- Stokes Solver on Compact Nonuniform Space Grids," Journal of Computational and Applied Mathematics 214, 2008, pp. 124 - 162.
  • Y. He and A. Wang, "A Simplified Two-Level Method for the Steady Navier-Stokes Equations," Comput. Methods Appl. Mech. Engrg. 197, 2008, pp. 1568 - 1576.
  • J.D. Gibbon, D.R. Moore, and J.D. Stuart, "Exact, Infinite Energy, Blow up Solutions of the Three-Dimensional Euler Equations," Nonlinearity 16, 2003, pp. 1823 - 1931.
  • P. Constantin, G. Gallavoti, A.V. Kazhikov, Y. Meyer, and S. Ukai, Mathematical Foundation of Turbulent Viscous Flows, Springer-Verlag, Berlin Heidelberg, 2003.
  • P. Penel and M. Pokorny, "Some New Regularity Criteria for the Navier-Stokes Equations Containing Gradient of the Velocity," Applications of Mathematics 49, No. 5, 2004, pp. 483 - 493.
  • Y. Zhou, "On a Regularity Criterion in Terms of the Gradient Pressure for the Navier-Stokes Equations in," Z. angew. Math. Phys 57, 2006, pp. 384 - 392.
  • S.K. Kao, "An Analytical Solution for Three-Dimensional Stationary Flows in the Atmospheric Boundary Layer over Terrain," Journal of Applied Meteorology, Vol. 20, 1980.
  • V. Christianto and F. Smarandache, "An Exact Mapping from Navier- Stokes Equation to Schrodinger Equation via Riccati Equation," Progress in Physics, Vol. 1, 2008.
  • F. Kamran, C. Zu-Chi, J. Xiaoda, and Y. Cheng, "Similarity Reduction of a (3+1) Navier-Stokes System," Engineering Computations: International Journal for Computer-Aided Engineering and Software, Vol. 23, No. 6, 2006, pp. 632 - 643. [10] A.V. Meleshko, "A Particular Class of Partially Invariant Solutions of the Navier-Stokes Equations," Nonlinear Dynamics 36, 2004, pp. 47 - 68. [11] K. Thailert, "One Class of Regular Partially Invariant Solutions of the Navier-Stokes Equations," Nonlinear Dynamics, 2005. [12] E.P. Symons and T.K. Labus, "Experimental Investigation of an Axisymmetric Fully Developed Laminar Free Jet," NASA Technical Notes, D-6304, 1971. [13] T. Eappen, "Exit Region of Submerged Laminar Jets," Thesis, Submitted to the Faculty of Graduate Studies, Department of Mechanical Engineering, University of Windsor, Ontario, Canada, 1991. [14] C. Farrel and A.K.S. Iyengar, "Experiments on the Wind Tunnel Simulation of Atmospheric Boundary Layers," Journal of Wind Engineering and Industrial Aerodynamics 79, pp. 11 - 35, 1999. [15] A. Cuoci, Frassoldati, G. Buzzi Ferraris, T. Faravelli, and E. Ranzi, "The Ignition, Combustion and Flame Structure of Carbon Monoxide/Hydrogen Mixtures. Note 2: Fluid Dynamics and Kinetic Aspects of Syngas Combustion," Int. J. Hydrogen Energy, 2007.