{"title":"Toward a New Simple Analytical Formulation of Navier-Stokes Equations","authors":"Gunawan Nugroho, Ahmed M. S. Ali, Zainal A. Abdul Karim","volume":27,"journal":"International Journal of Mechanical and Mechatronics Engineering","pagesStart":252,"pagesEnd":257,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/6484","abstract":"Incompressible Navier-Stokes equations are reviewed\nin this work. Three-dimensional Navier-Stokes equations are solved\nanalytically. The Mathematical derivation shows that the solutions\nfor the zero and constant pressure gradients are similar. Descriptions\nof the proposed formulation and validation against two laminar\nexperiments and three different turbulent flow cases are reported in\nthis paper. Even though, the analytical solution is derived for nonreacting\nflows, it could reproduce trends for cases including\ncombustion.","references":"[1] J.C. Kalita, A.K. Dass, and N. Nidhi, \"An Efficient Transient Navier-\nStokes Solver on Compact Nonuniform Space Grids,\" Journal of\nComputational and Applied Mathematics 214, 2008, pp. 124 - 162.\n[2] Y. He and A. Wang, \"A Simplified Two-Level Method for the Steady\nNavier-Stokes Equations,\" Comput. Methods Appl. Mech. Engrg. 197,\n2008, pp. 1568 - 1576.\n[3] J.D. Gibbon, D.R. Moore, and J.D. Stuart, \"Exact, Infinite Energy, Blow\nup Solutions of the Three-Dimensional Euler Equations,\" Nonlinearity\n16, 2003, pp. 1823 - 1931.\n[4] P. Constantin, G. Gallavoti, A.V. Kazhikov, Y. Meyer, and S. Ukai,\nMathematical Foundation of Turbulent Viscous Flows, Springer-Verlag,\nBerlin Heidelberg, 2003.\n[5] P. Penel and M. Pokorny, \"Some New Regularity Criteria for the\nNavier-Stokes Equations Containing Gradient of the Velocity,\"\nApplications of Mathematics 49, No. 5, 2004, pp. 483 - 493.\n[6] Y. Zhou, \"On a Regularity Criterion in Terms of the Gradient Pressure\nfor the Navier-Stokes Equations in,\" Z. angew. Math. Phys 57, 2006, pp.\n384 - 392.\n[7] S.K. Kao, \"An Analytical Solution for Three-Dimensional Stationary\nFlows in the Atmospheric Boundary Layer over Terrain,\" Journal of\nApplied Meteorology, Vol. 20, 1980.\n[8] V. Christianto and F. Smarandache, \"An Exact Mapping from Navier-\nStokes Equation to Schrodinger Equation via Riccati Equation,\"\nProgress in Physics, Vol. 1, 2008.\n[9] F. Kamran, C. Zu-Chi, J. Xiaoda, and Y. Cheng, \"Similarity Reduction\nof a (3+1) Navier-Stokes System,\" Engineering Computations:\nInternational Journal for Computer-Aided Engineering and Software,\nVol. 23, No. 6, 2006, pp. 632 - 643.\n[10] A.V. Meleshko, \"A Particular Class of Partially Invariant Solutions of\nthe Navier-Stokes Equations,\" Nonlinear Dynamics 36, 2004, pp. 47 -\n68.\n[11] K. Thailert, \"One Class of Regular Partially Invariant Solutions of the\nNavier-Stokes Equations,\" Nonlinear Dynamics, 2005.\n[12] E.P. Symons and T.K. Labus, \"Experimental Investigation of an\nAxisymmetric Fully Developed Laminar Free Jet,\" NASA Technical\nNotes, D-6304, 1971.\n[13] T. Eappen, \"Exit Region of Submerged Laminar Jets,\" Thesis,\nSubmitted to the Faculty of Graduate Studies, Department of\nMechanical Engineering, University of Windsor, Ontario, Canada, 1991.\n[14] C. Farrel and A.K.S. Iyengar, \"Experiments on the Wind Tunnel\nSimulation of Atmospheric Boundary Layers,\" Journal of Wind\nEngineering and Industrial Aerodynamics 79, pp. 11 - 35, 1999.\n[15] A. Cuoci, Frassoldati, G. Buzzi Ferraris, T. Faravelli, and E. Ranzi, \"The\nIgnition, Combustion and Flame Structure of Carbon\nMonoxide\/Hydrogen Mixtures. Note 2: Fluid Dynamics and Kinetic\nAspects of Syngas Combustion,\" Int. J. Hydrogen Energy, 2007.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 27, 2009"}