Effect of Mesh Size on the Viscous Flow Parameters of an Axisymmetric Nozzle

Authors: Rabah Haoui

Abstract:

The aim of this work is to analyze a viscous flow in the axisymmetric nozzle taken into account the mesh size both in the free stream and into the boundary layer. The resolution of the Navier- Stokes equations is realized by using the finite volume method to determine the supersonic flow parameters at the exit of convergingdiverging nozzle. The numerical technique uses the Flux Vector Splitting method of Van Leer. Here, adequate time stepping parameter, along with CFL coefficient and mesh size level is selected to ensure numerical convergence. The effect of the boundary layer thickness is significant at the exit of the nozzle. The best solution is obtained with using a very fine grid, especially near the wall, where we have a strong variation of velocity, temperature and shear stress. This study enabled us to confirm that the determination of boundary layer thickness can be obtained only if the size of the mesh is lower than a certain value limits given by our calculations.

Keywords: Supersonic flow, viscous flow, finite volume, nozzle

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1077367

References:

[1] Goudjo, J.A. Désidéri, " a finite volume scheme to resolution an axisymmetric Euler equations (Un schéma de volumes finis décentré pour la résolution des équations d-Euler en axisymétrique), " Research report INRIA 1005, 1989.
[2] R. Haoui, A. Gahmousse, D. Zeitoun, " Chemical and vibrational nonequilibrium flow in a hypersonic axisymmetric nozzle, " International Journal of Thermal Sciences, article n┬░ 8 , volume 40, (2001), pp787-795.
[3] R. Haoui, "Finite volumes analysis of a supersonic non-equilibrium flow around the axisymmetric blunt body," International Journal of Aeronautical and space Sciences, 11(2), (2010), pp59-68.
[4] R. Haoui," Application of the finite volume method for the supersonic flow around the axisymmetric cone body placed in free stream," WIT press, Fourteenth international conference on computational methods and experimental measurements, pp379-388, Southampton, 2009.
[5] B. Van Leer, "Flux Vector Splitting for the Euler Equations," Lecture Notes in Physics. 170, (1982), 507-512.
[6] R. Haoui, A. Gahmousse, D. Zeitoun, "Condition of convergence applied to an axisymmetric reactive flow," 16th CFM, n┬░738, Nice, France, 2003.
[7] H. Schlichting, "Boundary-layer theory," 7th edition, McGraw-Hill, New York, 1979.
[8] K. A. Hoffmann, "Computational fluid dynamics for engineers," Volume II. Chapter 14, Engineering Education system, Wichita, USA, pp.202-235, 1995.
[9] J.H. Ferziger & all, "Computational Methods for Fluid Dynamics," Chapter 8, Springer-Verlag, Berlin Heidelberg, New York, pp.217-259, 2002.