Effect of Mesh Size on the Viscous Flow Parameters of an Axisymmetric Nozzle
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.
[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.
[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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:60520", author = "Rabah Haoui", title = "Effect of Mesh Size on the Viscous Flow Parameters of an Axisymmetric Nozzle", 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", volume = "5", number = "11", pages = "2416-6", }