International Journal of Aeronautical and Space Sciences

The Korean Society for Aeronautical and Space Sciences (한국항공우주학회)
권호 표지
DOI QR코드

DOI QR Code

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

  • Haoui, Rabah (Department of Mechanical Engineering, University of Science and Technology)
  • Received : 2011.02.23
  • Accepted : 2011.05.21
  • Published : 2011.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

The viscous flow in an axisymmetric nozzle was analyzed while accounting for the mesh sizes in both in the free stream and the boundary layer. The Navier-Stokes equations were resolved using the finite volume method in order to determine the supersonic flow parameters at the exit of the converging-diverging nozzle. The numerical technique in the aforementioned method uses the flux vector splitting of Van Leer. An adequate time stepping parameter, along with the Courant, Friedrich, Lewis coefficient and mesh size level, was selected to ensure numerical convergence. The boundary layer thickness significantly affected the viscous flow parameters at the exit of the nozzle. The best solution was obtained using a very fine grid, especially near the wall at which a strong variation of velocity, temperature and shear stress was observed. This study confirmed that the boundary layer thickness can be obtained only if the size of the mesh is lower than a certain value. The nozzles are used at the exit of the shock tube in order to obtain supersonic flows for various tests. They also used in propulsion to obtain the thrust necessary to the displacement of the vehicles.

Keywords

References

  1. Ferziger, J. H. and Peric, M. (2002). Computational Methods for Fluid Dynamics. 3rd rev. ed. Berlin: Springer. pp. 217-259.
  2. Goudjo, J. and Desideri, A. (1989). A Finite Volume Schemes to Resolution an Axisymmetric Euler Equation (Research report INRIA 1005). National Institute of Research in Informatics and Automatic (NIRIA).
  3. Haoui, R. (2009). Application of the finite volume method for the supersonic flow around the axisymmetric cone body placed in free stream. The 14th International Conference on Computational Methods and Experimental Measurements, Algarve, Portugal. pp. 379-388.
  4. Haoui, R. (2010). Finite volumes analysis of a supersonic non-equilibrium flow around the axisymmetric blunt body. International Journal of Aeronautical and Space Sciences, 11, 59-68. https://doi.org/10.5139/IJASS.2010.11.2.059
  5. Haoui, R., Gahmousse, A., and Zeitoun, D. (2001). Chemical and vibrational nonequilibrium flow in a hypersonic axisymmetric nozzle. International Journal of Thermal Sciences, 40, 787-795. https://doi.org/10.1016/S1290-0729(01)01265-0
  6. Haoui, R., Gahmousse, A., and Zeitoun, D. (2003). Condition of convergence applied to an axisymmetric reactive flow. The 16th French Congress of Mechanic, Nice, France.
  7. Hoffmann, K. A. (1995). Computational Fluid Dynamics for Engineers Vol. II. Chap. 14. Engineering Education System. Wichita, KS: Engineering Education System. pp. 202-235.
  8. Schlichting, H. (1979). Boundary-Layer Theory. 7th ed. New York: McGraw-Hill.
  9. Van Leer, B. (1982). Flux-vector splitting for the Euler equations. In E. Krause, ed. Eighth International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics Vol. 170. Heidelberg: Springer Berlin. pp. 507-512. https://doi.org/10.1007/3-540-11948-5_66