International Science Index


Effect of Atmospheric Pressure on the Flow at the Outlet of a Propellant Nozzle


The purpose of this work is to simulate the flow at the exit of Vulcan 1 engine of European launcher Ariane 5. The geometry of the propellant nozzle is already determined using the characteristics method. The pressure in the outlet section of the nozzle is less than atmospheric pressure on the ground, causing the existence of oblique and normal shock waves at the exit. During the rise of the launcher, the atmospheric pressure decreases and the shock wave disappears. The code allows the capture of shock wave at exit of nozzle. The numerical technique uses the Flux Vector Splitting method of Van Leer to ensure convergence and avoid the calculation instabilities. The Courant, Friedrichs and Lewy coefficient (CFL) and mesh size level are selected to ensure the numerical convergence. The nonlinear partial derivative equations system which governs this flow is solved by an explicit unsteady numerical scheme by the finite volume method. The accuracy of the solution depends on the size of the mesh and also the step of time used in the discretized equations. We have chosen in this study the mesh that gives us a stationary solution with good accuracy.

[1] Haoui, R., “Design of the propelling nozzles for the launchers and satellites”, International Journal of Aeronautical and space Sciences, 15(1), 2014, pp91-96. DOI:10.5139/IJASS.2014.15.1.91.
[2] Haoui, R. Gahmousse, A. Zeitoun, D., “Condition of convergence applied to an axisymmetric reactive flow”, 16th CFM, n°738, Nice, France, 2003.
[3] 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.
[4] Van Leer, B., “Flux Vector Splitting for the Euler Equations”, Lecture Notes in Physics. 170, 1982, 507-512.
[5] Haoui, R., “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. DOI:10.5139/IJASS.2010.33.1.059
[6] Haoui, R., “Effect of Mesh Size on the Viscous Flow Parameters of an Axisymmetric Nozzle”, International Journal of Aeronautical and space Sciences, 12(2), 2011,
[7] Shapiro, A.H. (1954). The Dynamics and Thermodynamics of Compressible fluid flow. The Ronald Press Company, New York. Volume II. Ch.17.
[8] H. Schlichting, Boundary-layer theory, 7th edition, McGraw-Hill, New York, 1979.
[9] K. A. Hoffmann, Computational fluid dynamics for engineers, Volume II. Chapter 14, Engineering Education system, Wichita, USA, pp.202-235, 1995.
[10] Joel H. Ferziger & M. Peric, Computational Methods for Fluid Dynamics, Chapter 8, Springer-Verlag, Berlin Heidelberg, New York, 2002, pp.217-259,
[11] M-C. Druguet, “Contribution to the study of nonequilibrium reactive hypersonic Euler’s flows,” Thesis of Doctorate. University of Provence, France, 1992.
[12] L. Landau, E. Teller, “Theory of sound dispersion,” Physikalische Zeitschrift der Sowjetunion. 10, (1936), 34-43.