Application of De-Laval Nozzle Transonic Flow Field Computation Approaches

Authors: A. Haddad, H. Kbab

Abstract:

A supersonic expansion cannot be achieved within a convergent-divergent nozzle if the flow velocity does not reach that of the sound at the throat. The computation of the flow field characteristics at the throat is thus essential to the nozzle developed thrust value and therefore to the aircraft or rocket it propels. Several approaches were developed in order to describe the transonic expansion, which takes place through the throat of a De-Laval convergent-divergent nozzle. They all allow reaching good results but showing a major shortcoming represented by their inability to describe the transonic flow field for nozzles having a small throat radius. The approach initially developed by Kliegel & Levine uses the velocity series development in terms of the normalized throat radius added to unity instead of solely the normalized throat radius or the traditional small disturbances theory approach. The present investigation carries out the application of these three approaches for different throat radiuses of curvature. The method using the normalized throat radius added to unity shows better results when applied to geometries integrating small throat radiuses.

Keywords: De-Laval nozzles, transonic calculations, transonic flow, supersonic nozzle.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1336050

References:

[1] H. Kbab, "Développement et comparaison des méthodes de calcul des écoulements transsoniques”, MSc dissertation, Department of aeronautics, Saad Dahlab University, Blida, 2001.
[2] Th. Von Karman, "The similarity law of transonic flow”, J. Math. And Phys., 26, pp. 182-190, 1947.
[3] H. Yuan, and Y. He, "Transonic potential flows in a convergent divergent approximate nozzle”, J. Math. Anal. Appl., (2) 353, pp. 614-626, 2009.
[4] A.G. Kuz’min, "Boundary-Value Problems for Transonic Flow”, John Wiley & sons, West Sussex, 2002.
[5] V.S. Oliveira Leith, P.A. Sovicro, and D. Bastos-Netto, "Numerical evaluation of the flow inside the transonic nozzle of a direct-connect supersonic combustion research facility”, 18th ICME, Nov. 6-11, 2005.
[6] C. Wenxiang, "Applying numerical solution to analyze the performance of nozzles”, ICEET’2009, 16-18 Oct. 2009.
[7] A., Sauer, "General Characteristics of the Flow through Nozzles at Near Critical Speeds”, NACA TM-1147, 1947.
[8] I. M. Hall, "Transonic Flow in Two-Dimensional and Axially–Symmetric Nozzles”, Quarterly. Journal of Mechanics and Applied Mechanics, Vol. XV, Pt. 4, pp 487-508, 1962.
[9] J. R. Kliegel, and J. N. Levine, "Transonic Flow in Small Throat Radius of Curvature Nozzles”, AAIA journal, Vol. 7, N° 7, pp. 1375-1378, 1969.
[10] M. J. Zucrow, and J. D. Hoffman, "Gas Dynamics”, John Wiley & sons, 1976, vol. 2.
[11] L. H. Back, and R.F. Cuffel, "Flow Coefficients For Supersonic Nozzles With Comparatively Small Radius of Curvature Throats’, AAIA. Journal, Vol. 8, N° 2, pp.196-198, 1970.