Shock Waves DOI 10.1007/s00193-013-0458-3 ORIGINAL ARTICLE Numerical investigation of overexpanded nozzle flows Asymmetrical configuration and hysteresis phenomenon M. Sellam · G. Fournier · A. Chpoun · Ph. Reijasse Received: 31 October 2011 / Revised: 18 January 2013 / Accepted: 17 February 2013 © Springer-Verlag Berlin Heidelberg 2013 Abstract The flow in a planar overexpanded nozzle with a slope discontinuity is studied numerically by means of two- (2D) and three-dimensional (3D) Reynolds-averaged Navier–Stokes simulations and is compared to experimen- tal results. The nozzle pressure ratios (NPR) vary from 1.6 to 10. A good agreement is found between experimental and numerical results and two configurations are observed: under a certain critical NPR, the flow is shown to be asymmetrical with respect to the nozzle axis, while it is perfectly sym- metrical for higher NPRs. The value of the critical NPR is found to be very dependent on the turbulence model. Finally, an hysteresis phenomenon is evidenced since the NPR at which the change of flow configuration occurs is dif- ferent whether the NPR is increasing or decreasing in the nozzle. Keywords Overexpanded nozzle · Asymmetrical configuration · Hysteresis phenomenon · Reynolds-averaged Navier–stokes simulations Communicated by H. Olivier and K. Kontis. The paper was based on work that was presented at the 28th International Symposium on Shock Waves, 17–22 July. M. Sellam · G. Fournier (B ) · A. Chpoun Laboratoire de Mécanique et d’Energétique d’Evry, 40 rue du Pelvoux, 91020 Evry Cedex, France e-mail: guillaume.fournier@iup.univ-evry.fr M. Sellam e-mail: sellam@iup.univ-evry.fr Ph. Reijasse ONERA, 8 rue des vertugadins, 92190 Meudon, France 1 Introduction During ascent in low altitudes, space launchers experience high nozzle-exit-pressure leading to flow separation in the diverging part. Two flow separation regimes have been iden- tified: free shock separation (FSS) and restricted shock sep- aration (RSS) regimes [1]. The transition between these two regimes with potential asymmetry of the flow could lead to high side loads which are of great practical importance. Meanwhile, modern rocket nozzles are optimized for maxi- mum thrust during the entire ascent trajectory. In compliance with the launcher overall dimensions, the diverging part of these nozzles is truncated and the nozzle area-ratio is read- justed to satisfy the exit Mach number. Thus, the resulting thrust-optimised contour nozzle is characterised by a high angle of divergence at the throat compared to an ideal nozzle contour. As a consequence, an internal shock emanating from the nozzle throat region can interact with the shock waves system produced by flow separation at the end of the nozzle. Recently for the first time, the influence of the internal shock wave on the transition between free separation and restricted separation regimes has been questioned [2]. This work has had both a theoretical part by analysing shock waves interfer- ences inside the diverging part of the nozzle and an extensive experimental program during which measurements of both steady and unsteady pressures were obtained. In order to improve our understanding of the physical mechanisms that occur in that nozzle and to increase the num- ber of available data, it was decided to study the same prob- lem numerically. 2D and 3D numerical simulations have then been carried out at the Laboratoire de Mécanique et d’Ener- gétique in Evry, using the FASTRAN computational fluid dynamics code. This code has full 3D capability treating both structured and unstructured mesh. It solves the Reynolds- averaged Navier–Stokes (RANS) equations with different 123