Hydrodynamic instabilities and transverse waves in propagation mechanism of gaseous detonations Y. Mahmoudi 1 , K. Mazaheri n , S. Parvar Department of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran article info Article history: Received 3 May 2013 Received in revised form 4 June 2013 Accepted 7 June 2013 Available online 15 June 2013 Keywords: Detonation structure Richtmyer–Meshkov instability Kelvin–Helmholtz instability Transverse waves Keystone region abstract The present study examines the role of transverse waves and hydrodynamic instabilities mainly, Richtmyer–Meshkov instability (RMI) and Kelvin–Helmholtz instability (KHI) in detonation structure using two-dimensional high-resolution numerical simulations of Euler equations. To compare the numerical results with those of experiments, Navier– Stokes simulations are also performed by utilizing the effect of diffusion in highly irregular detonations. Results for both moderate and low activation energy mixtures reveal that upon collision of two triple points a pair of forward and backward facing jets is formed. As the jets spread, they undergo Richtmyer–Meshkov instability. The drastic growth of the forward jet found to have profound role in re-acceleration of the detonation wave at the end of a detonation cell cycle. For irregular detonations, the transverse waves found to have substantial role in propagation mechanism of such detonations. In regular detona- tions, the lead shock ignites all the gases passing through it, hence, the transverse waves and hydrodynamic instabilities do not play crucial role in propagation mechanism of such regular detonations. In comparison with previous numerical simulations present simula- tion using single-step kinetics shows a distinct keystone-shaped region at the end of the detonation cell. & 2013 IAA. Published by Elsevier Ltd. All rights reserved. 1. Introduction A detonation consists of a shock wave, which is coupled with a reaction zone propagating at supersonic speed. In reality all self-sustained detonations are unstable with three-dimensional transient cellular structure that is formed by an ensemble of interacting shock waves [1,2]. Because of the fundamental importance of the cyclic evolution of detonations structure, it is worthwhile to review the main features of a cellular detonation structure. A schematic of a detonation cell is shown in Fig. 1. The direction of propagation of the detonation is from left to right. The structure consists of a leading shock, involving Mach stems and incident waves. Shear layers and trans- verse shocks extend from the cell boundaries into the reaction zone behind the leading shocks. Triple points exist at the intersection of the leading shock front and the transverse waves. The transverse shocks sweep laterally across the structure behind the shock and collide with each other. They also interact and sometimes couple with the shear layers [3]. At the apex of a cell (point A in Fig. 1) the head-on collision of two triple points occurs. Subse- quent to the collision, a Mach stem and two transverse waves are formed. While the Mach stem propagates as the leading shock, the transverse shocks propagate away from each other. Upon the collision, a region of high tempera- ture and pressure is formed. The unreacted compressed gases are burnt rapidly in this region [4]. Such hot and burned materials generate a pair of forward and backward Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/actaastro Acta Astronautica 0094-5765/$ - see front matter & 2013 IAA. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actaastro.2013.06.009 n Corresponding author. Tel./fax: +98 218 288 3962. E-mail addresses: s.y.mahmoudilarimi@tudelft.nl (Y. Mahmoudi), kiumars@modares.ac.ir (K. Mazaheri). 1 Current address: Department Process and Energy, Section Fluid Mechanics, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands. Acta Astronautica 91 (2013) 263–282