Flame Acceleration and DDT in a Torus Geometry M. Kuznetsov, J. Yanez, and J. Grune Introduction The ignition, ﬂame propagation with a ﬂow ahead of the ﬂame, and shock waves generation with turbulent boundary layer behind the shock are the sequence of princi- pal events leading to the deﬂagration onset in smooth channels. A speciﬁc effect of geometry connected with boundary layer phenomena, turbulent ﬂow generation, and shock–ﬂame interaction might also be of the great interest for the deﬂagration-to-detonation transition (DDT) phenomena. An experimental and numerical study of detonation propagation in an annular structure was recently investigated with respect to rotating detonation engines (RDE) [1, 2]. A stability of gaseous detonation propagating in a coaxial cylinder was numerically and experimentally studied for hydrogen/oxygen/nitrogen mixtures. Due to a curvature of the annular tube, the size of cellular pattern along the concave wall is smaller than that along the convex wall. This implies that the detonation wave near the concave wall is convergent and therefore is stronger than that near the divergent convex wall [3]. A possibility of hydrogen combustion and then detonation in annular geometry was numerically analyzed for safety purposes of hydrogen–air mixtures in vacuum vessel of ITER fusion reactor [4]. The process of ﬂame propagation in coaxial annular geometry leads to additional stretching and acceleration of the ﬂame. A similar problem was experimentally investigated for methane–air mixtures in an open duct with 90 o bend [5]. Again, the stretching of the ﬂame and 1.5 times ﬂame veloc- ity increase observed experimentally and numerically modeled. Premixed ﬂame propagation in a closed duct with a 90  bend was experimentally and numerically studied in papers [6, 7]. It was shown that the ﬂame area at the bend part increased 3–4 times. It results in eight times faster propagation of the outer part of the concaved ﬂame. It was also shown that a 90  bend in a long tube had the ability to enhance ﬂame speeds and overpressures and shorten the run-up distance to DDT to a varying degree for a number of gasses [8]. Experimental and numerical results showed that ﬂame at the bend part could behave as a thrust resource for the unburned mixture to generate or induce very complex ﬂow ﬁelds which could facilitate unburned material that subsequently affects the ﬂame behavior [9]. This interaction between the ﬂame and the ﬂame-induced ﬂows results in higher dynamic pressure acting forward on the corner portions of the ﬂame front. The presence of a streamwise- oriented vortex pair near the inner surface of the bend and the high-pressure region near the outer surface signiﬁcantly affects the ﬂame dynamics. Most of the studies focus on the ﬂame propagation in linear geometry or straight channel combined with a bent part. It was found to have a strong promoting effect of bending of the channel for ﬂame acceleration and then DDT. The main advantage of the annular channel is that the ﬂame should propagate along two surfaces with different curvatures. It additionally can stretch the ﬂame with an increase of the ﬂame surface and in turn the ﬂame propaga- tion velocity. It should also produce a funnel of unburned material along outer surface with larger radius of curvature producing strong turbulent ﬂow within the shear layer. It may lead to additional ﬂame acceleration and DDT. There- fore, the problem of ﬂame acceleration and DDT in an annular geometry is of great interest for many practical applications. M. Kuznetsov (*)  J. Yanez Institute for Nuclear and Energy Technologies, Karlsruhe Institute of Technology, Hermann-von-Helmholtz Platz 1, Eggenstein-Leopoldshafen 76344, Germany e-mail: kuznetsov@kit.edu J. Grune Pro-Science GmbH, Parkstrasse 9, 76275 Ettlingen, Germany # Springer International Publishing AG 2017 G. Ben-Dor et al. (eds.), 30th International Symposium on Shock Waves 1, DOI 10.1007/978-3-319-46213-4_65 385