25 th ICDERS August 2–7, 2015 Leeds, UK Deflagration-to-detonation transition in narrow channels: Hydraulic resistance vs. flame folding L. Kagan and G. Sivashinsky School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel 1 Abstract This study is concerned with identification of the key interactions controlling deflagration-to-detonation transition (DDT) in narrow smooth-walled channels. Two agencies contributing to the transition are dis- cussed: hydraulic resistance for very thin channels (thick flames) and flame folding for wider channels (moderately thick flames). The dual nature of the DDT mechanism is reflected in the non-monotinicity of the dependency of the run-up time/distance on the channel width. 2 Outline of the problem Deflagration-to-detonation transition (DDT) occurring in smooth-walled thermally insulated channels, narrow enough to ensure the laminar character of the developing flow, is arguably the simplest system for theoretical/numerical exploration of the DDT. Yet, even under these benign conditions the emerg- ing dynamical picture is complex enough [1-4] for straightforward identification of the mechanisms involved. The present study is concerned with assessment of the relative impacts of hydraulic resistance and flame folding which have long been recognized as important players in the transition event [5-9]. To describe the DDT in a channel, a set of 2D Navier-Stokes equations for compressible reactive flows is employed; see Ref. [10] for details of equations and initial/boundary conditions. The reaction rate is modeled by a single-step second-order Arrhenius kinetics, W = Aρ 2 C exp (-E/RT ), where ρ is the gas density, C is the mass fraction of the deficient reactant, and A is the Arrhenius prefactor. Scaled variables and parameters appearing in the further discussion are defined as follows: Pr and Le are Prandtl and Lewis numbers; Ma = u p /a p , Mach number; u p , velocity of the isobaric deflagration relative to the burned gas; a p =  γ (c p - c v )T p sonic velocity at T = T p ; T p = T 0 + QC 0 /c p , adi- abatic temperature of burned gas (products) under constant pressure, P = P 0 ; T 0 , initial temperature of unburned gas; Q, heat release; γ = c p /c v ; c p ,c v , specific heats; C 0 , initial mass fraction of the deficient reactant; (ˆ u, ˆ v)=(u, v)/a p , scaled flow velocity; ˆ D = D/a p , scaled reaction wave velocity; (ˆ x, ˆ y)=(x, y)/x p , ˆ t = t/t p scaled spatio-temporal coordinates; x p = a p t p ; t p = A -1 Z exp (N p ), reference time; N p = E/RT p , scaled activation energy; Z = 1 2 Le -1 N 2 p (1 - σ p ) 2 , normalizing factor Correspondence to: kaganleo@post.tau.ac.il 1