Diffusion-Flame Ignition by Shock-Wave Impingement on a Hydrogen–Air Supersonic Mixing Layer

Abstract

Ignition in a supersonic hydrogen-air mixing layer interacting with an oblique shock wave is investigated analytically under conditions such that the post-shock flow is supersonic and the peak post-shock temperature prior to ignition remains below the crossover temperature. The study requires consideration of the flow structure in the post-shock ignition kernel found around the point of maximum temperature, which is assumed in this study to lie at an intermediate location across the mixing layer, as occurs in mixing layers subject to significant viscous dissipation. The ignition kernel displays a balance between the rates of chemical reaction and post-shock flow expansion, including the acoustic interactions of the chemical heat release with the shock wave leading to increased front curvature. The problem is formulated with account taken of the strong temperature dependence of the chemical heat-release rate characterizing the ignition chemistry in the low-temperature regime analyzed here. It is shown how consideration of a two-step reduced chemicalkinetic mechanism derived in previous work leads to a boundary-value problem that can be solved analytically to determine ignition as a fold bifurcation, with the turning point in the diagram of peak perturbation induced by the chemical reaction as a function of the Damköhler number providing the critical conditions for ignition.

Interaction of Oblique Shocks and Laminar Shear Layers

“…7, which affect mostly the temperature distribution outside the shear layer, are inconsequential for ignition. These results therefore indicate that the computation of critical ignition conditions can make use of the Moeckel-Chisnell theory in evaluating the postshock temperatures with good accuracy, as was done in earlier analyses [5,6].…”

“…apply to the downstream flow properties above the contact surface. Correspondingly, equations (4), (5), and (6) together with the two additional contact-surface conditions (p 4 /p 3 )(p 3 /p u ) = (p 5 /p u ) and ν t = ν i − ν r (7) provide a set of eleven algebraic equations that determine M 3 , M 4 , M 5 , σ r , σ t , ν i , ν r , ν t , p 3 /p u , p 4 /p u , and p 5 /p u as a function of M 1 , M 2 , and σ i for a regular refraction with a reflected shock wave. When the reflected wave is an expansion, however, the expressions (6) must be replaced, with σ r = sin −1 (M 3 ), by…”

“…where shocks generated in the air stream at wedged walls and fuel injectors impinge on the shear layer surrounding the fuel jets downstream from the injection point [2]. Although the flow is typically turbulent in these high-Reynoldsnumber applications, analyses of laminar flows have been shown to be instrumental in providing insightful information pertaining to mixing augmentation by vorticity production [3,4] and enhanced chemical reaction leading to ignition [5,6] behind the curved shock.…”

On the role of bulk viscosity in compressible reactive shear layer developments

“…In an attempt to better understand the behavior of the TKE, the analysis of the main terms involved in its transport equation is now carried out. The transport equation for the turbulent kinetic energy K is given by ∂ t (ρK) + ∇ · (ρũK) = P + ε + T + Π + Σ (12) In this equation, P is the production term, ε is the dissipation term, T denotes the turbulent transport term, Π is the pressure-strain term, and finally Σ the mass flux term. The budget (12) is deduced from the transport equation of the Reynolds tensor components: Fig.…”

“…Using direct numerical simulation (DNS), we investigate the impact of the bulk viscosity coefficient κ on the spatial development of reactive and non-reactive compressible mixing layers interacting with an oblique shock wave. Such a canonical flowfield is typical of the shock-mixing layer interactions that take place in compressible flows of practical interest [12]. For instance, supersonic jets at high nozzle-pressure ratio (NPR) give rise to complex cellular structures, where shocks and expansions waves interact with the turbulent outer shear layer [13].…”