Weak-Shock Interactions with Transonic Laminar Mixing Layers of Fuels for High-Speed Propulsion

Abstract

on the interaction between weak shocks and laminar boundary layers. As in that work, the analysis is carried out under linear-inviscid assumptions for the perturbation field, with streamwise changes of the base flow neglected, as is appropriate given the slenderness of the mixing-layer flow. The steady-disturbance profile is determined by taking a Fourier transform along the longitudinal coordinate. Closed-form analytical functions for the pressure field are derived in the small-and large-wave-number limits, and vorticity disturbances are obtained as functions of the pressure perturbations. The analysis is particularized to ethylene-air and hydrogen-air mixing layers, for which the dynamics are of current interest for hypersonic propulsion. The results provide, in particular, the effective distance of upstream influence of the pressure perturbation in the subsonic stream. The resulting value, which scales with the thickness of the subsonic layer, is much smaller than the upstream influence distances encountered in boundary layers. This study may serve as a basis to understand shock-induced autoignition and flameholding phenomena in simplified versions of non-premixed supersonic-combustion problems.

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

“…Ignition may, however, also be generated by weaker shocks that do not raise the gas temperature to crossover, if the critical value ∆ = ∆ c is exceeded. This would occur at sufficiently large values of the Damköhler number D in (22), of order unity. This ratio of cooling time to chemical time is affected by flow-configuration parameters, such as the thickness δ of the mixing layer and the order-unity nondimensional measure Λ of the rate of acoustic cooling, increasing in proportion to the ratio δ/Λ, which combines with U o to determine the relevant cooling time.…”

“…Pre-shock properties at the ignition kernel, M o , T o , p o , and Y o , have been obtained by computing the mixing-layer profiles for the above-mentioned feed-stream conditions (see ref. 22 for details). Contours of constant values of the air-stream shock angle σ ∞ and shock strength p ∞ /p are also shown in the figure, based on the Moeckel approximation, 14 suggesting that relatively weak incident shocks would be sufficient under these conditions.…”

Diffusion-flame ignition by shock-wave impingement on a supersonic mixing layer

“…In that case, the perturbations generated by the shock-wave impingement propagate upstream on the subsonic side, altering significantly the flow and deflecting the incoming mixing layer. Previous investigations of the resulting shock-reflection problem have been restricted to weak shocks (Riley 1960;Huete et al 2015), including upstream perturbations of small amplitude, a case for which the theory of shock-boundary layer interaction developed by Lighthill (1950Lighthill ( , 1953 was found to be instrumental in deriving analytical results. The interaction of transonic mixing layers with shocks of finite strength, including significant perturbations on the subsonic side upstream from the shock, appears to be a difficult problem not treated previously, in which the unknown location of the shock wave is coupled with the mixing-layer deflection.…”

“…These sample integrations including viscous dissipation neglect variations of the mean molecular weight and assume a fuel Lewis number of unity, with thermal diffusion neglected, as is appropriate for fuels that have properties close to those of air, such as ethylene, which has been employed in recent supersonic-combustion research (Dolvin 2008). A detailed description of the mixing-layer formulation employed in the integrations can be found in Huete et al (2015).…”

“…The blowup shows upstream mixing-layer profiles of temperature (thick curves) and fuel mass fraction (thin curves) obtained with M −∞ = 1.5 and T −∞ /T ∞ = 0.375 for M ∞ = 2.0 (dashed curves) and M ∞ = 5.0 (solid curves), with δ m = 2[D F x/U ∞ ] 1/2 representing the mixing-layer thickness, computed at a given downstream location x with use made of the fuel diffusivity D F and air-stream velocity U ∞ ; seeHuete et al (2015) for details of the associated computations.…”