Huete Ruiz de Lira, CésarUrzay Lobo, JavierSánchez Pérez, Antonio LuisForman, Williams A.2021-05-202021-05-202016-03AIAA Journal, 54(3), March 2016, Pp. 962-9750001-14521533-385X (online)https://hdl.handle.net/10016/32700This paper extends to transonic mixing layers an analysis of Lighthill ("Reflection at a Laminar Boundary Layer of a Weak Steady Disturbance to a Supersonic Stream, Neglecting Viscosity and Heat Conduction," Quarterly Journal of Mechanics and Applied Mathematics, Vol. 54, No. 3, 1950, pp. 303-325.) 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.14eng© 2015 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.PropulsionBoundary layer analysisAdverse pressure gradientSupersonic flowSupersonic combustionViscosityThermal diffusivityApplied mathematicsFlame holderFreestream Mach Numberresearch articleIngeniería IndustrialAeronáuticahttps://doi.org/10.2514/1.J054419open access9623975AIAA JOURNAL54AR/0000027286