Linear Stability Models for Reacting Mixing Layers

Abstract

We develop a physics-based reduced-order model of the aero-acoustic sound sources in reacting mixing layers as a method for fast and accurate predictions of the radiated sound. Instabilities in low-speed mixing layers are known to be dominated by the traditional Kelvin–Helmholtz (K–H)-type “central” mode, which is expected to be superseded by the “outer” modes as the chemical-reaction-based heat-release modifies the mean density, yielding new peaks in the density-weighted vorticity profiles. Although, these outer modes are known to be of lesser importance in the near-field mixing, how these radiate to the far-field is uncertain, on which we focus primarily, when the mixing layer is supersonic, but also report subsonic cases. On keeping the flow compressibility fixed, the outer modes are realized via biasing the respective mean density of the fast (oxidizer) or slow (fuel) side. In the linearized model that we use, the mean flow are laminar solutions of two-dimensional compressible boundary layers with an imposed composite turbulent spread rate, which we show to correctly predict the growth of instability waves by saturating them earlier, similar to in non-linear calculations, but obtained here via solving the linear parabolized stability equations (PSE). The chemical reaction is modeled via a single-step, single-product overall process which introduces a heat release term in the mean temperature equation. As the flow parameters are varied, modes that are unstable on the slow side are shown to be more sensitive to heat release, potentially exceeding equivalent central modes, as these modes yield relatively compact sound sources with lesser spreading of the mixing layer, when compared to the corresponding fast modes. In contrast, the radiated sound, obtained directly from the PSE solutions, seems to be relatively unaffected by a variation of mixture equivalence ratio, except for a lean mixture which is shown to yield a pronounced effect on the slow mode radiation by reducing its modal growth. For subsonic mixing layers, the sensitivity of central mode is explored, which in addition requires an acoustic analogy based method (e.g. the Lilley–Goldstein equations) to predict the sound from the linearized PSE sources, as used here, unlike in supersonic cases.