Interaction of a planar reacting shock wave with an isotropic turbulent vorticity field

Abstract

Linear interaction analysis (LIA) is employed to investigate the interaction of reactive and nonreactive shock waves with isotropic vortical turbulence. The analysis is carried out, through Laplace-transform technique, accounting for long-time effects of vortical disturbances on the burnt-gas flow in the fast-reaction limit, where the reaction-region thickness is significantly small in comparison with the most representative turbulent length scales. Results provided by the opposite slow-reaction limit are also recollected. The reactive case is here restricted to situations where the overdriven detonation front does not exhibit self-induced oscillations nor inherent instabilities. The interaction of the planar detonation with a monochromatic pattern of perturbations is addressed first, and then a Fourier superposition for three-dimensional isotropic turbulent fields is employed to provide integral formulas for the amplification of the kinetic energy, enstrophy, and anisotropy downstream. Transitory evolution is also provided for single-frequency disturbances. In addition, further effects associated to the reaction rate, which have not been included in LIA, are studied through direct numerical simulations. The numerical computations, based on WENO-BO4-type scheme, provide spatial profiles of the turbulent structures downstream for four different conditions that include nonreacting shock waves, unstable reacting shock (sufficiently high activation energy), and stable reacting shocks for different detonation thicknesses. Effects of the propagation Mach number, chemical heat release, and burn rate are analyzed.

Effect of equivalence ratio fluctuations on planar detonation discontinuities

“…The results shown in figures 3-5 are qualitatively similar to those obtained previously for the interaction of detonations with random vorticity perturbations (Jackson et al 1993;Huete et al 2017). However, a detailed comparison requires taking into account the diverse criteria used for normalization in different investigations.…”

“…Earlier work on the interaction of small-amplitude perturbations with detonation waves can be found in Massa, Chauhan & Lu (2011), , Jin et al (2016), Hussein (2018), Jackson, Kapila & Hussaini (1990); Jackson, Hussaini & Ribner (1993), Huete, Sánchez & Williams (2013, 2014, Griffond (2005) and Huete et al (2017). When the problem is addressed numerically, chemical kinetic models can be implemented Jin et al 2016;Hussein 2018), which allows the description of the detonation unstable modes.…”

“…(2016), Hussein (2018), Jackson, Kapila & Hussaini (1990); Jackson, Hussaini & Ribner (1993), Huete, Sánchez & Williams (2013, 2014), Griffond (2005) and Huete et al. (2017). When the problem is addressed numerically, chemical kinetic models can be implemented (Massa et al.…”

“…(1990, 1993) and Huete et al. (2013, 2014, 2017) may be applied. Employing the fast-reaction limit allows the detonation wave to be treated as a single discontinuity front, and the chemical process exclusively enters through the non-adiabatic RH curve.…”

Flame evolution in shock-accelerated flow under different reactive gas mixture gradients

“…Especially for the practical situations, inhomogeneity in the reactive gas mixture will have a significant influence on the flame evolution. Actually, at present, the influence of inhomogeneity of the reactive gas mixture on the combustion processes has aroused widespread interest [11][12][13][14], but few studies have been devoted to the shock-flame interaction topic. The investigation of the shock-flame interaction in the inhomogeneous reactive gas mixture will help us gain more insight, particularly when a high intensity shock wave is adopted.…”