Combustion Processes in Interfacial Instabilities

Fluid instabilities, particularly interfacial instabilities, have proven to be a powerful mechanism in driving and sustaining combustion processes in several devices of practical interest. Modern combustors are in fact designed to exploit the mixing and combustion characteristics associated with a broad class of canonical, interfacial instabilities. In spite of their relevance to combustor design, a detailed understanding of such flows has been elusive. While much progress has been made in gaining insights into the dynamics of shear-driven flows, an understanding of the interaction between combustion processes and other interfacial instabilities remains preliminary. In this chapter, we review recent results on Rayleigh-Taylor (RT) instability and the shock-driven Richtmyer-Meshkov (RM) instability in the context of combustion. The vast catalogue of research on non-reacting RT and RM flows has demonstrated these instabilities can be manipulated to achieve more efficient and aggressive mixing in comparison with the canonical Kelvin-Helmholtz (KH) problem. This has motivated recent efforts to understand RT/RM instability development in the presence of chemical reactions, leading to combustion and heat release – we present a review of these results and identify opportunities and challenges in this chapter

On the dynamics of Rayleigh-Taylor mixing

The self-similar evolution of a turbulent Rayleigh-Taylor (R-T) mix is investigated through experiments and numerical simulations. The experiments consisted of velocity and density measurements using thermocouples and Particle Image Velocimetry techniques. A novel experimental technique, termed PIV-S, to simultaneously measure both velocity and density fields was developed. These measurements provided data for turbulent correlations, power spectra, and energy balance analyses. The self-similarity of the flow is demonstrated through velocity profiles that collapse when normalized by an appropriate similarity variable and power spectra that evolve in a shape-preserving form. In the self-similar regime, vertical r.m.s. velocities dominate over the horizontal r.m.s. velocities with a ratio of 2:1. This anisotropy, also observed in the velocity spectra, extends to the Taylor scales. Buoyancy forcing does not alter the structure of the density spectra, which are seen to have an inertial range with a -5/3 slope. A scaling analysis was performed to explain this behavior. Centerline velocity fluctuations drive the growth of the flow, and can hence be used to deduce the growth constant. The question of universality of this flow was addressed through 3D numerical simulations with carefully designed initial conditions. With long wavelengths present in the initial conditions, the growth constant was found to depend logarithmically on the initial amplitudes. In the opposite limit, where long wavelengths are generated purely by the nonlinear interaction of shorter wavelengths, the growth constant assumed a universal lower bound value o

Rayleigh-Taylor and Richtmyer-Meshkov Instabilities: A Journey through Scales

Hydrodynamic instabilities such as Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities usually appear in conjunction with the Kelvin-Helmholtz (KH) instability and are found in many natural phenomena and engineering applications. They frequently result in turbulent mixing, which has a major impact on the overall flow development and other effective material properties. This can either be a desired outcome, an unwelcome side effect, or just an unavoidable consequence, but must in all cases be characterized in any model. The RT instability occurs at an interface between different fluids, when the light fluid is accelerated into the heavy. The RM instability may be considered a special case of the RT instability, when the acceleration provided is impulsive in nature such as that resulting from a shock wave. In this pedagogical review, we provide an extensive survey of the applications and examples where such instabilities play a central role. First, fundamental aspects of the instabilities are reviewed including the underlying flow physics at different stages of development, followed by an overview of analytical models describing the linear, nonlinear and fully turbulent stages. RT and RM instabilities pose special challenges to numerical modeling, due to the requirement that the sharp interface separating the fluids be captured with fidelity. These challenges are discussed at length here, followed by a summary of the significant progress in recent years in addressing them. Examples of the pivotal roles played by the instabilities in applications are given in the context of solar prominences, ionospheric flows in space, supernovae, inertial fusion and pulsed-power experiments, pulsed detonation engines and Scramjets. Progress in our understanding of special cases of RT/RM instabilities is reviewed, including the effects of material strength, chemical reactions, magnetic fields, as well as the roles the instabilities play in ejecta formation and transport, and explosively expanding flows. The article is addressed to a broad audience, but with particular attention to graduate students and researchers who are interested in the state-of-the-art in our understanding of the instabilities and the unique issues they present in the applications in which they are prominent

Rayleigh–Taylor and Richtmyer–Meshkov instabilities: a journey through scales

Hydrodynamic instabilities such as Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities usually appear in conjunction with the Kelvin–Helmholtz (KH) instability and are found in many natural phenomena and engineering applications. They frequently result in turbulent mixing, which has a major impact on the overall flow development and other effective material properties. This can either be a desired outcome, an unwelcome side effect, or just an unavoidable consequence, but must in all cases be characterized in any model. The RT instability occurs at an interface between different fluids, when the light fluid is accelerated into the heavy. The RM instability may be considered a special case of the RT instability, when the acceleration provided is impulsive in nature such as that resulting from a shock wave. In this pedagogical review, we provide an extensive survey of the applications and examples where such instabilities play a central role. First, fundamental aspects of the instabilities are reviewed including the underlying flow physics at different stages of development, followed by an overview of analytical models describing the linear, nonlinear and fully turbulent stages. RT and RM instabilities pose special challenges to numerical modeling, due to the requirement that the sharp interface separating the fluids be captured with fidelity. These challenges are discussed at length here, followed by a summary of the significant progress in recent years in addressing them. Examples of the pivotal roles played by the instabilities in applications are given in the context of solar prominences, ionospheric flows in space, supernovae, inertial fusion and pulsed-power experiments, pulsed detonation engines and Scramjets. Progress in our understanding of special cases of RT/RM instabilities is reviewed, including the effects of material strength, chemical reactions, magnetic fields, as well as the roles the instabilities play in ejecta formation and transport, and explosively expanding flows. The article is addressed to a broad audience, but with particular attention to graduate students and researchers who are interested in the state-of-the-art in our understanding of the instabilities and the unique issues they present in the applications in which they are prominent