Thermodynamics-Acoustics Coupling Studies on Self-Excited Combustion Oscillations Maximum Growth Rate

Abstract

Unlike electric vehicles and electric aircrafts, hydrocarbon-fuelled (fossil) engine systems are much noisier. By conducting one-step chemical reaction-thermodynamics-acoustics coupling studies and experimental measurements, we explore the universal physics of how hydrocarbon-fuelled combustion is a noise maker. We also explain that how combustion-sustained noise at a particular frequency ω is intrinsically selected. These frequencies correspond to the acoustic resonance nature of the combustor. We find that a reacting gas in which the rate of chemical reacting increases with temperature is intrinsically and naturally unstable with respect to acoustic wave motion, since its modal growth rate α is greater than 0. Acoustic disturbances tend to exponentially i.e. exp(αt) increased first and then are limited by nonlinear effects and finally grow into limit cycle oscillations. The growth rate α is found to increase first and then decrease with the gradient of the heat release rate with respect to the temperature change, i.e. heat capacity. The maximum (α/ω) max depends on the specific heat ratio γ, which is related to the speed of sound. The unstable nature could be changed by introducing some acoustic dissipative/damping mechanism, such as the boundary layer viscous drag and boundary losses. It is shown that such losses could lead to increased critical heat capacity, below which stable combustors can be designed. Finally, the acoustical energy consisting of both potential and kinetic energy is found to grow exponentially faster by 100% than the acoustic disturbance amplitude.

A time-domain method for free vibration responses of an equivalent viscous damped system based on a complex damping model

“…Equation (15) shows that the expression of displacement contains an exponential growth term. It means that smallamplitude acoustic disturbances at any frequency will be exponentially amplified.…”

“…It means that small-amplitude acoustic disturbances at any frequency will be exponentially amplified. 15 The growth rate of vibration responses is the important factor. 16 The growth item of free vibration responses is normaleαt.…”

Numerical investigation on low-frequency noise damping performances of Helmholtz resonators with an extended neck in presence of a grazing flow

“…Hence, the deflection angle of the extended neck significantly changes the resonance frequency. The modified Helmholtz resonators with extended necks with an optimum design could be applied to attenuate self-excited combustion oscillations, [46][47][48] thus enabling propulsion systems being operated stably.…”

Numerical Study on the Route of Flame-Induced Thermoacoustic Instability in a Rijke Burner

“…Two important parameters to evaluate the growth of thermoacoustic instability are the growth rate of the acoustic disturbances α and G. The definition and detail derivation of α and G can be found in the reference [44]. The time evolution of the pressure and heat release of the flame from 0 s to 0.4 s are illustrated in Figures 8 and 9.…”