Combustion of Energetic Materials in an Acoustic Field (Review)

Abstract

The review summarizes the long-term experience in theoretical research of combustion of gasifying condensed systems with periodically varied pressure. Most results are obtained within the framework of the Zel'dovich-Novozhilov theory. The main properties of the linear function of the burning rate response to harmonically varied pressure are discussed. The concept of nonlinear response functions is introduced, which is illustrated by the explicit form of a number of second-order response functions. A new phenomenon is described: bifurcations of response functions with a varied amplitude or frequency of pressure oscillations. For the simplest gunpowder model containing three parameters only, the sequence of bifurcations of doubling of the burning rate oscillation period is studied, which finally leads to a random combustion regime. An analytical relation between the linear response functions to harmonically varied pressure and to an oscillating radiant heat flux is noted. An example of calculating the response function with allowance for thermal inertia of the gas phase is presented.

Critical Review of Phenomenological Models for Studying Transient Combustion of Solid Propellants

“…Some works [28][29][30][31] were performed to estimate the effect of the heat propagation characteristic time in the gas phase on transient combustion behavior. Its account becomes important at relatively high pressures and high frequencies of gas phase oscillations.…”

“…The limiting case K = 0 corresponds to the formulation of problem in the form of [9] while the finite K-value corresponds to more realistic conditions. It is shown in [31] that when taking into account the value of K > 0, the calculated burning rate response to the acoustic pressure oscillations becomes higher in value (real part) and even exhibits the second resonance peak.…”

“…It has to be noted that [9,31] the principal difference in determination of the parameters in expressions (13) and (14). In (13), those parameters are "fitting" constants derived on the basis of generalization of numerous calculations without clear dependency on the combustion conditions (pressure, initial temperature).…”

“…In (14), all constants have clear physical meaning and can be obtained directly from experiment without making any assumptions about the combustion mechanism. This allows making consideration of nonlinear resonance phenomenon in combustion of SP [42,43].…”

Analysis of unsteady solid-propellant combustion models (review)

“…5 In the absence of detailed data, one has to calculate T s using ClausiusClapeyron type relations. The model has been widely used to calculate transition processes after ignition or with pressure variation and to find the combustion stability boundary (at constant pressure or in a chamber with outflow) and the acoustic conductivity of the burning surface [46].…”