Effect of particle size distribution on the laminar flame speed of iron aerosols

Iron particles in air burn in heterogeneous combustion mode and the flame speed is very sensitive to particle size. Previous numerical work on the propagation of flames in iron dust was based on average particle sizes. However, in practice, experiments are conducted with particle size distributions (PSD). This makes it challenging to compare different experiments as the samples used in those studies vary (the average particle size might be similar but not the particle size distribution). It is the aim of the current work to provide insight into the effect of particle size distribution on flame propagation. This involves identifying the minimum number of discrete averaged particle sizes (bins) required in the simulations to capture the burning characteristics of the PSD. Then, flame speed and flame structure for a narrow and broad distribution are investigated. It is shown that the equivalence ratio at which the maximum flame speed occurs for certain mean particle sizes varies with the width of the particle size distribution. The difference in the flame speed between the same average particle size but different standard deviation varies as a function of β (ratio between standard deviation and average particle size), not just the average particle size itself. For a constant β at a particular equivalence ratio, the difference in the flame speed between PSD and mono-dispersed aerosols is approximately the same irrespective of the particle size. The effects of the smaller and bigger particles in the PSD on the flame speed and flame structure are also systematically investigated. The findings in this study confirm that the particle width of the PSD plays a crucial role and that experiments and simulations can not be readily compared if different PSDs are used.</p

Stability criteria of two-port networks, application to thermo-acoustic systems

System theory methods are developed and applied to introduce a new analysis methodology based on the stability criteria of active two-ports, to the problem of thermo-acoustic instability in a combustion appliance. The analogy between thermo-acoustics of combustion and small-signal operation of microwave amplifiers is utilized. Notions of unconditional and conditional stabilities of an (active) two-port, representing a burner with flame, are introduced and analyzed. Unconditional stability of two-port means the absence of autonomous oscillation at any embedding of the given two-port by any passive network at the system’s upstream (source) and downstream (load) sides. It has been shown that for velocity-sensitive compact burners in the limit of zero Mach number, the criteria of unconditional stability cannot be fulfilled. The analysis is performed in the spirit of a known criterion in microwave network theory, the so-called Edwards-Sinsky’s criterion. Therefore, two methods have been applied to elucidate the necessary and sufficient conditions of a linear active two-port system to be conditionally stable. The first method is a new algebraic technique to prove and derive the conditional and unconditional stability criteria, and the second method is based on certain properties of Mobius (bilinear) transformations for combinations of reflection coefficients and scattering matrix of (active) two-ports. The developed framework allows formulating design requirements for the stabilization of operation of a combustion appliance via purposeful modifications of either the burner properties or/and of its acoustic embeddings. The analytical derivations have been examined in a case study to show the power of the methodology in the thermo-acoustics system application

Determining thermo-acoustic stability of a system whose boundary conditions are represented by strictly positive real transfer functions

The ultimate goal of the present research is to establish a methodology using which one can characterize the thermo-acoustic quality (figure of merit) of a given burner with flame. For this purpose, the probability of a certain burner/flame to be in either a stable or unstable regime when it is embedded in a randomly selected acoustic environment (similar to a combustor appliance) should be evaluated. An approach presented in this contribution consists of performing multiple calculations for the (in)-stability of a system composed of a known burner with flame and acoustically passive arbitrary upstream and downstream reflection coefficients. In this paper, a low order analytical network model of the acoustic system is used. Properties of strictly positive real functions are used to model the random frequency dependence of passive reflections. The implementation and testing of this particular method to generate random, frequency dependent acoustic embedding for the burner is the core subject of the present contribution. Within this method, initially, the roots of a Hurwitz polynomial are randomly selected and this polynomial is taken as the denominator of the impedance function, subsequently, the corresponding numerator polynomial coefficients are computed to obtain an impedance function that is strictly positive real. Then, this function is transformed to represent a reflection coefficient function in complex variable &#x1d460;&#x1d460; and is used as an embedding to evaluate the given burner’s flame stability by calculating the system’s complex eigen frequencies for various upstream and downstream reflection coefficients

Intrinsic thermo-acoustic instability criteria based on frequency response of flame transfer function

A study of Intrinsic Thermo-Acoustic (ITA) instability behavior of flames anchored to a burner deck is performed by introducing a mapping between the Flame Transfer Function, FTF(s), defined in the complex (Laplace) domain and the experimentally measured Flame Frequency Response, FFR(iω). The conventional approach requires a system identification procedure to obtain the FTF(s) from the measured FFR(iω). Next, root-finding techniques are applied to define the complex eigenfrequencies. The common practice is to fit the FTF(s) by a rational function that may lead to artifacts like spurious poles and zeros. The purpose of the present work is to establish instability criteria which are directly applicable in the frequency domain. The particular case is considered where the acoustic boundary conditions at both sides of the flame are anechoic. Therefore, the pure ITA mode is treated. First, the causality of the measured FFR(iω) is checked. Then, the criteria of the ITA mode instability applicable to the FFR(iω) phase and magnitude, are derived. Causality properties are used to find the unstable frequency, growth rate, and even the maximum possible value of the linear growth rate. In addition, a procedure is explained to reconstruct the flame transfer function in the complex plane s from the measured flame frequency response which could be an alternative method to study the FTF behavior in the complex domain instead of its estimation with a rational function