Perturbed flame dynamics perturbations

This chapter considers the first group of instabilities and introduces the analysis of processes implying an interaction with external flow-field perturbahons. This is exemplified by investigations of coupling between pressure waves and plane flames and also between an external acceleration field and flame fronts. The coupling between flow perturbations and flames giving rise to heat release unsteadiness and coupling with acoushc modes is considered in Chapter 5.2, which deals with the relationship between perturbed flame dynamics and radiated acoustic field, a fundamental process of thermo-acoustic instabilities. 

Perturbed Flame Dynamics and Thermo-Acoustic Instabilities... 

Flame dynamics is intimately related to combustion instability and noise radiation. In this chapter, relationships between these different processes are described by making use of systematic experiments in which laminar flames respond to incident perturbations. The response to incoming disturbances is examined and expressions of the radiated pressure are compared with the measurements of heat release rate in the flame. The data indicate that flame dynamics determines the radiation of sound from flames. Links between combustion noise and combustion instabilities are drawn on this basis. These two aspects, usually treated separately, appear as manifestations of the same dynamical process. 

The analysis of combustion dynamics is then intimately linked to an understanding of perturbed flame dynamics, the subsequent generation of unsteady rates of heat release, and the associated radiation of sound and resulting acoustic feedback. In practical configurations, the resonance loop involves the flow, the combustion process, and the acoustic modes of the system as represented schematically in Figure 5.2.2. 

In Chapter 5.2, S. Candel, D. Durox, and T. Schuller consider certain aspects of perturbed flame dynamics. The relation between combustion instability and noise generation is described by reference to systematic experiments. The data indicate that acoustic emission is determined by flame dynamics. On this basis, combustion noise can be linked with combustion instability. 

Dynamics of a methane-air conical flame submitted to a convective wave of equivalence ratio perturbations,/= 175 Hz, and = 0.1. The mass fraction perturbation is shown on the color scale. The flame is represented by temperature isocontours. Two cycles of modulation are displayed. 

T. Schuller, D. Durox, and S. Gandel. Dynamics of and noise radiated by a perturbed impinging premixed jet flame. Combust. Flame, 128 88-110, 2002. 

F. J. Higuera and A. Linan, Stability of Solid-Propellant Combustion to Non-Planar Perturbations in Dynamics of Flames and Reactive Systems, vol. 95 of Progress in Astronautics and Aeronautics, J. R. Bowen, N. Man son, A. K. Oppenheim and R. I. Soloukhin, eds.. New York American Institute of Aeronautics and Astronautics, 1984, 248-258, have shown that a similar phenomenon occurs for the model that led to equation (78). When transverse disturbances are admitted, the stability boundary in Figure 9.6 is changed to f... 

Schuller, T., Durox, D., and Candel, S. "Dynamics of and Noise Radiated by a Perturbed Impinging Premixed Jet Flame." Combustion and Flame 128 (2002) 88-110. 

The study of the response of nonlinear systems to external periodic perturbations leads to interesting information.Cool-flame, 9 oscillations occur in a number of combustion reactions, and we discuss an experimental study of the effect of external periodic perturbations on such systems. The application of perturbations to a chemical reaction can reveal important information about the stability, kinetics, and dynamics of the reaction. This technique is well known in the field of relaxation kinetics, in which perturbations are applied to a chemical system at equilibrium. In our work, periodic perturbations are first applied to the input rates of acetaldehyde and oxygen, one at a time, in the combustion of acetaldehyde in a CSTR. We measure periodic responses in five entrainment bands as we vary the frequency and amplitude of the external periodic perturbation. Outside of entrainment bands we find quasi-periodic responses. Next-phase rnapslO, of the experimental results are constructed in real time and used in the observation and interpretation of entrainment and quasi-periodic behavior. Within the fundamental entrainment band, we measure critical slowing down and enhancement of the response amplitude. As the bath temperature is increased, so that the oscillatory system approaches a Hopf bifurcation, we observe an increase in the amplitude enhancement. The predictions of a five-variable thermokinetic model agree well with the experimental results. 

Thus, in these models, the fluid dynamical field on either side of the flame is assumed to be inviscid and incompressible, with given density jump [p]. If in addition Sf is known, a complete description of the problem is given in principle by solving Euler s equations subject to the conditions (l)-(3) and the equation prescribing S. For example, Landau [6] and Darrieus [2] assumed the flame speed of a perturbed flame... 

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