On the nonlinear dynamics of convective-diffusive-reactive waves

The burning of fossil fuels will play a crucial role for both power generation and transportation sectors over the next fifty years according to the forecasts of regulatory bodies in these sectors. The combustion of these fuels contributes to climate change, air pollution, and environmental noise and consequently affects the health and quality of human life. Public awareness and governmental legislations over these issues have improved substantially in recent years. As a result, heat engine manufacturers have to meet international standards for noise and pollutant emissions which are continually lowering the acceptable levels. The manufacturers of gas turbine engines which are used widely for propulsion and power generation are investing continually into extensive research that will enable them to meet the ever more stringent targets of NOx emissions and perceived noise. It is widely acknowledged among gas turbine manufacturers that lean premixed combustors fuelled by hydrogen blends is the most effective solution. The burning of fuels containing hydrogen results in reductions of all emissions compared to the levels produced from the burning of conventional fuels with the exception of NOx. Significant reductions of NOx emissions is the primary role of lean premixed combustion systems. These systems also provide reduced fuel consumption that results in less CO2 and H2O production because they operate close to the fuel-lean blowout limit. That is, these systems burn a fuel-air ratio that is lower than stoichiometry. Lean premixed combustors are effective in achieving low NOx emissions but their operating range is severely limited due to their susceptibility to a range of dynamical problems including combustion instabilities and flame flashback. Furthermore, these combustors are more noisy compared to other combustion systems for two reasons. Firstly, the flame dynamics are more unsteady and hence, more energy is supplied to the acoustic field. Secondly, the cooling air that flows around the combustor liner and acts as an acoustic insulation layer is relatively much less. The requirement for fuel flexibility makes these problems more challenging to solve as the chemical composition of the fuel significantly influences the combustion dynamics. Combustion instabilities are characterised by strong pressure oscillations that can destroy the combustor. These are a result of coupling of the flame heat release with flow perturbations through a feedback mechanism that is usually the combustor acoustics. In the multiphysics environment of a combustor there are various processes that cause flow perturbations and hence, the problem of combustion instability is extremely complex. The flow perturbations could be the result of other dynamic phenomena such as flame flashback and advecting entropy waves and these are the subject of the current work. The former is a highly transient phenomenon characterised by the sudden upstream propagation of the flame. The entropy waves are hot parcels of fluid that are generated by an oscillatory heat release at the flame and advect with the flow to generate acoustic waves known as entropy noise during their passage through the combustor exit nozzle. The flashback frequency of a flame periodically moving upstream or the frequency of entropy noise could coincide with an acoustic mode of the combustor, thus resulting in combustion instability. Even if the phenomena do not cause combustion instability they are problems in their own right. Flame flashback can damage upstream components of the combustor that are not designed to operate at high temperatures. On the other hand, entropy noise contributes to engine noise. Investigation of flashback requires multiple, simultaneous diagnostics without prior knowledge of the relevant time and length scales of the physical processes involved. Detection, accordingly, deals with post-event characterization. The current work, attempts to detect subtle dynamics prior to flashback using for the first time nonlinear time series analysis tools to process existing pressure time series from flashback experiments. Time and frequency domain methods are unable to detect precursors of flashback as will be demonstrated. However, these conventional methods of time series analysis operate on the assumption that the source of the time series is linear. The highly transient nature of flashback clearly indicates that the phenomenon is a consequence of nonlinear dynamics. Following standard nonlinear time series analysis, the trajectory of the system in phase space is constructed from the time series data. Subsequently, the orbit of the trajectory is analysed using a running window to plot its translation error and recurrence quantification measures of its recurrence pattern as a function of time. The translation error analysis is applied to time series from a flashback experiment in stable combustion. The recurrence analysis is applied to time series from a flashback experiment in a different burner with unstable combustion. In both cases, it is found that the determinism of the system dynamics gradually increases as flashback is approached. The influence of entropy noise on combustion instabilities is still a subject of contention. Experimental investigations are again difficult because entropy noise cannot be distinguished from noise generated at the flame in acoustic measurements. Hence, experimental investigations rely on measuring the temperature perturbations before their passage through the combustor exit nozzle. However, this brings about another difficulty, that of measuring high frequency temperature oscillations. Nonetheless, once the temperature measurements are made there is a need for a comprehensive theory to convert them to entropy noise. For this reason, research in this area has focused mainly on the acoustic response of nozzles to entropic forcing. The equally important stage of the phenomenon, that of the attenuation of advecting entropy waves through the combustor flow field has received little attention. Existing low order models of an advecting entropy wave are one-dimensional, linear, and purely phenomenological. The current work, carries out a direct numerical simulation of an entropy wave advecting in a compressible turbulent channel flow with adiabatic and convectively cooled walls. Time series from the direct numerical simulation are subsequently processed using a novel methodology to develop a model that retains the two-dimensional shape and amplitude of the entropy wave. The model is capable of simulating the adiabatic and heat transferring cases using only a small fraction of the data from the direct numerical simulation. It is shown that a nonlinear model is more appropriate even for entropy waves with an amplitude that until now has been considered small. Also, it is found that heat loss at the walls significantly influences the advecting entropy wave.