Arturo Pagano

Experimental analysis of thermo-acoustic combustion instability

Thermo-acoustic instabilities are dynamic phenomena that represent a major threat for most modern combustion systems. Many studies, mainly undertaking a linear analysis of experimental data, have been carried out to provide a deeper understanding of the underlying phenomena. However, linear analysis may lead to an oversimplified view of the problem, which involves many complex non-linear interactions, and a more detailed non-linear analysis may be necessary. This paper presents both linear and non-linear analyses of experimental measurements observed in a methane-fuelled laboratory combustor. The linear analysis aims to verify the existence of thermo-acoustic instabilities and consists of the elaboration of both power-spectral density distribution and Rayleigh Index of the experimental time series. Non-linear analysis aims to investigate dynamic behaviours by means of the deterministic chaos theory. Results of the analyses show that combustion instabilities occur in all the experimental operating conditions. Moreover, the existence of a chaotic source in the combustion system under study is demonstrated.

Neural prediction of combustion instability

Abstract Combustion instabilities consist in self–exited oscillations in combustion chambers and can cause structure degradations. When combustion instabilities occur, the combustion process is characterised by the coupling of various non-linear phenomena, which can lead to the formation of either a limit cycle or chaos. The intrinsic highly non-linear behaviour, especially when chaos arises, poses a major problem for the formulation of good predictions and the design of reliable control systems. Due to the relevant number of degree of freedom and to the non-linear coupling of different phenomena, the mathematical modeling of combustion instabilities is computationally heavy and may produce an unsatisfactory correspondence between simulated and experimental data. Analogous problems arise also from the uncertainty for the parameters of the process, such as the local velocity of the flame front (and, hence, the reaction rate and the exhausted temperatures), and their unpredictable variations. In fact, note that most of the chemical and thermo-physical variables both strongly depend and influence the instantaneous displacement of the flame front, which is positioned on the unstationary eddies external surface. In order to obtain a reliable model for thermo-acoustic combustion instabilities, a different approach was chosen in this paper. The black-box identification of an experimental combustion chamber was obtained by means of a generalized NARMAX model. The model was implemented by training a Multilayer Perceptron artificial neural network with input-output experimental data. The main advantages of the proposed approach consisted in the natural ability of neural networks in modeling nonlinear dynamics in a fast and simple way and in the possibility to address the process to be modeled as an input-output black box, with little or no mathematical information on the system. Satisfactory agreement between simulated and experimental data was found and results show that the model successfully predicted the temporal evolution of thermo-acoustic combustion instabilities.

Clustering of chaotic dynamics of a lean gas-turbine combustor

This work deals with the dynamic behaviour of a lean premixed gas turbine combustor. The study aims to achieve a classification of experimental burner dynamic behaviour and is based on the geometrical properties of the attractors of the system variables. Several experiments were performed varying the flame stoichiometric ratio [lambda] and the pilot fuel percentage PFP. The dynamics of the experimental time series of the flame front heat release were described by using vectors collecting information on the topological distribution of the attractors. Therefore, unsupervised Kohonen associative memories were trained to create clusters of operating conditions characterised by similar dynamical behaviours. Kohonen associative memories were able to divide the experimental operating conditions into different clusters according to the different values of the flame stoichiometric ratio. The results of the clustering underline the possibility of being able to define an algorithm for combustion-instability pattern recognition that takes into account the highly non-linear effects which govern combustion processes.

Stability maps for rectangular circulation loops

This study aims to define a methodology for the construction of stability maps of rectangular natural circulation loop. The interest for these maps derives from their ability to present in synthetic form the results of stability analysis. In fact, the proposed methodology is based on the linear stability analysis around equilibrium points of a high order nonlinear mathematical model describing the dynamical behaviour of the non-dimensional flow velocity and temperature inside the loop. Imposed heat flux at the loop walls has been assumed at the boundaries; in particular, it has been considered that the fluid is heated and cooled during its passage in the horizontal sections, respectively, at bottom and top of the loop, whereas the vertical legs are supposed adiabatic. Hence, the stability analysis was performed considering the effect of the variation of the modified Grashof number, Grm, for a wide range of loop geometrical configurations, assuming various aspect ratios (ratio of the vertical to the horizontal length of the tube) and inner tube diameters.

Appearance of quasiperiodicity within a period doubling route to chaos of a swaying thermal plume

The birth, evolution and disappearance of quasiperiodic dynamics in buoyancy-driven flow arising from an enclosed horizontal cylinder are analysed here, by numerical means, in the limit of the 2D approximation. The governing equations are solved on orthogonal Cartesian grids, giving special treatment to the internal, non-aligned boundaries. Thanks to the adoption of a high level of refinement of the Rayleigh number range, quasiperiodicity was observed to emerge from a periodic limit cycle (P1), and to turn into its omologous orbit with doubled period (P2), eventually evolving into a classical period-doubling route to chaos, for further increases of the Rayleigh number. The present study gives a deeper insight to what appears to be an imperfect period doubling bifurcation through a quasiperiodic T2-torus. The approach used is based on the classical tools for time series analysis. The distribution of the power spectral densities is used to search for and characterise the existence of relations between the frequencies of the P1, T2 and P2 dynamics. The topology of the orbits, as well as their evolution within the quasiperiodic window, are analysed with the aid of phase space representation and Poincare maps.

Heat transfer along the route to chaos of a swaying thermal plume

Detailed analyses have been recently reported on the low order dynamics of a thermal plume arising from a horizontal cylindrical heat source concentric to an air-filled isothermally cooled square enclosure, together with those of the related flow structures, in the limit of the 2D approximation. In particular, within the range of 0 < Ra < 3Racr, with Racr corresponding to the loss of stability of the stationary buoyant plume, the entire evolution from a periodic limit cycle (P1) to the birth of chaos through a period-doubling cascade has been fully explored. With this respect, special attention has been given to the window of quasiperiodic dynamics onto a T2-torus that is observed to separate the monoperiodic dynamics from the biperiodic dynamics onto a P1 and a P2-limit cycle, respectively. The results of these analyses hint at the bimodal nature of the overall dynamics, in general, and of the subharmonic cascade, in particular, which are still under investigation. Although relevant on a dynamical perspective, a with a main reflection on the laminar-turbulent transition, the observed oscillations appear to be characterised by comparable amplitudes and to be determined by similar evolutions of the flow pattern evolutions, so that their role on the overall heat transfer rate is expected to be marginal. Within this frame, the present study aims at reporting the influence played by the observed dynamics of the thermal plume and of the flow structures on the global heat transfer rate. In particular, the aim is the assessment of the correlation between the Rayleigh number and the average Nusselt number on the cylinder surface, as well as the effect on the latter of the observed series of bifurcations.

Application of Recurrence Analysis to the period doubling cascade of a confined buoyant flow

Recurrence Analysis (RA) is a promising and flexible tool to identify the behaviour of nonlinear dynamical systems. The potentialities of such a technique are explored in the present work, for the study of transitions to chaos of buoyant flow in enclosures. The case of a hot cylindrical source centred in a square enclosure, is considered here, for which an extensive database of results has been collected in recent years. For a specific value of the system aspect ratio, a sequence of period doublings has been identified, leading to the onset of chaos. RA is applied here to analyse the different flow regimes along the route to chaos. The qualitative visual identification of patterns and the statistics given by the quantitative analysis suggest that this kind of tool is well suited to the study of transitional flows in thermo-fluid dynamics.

Flow Transitions and Bifurcations of Buoyancy-Induced Flows From an Enclosed Cylindrical Heat Source

ABSTRACT The study presents a numerical analysis of the dynamicsof transitional natural convection flow regimes, generated by aconfined thermal source. The system considered is a 2D enclo-sure of square cross-section, containing a horizontal cylindricalsource, placed in central position. The heat carrier fluid is airwith Prandtl number Pr =0:7. The resulting flow is investigatedwith respect to the variation of the Rayleigh number, based onthe minimum gap width H between the cylinder and the enclo-sure walls. Three values of the aspect ratio A are considered(A = 2:5;3:3¯;5;). The first bifurcation of the low-Ra fixed-pointsolution is tracked for each A-value. The transition to unsteady,chaotic flow is detailed for A =2:5. The supercritical behaviourof the system is investigated using nonlinear analysis tools andphase space representations of the computed time series. NOMENCLATURE A =L=H aspect ratioD cylinder diameter [m]CFL Courant numberGr =(gbT ref H 3ref )=n 2 Grashof numberH vertical gapi; j grid indicesf frequency [Hz]

Phase Space Description of Unstable Dynamics of a Lean Premixed Gas Turbine Combustor

This work describes unstable phenomena of a lean premixed gas turbine combustor considering the geometrical properties in a phase space representation. Several experiments have been performed in which the air excess ratio λ and the percentage of pilot fuel PFP have been varied. The time series of experimentally measured pressure and heat release fluctuations inside the duct have been analysed using vectors collecting topological parameters of the attractors of experimental acoustical and optical sensors. Therefore, unsupervised Kohonen associative memories have been trained to create clusters of operating conditions characterised by similar dynamical behaviours. The results of the clustering underline the practical possibility of defining an algorithm for instability pattern recognition, which could be effective for either a diagnostic or a control system.

A MODELING STRATEGY FOR RECTANGULAR THERMAL CONVECTION LOOPS

Abstract In this paper a new modelling strategy based on the approximation of the Fourier series expansion of the analytic model of a rectangular thermal convection loop is proposed. This strategy has been derived in order to improve the accuracy of previous existing models. The computation of accurate models is an important step towards the design of suitable control strategies able to prevent the occurence of oscillations in the loop. The obtained model has been validated through extensive comparison between simulated and experimental data.