Computational Bifurcation Analysis of Radiative Diffusion Flames

76 σ.Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Εφαρμοσμένη Μηχανική”Στην εργασία αυτή, αναλύεται η δυναμική του μοντέλου που περιγράφει μια επίπεδη φλόγα διάχυσης με θερμικές απώλειες ακτινοβολίας, η οποία συμπεριλαμβάνει κινητική απλού βήματος για αριθμό Lewis ίσο με τη μονάδα. Κατασκευάζεται το ολοκληρωμένο διάγραμμα διακλάδωσης συναρτήσει του αριθμού Damkohler, το οποίο περιλαμβάνει και τους κλάδους των ταλαντευόμενων λύσεων. Βάσει αυτής της ανάλυσης, βρέθηκαν ομοκλινικές διακλαδώσεις, οι οποίες σηματοδοτούν την απότομη εξαφάνιση των μη γραμμικών ταλαντώσεων της φλόγας κοντά στην απόσβεσή της, το οποίο έχει παρατηρηθεί τόσο σε πειράματα όσο και σε πραγματικές διατάξεις καύσης.We analyse the dynamics of a model describing a planar diffusion flame with radiative heat losses incorporating a single step kinetic for Lewis number equal to one. We construct the full bifurcation diagram with respect to the Damk¨ohler number including the branches of oscillating solutions. Based on this analysis we found, for the first time, homoclinic bifurcations that mark the abrupt disappearance of the nonlinear oscillations near extinction as reported in experiments.Δημήτρης Μ. Μανιά

Static analysis of gradient elastic nanobeams in Winkler Foundation

165 σ.Στην εργασία αυτή διατυπώνεται ένα απλοποιημένο μοντέλο βαθμίδας ελαστικότητας για λεπτές δοκούς, βασισμένο στη θεωρία της βαθμίδας ελαστικότητας του Mindlin και στις υποθέσεις των Bernoulli‐Euler, συμπεριλαμβανομένων της ελαστικής θεμελίωσης και της στρεπτικής ροπής των τύπων του Winkler. Ο σκοπός της παρούσας εργασίας είναι να μελετηθεί η συμπεριφορά του μοντέλου αυτού στη στατική ανάλυση νανοσωλήνων άνθρακα μονού τοιχώματος. Η εξίσωση που χαρακτηρίζει το μοντέλο, μια 6ου βαθμού μερική διαφορική εξίσωση, μαζί με τις σχετικές συνοριακές και αρχικές συνθήκες, επάγεται από την εφαρμογή της αρχής της μεταβολής των Hamilton‐Lagrange, και εξάγει την ακριβή αναλυτική λύση. Στη συνέχεια, παρουσιάζονται η αναλυτική στατική λύση και οι ιδιοτιμές ταλάντωσης λυγισμού. Αρκετά παραδείγματα παρατίθενται, χρησιμοποιώντας δεδομένα “αντίστοιχων δοκών” για νανοσωλήνες άνθρακα (Carbon Nanotubes‐CNTs) και συγκρίνονται τα αποτελέσματα με αυτά της κλασικής θεωρίας.In this thesis we formulate a simplified gradient elastic model for slender beams based on Mindlin's gradient elasticity theory and the Bernoulli‐Euler hypothesis, including a Winklertype elastic foundation and rotary inertia. Our aim is to examine the relevance of this model for the static analysis of single‐walled carbon nanotubes (CNTs). The model governing equation, a 6th order partial differential equation, along with the relevant boundary and initial conditions, is derived by application of the Hamilton‐Lagrange variational principle. In the sequel we present the analytical static solution and the buckling eigenvalues. Several examples are presented, using "equivalent beam" data for CNTs and comparisons with results of other researchers in the field, as well as with those of the classical beam theory, are made.Δημήτρης Μ. Μανιά

CH4/air homogeneous autoignition: A comparison of two chemical kinetics mechanisms

Reactions contributing to the generation of the explosive time scale that characterise autoignition of homogeneous stoichiometric CH4/air mixture are identified using two different chemical kinetics models; the well known GRI-3.0 mechanism (53/325 species/reactions with N-chemistry) and the AramcoMech mechanism from NUI Galway (113/710 species/reactions without N-chemistry; Combustion and Flame 162:315-330, 2015). Although the two mechanisms provide qualitatively similar results (regarding ignition delay and profiles of temperature, of mass fractions and of explosive time scale), the 113/710 mechanism was shown to reproduce the experimental data with higher accuracy than the 53/325 mechanism. The present analysis explores the origin of the improved accuracy provided by the more complex kinetics mechanism. It is shown that the reactions responsible for the generation of the explosive time scale differ significantly. This is reflected to differences in the length of the chemical and thermal runaways and in the set of the most influential species

The mechanism by which CH2O and H2O2 additives affect the autoignition of CH4/air mixtures

When the fast dissipative time scales become exhausted, the evolution of reacting processes is characterized by slower time scales. Here the case where these slower time scales are of explosive character is considered. This feature allows for the acquisition of significant physical understanding; among others, the identification of intermediates in the reacting process that can be used as additives for the control of the ignition delay. The case of the homogeneous autoignition of CH4/air mixtures is analyzed here and the effects of adding the stable intermediates CH2O and H2O2 to the fuel. These two species are identified as those relating the most to the explosive mode that causes autoignition, throughout the largest part of the ignition delay. Small quantities of these species in the initial mixture decrease considerably the ignition delay, by expediting the development of the thermal runaway

Algorithmic Analysis of Chemical Dynamics of the Autoignition of NH3–H2O2/Air Mixtures

The dynamics of a homogeneous adiabatic autoignition of an ammonia/air mixture at constant volume was studied, using the algorithmic tools of Computational Singular Perturbation. Since ammonia combustion is characterized by both unrealistically long ignition delays and elevated NO x emissions, the time frame of action of the modes that are responsible for ignition was analyzed by calculating the developing time scales throughout the process and by studying their possible relation to NO x emissions. The reactions that support or oppose the explosive time scale were identified, along with the variables that are related the most to the dynamics that drive the system to an explosion. It is shown that reaction H 2 O 2 (+M) → OH + OH (+M) is the one contributing the most to the time scale that characterizes ignition and that its reactant H 2 O 2 is the species related the most to this time scale. These findings suggested that addition of H 2 O 2 in the initial mixture will influence strongly the evolution of the process. It was shown that ignition of pure ammonia advanced as a slow thermal explosion with very limited chemical runaway. The ignition delay could be reduced by more than two orders of magnitude through H 2 O 2 addition, which causes only a minor increase in NO x emissions

Topological and chemical characteristics of turbulent flames at MILD conditions

Dominant physical processes that characterize the combustion of a lean methane/air mixture, diluted with exhaust gas recirculation (EGR), under turbulent MILD premixed conditions are identified using the combined approach of Computational Singular Perturbation (CSP) and Tangential Stretching Rate (TSR). TSR is a measure to combine the time scale and amplitude of all active modes and serves as a rational metric for the true dynamical characteristics of the system, especially in turbulent reacting flows in which reaction and turbulent transport processes compete. Applied to the MILD conditions where the flame structures exhibit nearly distributed combustion modes, the TSR metric was found to be an excellent diagnostic tool to depict the regions of important activities. In particular, the analysis of turbulent DNS data revealed that the system’s dynamics is mostly dissipative in nature, as the chemically explosive modes are largely suppressed by the dissipative action of transport. On the other hand, the convective transport associated with turbulent eddies play a key role in bringing the explosive nature into the system. In the turbulent MILD conditions under study, the flame structure appears nearly in the distributed combustion regime, such that the conventional statistics conditioned over the progress variable becomes inappropriate, but TSR serves as an automated and systematic way to depict the topology of such complex flames. In addition, further analysis of the CSP modes revealed a strong competition between explosive and dissipative modes, the former favored by hydrogen-related reactions and the convection of CH4, and the latter by carbon-related processes. This competition results in a much smaller region of explosive dynamics in contrast to the widespread existence of explosive modes

Investigation of the turbulent flame structure and topology at different Karlovitz numbers using the tangential stretching rate index

Turbulent premixed flames at high Karlovitz numbers exhibit highly complex structures in different reactive scalar fields to the extent that the definition of the flame front in an unambiguous manner is not straightforward. This poses a significant challenge in characterizing the observable turbulent flame behaviour such as the flame surface density, turbulent burning velocity, and so on. Turbulent premixed flames are reactive flows involving physical and chemical processes interacting over a wide range of time scales. By recognizing the multi-scale nature of reactive flows, we analyze the topology and structure of two direct numerical simulation cases of turbulent H2/air premixed flames, in the thin reaction zone and distributed combustion regimes, using tools derived from the computational singular perturbation (CSP) method and augmented by the tangential stretching rate (TSR) analysis. CSP allows to identify the local time scale decomposition of the multi-scale problem in its slow and fast components, while TSR allows to identify the most energetic time scale during both the explosive and dissipative regime of the reactive flow dynamics together with the identification of the flame front in an unambiguous manner. Before facing the complexity of the turbulent flow regime, we carry out a preliminary analysis of a one-dimensional laminar premixed flame in view of highlighting similarities and differences between laminar and turbulent cases. Subsequently, it is shown that the TSR metric provides a reliable way to identify the turbulent flame topologies

Analysis of hydrogen/air turbulent premixed flames at different Karlovitz numbers using computational singular perturbation

The dynamics and structure of two turbulent H2/air premixed flames, representative of the corrugated flamelet (Case 1) and thin reaction zone (Case 2) regimes, are analyzed and compared, using the computational singular perturbation (CSP) tools, by incorporating the tangential stretch rate (TSR) approach. First, the analysis is applied to a laminar premixed H2/air flame for reference. Then, a two-dimensional (2D) slice of Case 1 is studied at three time steps, followed by the comparison between two representative 2D slices of Case 1 and Case 2, respectively. Last, statistical analysis is performed on the full three-dimensional domain for the two cases. The dominant reaction and transport processes are identified for each case and the overall role of kinetics/transport is determined