Insight into CO2 dissociation in plasmas from numerical solution of a vibrational diffusion equation

The dissociation of CO2 molecules in plasmas is a subject of enormous importance for fundamental studies and the recent interest in carbon capture and carbon-neutral fuels. The vibrational excitation of the CO2 molecule plays an important role in the process. The complexity of the present state-to-state (STS) models makes it difficult to find out the key parameters. In this paper we propose as an alternative a numerical method based on the diffusion formalism developed in the past for analytical studies. The non-linear Fokker-Planck equation is solved by the time-dependent diffusion Monte Carlo method. Transport quantities are calculated from STS rate coefficients. The asymmetric stretching mode of CO2 is used as a test case. We show that the method reproduces the STS results or a Treanor distribution depending on the choice of the boundary conditions. A positive drift, whose energy onset is determined by the vibrational to translational temperature ratio, brings molecules from mid-energy range to dissociation. The high-energy fall of the distribution is observed even neglecting VT processes which are normally believed to be its cause. Our study explains several puzzling features of previous studies, provides new insights into the control of the dissociation rate and a much sought compression of the required data for modeling

Minimal Curvature Trajectories: Riemannian Geometry Concepts for Model Reduction in Chemical Kinetics

In dissipative ordinary differential equation systems different time scales cause anisotropic phase volume contraction along solution trajectories. Model reduction methods exploit this for simplifying chemical kinetics via a time scale separation into fast and slow modes. The aim is to approximate the system dynamics with a dimension-reduced model after eliminating the fast modes by enslaving them to the slow ones via computation of a slow attracting manifold. We present a novel method for computing approximations of such manifolds using trajectory-based optimization. We discuss Riemannian geometry concepts as a basis for suitable optimization criteria characterizing trajectories near slow attracting manifolds and thus provide insight into fundamental geometric properties of multiple time scale chemical kinetics. The optimization criteria correspond to a suitable mathematical formulation of "minimal relaxation" of chemical forces along reaction trajectories under given constraints. We present various geometrically motivated criteria and the results of their application to three test case reaction mechanisms serving as examples. We demonstrate that accurate numerical approximations of slow invariant manifolds can be obtained.Comment: 22 pages, 18 figure

A variational principle for computing slow invariant manifolds in dissipative dynamical systems

A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing such manifolds for kinetic models using trajectory optimization. The corresponding objective functional reflects a variational principle that characterizes trajectories on, respectively near, slow invariant manifolds. For a two-dimensional linear system and a common nonlinear test problem we show analytically that the variational approach asymptotically identifies the exact slow invariant manifold in the limit of both an infinite time horizon of the variational problem with fixed spectral gap and infinite spectral gap with a fixed finite time horizon. Numerical results for the linear and nonlinear model problems as well as a more realistic higher-dimensional chemical reaction mechanism are presented.Comment: 16 pages, 5 figure

Analysis and simplification of chemical kinetics mechanisms with CSP-based techniques

The computational singular perturbation (CSP) method is exploited to build a comprehensive framework for analysis and simplification of chemical kinetic models. The necessity for both smart post-process tools, able to perform rational diagnostics on large numerical simulations of reactive flows, and affordable reduced kinetic mechanisms, to make the simulations feasible, is the driving force behind this work. The ultimate goal is to improve the understanding of the fundamentals of chemically reacting flows. The CSP method is a suitable candidate for extracting physical insights from reactive flows dynamics that can be employed for both the generation of simplified kinetic schemes and the calculation of smart and compact diagnostic observables. Among them, the tangential stretching rate (TSR) is an estimate of the system’s driving chemical timescale that can be profitably employed for characterising the reactive flow dynamics in terms of combustion regimes and role of transport with respect to kinetics. The potentials of TSR are extensively highlighted, starting from prototypical combustion models, such as batch reactor and unsteady laminar flamelet, and getting to real-life usage on 3-dimensional direct numerical simulation datasets. The CSP mathematical foundations are then employed for mechanism simplification purposes, where small and accurate kinetic mechanisms are sought after. An existing CSP-based simplification algorithm is improved, aiming at the minimisation of the required user knowledge, which becomes a critical feature of the algorithm when dealing with new fuels. Practical applications of the revised algorithm are shown and discussed. Finally, the focus is shifted from the quest for tight accuracy in the simplified mechanisms towards a much broader question regarding confidence in detailed kinetic schemes. Uncertainty in the kinetic model parameters, such as Arrhenius coefficients, can jeopardize the efforts spent in the reduction challenge. A new, uncertainty-aware, robust CSP simplification strategy is proposed, discussed and employed, and its robustness demonstrated in a test case involving an uncertain -in its Arrhenius pre-exponential coefficients- kinetic scheme

A Numerical and Experimental Investigation on the Thermal Structure of Oxy-fuel Combustion

This thesis presents a numerical and experimental investigation on the characteristics of oxy-fuel combustion utilising CH4 as a fuel. An emphasis is placed on investigating the thermal structure and the impact of the oxidiser diluent on oxy-fuel flames. The numerical portion of this thesis sheds light on off-stoichiometric temperature peaking (OTP), which is a phenomenon whereby the flame temperature does not peak at exactly stoichiometry, but rather near stoichiometry. Specifically, OTP in equilibrium calculations (0D OTP) and opposed-flow diffusion flame simulations (1D OTP) is explored for N2, CO2 and H2O diluted flames examining the significance of reactivity, dissociation, diffusivity, conductivity, finite-rate chemistry, heat release, and specific heats. Results from both 0D OTP and 1D OTP analysis indicate that all investigated flames possess some degree of OTP, with the CO2 diluted oxidiser case displaying the largest degree of OTP. Parametric analysis utilising concepts of imaginary species and post-simulation equilibrium calculations are shown to be valuable tools to determine the dominant mechanism causing OTP for the different simulation results examined. Experimentally, the development and application of a planar hydroxyl radical (OH) laser induced fluorescence thermometry technique to a laminar oxy-fuel counter-flow diffusion flame is presented. The resulting temperature profiles obtained by a spectrally integrated two-line technique are found to agree well with the simulated thermal structure to within a 2% difference. Further, this thesis also presents the detailed design of a counter-flow burner and laser pulse stretcher for the application Raman scattering in oxy-fuel flames for future experiments

LAURA Users Manual: 5.6

This users manual provides in-depth information concerning installation and execution of Laura, version 5. Laura is a structured, multiblock, computational aerothermodynamic simulation code. Version 5 represents a major refactoring of the original Fortran 77 Laura code toward a modular structure afforded by Fortran 95. The refactoring improved usability and maintainability by eliminating the requirement for problem-dependent recompilations, providing more intuitive distribution of functionality, and simplifying inter- faces required for multi-physics coupling. As a result, Laura now shares gas-physics modules, MPI modules, and other low-level modules with the Fun3D unstructured-grid code. In addition to internal refactoring, several new features and capabilities have been added, e.g., a GNU-standard installation process, parallel load balancing, automatic trajectory point sequencing, free-energy minimization, and coupled ablation and flow field radiation