Instabilities and soot formation in high-pressure, rich, iso-octane-air explosion flames - 1. Dynamical structure

Simultaneous OH planar laser-induced fluorescence (PLIF) and Rayleigh scattering measurements have been performed on 2-bar rich iso-octane–air explosion flames obtained in the optically accessible Leeds combustion bomb. Separate shadowgraph high-speed video images have been obtained from explosion flames under similar mixture conditions. Shadowgraph images, quantitative Rayleigh images, and normalized OH concentration images have been presented for a selection of these explosion flames. Normalized experimental equilibrium OH concentrations behind the flame fronts have been compared with normalized computed equilibrium OH concentrations as a function of equivalence ratio. The ratio of superequilibrium OH concentration in the flame front to equilibrium OH concentration behind the flame front reveals the response of the flame to the thermal–diffusive instability and the resistance of the flame front to rich quenching. Burned gas temperatures have been determined from the Rayleigh scattering images in the range 1.4⩽ϕ⩽1.9 and are found to be in good agreement with the corresponding predicted adiabatic flame temperatures. Soot formation was observed to occur behind deep cusps associated with large-wavelength cracks occurring in the flame front for equivalence ratio ϕ⩾1.8 (C/O⩾0.576). The reaction time-scale for iso-octane pyrolysis to soot formation has been estimated to be approximately 7.5–10 ms

On Factorization of Molecular Wavefunctions

Recently there has been a renewed interest in the chemical physics literature of factorization of the position representation eigenfunctions \{$\Phi$\} of the molecular Schr\"odinger equation as originally proposed by Hunter in the 1970s. The idea is to represent $\Phi$ in the form $\varphi\chi$ where $\chi$ is \textit{purely} a function of the nuclear coordinates, while $\varphi$ must depend on both electron and nuclear position variables in the problem. This is a generalization of the approximate factorization originally proposed by Born and Oppenheimer, the hope being that an `exact' representation of $\Phi$ can be achieved in this form with $\varphi$ and $\chi$ interpretable as `electronic' and `nuclear' wavefunctions respectively. We offer a mathematical analysis of these proposals that identifies ambiguities stemming mainly from the singularities in the Coulomb potential energy.Comment: Manuscript submitted to Journal of Physics A: Mathematical and Theoretical, May 2015. Accepted for Publication August 24 201

The turbulent burning velocity of iso-octane/air mixtures

Turbulent burning velocities of iso-octane air mixtures have been measured for expanding flame kernels within a turbulent combustion bomb. High speed schlieren images were used to derive turbulent burning velocity. Turbulent velocity measurements were made at u’ = 0.5, 1.0, 2.0, 4.0, 6.0 m/s, equivalence ratios of 0.8, 1.0, 1.2, 1.4 and pressures of P = 0.1, 0.5, 1.0 MPa. The turbulent burning velocity was found to increase with time and radius from ignition, this was attributed to turbulent flame development. The turbulent burning velocity increased with increasing rms turbulent velocity, and with pressure; although differences were found in the magnitude of this increase for different turbulent velocities. Generally, raising the equivalence ratio resulted in enhanced turbulent burning velocity, excepting measurements made at the lowest turbulent velocity. The results obtained in this study have been compared with those evaluated for a number turbulent burning velocity correlations and the differences are discussed

Laser ignition of iso-octane air aerosols

Iso-octane aerosols in air have been ignited with a focused Nd:YAG laser at pressures and temperatures of 100kPa and 270K and imaged using schlieren photography. The aerosol was generated using the Wilson cloud chamber technique. The droplet diameter, gas phase equivalence ratio and droplet number density were determined. The input laser energy and overall equivalence ratio were varied. For 270mJ pulse energies initial breakdown occurred at a number of sites along the laser beam axis. From measurements of the shock wave velocity it was found that energy was not deposited into the sites evenly. At pulse energies of 32mJ a single ignition site was observed. Overall fuel lean flames were observed to locally extinguish, however both stoichiometric and fuel rich flames were ignited. The minimum ignition energy was found to depend on the likelihood of a droplet existing at the focus of the laser beam

A Derivation of Moment Evolution Equations for Linear Open Quantum Systems

Given a linear open quantum system which is described by a Lindblad master equation, we detail the calculation of the moment evolution equations from this master equation. We stress that the moment evolution equations are well-known, but their explicit derivation from the master equation cannot be found in the literature to the best of our knowledge, and so we provide this derivation for the interested reader

Lyapunov Stability Analysis for Invariant States of Quantum Systems

In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In contrast to many previously studied convergence analysis methods for invariant density operators which use weak convergence, in this article we analyze the convergence of density operators by considering the set of density operators as a subset of Banach space. We show that the set of invariant density operators is both closed and convex, which implies the impossibility of having multiple isolated invariant density operators. We then show how to analyze the stability of this set via a candidate Lyapunov operator.Comment: A version of this paper has been accepted at 56th IEEE Conference on Decision and Control 201