A numerical study of quasi-steady burning characteristics of a condensed fuel: effect of angular orientation of fuel surface

A numerical study of laminar diffusion flames established over a condensed fuel surface, inclined at several angular orientations in the range of –90°?θ?+90° with respect to the vertical axis, under atmospheric pressure and normal gravity environment, is presented. Methanol is employed as the fuel. A numerical model, which solves transient gas-phase, two-dimensional governing conservation equations, with a single-step global reaction for methanol–air oxidation and an optically thin radiation sub-model, has been employed in the present investigation. Numerical results have been validated against the experimental data from the present study. Thereafter, the model is used to investigate the influence of angular orientation of fuel surface on its quasi-steady burning characteristics. Results in terms of fuel mass burning rate, flame stand-off distances, temperature field, velocity profiles and oxygen contours have been presented and discussed in detail. It is observed that orientation angles in the range of –45°?θ? –30° (fuel surface facing upwards), yield the maximum mass burning rates. The flame anchoring location near the leading edge of the fuel surface, normal gradient of fuel vapor mass fraction at the surface and oxygen contours have been used to explore this unique behavior. Based on the numerical results, a theoretical correlation to predict the mass burning rate as a function of fuel surface orientation is also proposed. Furthermore, a discussion on the differences in the structure of laminar diffusion flame established over fuel surface as a function of its angular orientation is included.     

Effect of flame thickness variation on the mass burning rate of premixed counterflow flames with an oscillating strain rate

The mass-based stretch rate is used to study the response of premixed axisymmetric counterflow flames subject to an oscillating strain rate. Integral analysis is used to estimate the mass burning rate of the oscillating counterflow flames. From this study it can be concluded that the flame responds in a nonlinear manner. With an increase of the applied strain frequencies, it is found that unsteady stretch effects arising due to flame thickness variations become significant and the mass-based stretch rate is able to capture these nonlinear effects. The inclusion of these unsteady stretch effects in the mass-based stretch helps the integral analysis to predict the mass-burning rate of oscillating flames more accurately.     

A theoretical and numerical consideration of the longitudinal and transverse relaxations in the rotating frame

We previously derived a simple equation for solving time-dependent Bloch equations by a matrix operation. The purpose of this study was to present a theoretical and numerical consideration of the longitudinal (R_1ρ = 1/T_1ρ) and transverse relaxation rates in the rotating frame (R_2ρ = 1/T_2ρ), based on this method. First, we derived an equation describing the time evolution of the magnetization vector (M(t)) by expanding the matrix exponential into the eigenvalues and the corresponding eigenvectors using diagonalization. Second, we obtained the longitudinal magnetization vector in the rotating frame (M_1ρ(t)) by taking the inner product of M(t) and the eigenvector with the smallest eigenvalue in modulus, and then we obtained the transverse magnetization vector in the rotating frame (M_2ρ(t)) by subtracting M_1ρ(t) from M(t). For comparison, we also computed the spin-locked magnetization vector. We derived the exact solutions for R_1ρ and R_2ρ from the eigenvalues, and compared them with those obtained numerically from M_1ρ(t) and M_2ρ(t), respectively. There was excellent agreement between them. From the exact solutions for R_1ρ and R_2ρ, R_2ρ was found to be given by R_2ρ = (2R₂ + R₁)/2 − R_1ρ/2, where R₁ and R₂ denote the conventional longitudinal and transverse relaxation rates, respectively. We also derived M_1ρ(t) and M_2ρ(t) for bulk water protons, in which the effect of chemical exchange was taken into account using a 2-pool chemical exchange model, and we compared the R_1ρ and R_2ρ values obtained from the eigenvalues and those obtained numerically from M_1ρ(t) and M_2ρ(t). There was also excellent agreement between them. In conclusion, this study will be useful for better understanding of the longitudinal and transverse relaxations in the rotating frame and for analyzing the contrast mechanisms in T_1ρ- and T_2ρ-weighted MRI.     

The mass transfer process and the growth rate of NaCl crystal growth by evaporation based on temporal phase evaluation

The mass transfer process and the crystal growth rate have been proved to be very important in the study of crystal growth kinetics, which influence the crystal quality and morphological stability. In this paper, a new method based on temporal phase evaluation was presented to characterize the mass transfer process in situ and determine the crystal growth rate. The crystallization process of NaCl crystal growth by evaporation was monitored in situ by a Mach-Zehnder interferometer, and the absolute concentration evolution, the evaporation rate and the real-time supersaturation of solution were obtained using temporal phase analysis, which acted as a novel technique to extract phase variation along time axis recently. Based on the evaporation rate and the absolution concentration, a new method to calculate mass transfer flux during the crystal growth without the knowledge of the mass transfer coefficient was proposed, and then the crystal growth rate could also be retrieved under the hypothesis of cubic crystals. The results show that the crystal growth rate increases with the supersaturation linearly. It is in agreement with the diffusion theories, which presume that matter is deposited continuously on a crystal face at a rate proportional to the difference in concentration between the points of deposition and the bulk of solution. The method is applicable to the research of crystallization process based on evaporation or vapor diffusion of which the precise conditions of nucleation and supersaturation are usually unknown because of the complexity of the evaporation rate and crystal growth rate.     

Reaction mechanism and rate constants of the CH+CH4 reaction: a theoretical study

Ab initio and density functional calculations have been performed to elucidate the mechanism of CH radical insertion into methane. The results show that the reaction can be viewed to occur via two stages. On the first stage, the CH radical approaches methane without large structural changes to acquire proper positioning for the subsequent stage, where H-migration occurs from CH₄ to CH, along with a C–C bond formation. Where the first stage ends and the second begins, a tight transition state was located using the B3LYP/6-311G(d,p) and MP4(SDQ)/6-311++G(d,p) methods. Using a rigid rotor – harmonic oscillator approach within transition state theory, we show that at the MP5/6-311++G(d,p)//MP4(SDQ)/6-311++G(d,p) level the calculated rate constants are in a reasonably good agreement with experiment in a broad temperature range of 145–581 K. Even at low temperatures, the insertion reaction bottleneck is found about the location of the tight transition state, rather than at long separations between the CH and CH₄ reactants. In addition, high level CCSD(T)-F12/CBS calculations of the remainder of the C₂H₅ potential energy surface predict the CH+CH₄ reaction to proceed via the initial insertion step to the ethyl radical which then can emit a hydrogen atom to form highly exothermic C₂H₄+H products.