Investigation over the recirculation influence on the combustion of micro organic dust particles

This paper investigates the role of recircnlation and non-unity Lewis number on the combustion of organic dust particles. Since recirculation effect is more noticeable in micro-combustors, it is necessary to propose a modeling approach of this phenomenon to better simulate the performance of micro-combustors. In this research, in order to model the combustion of organic dust particles, it is assumed that the dust particles va- porize first to yield a known chemical structure which is oxidized in the gas phase, and the chemical structure of this gaseous fuel is assumed methane. To study the flame structure and solve the governing equations, it is considered that the flame structure consists of three zones titled the preheat-vaporization zone, the narrow reaction zone and finally the post flame zone. The recirculation phenomenon is evaluated by entering the exhausted heat from the post flame zone into the preheat zone. The solution is based on the follow- ing approach. First, the governing equations in each zone are nondimensionalized. Then the needed boundary and matching conditions are applied in each zone. After that, these equations and the required boundary and matching conditions are simultaneously solved with the analytical model. Consequently, the remarkable effects of recirculation and non- unity Lewis number on the combustion characteristics of the organic dust particles such as burning velocity and temperature profiles for different particle radii are obtained. The results show reasonable agreement with published experimental data.     

Using nonlinear functions to approximate a new quasi-Newton method for unconstrained optimization problems

Numerical Algorithms - In order to get a higher order accuracy of approximating the Hessian matrix of the objective function, we use the chain rule and propose two modified secant equations. An...     

The discrete heat source approach to dust cloud combustion

In the present paper, combustion of dust clouds from the discrete point heat source method has been addressed. Time-place temperature profile generated by single particle burning has been obtained to study the dust combustion. The summation of the temperature profiles of burned and burning particles predict the temperature in the preheating zone so that the ignition time of layer in flame front can be determined. Consequently the flame propagating speed was obtained based on the dust concentration corresponding to particles spacing and particle diameter. This method has been validated with aluminum dust cloud combustion. Decrease in the dust concentration leads to the lean limit of dust combustion. Increase in particles diameter or reduction in the dust concentration causes higher lean limit and also reduction in the flame propagating speed. Adding the ignition energy as igniter to this system, provides the path to study the effects of ignition energy in the dust combustion.     

An asymptotic approach to heat recirculation in diffusion flames fueled by organic particles

Journal of Thermal Analysis and Calorimetry - Owing to their safety, stability and controllability, diffusion flames have found extensive applications in medicine and power generation. Regarding...     

A two-step superlinearly convergent projected structured BFGS method for constrained nonlinear least squares

We present an exact penalty approach for solving constrained non-linear least-squares problems, when the projected structured Hessian is approximated by a projected version of the structured BFGS formula and prove its local two-step Q-superlinear convergence. The numerical results obtained in an extensive comparative testing experiment confirm the approach to be reliable and efficient.     

Superlinearly Convergent Exact Penalty Methods with Projected Structured Secant Updates for Constrained Nonlinear Least Squares

We present a superlinearly convergent exact penalty method for solving constrained nonlinear least squares problems, in which the projected exact penalty Hessian is approximated by using a structured secant updating scheme. We give general conditions for the two-step superlinear convergence of the algorithm and prove that the projected structured Broyden–Fletcher–Goldfarb–Shanno (BFGS), Powell-symmetric-Broyden (PSB), and Davidon–Fletcher–Powell (DFP) update formulas satisfy these conditions. Then we extend the results to the projected structured convex Broyden family update formulas. Extensive testing results obtained by an implementation of our algorithms, as compared to the results obtained by several other competent algorithms, demonstrate the efficiency and robustness of the proposed approach.     

A simplified mathematical study of thermochemical preparation of particle oxide under counterflow configuration for use in biomedical applications

This study mathematically presents a counterflow non-premixed thermochemical technique for preparing a particle oxide used for cancer diagnosis and treatment. For this purpose, preheating, reaction, melting, and oxidation processes were simulated considering an asymptotic concept. Mass and energy conservation equations in dimensional and non-dimensional forms were solved using MATLAB^®. To preserve the continuity in the system and calculate the locations of melting and flame fronts, promising jump conditions were derived. In this research, variations in flame temperature, flame front location and mass fractions of the particle, particle oxide and oxidizer, with position, Lewis number and initial temperature of the particles were investigated. The simulation results were compared with those obtained from an earlier experimental study under the same conditions. Regarding the comparison, an appropriate compatibility was observed between the results. Based on the simulation results, flame temperature was found to be about 1310 K. Positions of flame and melting fronts were found to be ??1.8 mm and ??1.78 mm, respectively.

     

Semi-analytical modeling of non-premixed counterflow combustion of metal dust

In this study, a semi-analytical model is developed for non-premixed combustion of metal dusts in counterflow configuration. Combustion domain is divided into three separate zones, each of which possesses corresponding mass and energy conservation equations as well as boundary and jump conditions. Metal dust, assumed to be aluminum, undergoes an Arrhenius-type reaction with oxidizer, when it is heated enough to reach the ignition temperature. Dimensionless forms of conservation equations are derived and utilized to elucidate the combustion characteristics. The effects of oxidizer Lewis number and fuel mass concentration on the flame position and temperature are discussed thoroughly. In addition, temperature distribution of the whole domain is calculated by numerically solving the system of partial differential equations. In order to track particles through combustion domain, Lagrangian equations of motion are solved either mathematically or numerically, considering thermophoretic, weight, buoyancy and drag forces. The effects of thermophoretic force on the particle path are investigated, and the deviation of particle from carrier neutral gas direction is obtained. The results showed a great agreement with the data reported in the literature highlighting the fact that the presented model is an efficient one to accurately model the non-premixed counterflow combustion of metal dust.