KINETIC CHARACTERISTICS OF IGNITION DISPERSED CONDENSED SUBSTANCE SINGLE HEATED TO A HIGH TEMPERATURE OF THE PARTICLES

Kinetic parameters of ignition are defined by the results of performed experimental and theoretical investigations of regularities of the process ignition dispersed solid condensed substance when interacting with a high-temperature metal particles.


Introduction
The use of traditional solid fuels, such as low-calorie coal, is one of the actual directions of development heat power engineering [1].Any condensed substance (CS) in particulate (dispersed) state burn up in the furnaces of steam boilers more efficiently [2].If there is some grinding mechanoactivation substances [2], which resulted in the change process performance termokinetics ignition and subsequent burning fuels.Interaction shredded combustible materials with "hot" particles formed as a result of friction or shock, characterized by a high risk of transport and storage of such fuels [3].Well researched conditions and ignition characteristics of a large group uncomminuted condensed substances (HF), for example, composite solid propellants [4][5][6], forest fuels [7,8], liquid fuels [9,10] local energy sources.Well researched conditions and ignition characteristics of a large group uncomminuted condensed substances CS), for example, composite solid propellants [4][5][6], combustible forest materials [7,8], liquid fuels [9,10] local energy sources.Regularities of ignition dispersed CS studied to a much lesser extent [11].
Results [3][4][5][6][7][8][9][10] and theoretical investigation [12][13][14] can not be directly used to predict the conditions and the ignition characteristics of crushed solid fuels.On the example of wood sawdust [11] established significant differences in the mechanisms of heat transfer layer dispersed CS and monolithic condensed matter.Therefore, the kinetic characteristics of the ignition processes in these two cases may differ materially.Therefore to present day is no information about these characteristics the even for prevalent used in the heat-and-power engineering of solid fuels.
The purpose of this work is determination of thermochemical characteristics (activation energy and pre-exponential factor) for reaction of gas-phase dispersed condensed substance ignition (coal dust) according to experimental studies results.

Experimental technique
a Corresponding author: bet@tpu.ruThe experimental investigations of ignition for solid CS by the single steel particle warmed to high temperatures was held used the plant according the methods [5].Analysis and generalization of experimental data [3,5,7,8] on dependence of ignition delay time on initial temperature of heating source allow formulating an important statement regulating experimental conditions for determination of kinetic parameters.It is reasonable to conduct an experiment at the maximum possible initial temperature (T p ) of the particle (source of energy) for ensuring minimal errors of ignition delay time (t ign ) measurements.
The results of experiments performed with the dispersed coal in the form of relation t ign =f(T p ) are shown in Fig.The experimental results are shown in Fig. 1.The kinetic parameter values of ignition reaction -E 1 (activation energy) and the product Q o k 1 0 (product of the thermal effect of the reaction on the preexponential factor) were calculated by the expression [15]: Nomenclature were accepted: t ignignition delay time, sec; T 0initial temperature of air and CS, K; T p -initial temperature of "hot" particle, K; C -specific heat, J/(kg•K); Q оthermal effect of oxidation reaction, J/kg; k 1 0preexponential factors, s -1 ; Е 1activation energy of oxidation reaction, J/mol; R t -absolute gas constant, J/(mol•K).
Two points of the experimental curve (Fig. , curve 1) were used for calculating of two unknowns.The points make a connection between T p and t ign in area of relatively high initial temperatures of energy source.Thus it is sufficiently to solve a system of two transcendental equations for determination the kinetic parameters.
The kinetic parameters values of the oxidation reaction were calculated for the variation range of the hot particle initial temperature from 1050 K to 1200 K: The verification of the findings characteristics of the ignition process.Toward this end we solve the problem in describing the process under study the mathematical model [13,14] developed for the heating conditions of liquid fuels "hot" particles.

Mathematical model
Mathematical modeling of physical and chemical processes taking place during the ignition has been realized in system "dispersed CSenergy source with limited heat content-air".It was assumed that the local energy sourcethe small-size (r p =r 1 =3·10 -3 m, h p =z 2 -z 1 =3·10 -3 m) disk-shaped steel particle heated to high temperature is deposited on the surface of the dispersed coal.
The objective of this analysis is to assessment of reliability of the determined values of the kinetic ignition parameters by means of Arrhenius dependence (Fig. 1, curve 1) of the rate of oxidation reaction on the local energy source's initial temperature.
The following complex of ignition criteria was used which allows considering that specific features of the heat-and-mass transfer processes in the system with the local power source during the induction period: 1. Energy released by the oxidation reaction of the gaseous products of thermal decomposition of dispersed CS's particles is greater than heat transferred from the heating source to the reaction zone.
2. The gas mixture temperature is greater than the initial temperature of the hot particle in the reaction zone of intensive oxidation.
The ignition problem has been solved in an axially symmetric formulation in a cylindrical coordinate system with the origin coincident with the symmetry axis of the hot particle.The given below system of nonlinear non-stationary differential equations describes a complex of the heat and mass transfer processes with the phase transformations and chemical reactions at 0<t<t d .
The energy equation for the gas mixture of oxidant (air) with gas components of porous CS particles thermal decomposition ( 1 where is mass rate of combustible gases oxidation in the air [15].
The heat transfer equation for the metallic particle ( The energy equation for porous CS ( 0 where is mass rate of porous CS particles thermal decomposition [15].
The diffusion equation for the combustible gases in the oxidant (air Thermophysical Basis of Energy Technologies 2015 The balance equation for the gas mixture ( 1 Nomenclature were accepted: r, zcoordinates of the rectangular system, m; r l , z hsolution domain extent, m; λ -thermal conductivity, W/(m•K); ρ is density, kg/m 3 ; Q 3thermal effect of gasification reaction, J/kg; k 3 0preexponential factors, s -1 ; Е 3activation energy of gasification reaction, J/mol; С f 1dimensionless mass concentration of combustible gases in the gas mixture (0<С f 1 <1), С о 1dimensionless mass concentration of oxidant (air) in the gas mixture; subscripts "1", "2", "3" correspond to gas mixture, steel particle, dispersed condensed substance.Initial conditions at t=0: Boundary conditions at 0<t<t d : 1.On symmetry axis and external borders we set for all equations the condition of gradients vanishing of corresponding functions: r=0, 0<z<z 1 ; r=r l , 0<z<z 1 : 2. Thermal interaction between system components was described by boundary condition of type IV with allowance for finely grinded coal particles gasification on the site of a surface closed by "hot" metallic particle: z=z 2 , 0<r<r 1 : z=z 1 , 0<r<r 1 : Gasification rate of dispersed CS particles on the surface closed by a "hot" particle was defined by a ratio: Total gas-arrival g W ¦ was distributed in a small vicinity of a particle according to expression: W r is mass rate of gasification on k th step along an axis r without additional gas-arrival from the site of a surface closed by a "hot" particle; ( ) W r is total gasification rate on k th step along an axis r in a vicinity of a "hot" particle.
Thermophysical Basis of Energy Technologies 2015 The set of nonlinear non-stationary differential equations in private derivatives ( 2)-( 6) with the corresponding initial and boundary conditions was solved by the method of final differences with use of algorithms [9,10].

Results and discussion
The numerical investigation was carried out for the following values of parameters: CS and air initial temperature T 0 =300 K, steel particle initial temperature T p =1050÷1200 K; volume fraction of a substance capable of chemical reaction φ 3 =0.5;kinetic parameters of the thermal decomposition reaction of CS -Е 3 =195·10 3 J/mol, Q 3 k 3 0 =25.5·10 14 J/(kg·s); kinetic parameters of the oxidation reaction of the gas mixture were calculated by the experimental dependence t ign =f(T p ): Thermophysical characteristics of substances are listed below: Has been found (Fig. 1) that the experimental (curve 1) and calculated (curve 2) as a result of solving the problem (2)-(20) values of t ign (for identical temperatures) differ nearly by 25 % providing by relatively low values of T p .The reasons for rejection t ign , can be explained by the features of gasphase ignition with local heating of substance as well as by the specificity of heat and mass transfer in the heated layer of dispersed solid fuel.
For a formal description of the ignition process the analysis of received experimental data has been executed considering a possible dependence between the pre-exponential factor and temperature.The following approximation expression was received: The Fig.
shows the theoretical dependence t ign =f(T p )curve 3 obtained by numerical simulation of the ignition process using the approximated expression (21).An acceptable agreement between the experimental and calculated values of the ignition delay times at low temperatures is can be noted.The extreme deviations of the t ign represent less than 3.5% that does not exceed the error of the experimental values t ign .The type of the approximation dependence (21) allows to suggest that the model (1) gives a very good description of the actual process due to some "redundancy" of heat entering to the reaction zone.The heat transfer conditions in the case of dispersed substance as well as for the mixture of fuel and oxidant have a little effect on the chemical reaction rate if T p is greater than some limiting value (in that case T p ≈1180 K).At relatively low temperature of local source the conditions of energy supply to the zone of intensive interactions have a prior importance.Summarizing the results of the research it can be concluded that we can always choose such variation range of the initial temperature of the heat source where the kinetics of the ignition process can be 01021-p.6determined by the formula (1) [15] with high accuracy for the ignition of dispersed CS at local heating conditions.At low T p is necessary to consider the effect of temperature on the kinetic constants.

Conclusions
Investigation results allow making a conclusion about the possibility to determine the kinetic characteristics of the gas-phase ignition of dispersed CS by a local source at high temperatures using relatively simple approach developed long ago [15].This work was supported by RFBR grant № 13-08-90710.

Figure 1 .
Figure 1.The dependence of the ignition delay time t d on the initial temperature T p of "hot" particle: 1experimental curve, 2theoretical curve at Q o k 1 0 =const, 3theoretical curve at Q o k 1 0 =f(T p ).