Laminar Flame Propagation Research Articles

The theory of steady laminar spherical flame propagation: Analytical solutions

Spherical steady laminar flame propagation is considered. Analytical solutions have been obtained for the cases of (a) Step-function reaction-rate curves, and (b) Adams-type reaction-rate curves. It is shown that the effective radius of a spherical flame is under-estimated if one uses the thin-flame approximation. The error decreases as the rate of injection and the laminar flame speed of the mixture increase. Graphical comparison has been made with numerical and analogue solutions. Curves are presented which can be used with fair accuracy with any realistic reaction-rate function.

Flame propagation by non-branching chain reactions

Steady, one-dimensional, laminar flame propagation, proceeding by a non-branching chain reaction with negligible chain breaking is considered. Some exact analytical solutions for the temperature gradient, radical concentration and flame propagation speed are obtained for particular systems of reaction rate functions. Approximate methods are developed by means of which the flame propagation speed for any given reaction scheme may be determined.

The theory of steady laminar spherical flame propagation: Analogue solutions

Steady spherical laminar flame propagation is considered in gases with temperature-explicit reaction-rate curves. The temperature distribution has been calculated by means of a resistance network analogue computer. It is shown that the effective radius of a spherical flame is under-estimated by the thin-flame approximation. The error decreases as the rate of injection and the laminar flame speed of the mixture increase. Comparison has been made with the results obtained by numerical means.

The spectral theory of turbulent-flame propagation

This paper is concerned with turbulent-flame propagation. An analytical formulation for large or small scale, low-intensity turbulent flames is based on the distribution of eddy sizes present in the flow stream. The validity of several turbulent-flame theories is checked as well as the reactionzone-model criterion of Kovasznay, with a modified Powling type burner to produce a low-pressure stream of propane and air with small-scale, low-intensity isotropic turbulence. The basic assumption involved in the analysis is that the large-scale turbulence wrinkles the flame surface, thereby increasing the combustion area, but does not affect the laminar-flame propagation rate. The small-scale turbulence is assumed to alter the laminar-flame propagation by virtue of a change in the transport processes. Both effects are believed to occur simultaneously, producing an increase in the rate of flame propagation. The spectral theory weights the contributions of large and small eddies by considering the distribution of kinetic energy in the velocity fluctuations. The experimental data obtained correspond to the upper limiting condition of the spectral theory, although published data are shown to fall close to a lower limit. In the former case, nearly all the eddies are of smaller or comparable size to that of the reaction zone thickness; whereas, in the latter case, the scale is of larger size. The Kovasznay parameter correlated the experimentally obtained data and correctly described the reaction-zone structure as observed during the testing. The turbulence intensity of ambient air behind a 3/32 inch mesh grid and an x/M position of 50.7 was found to decrease 70 per cent as the pressure varied from 1 to 0.1 atmos. The experimental data of this study were found to be larger in magnitude than that predicted by the Scurlock-Grover Theory but consistent with the experimental results of Grover, et al. This difference may be indicative of the effect of anisotropy on turbulent-flame propagation. The ratio of turbulence microscale to laminar-flame thickness did not appear to be a valid criterion for predicting the reaction-zone structure. Within the limits of the approximations made, the following general conclusions were made. (1) The spectral theory correctly describes turbulent-flame propagation for large- or small-scale, low-intensity flames. (2) The Kovasznay parameter accurately predicts the reaction-zone structure for small-scale, low-intensity turbulent flames. (3) Grid-generated turbulence intensity is dependent on the pressure of the system. (4) The ratio of turbulence microscale to laminar-flame thickness does not constitute a sufficient measure for the prediction of the reaction-zone structure.

The theory of steady laminar spherical flame propagation: Equations and numerical solution

The combustible gas is supposed to emerge steadily from a point source immersed in an combustions products. The differential energy equation is solved numerically and shown that the effective radius of the spherical flame is larger than that from the assumptions that the flame is very thin and that it has the same rate per unit area as a plane flame. The error interest as the rate of injection and the Laminar flame of the mixture decrease. The thermal conductivity of the gas is constant in the numerical analysis, but it is shown the resulting data can be cases for which depends upon temperature.

Structure and propagation of laminar flamesnear a heat sink

This paper presents the results obtained in a theoretical investigation of the problem of laminar flame propagation near a heat sink, the temperature of which may be either high or low as far as the chemical reaction rate is concerned. The results presented consist of two parts: first, effects on the burning velocity of an adiabatic laminar flame due to a change in the temperature of the unburnt mixture; and secondly, effects on the structure and the burning velocity of a laminar flame when the rate of heat loss per unit volume inside the flame in the direction normal to the mixture velocity and the raw of heat loss per unit area at the hot boundary in the direction parallel to the flow are prescribed by arbitrary functions. In all cases, the burning velocity is found to vary approximately with the temperature of the combustion product at the hot boundary according to an expression of the following form Su ȣ exp (ȡTc/Tb) where Su is the burning velocity. Tb is the temperature of the combustion product, and Te is a characteristic temperature, the value of which depends on the specific case under consideration. Some of these observations have also been found to agree with the experimental results. For the special case where heat loss occurs only at the hot boundary in the direction parallel to the flow, there is a lower limit for the temperature of the combustion product, below which no steady-state solution for the burning velocity can be found. This limit is in addition to the one deduced from stability considerations.

The limits of the eigenvalue of the laminar flame equation in terms of the reaction rate-temperature centroid

The differential equation describing one-dimensional laminar flame propagation for temperature explicit reaction-rate functions is considered. It is shown that for a fixed centroid of the reaction-rate function, the burning velocity must lie within certain limits, which are independent of the type of reaction considered.

The present status of the theory of laminar flame propagation

Summary Summarizing our considerations concerning the present status of the theory of laminar flame propagation, I wish to state: o (1) That it appears in cases in which the reaction-scheme and the corresponding chemical kinetics are well-defined, a semianalytical method, as presented in this paper, makes a relatively easy determination of the flame velocity possible. There is no necessity for radical simplifying assumptions such as are introduced, for example, in the pure diffusion theories. (2) There is no necessity to take recourse to laborious numerical integration of the differential equations, although the use of digital computers may facilitate such methods. (3) It appears that in the cases dealt with until now, the steady-state assumption facilitates a rather quick determination of the flame velocity of a chain reaction, even in those cases where it does not furnish an exact picture for the distribution of the radicals through the flame zone. (4) It is believed that in order to make further progress in the theory, the most urgent need is a better knowledge of the reaction schemes and the chemical kinetics of the important chain reactions. Especially more exact data are necessary concerning the presence and distribution of the radicals involved. A paper by K. A. Wilde [J. Chem. Phys. 22 , 1788. (1954)] has recently come to our attention. The procedure used by this author for the integration of the simple one-step flame reaction is the same as that used in our first approximation except that ∈ is assumed to vary as ([ϱ=ϱ o )/(1-ϱ o )] n+1 . Here the exponent n is determined by equating the limiting slope of [(ϱ-ϱ o )/(1-ϱ o )] n to the limiting slope of [exp [-ϱ a (1-ϱ)/ϱ }. This procedure leads to the relation 1 Λ = 2 I 1 − θ 0 [ 1 + 2 θ α ( 1 − θ 0 ) ( A − 1 ) which is similar to our Equation (19). For, sufliciently large values of ϱ a , i.e., small values of I, Equations (A-1) and (19) become evidently equivalent. We have evaluated 1 / Λ according to Equation (A-1) and find the results to be less accurate than our second approximation for ϱ a ≥5 but to be better at smaller values of ϱ a . Equation (A-1) gives results which are superior to those determined from Equation (19) for ϱ a Λ about as much too small according to Equation (A-1) as it is too large according to Equation (19) for larger values of ϱ a

The propagation and stability of the decomposition flame of hydrazine

Pre-eminent among problems facing the theory of laminar flame propagation is the prediction of the properties of flames from the kinetics of the chemical reactions occurring in them. Such predictions require, inter alia, knowledge of the kinetic order and activation energy of the over-all decomposition reaction under the conditions of the flame. This in turn requires extrapolation of experimental data on reaction kinetics, usually far beyond the range in which their validity is sure. An alternative approach uses measurements made on the laminar flame to derive the form of kinetic equations governing reactions in the flame, and then compares this with the kinetic behavior observed at lower temperatures. This approach is adopted here. The rigorous solution of the flame equations for even an elementary, single-step, reaction requires lengthy calculations and for this reason their excessive chemical complexity hinders the use of this information in testing flame theories, although in the past most information has been derived from studies of hydrocarbon flames. Flames which are chemically much less complicated may be expected to supply suitable data more readily. The most simple flames known are those supported by the exothermic breakdown of a single compound and among these the hydrazine decomposition flame stands out. Hydrazine decomposition produces only nitrogen, hydrogen and ammonia. Thus, chemical analysis is easy and stoichiometry and thermoehemistry are clear cut. The kinetics of the initial step in homogeneous decomposition ( N N bond fission) are known I as a function of temperature. The spontaneous 2,a and spark 4 ignitions have been observed. The gaseous decomposition flame has been stabilized on burners 5, G at atmospheric pressure. The decomposition flame has been burned above the surface of the liquid J. s Furthermore, some theoretical work has also been done on this system 9, 10 in an a t tempt to predict the flame velocity from the kinetics of the initial step in homogeneous decomposition. Two fundamental properties of the hydrazine flame are (1) the dependence of flame speed on pressure from which the over-all kinetic order of reaction may be found, and (2) the dependence of flame speed on temperature from which the over-all activation energy may be found. The primary purpose of this work is to supply this information experimentally, to examine its theoretical implications, and to see how they may be interpreted. Two experimental methods have been used. In the first, flame speeds of gaseous hydrazine have been measured by the closed vessel method. This permits the accurate control of initial pressure and temperature and avoids the hazards of the considerable flow of heated hydrazine necessary for a normal burner technique. The pressure range which can be studied in a glass vessel extends from very tow values up to about 10 cm Hg. In the second method the pressure range between 10 cm Hg and atmospheric has been examined by burning liquid hydrazine in narrow tubes.S. 7 This provided the secondary purpose of this work-to examinc the validity of this simple technique. In tubes, the flame is not adiabatic but subject to strong quenching influences as a result of lateral heat losses. This difficulty has been pointed out by Gray and Kay s but not previously overcome. An at tempt has now been made to allow for these varying heat losses.

The theory of flame phenomena with a chain reaction

For single-step reactions there is a unique relation between reaction rate and reactedness for a given combustible mixture at a specified pressure and initial temperature. This paper examines whether the relation is still unique when chain reactions are present, by considering three types of flame—spontaneous ignition, laminar-flame propagation, and the homogeneous steady-flow reaction zone—with a chain-reaction scheme proposed by Adams & Stocks for the decomposition of hydrazine. It is found that the relation is not unique but that similarities exist between the relation for laminar-flame propagation and the relation for the homogeneous reaction zone. Incidentally, a general method of calculating laminar-flame speeds with reaction schemes of arbitrary complexity is presented. When applied to the hydrazine decomposition flame the predictions of the theory are in fair agreement with experimental results. In particular, the variation of flame speed with temperature is correctly predicted. It is shown that the use of the Karman-Penner 'steady-state assumption' would lead to an overestimate of the flame speed. Consideration of the changes which would result if the chain reaction should branch shows that there would once again tend to be a unique reaction rate versus reactedness relation, and that the laminar-flame speed would be increased by a factor of about three for the hottest flame considered but by larger factors for cooler flames.

The Influence of Turbulence on Flame Propagation Rates

A technique for the experimental study of laminar and turbulent flame propagation is presented. The method consists of igniting, by a single spark discharge, a smal l zone in a free jet of fuel-air mixture. This approximately spherically shaped burning zone, called a flame globule , was shadowgraphed, us ing a high-speed mot ion picture camera, as it passed downstream with the mixture. Measurements taken from the photographs resulted in the flame speed data. 1 The experimental technique appears to have considerable value for the study of the propagation of laminar and turbulent flames. The data are quite consistent and reproducible, and are adaptable to the study of the transient phase of the turbulence effect. 2 The measured laminar flame speeds are in good agreem e n t with those obtained by other investigators. 3 An encouraging quantitat ive correlation between an empirical equation and the experimental data is shown, but the relation to the scale of the turbulence was satisfactory for only one of the two screens used. The correlation was unsuccessful for very lean and rich mixtures . This was due to the fact tha t the rate of turbulent flame growth, for these cases, was lower t h a n the laminar values.