Derek Bradley

The measurement of laminar burning velocities and Markstein numbers for iso-octane-air and iso-octane-n-heptane-air mixtures at elevated temperatures and pressures in an explosion bomb

Abstract Spherically expanding flames have been employed to measure flame speeds, from which have been derived corresponding laminar burning velocities at zero stretch rate. Two burning velocities are defined, one based upon the rate of propagation of the flame front, the other on the rate of formation of burned gas. To express the effects of flame stretch upon burning velocity, Markstein lengths and numbers for both strain and curvature also have been obtained from the same measurements of flame speed. The effects of the initial mixture temperature and pressure on these parameters also have been examined and data have been obtained for iso-octane–air mixtures at initial temperatures between 358 K and 450 K, at pressures between 1 and 10 bar, and equivalence ratios, φ, of 0.8 and 1.0. Burning velocities and Markstein numbers also are reported for a fuel comprised of 90% iso-octane and 10% n-heptane, with air, for the same range of pressures, temperatures, and equivalence ratios. An important observation is that, as the pressure increases, a cellular flame structure develops earlier during flame propagation. The reasons for this are discussed. As the flame surface becomes completely cellular there is an increase in flame speed and this continues as the flame propagates. The increase in the rate of flame propagation due to flame cellularity has been carefully charted. General expressions are presented for the increase in stretch-free burning velocity with initial temperature and its decrease with pressure. The measured burning velocities are compared with those of other researchers and reasons for the differences discussed.

Burning velocities, Markstein lengths, and flame quenching for spherical methane-air flames: A computational study

Computations are for three modes of spherical laminar flame propagation: explosion, implosion, and stationary. The reduced kinetic, C1, scheme of Mauss and Peters is employed for a range of equivalence ratios under atmospheric conditions, with flame propagation at constant pressure. Save for the richest mixture, the scheme is fully adequate for present purposes. Two burning velocities are computed, one based on the rate of disappearance of unburned gas, the other on the rate of appearance of burned gas. These give the same laminar burning velocity when extrapolated to zero stretch rate. It is necessary to account for two different contributions to the flame stretch rate: one due to the flow field strain rate, the other to the flame curvature. These give rise to different values of Markstein length, which have been evaluated from the three modes of propagation. Flame quenching stretch rates are derived from corresponding Markstein lengths and the mode of quenching is discussed. The relevance of the results to laminar flamelet modeling of turbulent combustion also is discussed. Finally, experimental procedures are suggested for the measurement of the stretch-free laminar burning velocity and the different Markstein lengths.

The burning velocity of methane-air mixtures

Results are presented for the variation of burning velocity with equivalence ratio for methane-air mixtures at one atmosphere pressure. Values were determined by the bomb-hot wire and corrected density ratio techniques, for combustion during the prepressure period. The former of these methods gives a maximum burning velocity of 45 + 2 cm/see, at an equivalence ration of 1.07. Results are compared with those of other workers and the reasons for discrepancies are discussed. The influence of pressure and unburnt gas temperature upon burning velocity are discussed also.

Turbulent burning velocities: a general correlation in terms of straining rates

All known experimental values of turbulent burning velocity have been scrutinized. These number 1650, a significant proportion of which at the higher turbulent Reynolds numbers we measured in a fan-stirred bomb. Dimensionless correlations which have a theoretical basis are presented. These are in terms of flame straining rates and the effective r. m. s. turbulent velocity, as well as the laminar burning velocity of the mixture. When a flame develops from an ignition source it is not initially exposed to the lower frequencies of the turbulent spectrum. As the kernel grows the flame is affected by ever-lower frequencies and the turbulent burning velocity increases towards a fully developed value. An experimental dimensionless power spectral density function is presented, and used to show how both effective r. m. s. turbulent velocity and flame straining rate develop in an explosion. The results are relevant to a variety of practical devices, including gasoline engines, as well as atmospheric explosions.

Determination of burning velocities: A critical review

A critical survey is presented of the different experimental techniques for the measurement of burning velocity. Where possible, correction factors are derived to compensate for errors. The survey is carried out with particular reference to the maximum burning velocity of methane-air mixtures. Recommendations are made as to the most suitable methods of measuring burning velocity for both closed vessels and burners. The recommended value of the maximum burning velocity of methane-air is 45 ± 2 cm/sec at 1 atm and 298°K.

Turbulence and turbulent flame propagation—A critical appraisal

Abstract Current theories of turbulence that seem relevant to the structure of turbulent flames are reviewed. The compatibility of such theories with different turbulent flame models is discussed. It is suggested that the turbulent Reynolds number, Rλ, of the reactants is an important controlling parameter in turbulent flame propagation. When Rλ>100, a wrinkled laminar flame structure is unlikely and the turbulent flame propagation is probably associated with small dissipative eddies. It is proposed that the ratio of turbulent burning velocity to laminar burning velocity can be correlated with Rλ.

Flame Stretch Rate as a Determinant of Turbulent Burning Velocity

A rational basis for correlating turbulent burning velocities is shown to involve the product of the Karlovitz stretch factor and the Lewis number. A generalized expression is derived to show how flame stretch is related to the velocity field. A new dimensionless correlation of experimental values of turbulent burning velocities is presented. Dimensionless groups also are used in correlations of laminar and turbulent flame extinction stretch rates. A distribution function of stretch rates in turbulent flames, based on an earlier one of Yeung et al., is proposed and the experimental data are well predicted by a theory based on flamelet extinction by flame stretch with this distribution. Uncertainties arise concerning the role of negative stretch rate. Laminar flamelet modelling of complex combustion appears to have a broader validity than might be expected and some explanation for this is offered.

How fast can we burn

The roots of our present understanding of tubulence, flame chemistry and their interaction are traced. Attention is then focused on premixed turbulent combustion and the different analyses of stretch—free theories of turbulent burning velocity, u t , are reviewed and new work presented. The various expressions for u t are very different and this becomes more important when allowance must be made for flame stretch. On the basis of previous asymptotic analyses the appropriate dimensionless groups emerge for the correlation of experimental values of u t and a correlation based on these is presented save that,‘pro tem’, the Lewis rather than the Markstein number is employed. The presented correlations are used as a test bed for a stretched flame, Reynolds stress, laminar flamelet model of turbulent combustion. Computed laminar flame data on flame quenching by stretch are generalised and used in the model. The problems of appropriate probability density functions of both stretch and temperature are discussed. There is good agreement between model predictions and experiment over a wider range than would be distance scale should be greater than the laminar flame thickness. The reasons for this wider applicability are discussed, particularly in relation to recent direct numerical simulations. Some of the concepts discussed are applied to spherical explosions and continuous swirling combustion. There is wide diversity in burning rates because of widely different circumstances, but our knowledge is becoming adequate enough to develop reasonably accurate mathematical models for the wide range of engineering applications.

The venting of gaseous explosions in spherical vessels. I—Theory

A study is made of the required vent areas for pressure relief during explosions with normal flame propagation. Two idealised analyses are presented for what is shown to be the worst case of central ignition in a spherical vessel with venting of unburnt gas: one is simple and for a particular condition, whilst the other is based on a comprehensive computer model. Initial internal and external pressure are taken to be atmospheric. Results are presented in a recommended form of values of maximum pressure rise plotted against AS0, where A is the product of vent area and coefficient of discharge divided by the total sphere area, and S0 is the ratio of gas velocity just ahead of the flame front to the acoustic velocity in the unburnt gas just after ignition. Comparisons are made on this basis with the results of previous workers. Solutions are also presented for burnt gas venting. The gas velocity ahead of the flame front, during venting, is computed and the generation of pressure waves discussed.

Modes of reaction front propagation from hot spots

The results of computations with detailed chemical kinetic schemes for the autoignition of stoichiometric H2-CO-air and H2-air mixtures at high pressure and high temperature are reported, with and without a single hot spot. Autoignition delay and excitation times first are computed in zero-dimensional, homogeneous mixture, simulations. Spherical hot spots of three different radii are then studied, for a range of temperature differences between the centre of the hot spot and the surrounding mixture. The effects of the resulting localised initial temperature gradients on the propagation modes of the ensuing reaction waves are examined, with particular regard to possible transitions to a developing detonation. Five modes of reaction front propagation are identified and demonstrated. One mode involves normal flame deflagration, the other four involve different types of hot spot autoignition. These modes depend upon the value of the initial hot spot temperature gradient normalised by the critical temperature gradient for a developing detonation. The latter is conveniently obtained from the homogeneous computations. Upper and lower limits of this normalised temperature gradient, ξ, are observed for a developing detonation. The bounds for this also depend upon the ratio of the hot spot acoustic time to the heat release rate excitation time. A tentative first attempt is described to quantify the bounds for all the modes, in terms of the two dimensionless groups.