Laminar diffusion flamelet models in non-premixed turbulent combustion

Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations

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.

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

The lift-off heights and visible-flame lengths of jet diffusion flames in still air have been determined for hydrogen, propane, methane and ethylene. The flame lift-off height varies linearly with the jet exit velocity and is independent of the burner diameter for a given gas. The results support the assumption that if the burner exit flow is choked the burner can be approximated by an equivalent convergent-divergent nozzle at whose exit the flow has expanded to ambient pressure. The data for different gases can be collapsed onto a single curve if they are plotted in terms of the appropriate non-dimensional groupings. These results and previous results for blow-out stability suggest that diffusion flames blow out when the base is lifted to between 0.65 and 0.75 times the height at which stoichiometric concentration is reached at the jet axis. It can be deduced from the experimental results that, at the base of the flame. the ratio of turbulent burning velocity to laminar burning velocity varies a...

Lift-Off Heights and Visible Lengths of Vertical Turbulent Jet Diffusion Flames in Still Air

A turbulent non-premixed burning mixture is considered at a state close to extinction. The turbulent flame is conceived as an ensemble of thin laminar diffusion flamelets that are highly distorted and stretched such that they may be quenched locally. The structure of the laminar diffusion flamelets is analysed in the limit of a large activation energy and the results of Linan's analysis of counterflow diffusion flames are used to derive the quenching condition. This condition is expressed by an instantaneous scalar dissipation rate. Statistics of the scalar dissipation rate are discussed on the basis of Kolmogoroff's third hypothesis. Extinction condition of the whole turbulent flame are derived on the basis of the percolation theory.

Local Quenching Due to Flame Stretch and Non-Premixed Turbulent Combustion

Turbulence and turbulent flame propagation—A critical appraisal

Turbulent burning velocities have been measured in an explosion vessel equipped with four fans driven by air turbines. This arrangement created a central region of uniform isotropic turbulence in which measurements were made of flame speed, turbulent burning velocity and gas velocity just ahead of the flame front. Two techniques were used for such measurements: one involving anemometer measurements of the gas velocity ahead of the flame and the other involving the creation of two kernels of gas originating from two separated, simultaneous sparks. Measurements were made for a range of methane-air and ethylene-air mixtures at an initial pressure of one atmosphere and at different fan speeds. An increase in fan speed resulted in increases in flame speed and turbulent burning velocity, but the gas velocity ahead of the flame showed little change. This last is explained by significant increase in flame thickness with fan speed. A consideration of current ideas of turbulent structure suggests a rational basis for the correlation of burning velocity data is to plot the ratio of turbulent to laminar burning velocity against the turbulent Reynolds number for the unburnt gas. An increase in fan speed gives an increase in the Reynolds number. The experimental results show there is indeed a primary correlation between this ratio and the turbulent Reynolds number. Reference to results of other workers also gives some confirmation of this.

S.B. Lwakabamba

Papers

Turbulence and turbulent flame propagation—A critical appraisal

Measurement of turbulent burning velocity for large turbulent Reynolds numbers

Energy in Africa

Response to comment of forman A. Williams