Laminar Flame Theory By Eng. Mohamad Okour UINVERSITY OF JORDAN MECHANICAL ENGINEERING DEPARTEMENT

Laminar Flames  Premixed flames  Partial premixed flames  Diffusion flames

Premixed flames are characterized by  Laminar flame speed  Flame structure  Flame thickness

THE LAMINAR FLAME SPEED  The flame velocity, which is also called the burning velocity, normal combustion velocity, or laminar flam speed  Defined as: The velocity at which unburned gases move through the combustion wave in the direction normal to the wave surface. The velocity at which unburned gases move through the combustion wave in the direction normal to the wave surface.

The theoretical approaches to calculate the laminar flame speed can be divided into three categories  (a) Thermal theories  (b) Diffusion theories  (c) Comprehensive theories In thermal theories The flame zone according to Mallard and Le Chatelier consist of two zones broken up by the point where the next layer ignites, as shown in the Figure.

 In thermal theories The flame zone according to Mallard and Le Chatelier consist of two zones broken up by the point where the next layer ignites, as shown in the Figure.

The Theory of Mallard and Le Chatelier  Mallard and Le Chatelier stated that the heat conducted from zone II in Fig.1 equaled that necessary to bring the unburned gases to the ignition temperature (the boundary between zone I and II). The enthalpy balance then becomes (1) (1) Where is the thermal conductivity and is the mass rate into the combustion wave.

(2) (2) Where is the density, A the cross-sectional area, u the velocity of the gases, and S L the laminar flame speed. Because unburned gases enter normal to the wave, by definition Equation (1) then becomes Or(3)

Since is the reaction zone thickness. Thus (4) Where is the reaction time and is the reaction rate. Substituting this expression into Equation (4), obtains Substituting this expression into Equation (4), obtains Where is the thermal diffusivity and RR is the reaction rate.

 In order to calculate the laminar flame speed one must know the thermophysical properties of a mixture at high temperatures and have accurate reaction rate data.

Flame Speed Measurements  Different measuring techniques can be used to measure the laminar flame speed such as: 1- Bunsen burner method 2- Flame in tubes 3- Soap bubble method 4- Flat flame methods These methods are arranged in order of decreasing complexity of flame surface and correspond to an increasing complexity of experimental arrangement. In this amount we will discuses the Bunsen Burner Method only.

Bunsen burner method  In this method premixed gases flow up a cylindrical jacketed tube long enough to insure streamline flow at the mouth.The gas burns at the mouth of the tube and the shape of the Bunsen cone is recorded and measured by various ways.

 The burning velocity is not constant over the cone.The velocity near the tube wall is lower because of cooling by the walls. Thus there are lower temperature; therefore, lower flame speeds.  Actually, if one measures SL at each point he will see that it varies along every point for each velocity vector and it is not really constant. This is the major disadvantage of this method.

 The earliest procedure of calculating flame speed by this method was to divide the volume flow rate by the area of flame cone.  Two disadvantages of the Bunsen method are: 1-One can never completely eliminate wall effects. 2-One needs a steady source of supply of gas, which for rare or pure gases can be a severe problem.

Effects of Chemical Variables on Flame Speed  Effect of Mixture ratio * The vibration of laminar flame speed with fuel-oxidant ratio is governed by variation of the temperature with the mixture ratio. * The mixture with maximum flame temperature is a mixture with maximum flame speed

 Effect of Fuel Molecular * As the fuel molecular weight increases, the range of flammability becomes narrow * The difference in SL for fuels containing different numbers of carbon is due to the changes in the thermal diffusivity which is function of fuel molecular weight.

 Effect of additives * The purpose of using additives is to raise the ignition temperature and reduce the tendency to preignition as knocking. * Additives such as acetone, benzene and so on which studies for oxidation intermediates in low–temperature expected to decrease the induction period and thus increase the flame velocity.

Effects of physical Variables on Flame Speed  Effect o Pressure * The pressure effect is straightforward ; the flame speed varies as  Effect of initial temperature * The effect of the initial temperature on the flame propagation rate appears upon the effect on the final or flame temperature.

* Generally, small changes of initial temperature have little effect on the flame temperature * The flame propagation expression contains the flame temperature in an exponential term; thus small changes in flame temperature can give noticeable changes in flame propagation rates.

 Effect of Thermal Diffusivity * The flame speed in helium (He) mixture is higher than that in Argon (Ar) mixture that is due to the thermal Diffusivity of helium He which is much larger than Ar because the molecular weight of He is much smaller.

Diffusion Flames  Diffusion flame defined as: *Flame in which the fuel and oxidizer are initially separated (non-premixed). *Systems in which mixing is slow compared with reaction rate so that mixing controls the burning rate, these systems are called diffusion flames.  For example a pan of oil burning in air and a lighted candle produced diffusion flames

Types of Diffusion Flames  Gaseous fuel jets  Burning of condensed phase (liquid or solid)  Catalytic combustion

Gaseous Fuel Jets In combustion field gaseous diffusion flames have received less attention than premixed flame, on the other hand diffusion flames have greater practical application. The difficulty with gaseous diffusion flames is that there’s no fundamental characteristic like flame velocity which can be measured.

Appearance of gaseous fuel jet flames

 Appearance the shape of a laminar jet of fuel depends on the mixture strength (the quantity of air supplied ). If an excess of air is present the flame is a closed, elongated figure. Such flames occur when two coaxial jet are used, the inner contain fuel and the outer contain an excess of air. As shown in the figure.

 Structure The diffusion flame has a wide region over which the composition of the gases changes. Where the actual reaction take place in a narrow zone. It’s most important to release that the diffusion establishes a bulk velocity in the direction x (or r).

Burning of condensed phases When liquids or solids projected to atmosphere combustible mixture formed and when this mixture is ignited,a flame surrounded the liquid or solid phase. The diffusion flame happened when the mixture projected to very lowest pressures around Torr.

 Condensed phase occurrence If considered a liquid fuel and gaseous oxidizer as oxygen, then fuel is evaporated from the liquid interface and diffuses to the flame front as the oxygen moves from the surroundings to the burning front.

Conclusion  Premixed flame: Mixing before combustion Mixing before combustion Reacts rapidly Reacts rapidly Propagates as thin zone Propagates as thin zone  Diffusion flame Mixing during combustion Mixing during combustion Reaction occurs at Fuel / Air interface Reaction occurs at Fuel / Air interface Controlled by the mixing of the reactants Controlled by the mixing of the reactants

 References: 1- IRVIN GLASSMAN, “Combustion”, Roger A. Strehlow, “Combustion Fundamentals” Internet sites.