Linear burning velocity

The linear burning velocity S is defined as the normal velocity of approach of the unbumt gas towards the flame front. Alternatively, the mass burning velocity M is the mass rate of consumption of reactant mixture per unit area of flame surface. By continuity, M is constant through a one-dimensional flame, and is given by... 

In any gas burner some mechanism or device (flame holder or pilot) must be provided to stabilize the flame against the flow of the unbumed mixture. This device should fix the position of the flame at the burner port. Although gas burners vary greatly in form and complexity, the distribution mechanisms in most cases are fundamentally the same. By keeping the linear velocity of a small fraction of the mixture flow equal to or less than the burning velocity, a steady flame is formed. From this pilot flame, the main flame spreads to consume the main gas flow at a much higher velocity. The area of the steady flame is related to the volumetric flow rate of the mixture by equation 18 (81,82)... 

It is apparent from Fig. 4.14 that it is difficult to select a particular linear flow rate of unbumed gas up to the flame and regard this velocity as the burning velocity. 

For a given set of flow parameters, the strained flame speed is taken as the fluid velocity at the minimum in the profile just upstream of the flame. Law and collaborators developed an analysis that uses a series of variously strained flames to predict strain-free laminar burning velocities [238,438,448]. As the strain rate is decreased, the strained flame speed decreases and the flame itself moves farther from the symmetry plane. There is an approximately linear relationship between the strained flame speed and the strain rate. Thus, after measuring the velocity profiles (e.g., by laser-dopler velocimetry) for a number of different strain rates, the strain-free burning velocity can be determined by extrapolating the burning velocity to zero strain. 

The effects of high gas velocity upon linear burning rate can be expressed in terms of an erosion coefficient. Two different methods for its calcn are given in Ref 13... 

The effect on the linear burning rate that is related to the velocity at which hot combustion gas flows over the burning surfaces is known as the erosive-burning effect(Rei 13)... 

The results indicate that the burning times are not exactly linear, but the columns appear to be burning a little faster with increasing length. This may be due to length of column needed to reach maximum burning velocity. 

The linear burning rate of a propellant is the velocity with which a chemical reaction progresses as a result of thermal conduction and radiation (at right angles to the current surface of the propellant). It depends on the chemical composition, the pressure, temperature and physical state of the propellant (porosity particle size distribution of the components compression). The gas (fume) cloud that is formed flows in a direction opposite to the direction of burning. 

The burning rate describes the velocity with which the volume of the burning propellant changes. It is proportional to the linear burning rate and in addition it depends on the specific shape of the propellant (size of the powder elements and conformation, e.g. flakes, spheres, tubes, multi-perforated tubes etc. extending to the most complicated shapes of rocket propellant charges). 

If we consider a combustion wave as an infinite plane moving through a reaction system, then with respect to the plane itself considered as stationary the unburiied gases move toward it at a velocity while far behind it the burned gases leave with a velocity Vh- The difference in velocities is due to the difference in densities of the burned and unburned gases, p and pw. The law of conservation of mass requires that the mass flow rate across any surface be constant, so that, if v is the linear gas velocity at any point with reference to the stationary flame front, the mass velocity Th = pv constant at every point and, in particular, far from the flame front on either side... 

Special situations exist for which this procedure simplifies considerably. If the intermediary under consideration is not a chain carrier but is merely produced and consumed through unimportant side reactions, then the burning velocity and the composition profiles of all other species in the flame are virtually unaffected by the presence of this intermediary. The structure of the flame (excluding the X profile) can therefore be determined completely by setting = 0 in the flame equations. After this structure is determined, a, b and the coefficients of the linear differential operator Si X ) are known functions of t. Therefore, equation (90) reduces to a linear nonhomogeneous differential equation with known variable coefficients,... 

If an attempt is made to define burning velocity strictly for such a system, it is found that no definition free from all possible objections can be formulated. Moreover, it is impossible to construct a definition that will, of necessity, determine the same value as that found in an experiment using a plane flame. The essential difficulties are as follow. (1) Over no range of r values does the linear velocity of the gas have even an approximately constant value and (2) in this ideal system, the temperature varies continuously from the center of the sphere outward and approaches the flame surface asymptotically as r approaches infinity. So no spherical surface can be considered to have a significance greater than any other. 

The burning velocity has been found to vary linearly with ozone concentration in oxygen-ozone mixtures." It ranges from a low of 9.2cm/sec in a 17 mole % ozone-83 mole % oxygen mixture to a high of 475 cm/sec in pure ozone. 

A flame is said to be stabilized when the flame front remains stationary in space. This is achieved when the linear velocity of the unburnt gases is equal and opposite to the normal burning velocity. This criterion implies a very delicate balance between gas flow and composition however, in practice very broad limits of stability are observed for burner flames (Fig. 3.4). It is true that, at very low unburnt gas flow rates, the flame may flash back down the burner tube, while for very high flow, blow off may occur. However since the flame is stable over a wide range of intermediate flows, there cannot be any delicacy in the stabilization mechanism. 

The key to this paradox is found in Fig. 3.1 which shows that the burning velocity is a linear function of the hydrogen atom concentration. The walls of the burner, or other stabilizing body, will act as a sink for hydrogen atoms, whether their function is to conduct heat or, more probably, to diffuse ahead of the reaction zone and initiate combustion chains. There will therefore be a concentration gradient... 

A hydrogen/air premixed flame has a burning velocity of the order of 0 5 m s which the linear gas flow must exceed. A typical value would be 1-0 m s . Such a flame would show a slight contraction if burned isothermically. However the burnt gases are actually at a temperature of the order of 2000 K, so there is a sevenfold expansion. Some part of this is taken up by a transverse expansion, but a significant portion produces an acceleration of the burnt gas, with a resultant back pressure across the flame front. The burnt gases pass up the flame with a velocity of the order of 2-0 m s 1 cm height corresponds to 500 fis. Several techniques are available to study flames which have a spatial resolution of 100 fis. The flame photometer in particular can resolve measurements at intervals of 10 /is. 

These results lead to the assumption that should be proportional to the square root of the product u L. This linear correlation was suggested several years ago by Bradley on the basis of a statistical evaluation of turbulent burning velocity results from various experimental systems described in literature. 

The same experiments were performed with two and three grids of type 6. The results are analogue to those just mentioned, and it is evident that a successive increase in the number of grids leads to somewhat stronger acceleration of the flame front. However, it is important to note that the burning velocity does increase less than linear with the number of grids. 

It is interesting to see that the burning velocity in the wake of the second and even third grid corresponds to the same linear relation (S Vu L ) as described for the single grid experiments (Fig. 16). 

Inserting a second or third grid in the flame path leads to a somewhat stronger acceleration, but the burning velocity increases much less than linear with the number of grids. 

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