Linear burning rate law

This universally accepted concept is known as Piobert s law and is supported by the experience of many investigators drawing their conclusions from many different approaches. The linear burning rate vs pressure behavior of a gun propellant (the rate at which burning proceeds normal to the surface) is a characteristic of the composition and is a required input for most interior ballistics calculations. 

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. 

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... 

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