Lectures on Mathematical Combustion. Lecture 3. General Deflagrations.
Interim technical rept.,
CORNELL UNIV ITHACA NY DEPT OF THEORETICAL AND APPLIED MECHANICS
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In the last lecture we examined the plane, steady, adiabatic, premixed flame and deduced an explicit formula for its speed. By using judicious choice of parameters this formula can be made to agree roughly with experiment precision is not a reasonal goal, given the crude nature of our model. Noteworthy is the extreme sensitivity of the speed to variations in the flame temperature an 01 change generates an exponentially large change in flame speed. Such variations in speed caused, for example, by changes in mixture strength are not excessive numerically at least for fuels burnt in air, because activation energies and fractional changes in temperature are modest but in an asymptotic analysis they present a potential obstacle to discussion of multidimensional andor unsteady flames. Then signigicant variations, spatial andor temporal, in the flame temperature can be expected and, if the sensitivity mentioned above is any guide, there will be correspondingly large spatial andor temporal variations in the flame speed. A mathematical framework in which to accomodate these is not obvious. The first lecture dealt with special circumstances for which such variations were manageable.
- Numerical Mathematics
- Combustion and Ignition