THEORY OF FLAME HISTORIES IN DROPLET COMBUSTION AT SMALL STOICHIOMETRIC FUEL-AIR RATIOS

摘要

Motivated by observations on the spherically symmetrical burning of single, free heptane droplets in quiescent helium-oxygen atmospheres, made in Spacelab aboard the Space Shuttle, the theory of droplet burning is extended for conditions under which the Burke-Schumann flame sheet lies in the outer transient zone. Account is taken of Lewis numbers different from unity and of radiant energy loss hat sometimes leads to extinction. The asymptotic analysis employs the squares root of the ratio of the gas to liquid density as small parameter. In suitably scaled outer variables, the droplet then appears as a time-varying point source, and the flame radius first grows then decreases in size. Numerical integrations of the outer parabolic partial differential equations provide flame histories and histories of the outer temperature and concentration fields. An analytical criterion for flame extinction enables the extinction point along the flame history to be determined, when extinction is caused by radiative energy loss. The theoretical results can be useful for comparison with experiment and for predicting whether radiative extinction will occur in droplet combustion.