Flame and droplet interaction effects during droplet-stream combustion at zero reynolds number

Transient gas phase interaction effects during droplet-stream combustion

“…Deviations of less than 1% between numerical and analytical results for the droplet mass vaporization rate and flame stand-off distance were obtained. Besides, these analytical solutions were used to calibrate the clustering parameter (c*) introduced by the coordinate transformations (Leiroz and Rangel, 1997). Typical value used was c* = 1.01.…”

“…The transient term is discretized using a forward first-order scheme. The resulting forward-time centeredspace (FTCS) scheme (Roache, 1972) leads to a system of algebraic equations with the same matrix structure as in the quasi-steady case (Leiroz and Rangel, 1995;Leiroz and Rangel, 1997). Therefore, the iterative procedure used for quasi-steady simulations (Leiroz and Rangel, 1997) remains appropriate for each transient calculation time step.…”

“…Therefore, despite generating profiles which depend on the axial position, steady-state solutions for infinite droplet streams are not able, in general, to satisfy the ambient conditions imposed by the vaporization or combustion phenomena. The study also shows that truncating the originally semi-infinite solution domain allows quasi-steady solutions to be obtained (Leiroz, 1996). The effect of the domain truncation distance on the results are necessary in order to validate the approximation (Leiroz and Rangel, 1995).…”

“…Numerical and analytical studies of an infinite stream of droplets poses the question on the existence of steady-state solutions for the governing equations. A purely-diffusive cylindrically-symmetric model problem, which allows an analytical solution through the separation of variables method was used to analyze the transient aspects of the solution (Leiroz, 1996). Droplet streams are approximated as liquid cylinders with axially varying surface potentials.…”

“…The results show the existence of different flame regimes ranging from isolated to merged flame conditions and similar vaporization rate evolution for different interdroplet distances. Differences between transient results and available quasi-steady data (Leiroz, 1997) are explored. Droplet mass vaporization rate results show that gas-phase unsteadiness inhibits interference effects for small times.…”