Thin-flame theory for the combustion of a moving liquid drop: effects due to variable density

Abstract

Follow this and additional works at: http://repository.upenn.edu/meam_papers Part of the Mechanical Engineering CommonsSuggested Citation: Gogos, George S., et. al. (1986) The combustion of a moving liquid fuel drop has been investigated. The drop experiences a strong evaporation-induced radial velocity while undergoing slow translation. In view of the high evaporation velocity, the flow field is not in the Stokes regime. The combustion process is modelled by an indefinitely fast chemical reaction rate.While the flow and the transport in the continuous phase and the drop internal circulation are treated as quasisteady, the drop heat-up is regarded as a transient process. The transport equations of the continuous phase require analysis by a singular perturbation technique. The transient heat-up of the drop interior is solved by a series-truncation numerical method. The solution for the total problem is obtained by coupling the results for the continuous and dispersed phases.The enhancement in the mass burning rate and the deformation of the flame shape due to drop translation have been predicted. The initial temperature of the drop and the subsequent heating influence the temporal variations of the flamefront standoff ratio and the flame distance. The friction drag, the pressure drag and the drag due to interfacial momentum flux are individually predicted, and the total drag behaviour is discussed. The circulation inside the drop decreases with evaporation rate. A sufficiently large non-uniform evaporation velocity causes the circulation to reverse.

Simplified model for droplet combustion in a slow convective flow

“…Equation (29) shows how the mixture-fraction field emanating from the spherical burning droplet responds to this uniform flow in the outer region. This nontrivial nonspherical order-ε solution for Z in the outer zone has been seen previously [6,7,11] and is significant in inducing perturbations in Z in both the inner and the outer zones at higher order.…”

“…The condition preceding that, which applies to a rigid porous sphere or to a high-viscosity liquid droplet, excludes tangential motion at the droplet surface; it is selected largely for the simplicity of avoiding the necessity of introducing additional parameters, such as the liquid viscosity, under the realization that much of the earlier work [5][6][7][8] has addressed various influences involving surface motion and that the other parameter-free approximation, (∂u/∂r) = 0, the opposite limit, is less realistic. In the first condition given in Eq.…”

“…Fendell's model contained many simplifying approximations, but more recent and more extensive investigations by Ayyaswamy and co-workers [5][6][7][8] removed many of these approximations. Similar analyses of the combustion of spherical carbon particles at low convection Reynolds numbers have been performed by Blake and Libby [9] and Blake [10].…”

Microgravity n-Heptane Droplet Combustion in Oxygen-Helium Mixtures at Atmospheric Pressure

“…18 ;25 It appears that closer attention may have to be paid to the relative velocity of droplet and gas to explain the results completely. In this work, use may be made of previous results, such as theoretical studies of convective effects on droplet combustion at low Reynolds numbers, 54 as well as correlationsfor higher Reynolds numbers. 55 Although the convective effects to be explained here are not large, typically less than 20%, more study of their sources is desirable.…”

Fluid Dynamical Analysis of a Particle with Large Vapor Transport in Poiseuille Flow

“…The model was further generalized to a larger set of transport problems by Sadhal, 2 which led to the development of a new class of polynomials particularly suited for systems involving large vapor transport on spherical drops and solid particles. The original model has been applied to the problem of condensation with heat/mass transfer analysis 3 as well as combustion 4 . In other subsequent developments, Jog, Ayyaswamy, and Cohen, 5 as well as del Alamo and Williams, 6 carried out the analysis of the droplet combustion problem to higher order in terms of the perturbation parameter ɛ that represents the translational Reynolds number.…”