| dc.description.abstract | The work is a theoretical study on the ignition of a pool of liquid fuel at subflash temperatures under the action of localized ignition sources. While a few experimental results are available in the literature, no theoretical study exists to explain the observed effects and elucidate the factors that influence ignition.
Of particular importance is the fact that ignition delay times in the case of liquid fuel pools are substantially larger (sometimes as much as 3 to 4 orders of magnitude) than the corresponding values for solid fuels under similar conditions. Experimental evidence indicates strong sub-surface currents preceding the ignition event, resulting in a large body of liquid being heated before the critical conditions for ignition are achieved.
Two probable mechanisms for the observed liquid motions have been advanced, viz., a surface tension drive due to the variation of surface tension with temperature along the liquid surface and a buoyancy drive due to density differences in the bulk of the liquid. Other important observations include the effect on ignition delay of:
i) geometric factors such as the depth and extent of the pool,
ii) nature of the substrate on which the fuel rests,
iii) additives which modify the physical properties of the liquid, and
iv) the magnitude and distribution of heat flux.
The present work is undertaken to clarify the role of the various factors that influence ignition, thereby substantiating the experimental observations and predicting possible new effects. The work particularly aims to clarify the relative roles of surface tension and buoyancy.
Two numerical schemes were tried:
i) an implicit Hopscotch scheme, and
ii) an Alternating Direction Implicit (ADI) scheme.
For both schemes, the spatial discretization is kept similar and has the following features:
a) conservative differencing over variable meshes in both spatial directions, and
b) an option for upwind, central, or hybrid upwind/central schemes for the convective terms.
Studies performed on a model set of parameters reveal a number of interesting features. The Hopscotch method is prone to non-linear instability when the wall vorticity is lagged by one time step and performs very poorly, even though on an operation count basis it is the most attractive. The instability is readily cured by iterative improvement of the solution, but in the process, the method loses its competitiveness. The ADI method performs quite well and results in smooth and accurate solutions. Contrary to what is generally believed, this method gives time-accurate solutions up to a Courant number of 5.0, even though economical computations are obtained around a Courant number of 3.0.
In addition to evaluating the two differencing schemes, the influence of factors like artificial viscosity, the type of treatment of energy boundary conditions, and the stretching of the numerical grid on the accuracy of the numerical solutions is brought out.
Fairly extensive numerical results are presented for the case of a plane two-dimensional pool with a strip source of heating for a range of physical parameters representative of alcohols. The geometry and heating conditions closely correspond to the situation obtained in the experiments of Burgoyne, wherein the ignition of a two-dimensional liquid pool was effected by means of a flame stabilized on a wick. The numerical results on ignition delays and the details of the fluid flow compare quite favorably with the experimental results.
Although a fairly broad-based coverage in the non-dimensional parametric space is not possible due to the large computational times (some parameter sets take more than 4 hours of CPU time on a DEC-1090 system), sufficient results are obtained to clarify the role of various parameters like buoyancy, liquid depth, initial temperature, lateral extent of the channel, and heat exchange conditions at the bottom of the pool. | |
