AIAA 93 - 0901 On the Interaction of a Dense Spray Diffusion Flame and a Potential Vortex

I h e interaction of a dense spray diffusion flame with a non-decaying potential vortex has been investigated theoretically. A similwity solution for the local ~tmctiire of the diffusion flamelet in the vortex field has been determined. The global diffusion flame contour generated by the vortcx has been determined by patching the flamelet solutions at different distances from the vortex center together. The initially plane spray is assumed to he sufficiently dense so that burning occurs in the sheath combustion mode. The local flamelet analysis shows that with respect to an inertial cwrdinnte frame the spray flamelet moves into the gaseous oxidizer, away from the spray while the edge of the spray moves in thc opposite direction with a much smaller velocity. The flamelet motion depends on the properties of the spray and the bounding oxidizer. The local diffusion layer structure of the Ileme is found to be self similar i n terms of the parameter Tt / 2 d The global flame contour is shown to he governed by the circulation diffusivity ratio r/2nDo. The flame contoLir is found to hound a spray engulfment and reacted core region near the vortex center where combustion is no longer possible. The radius of this core, which contains reaction products and unburned spray, is found to he proportional to (r l 2 n I l ) ' ~ ~ . The augmentation of fuel consumption due to the vortex spray has been calculated and is shown to be independent of time and proportional to (r l 2 ~ D ) ~ f i . The present results, based on a potential vortex are found to be a good approximation to those for a viscous vortex with the same value of r /2nD as long as this parameter is sufficiently large. While many approximations have been made in this analysis, some of the key parameters governing spray flame vortex intcraction have heen identified. I N T R O D U C T I O N Thc interaction bctwccn a diffusion flamc and a v ~ r t e x has recently bccn studicd extensively by many invcstigatorsi-8. The flamclvortex intesaction problem is of great intcrcst due to its rclcvance to the theoretical study of turhulcnt diffusion flames. According to Marble', who first studied this problem. thc flamelvortcx interaction can bc rcsolvcd into a local flamelet analysis and based on thcsc local rcsults the global propcrty of the interaction ficld can then hc csvahlishcd with rclative simplicity. Two simplifying fcaturcs of the original Marble problem are that the density is assumcd constant, and that the fucl and oxidizcr placcd in the vortcx I ~ l ~ ~ w c v c r , if thc fuel and oxidizcr arc not in stoichiometric proportions or if the gascous fucl is replaced by a dcnse liquid fuel spray, thcre will be rclativc motion hctwcon thc diffusion Ilamc and thc vortex. In thcsc situations thc resultant flamc coninur can n o longcr he dctcrmincd using only vortex kincmatics: it bccomcs ncccssary to b k c into account thc local I1;lnrclct motion. complicating the analysis of the original Mxhlc problcm. In a previous papcr nf the prcscnt authors8, the cffcct of Ilamc motion was rcsolvcd; however, a non-decaying potcntial vortcx rather than a viscous vortcx was considered in wdcr to simplify thc analysis. The rcsults showcd that I1:imcIct motion, govcrncd by thc background cquivalcncc ratio 4 for thc diffusion flame, will occur such that flamclets mnvc toward the oxidizcr for @ > 1, and toward the fucl, for q5 < I . A patching method was then dcvelopcd for computing contours of thcse non-stationary flames, and the flamc c n n t ~ ~ u r s thus obtained wcrc shown to he similar to the inomcrical results rcportcd by Lavcrdant and Candcl4, thus justifying thc applicability of the patching method. It should bc noted that the background cquivalcncc ratio @ as used here ~ c f c r s to the initial concentration of the fuel and oxidizer on the two sides of the diffusion flamc shcct. The prcscnt papcr is a continuation of this study8 and considcrs tlic intcraction of a planar spray diffusion flame with a potcntial non-decaying vortcx. Thc focus is placed on the flame contour, thc sizc of thc reacted region, and thc :iugmcntation in global fucl consumption rate. The spray coiisists of saturated fucl droplets with a large hcat of v;ipol-imtion and inert gas and is assumcd sufficiently dense so tha t combustion of the spray is govcrned by thc sheath comhustion mode dcscribcd by Sichcl and Palaniswamy9. l h c n the resultant llamc will he external to the spray and vaporization of the spray is confined to a thin sheath or inwardly propagating vaporizing wave at the edge of the spray while the spray intcrior is unaffcctcd and rcmains cool and satul-;ltcd. The spray flamelct analysis is based on the assumptions of conslant density and transport coefficients, thc Burkc-Schumann flame sheet approximation, and the locally one-dimcnsional approximation used by Marble'. Thc vortexdistortcd spray flamc contour is constructed by thc patching method dcvelopcd in Ref. 8. for treating the gaseous nonstoichiometric diffusion flame. For intcrpretation, thc casc of an octane spraylair diffusion flamc is studicd for several valiics of the vortcx circulation diffusiviiy ratio, r iD, and of tl1c spray droplet mass fraction. Yd. bJ ficld are in stoichiometric proportions, fbr then the resultant diffusion flame docs not move rclativc to the fluid so that its contour can be dctcrmincd using vortex kincmatics nnly. Copyright