(694a) "Bi-Variate Population-Balance Analysis of Ethanol-Fueled Continuous Flow Spray Combustors"

We formulate/present here results of our recent bi-variate Population Balance (PB-)-based theoretical analysis of the performance of well-(macro-)mixed adiabatic combustors fed by EtOH-containing sprays of prescribed DSD and composition^1-3. Our ?pre-bio-fuel? historically relevant/instructive example is the well-documented liquid fuel-cooled V-2 rocket-------which used 75 wt pct EtOH + H2O solution, along with the cryogenic oxidizer O2(L) at a chamber pressure of 15 atm. Of special interest are our predicted combustion intensities (GW/m^3), and efficiencies (EtOH fraction vaporized) at each ?vaporization Damkohler number? [ratio of combustor mean residence time to feed-SMD QS-vaporization lifetime]^4. Our droplet evaporation rate-controlled formulation exploits a Quasi-Steady gas-diffusion-controlled and internally well-mixed individual droplet evaporation rate law, and we exploit the formally exact method of characteristics to solve (numerically) the associated first-order PB-PDE governing the joint pdf(m1,m2) exiting such a chamber, where m1 = EtOH mass/droplet, and m2 = H2O mass/droplet. This function also enables predictions of corresponding unconditional DSDs, and the possibly (remotely-) measurable jpdf(diam,droplet temperature). Apart from their intrinsic multi-phase chemical reaction-engineering interest as an instructive, tractable limiting case, our numerically exact formulation/results can also serve as valuable ?meter-sticks? for computationally convenient approximate methods (BV-QMOM- and spectral/weighted residuals) to predict such ?correlated? bi-variate pdfs in more realistic spray combustor environments. We also demonstrate the inability of a seemingly plausible ?pseudo-unary? approximation to capture key features of the performance of combustors fueled by alcohols capable of absorbing their own combustion product : H2O. ______ *Supported at Yale University by Yale NSF Grant : CTS 0522944 1 Rosner, DE , Ind.Eng.Chem Res. Vol 48, 6453-6464(2009) 2 Rosner, DE and Arias Zugasti, M, AIChE J (submitted May, 2010) 3 Rosner, DE and Arias Zugasti, M, AIAA-J Prop.Power, vol 25(3)826-828(2009) 4 Rosner, DE, Arias-Zugasti,M and Labowsky, M., Chem. Eng. Sci. vol 63, 3909-3920(2008) ________________________________________