Bivariate population balance model of ethanol-fueled spray combustors

Authors

  • Daniel E. Rosner,

    Corresponding author
    1. High Temperature Chemical Reaction Engineering Laboratory and Yale Center for Combustion Studies, Dept. of Chemical and Environmental Engineering, Yale University, New Haven, CT 06520
    • High Temperature Chemical Reaction Engineering Laboratory and Yale Center for Combustion Studies, Dept. of Chemical and Environmental Engineering, Yale University, New Haven, CT 06520-8286
    Search for more papers by this author
  • Manuel Arias-Zugasti

    1. Departamento de Física Matemática y de Fluidos, Facultad de Ciencias UNED, Apdo: 60141, 28080 Madrid, Spain
    Search for more papers by this author

  • Preliminary versions of portions of this article were presented at AIChE 2008 Annual Meeting (Philadelphia) Paper #156d, and AIChE 2010 Annual Meeting (Salt Lake City) Paper #694a.

Abstract

We present a bivariate population balance-based formulation of the performance of well-mixed adiabatic combustors fed by ethanol (EtOH)-containing sprays of prescribed droplet size distribution (DSD) and composition. Our historically interesting example is the fuel-cooled V-2 chemical rocket—using 75 wt % EtOH + H2O solution, and oxidizer O2(L). Of special interest are the predicted combustion “intensity” (GW/m3) and efficiency (EtOH fraction vaporized) at each ratio of combustor mean residence time to feed-droplet characteristic vaporization time. Our formulation exploits a quasi-steady, gas-diffusion-controlled individual droplet evaporation rate law, and the method-of-characteristics to solve the associated first-order population balance partial differential equation governing the joint distribution function n(m1, m2) of the fuel spray exiting such a chamber, where m1 = EtOH mass/droplet, and m2 = H2O mass/droplet. Besides the combustor efficiency and intensity, this bivariate distribution function enables predictions of corresponding unconditional DSD, and the joint distribution function(diam., droplet temperature)—perhaps measurable. Our numerically exact formulation/results also provide valuable test cases for convenient approximate methods (bivariate moment and spectral/weighted residual) to predict these “correlated” bivariate distribution functions in more complex situations. © 2011 American Institute of Chemical Engineers AIChE J, 2011

Ancillary