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Bivariate population balance model of ethanol‐fueled spray combustors
Author(s) -
Rosner Daniel E.,
AriasZugasti Manuel
Publication year - 2011
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.12552
Subject(s) - bivariate analysis , population , chemistry , combustor , mathematics , combustion , thermodynamics , distribution (mathematics) , mass fraction , mechanics , statistics , physics , mathematical analysis , demography , organic chemistry , sociology
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 + H 2 O solution, and oxidizer O 2 (L). Of special interest are the predicted combustion “intensity” (GW/m 3 ) 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(m 1 , m 2 ) of the fuel spray exiting such a chamber, where m 1 = EtOH mass/droplet, and m 2 = H 2 O 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