Intensity and efficiency of spray fuel-fed well-mixed adiabatic combustors

Motivated by the insights it can provide, we revisit the classical problem of liquid fuel-fed idealized steady-flow combustors. New quadrature-based results are presented for the theoretical combustion intensity and corresponding efficiency for well-stirred adiabatic vessels fed with a prescribed polydispersed spray. Each droplet of the spray is assumed to evaporate according to a non-quasi-steady (non-QS) gas-phase energy/mass diffusion-controlled rate for the pseudo-single-component fuel. As a byproduct, we calculate the complete droplet size distribution (DSD) function exiting the chamber, of interest for the design of downstream components. We explicitly assume that the volumetric rate of chemical energy release in such “primary” combustion chambers is controlled by the liquid fuel physical vaporization process (with negligible lags due to propellant droplet heat-up or vapor-phase ignition). In this instructive asymptotic limit, two decisive non-dimensional parameters are shown to be: (1) a vaporization Damköhler number (defined by the ratio of the mean residence time of the chemically reacting vapor mixture in the combustion space, to the reference value of the vaporization lifetime of a droplet with the injector-Sauter-mean diameter, and (2) a single dimensionless non-QS parameter. Illustrative numerical results for a kerosene-like fuel burning in air at pressures up to 24 atm are displayed for the case of a log-normal feedstream DSD with a range of spreads. Our results reveal the existence of an optimum vaporization Damköhler number which maximizes the combustion intensity—with maximum intensities, occurring well before nearly complete fuel evaporation, being quite sensitive to the non-QS parameter at high pressures. These deliberately idealized mathematical model results, spanning more than a 1000 combinations of operational parameters, set instructive bounds to the achievable performance of “real” spray combustors. Even without tractable enhancements (see Section 5.2), this approach can be used to economically map the sensitivity of spray combustor performance to a large number of important design and control parameters.