Uncertainty and sensitivity analysis of boundary conditions during water droplet phase change regimes

Abstract

This paper presents the heat and mass transfer model of a liquid droplet in the consistently changing condensation, transit and equilibrium evaporation regimes, and iterative scheme of numerical simulation of the instantaneous temperature of a semi-transparent droplet in the case of complex radiative-convective heating. The whole cycle of the phase transition regimes of medium and large water droplets flowing in the flue gas was modeled, taking into account the application of water spraying into the flue gas of a biofuel furnace. Simulation results expressed as thermal, energy and phase transformation parameters of water droplets are analyzed in the universal Fourier time scale. The factors defining the change of heat transfer regime of a water droplet are termed as the suppression of droplet slipping in flue gas flow at initial phase transformation stage, and the decrease of radiation absorption at the final stage. Particular attention is paid to the evaluation of the influence of parameters defining the interaction of complex transfer processes on the droplet's phase transformations performing the sensitivity analysis of the heat and mass transfer parameters for the “hypothetical” droplet case (the diameter and the slipping velocity in to gas did not change). It is substantiated, that the main parameters defining the sensitivity of water droplets equilibrium evaporation temperature are flue gas humidity, droplets dispersity, flue gas temperature and droplets slipping velocity.The performed statistical uncertainty and sensitivity analysis showed that the uncertainty of heat and mass transfer parameters describing the phase transformations of a water droplet until equilibrium evaporation regime is affected mostly by droplet dispersity, slipping velocity, flue gas temperature and pressure. The size of droplets and their slip velocity in the flue gas flow were identified as very important parameters for the interaction of complex heat and mass transfer processes of a sprayed water. The main uncertainties were defined at the transition from condensing to transit evaporation regime, and it was defined that with a confidence interval of at least 95 % and accepting a tolerance limit with a probability of at least 95 %, the transit evaporation regime starts at the range Fo ≈ (0.02–0.1). The droplet surface temperature, i.e. parameter determining the droplet phase transformations and its dynamics, could be assessed with a mean error of ±10 %, accepting 95 % probability with 95 % confidence level.