Droplet size distribution in condensing flow

Abstract

In this thesis, the problem of predicting the droplet size distribution in condensing ow is in- vestigated numerically and analytically. The work focuses on two types of problems: one where condensation occurs during the transonic expansion of a vapor-mixture, and a second one where condensation takes place in a synthetic turbulent ow, reminiscent of atmospheric clouds. For single-component condensing nozzle ow, three master equations for the prediction of the droplet size distribution are evaluated: the kinetic equation (KE), and two of its approximations, i.e., the general dynamic equation (GDE) and the Fokker-Planck equation (FPE). Large dierences are observed between the equilibrium distributions of the FPE and KE, whereas no equilibrium distribution exists for the GDE. For a simulated nucleation pulse experiment, good agreement is found between the results of the KE, FPE and GDE. For a simulated condensing nozzle ow, signicant dierences between the GDE- and the KE-distributions are observed due to failure of the quasisteady-nucleation-assumption for the GDE. The method of moments for single-component condensing ow is evaluated for Hill's method of moments and the quadrature method of moments (QMOM, DQMOM). It is found that the former is robust but does not allow for control of the closure error, whereas the quadrature methods severely suer from a lack of robustness as well as an inability to predict the correct equilibrium moments. An evaluation is made of a ow model with two-component condensation. Comparison of pre- dicted and measured temperatures and pressures at condensation-onset for a nozzle ow shows a fair agreement. Furthermore, it is found that the usual assumption of quasisteady nucleation is not satised. Finally, the condensation of micro-droplets in a turbulent ow is investigated. Droplets are traced through a synthetic ow eld composed of random Fourier modes, incorporating all relevant length scales that are typical for atmospheric clouds. Simulations with a one-way coupled model reveal a signicant broadening of the droplet size distribution. For simulations with two-way coupling, it is found that the predicted droplet size distributions are still very broad, despite the stabilizing eects of vapor depletion and latent heat release on droplet growth.