A numerical study of a droplet evaporating in a turbulent airflow

The effect of turbulence intensity on the drag coefficient of a sphere immersed in a turbulent airstream with Reynolds number, Re = U infinityd/nuinfinity, ranging between 10 and 250 and freestream* turbulence intensity, u'infinity /Uinfinity, of up to 60% is investigated numerically. Three-dimensional Reynolds-Averaged Navier-Stokes (RANS) equations along with mass conservation equation are solved in Cartesian coordinates by using a blocked-off technique in conjunction with a finite volume scheme. Closure for the turbulence stress term is accomplished by testing four different turbulence closure models. The predictions of the sphere drag coefficient in laminar flow conditions compare well with numerical and experimental published data. However, predictions of the sphere drag coefficient in turbulent airstream show that different turbulence closure models produce different trends in the range of Reynolds number up to Re =100, and this difference is demarcated by the non-agreement between the turbulent predictions and the well known sphere "standard"† drag coefficient. However, the results obtained by using Menter's SST turbulence model show fair agreement with the sphere "standard" drag coefficient over the range of test conditions explored here. Thus, the present results confirm recently published findings, which suggest that the freestream turbulence intensity does not have a significant effect on the sphere mean drag.; The three-dimensional numerical model used for predicting sphere drag coefficient is extended to investigate the effect of turbulence on mass transfer from a single droplet exposed to a freestream of air. The governing equations for the gas-phase are mass, momentum (i.e., Reynolds-Averaged Navier-Stokes), energy and fuel mass fraction, whereas the governing equations for the liquid-phase (droplet) are mass, momentum and energy. Turbulence terms in the conservation equations of the gas-phase are modeled by using only the shear-stress transport (SST) model for the case of elevated temperature of freestream conditions and by using both the SST and LRN k-epsilon models in the case of freestream standard‡ pressure and temperature conditions. The freestream temperature, turbulence intensity and Reynolds number are varied to provide a wide range of test conditions while the ambient pressure is kept atmospheric. The set of governing equations of the gas- and liquid-phases are solved by using the same technique as in the case of the sphere drag coefficient. The numerical results obtained at ambient standard pressure and temperature conditions show that the predictions based on the SST model agree reasonably well with published data. Furthermore, the vaporization Damkohler number proposed in the literature to correlate the effect of turbulence on the droplet's vaporization rate is found to be invalid at airstream temperatures higher than room temperature. Finally, a turbulent droplet's mass transfer correlation expressed in terms of Sherwood number is proposed.; *In the present manuscript, the word "freestream" means "airstream". †Standard drag coefficient refers to the well established sphere drag coefficient by Roos and Willmarth (1971) in laminar flow condition. ‡Standard conditions mean room temperature and atmospheric pressure conditions.