Gas-Droplet Flows

Problem Definition:

The assumed evaporation model is classical evaporation model by Spalding [32]. It is the simplest of all the evaporation model available having the assumption that thermal diffusivity of the droplet is infinite. This model is also known as rapid mixing model or infinite conductivity model. This model assumes that temperature within the droplet is spatially uniform although time varying. It is assumed that a two way coupling for momentum and one way coupling for temperature i.e., we are not solving for gas temperature, gas temperature is not effected by droplet evaporation. All results of evaporation model validation are of single isolated stationary/moving droplet evaporating in a quiescent environment. For stationary droplets the evaporation is due to temperature difference only but evaporation is also dependent on the properties of the droplet and gas phase, initial droplet diameter and if convection is there then also dependent on the velocities. During unsteady evaporation droplet attains its saturation temperature and later on steady state evaporation which comprises of constant temperature droplet diameter decrease. Here the evaporation model is validated for n-heptane droplets. The validation of the evaporation model is done on the following geometry. A uniform hexahedral grid of 1600 cells has been used to mesh the flow domain. Other problem parameters are





Figure 2.1: The schematic diagram of the physical domain.


The test case considered for this case is n-heptane droplet evaporating in a constant velocity air stream. 1.052 mm diameter droplets having temperature of 300 K is evaporating in a air stream of temperature 356 K and having a constant velocity of 3.2 m/s. For validation we are taking a test case of Kolaitis [33] which is hexane droplets are evaporating in a constant velocity environment. 1.76 mm diameter droplets having temperature 281 K is introduced in air stream having constant velocity of 1.584 m/s and temperature of 437 K. It is seen that droplet diameter decreases with time due to evaporation and it is also confirmed that evaporation model is independent of fluid. If we compare the above two test cases of Kolaitis [33] it is seen that to diminish 1.052 mm diameter droplet it is taking 6 sec almost and to diminish 1.76 mm diameter it is taking around 8 Sec and it is quite reasonable because to diminish a larger droplet more time required as compared to a smaller droplet diminish.


Figure 2.2: Change in diameter with time for initial droplet diameter dd=1.052 mm




Figure 2.3: Change in diameter with time for initial droplet diameter d0=1.76 mm