An Investigation of Simple Evaporation Models Used in Spray Simulations

Abstract

In the present work, an unified derivation of simple evaporation models used in spray simulation is described and a new evaporation model is formulated. In the model, the Nusselt number, Sherwood number, and evaporation mass flux are derived using the traditional film theory. However, instead of determining the film thicknesses using the Nusselt and Sherwood numbers derived in the absence of high mass transfer rate, the film thicknesses are calculated from those derived from the fully numerical solutions which represent the realistic heat and mass transfer processes around a droplet. The model predictions are compared with the fully numerical solutions.

Models for droplet transient heating: Effects on droplet evaporation, ignition, and break-up

“…As in the case of heat transfer, approximation (8) gives the results close to those predicted by other approximations [5,9]. The effect of thermal film thickness is considered to be small [30]. Droplet swelling due to thermal expansion was taken into account.…”

“…(3) are not expected to influence the conclusions of this paper. Moreover they can, on some occasions, even marginally decrease the accuracy of calculations of the mass flow rate of evaporated fuel [30]. Heat removed from the gas is described by Eq.…”

Lagrangian modelling of turbulent spray combustion under liquid rocket engine conditions

“…The closure of the third term often relies on the classical droplet vaporization model associated with the conduction limit, which leads to the well-known d 2 -law, i.e., r 2 k (t)=r 2 0,k (t) − K 0,k t where K 0,k is a positive constant. However, in the present work, the vaporization rate is evaluated using the model of Yao et al [12] associated with the rapid mixing limit [13,14]. Thus, the effects associated with variable properties and transient liquid heating, as well as the influence of the Stefan flow on the thickness of both thermal and mass boundary layer are incorporated.…”

“…In the approach described by Yao et al [12] and based on the film theory, the mass transfer between gas and droplet is fully controlled by the mass diffusion in the droplet boundary layer. As a consequence, the composition outside this latter is assumed to be homogeneous and equal to the mean composition in the considered volume, which leads to:…”

“…The modelling issue is indeed moved to the determination of the vaporized mass flow rateṁ k , dashed boxed in Fig. 1, which is represented using the vaporization model of Yao et al [12], in light grey in Fig. 1:…”