A modified lumped heat capacity model for droplet flash cooling

Abstract

Using lumped heat capacity model (LHCM) to describe a droplet evaporation process is one of the most convenient and simplest approaches. However, its assumption of infinitely fast heat conduction within the droplet is constantly beyond the reality in droplet flash cooling, in which the process is typically dominated by the internal heat conduction. Alternatively, an effective heat conduction model (EHCM) considers the limited heat conduction with temperature non-uniformity within the droplet and hence more physics-sound than LHCM. Yet, its governing equations are also much more complicated than the ones of LHCM. Consequently, applying EHCM could be very difficult in the parametric modeling of many spray flash applications, especially in the point-based discrete phase modeling and associated numerical simulation. Therefore, this paper proposes a modified LHCM for spray flash cooling, which preserves both the accuracy of EHCM and the mathematical simplicity of LHCM. Specifically, a non-dimensional EHCM for droplet flash is developed to provide guidance for determining a case-independent modified evaporation coefficient of LHCM, accompanied with four dimensionless parameters, namely, Fourier number (Fo), flash number (β*), Biot number (Bi), and radiation number (E*), which are reflecting the characteristic time and heat transfer intensities of latent heat, convection, and radiation, respectively. The corrective coefficient represents the ratio of predicted evaporating rates between EHCM and LHCM, which is a function of Fo and affected by other three operating parameters (β*, Bi, and E*). The prediction on droplet cooling characteristic (temperature) by modified LHCM matches those of EHCM and available experimental data. The relative errors between the modified LHCM and EHCM are evaluated in cases of a wide operating range (droplet diameters from 0.01 to 1 mm, superheat levels from 1.06 to 1.67), and their values are within 3.4%. Parametric studies show the value of the modified coefficient follows a negative correlation with β* and a positive correlation with Fo. Meanwhile, the heat convection and thermal radiation have negligible impacts (less than 0.1%) on the flash cooling process in our cases, in which values of Bi and E* are relatively small. The most dominant parameter β* can be used to judge the importance in adopting the corrective coefficient on LHCM.