Taylor analogy breakup model

In the CAB model the breakup condition is determined by means of the drop deformation dynamics of the standard Taylor analogy breakup model [5] (cf. TAB model above). In this approach, the drop distortion is described by a forced, damped, harmonic oscillator in which the forcing term is given by the aerodynamic droplet-gas interaction, the damping is due to the liquid viscosity and the restoring force is supplied by the surface tension. More specifically, the drop distortion is described by the deformation parameter, y = Ixjr, where x denotes the largest radial distortion from the spherical equilibrium surface, and r is the drop radius. The deformation equation in terms of the normalized distortion parameter, y, as provided in Eq. 9.29 is... 

Abstract In an effort to characterize fuel sprays using Computational Fluid Dynamics (CFD) codes, a number of spray breakup models have been developed. The primary atomization of liquid jets and sheets is modeled considering growing wave instabilities on the liquid/gaseous interface or a combination of turbulence perturbations and instability theories. The most popular approaches for the secondary atomization are the Taylor Analogy Breakup (TAB) model, the Enhanced-TAB (E-TAB) model, and the WAVE model. Variations and improvements of these models have also been proposed by other researchers. In this chapter, an overview of the most representative models used nowadays is provided. 

Based on an analogy between the oscillations of a two-dimensional (2D) droplet and a mass spring system (similar to the Taylor analogy breakup (TAB) model), we assume that the deformation of our 2D liquid droplet is dependent on the viscous (Fv), surface tension (Fj), and inertial (Fa) forces. So, performing a force balance in the X2-direction for the half element (shaded) in Fig. 29.2c, we can write... 

The maj or limitation of the TAB model i s that it can only keep track of one oscillation mode, while in reality there are many oscillation modes. Thus, more accurately, the Taylor analogy should be between an oscillating droplet and a sequence of spring-mass systems, one for each mode of oscillations. The TAB model keeps track only of the fundamental mode corresponding to the lowest order spherical zonal harmonic 5541 whose axi s i s aligned with the relative velocity vector between the droplet and gas. Thi s is the longest-lived and therefore the most important mode of oscillations. Nevertheless, for large Weber numbers, other modes are certainly excited and contribute to droplet breakup. Despite this... 

---