Role of Weber number in primary breakup of turbulent liquid jets in crossflow

Atomization of liquid fuel controls combustion efficiency and pollutant emissions of internal combustion engines and gas turbines (Lefebvre 1998). The liquid jet in crossflow (LJCF) finds application in lean premixed prevaporized (LPP) ducts, afterburners for gas turbines, and combustors for ramjets and scramjets. This flow configuration, which consists of a turbulent liquid jet injected transversely into a gaseous laminar or turbulent crossflow, has been the focus of several experimental studies with the primary objective of proposing scaling laws and regime diagrams for liquid breakup (Sallam et al. 2004; Lee et al. 2007; Bellofiore, A. 2006). A typical turbulent LJCF exhibits a Kelvin-Helmoholtztype instability wave on the windward side of the liquid column (see schematic in Fig. 1). These waves travel along the liquid column and ultimately lead to its breakup around the time the liquid jet reaches the maximum penetration in the transverse direction. For high crossflow Weber number and momentum flux ratios, a turbulent liquid jet with a circular cross-section gradually changes into an almost crescent shape. Ligaments, drops, and other liquid structures, which are termed dispersed phase elements (DPEs) in the rest of this brief, are shed along the sides of the liquid column especially along the crescent edges. The shedding of DPEs is more prominent at the location of the traveling waves and might be a primary source of DPE production in the LJCF. Primary breakup in the context of a LJCF refers to this first stage of liquid jet breakup, which involves the shedding of DPEs from the liquid column owing to various processes inside the liquid jet and the ambient gas. In the primary breakup stage, DPEs that are shed from the liquid column need not be spherical in shape (see Fig. 1). Depending on the size and velocity of the DPEs (as characterized, say, by the Weber number and Reynolds number corresponding to these structures) that are shed from the liquid column as a result of primary breakup, these DPEs undergo further breakup. This second stage of breakup is termed secondary breakup. Experiments report the drop size distribution that results after primary and secondary breakup, in addition to coalescence of drops and ligaments further downstream, and possibly other sources of drop formation (for instance, satellite drop formation as a result of rebounding drops). Thus a primary breakup model for the LJCF must be able to capture the size distribution (or more precisely, the volume distribution) and possibly other geometrical features of the DPEs immediately after being shed from the liquid column in order to be predictive. This information would be supplied to a secondary breakup model, which then predicts a drop size distribution that can be employed in numerical calculations of multiphase reactive flows with sprays. Several experiments have shed light on various regimes of breakup and scaling laws for various statistics such as liquid jet penetration and trajectory, Sauter mean diameter of drops and wavelength of liquid surface instabilities have been proposed. Yet,