Correlations for penetration height of single and double liquid jets in cross flow under high-temperature conditions

In previous researches on a jet in cross flow (JICF), which is applied for the liquid jet injection system of airbreathing propulsion systems or rocket engine systems, more than 20 different correlations of jet penetration have been proposed. In these proposed correlations, the relationships between jet penetration and the various flow parameters (momentum flux ratio, Reynolds number, Weber number, viscosity ratio, etc.) were defined. But most of these studies were carried out using the single orifice injector (SOI). In this study, in order to define the interference effects of liquid jet penetration in cross flow, the double orifice injector (DOI) is adopted. First, the jet penetration correlation of the SOI according to the cross-flow temperature controlled by the vitiated air heater is proposed. The jet penetration height for heated cross flow is lower than that for cold cross flow because of the increase of cross-flow velocity despite the lower density. The jet penetration correlation of the DOI is derived for variations of injector orifice spacing. In the case of the DOI, since the front liquid jet acts as a shield of the rear liquid jet, the jet penetration with the DOI is higher than that with the SOI. With the double DOI, the rear jet penetration height is increased as the nozzle spacing is decreased. The penetration height correlation for the rear liquid jet with the DOI was developed. As the nozzle spacing increases, the jet penetration height decreases; therefore, an inverse relationship between nozzle spacing and jet penetration height is expected.