An experimental and theoretical investigation of spray characteristics of impinging jets in impact wave regime

Abstract

The current study focuses on experimentally and theoretically improving the characterization of the drop size and drop velocity for like-on-like doublet impinging jets. The experimental measurements were made using phase Doppler anemometry (PDA) at jet Weber numbers We _j corresponding to the impact wave regime of impinging jet atomization. A more suitable dynamic range was used for PDA measurements compared to the literature, resulting in more accurate experimental measurements for drop diameters and velocities. There is some disagreement in the literature regarding the ability of linear stability analysis to accurately predict drop diameters in the impact wave regime. This work seeks to provide some clarity. It was discovered that the assumed uniform jet velocity profile was a contributing factor for deviation between diameter predictions based on models in the literature and experimental measurements. Analytical expressions that depend on parameters based on the assumed jet velocity profile are presented in this work. Predictions based on the parabolic and 1/7th power law turbulent profiles were considered and show better agreement with the experimental measurements compared to predictions based on the previous models. Experimental mean drop velocity measurements were compared with predictions from a force balance analysis, and it was observed that the assumed jet velocity profile also influences the predicted velocities, with the turbulent profile agreeing best with the experimental mean velocity. It is concluded that the assumed jet velocity profile has a predominant effect on drop diameter and velocity predictions.

Appendix

For the assumption of a parallel-sided sheet, instead of an attenuating sheet, the sheet thickness is constant. Therefore, as outlined in Senecal et al. (1999), the following expression can be used as a condition for breakup:

$$ \frac{{x_{\text{b}} \beta_{{{\text{r,}}\hbox{max} }} }}{{U_{\text{s}} }} = 12. $$

(36)

In keeping with the long-wave approximation (kh/2 ≪ 1), an analytical expression can also be derived for drop diameter. This expression depends on the jet Weber number We _j , ratio of sheet velocity to mean jet velocity α, dimensionless sheet thickness parameter K*, and ratio of ambient gas density to liquid density s:

$$ \frac{{d_{D} }}{{d_{0} }} = \frac{{1.30\left( {K^*} \right)^{1/3} }}{{\alpha^{2/3} s^{1/6} We_{j}^{1/3} }}. $$

(37)

Figure 11 presents a comparison of the experimental MMD to the predicted diameters given by the two-step breakup mechanism with the parallel-sided sheet for parabolic, turbulent, and uniform jet velocity profiles. The parallel-sided sheet assumption is useful for predictions for viscous Newtonian and non-Newtonian liquids, where the inviscid assumption cannot be justified.

Fig. 11

Dimensionless mass median diameter and predicted drop diameters versus jet Weber number for two-step breakup mechanism with parallel-sided sheet