*4.3. The E*ff*ects of Ca, La1, Njm, and* δ

The above three dimensionless groups are mainly based on the variable factor of injection velocity. Nevertheless, the variables of the angles are also important variable parameters, such as the relative angle of the upper and lower side nozzle, the horizontal angle of the upper side nozzle, the horizontal angle of the lower side nozzle, etc. and dimensionless group δ is the group of the related angle. Therefore, the dimensionless group δ is introduced here to study the expression of the dimensionless group of mixing time under the action of these four dimensionless groups. The following Table 8 shows multiple linear regression data for the experimental values of four dimensionless groups to the mixing time:

**Table 8.** Value and standard error of lg Ca, lg La1, lg N*jm* and lg δ by multiple linear regression for the upper side nozzle and lower side nozzle.


Based on the data in Table 8, the following equations of the mixing time dimensionless group of the upper side nozzle and the mixing time dimensionless group of the lower side nozzle can be obtained, respectively:

$$\tau = \frac{D\_s}{V\_{us}} \left( \text{Ca}^{-1.88} \text{La}\_1 \text{ }^{-2.71} \text{N}\_{jm} \text{ }^{5.33} \delta^{0.11} \right) \tag{19}$$

$$\tau = \frac{D\_s}{V\_{ls}} \text{(Ca}^{-1.85} \text{La}\_1 \text{ }^{-2.61} \text{N}\_{jm} \text{ }^{4.77} \text{\\$}^{-0.40}) \tag{20}$$

Finally, by comparing the experimental values of the dimensionless group of mixing time with the calculated value of the dimensionless group, it can be seen that the experimental value of the dimensionless group has a good linear relationship with the calculated value of the dimensionless group (cf. Figure 9a,b), and it can also be seen from Figure 10a–f that there is a high consistency between the figure τ1, τ2, τ<sup>3</sup> (cf. Figure 10) and τ (cf. Figure 9).

**Figure 9.** Comparison of experimental lgτ*Vs*/*Ds* with calculated ones for upper side nozzle (**a**) and lower side nozzle (**b**), respectively, using proposed Equations (19) and (20).

**Figure 10.** Comparison of experimental lgτ*Vs*/*Ds* with calculated ones for upper side nozzle (**a**–**c**) and lower side nozzle (**d**–**f**), respectively, using τ1, τ2, τ3.
