## 3 PIV Experimental Apparatus  
The two-dimensional (2D) PIV system (Microvec Pte Ltd, Beijing, China) adopted in the present work consisted of a dual Vlite series 532 nm dual pulse laser (Beamtech Optronics Co., Ltd., 500 mJ, 10 Hz, Beijing, China), a high-resolution CCD camera with 6600 \(\times\) 4400 pixels, a synchronizer, and the commercial software MicroVec-V3.6. The experimental setup is shown in Figure 3. An electromagnetic phase-locking device was used to obtain the phase-resolved measurements. The signals triggered by the shaft once per revolution were used to synchronize the blade angular position, image acquisition, and laser firing. In all of the experiments, the vertical laser plane was placed at a \(5^{\circ}\) angle from the nearest baffle, passing through the vessel axis to give a clear and undistorted image of fluid flow [29]. Only half of the plane was measured due to symmetry.  
The tracer particles used in this experiment were hollow glass particles with a diameter of 10 to 20 \(\upmu\)m and a density of 1030 kg\(\cdot\)m\({}^{-3}\), which was quite close to the liquid density, so as to better track the liquid velocity. The selected interrogation area was 64 \(\times\) 64 pixels, and the overlap area was 50% during the correlation. Considering the accuracy of the experimental data and the efficiency of the image processing, 500 pairs of collected images were processed to obtain the time-average flow field in each condition.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Tank diameter & \(T\) & 288 mm \\ Liquid height & \(H\) & T \\ Baffle width & \(W_{b}\) & 0.1 T \\ Off-bottom clearance & C & 0.25 T \\ Impeller diameter & \(D\) & 0.5 T \\ Blade width & \(W_{i}\) & 41 mm \\ Blade length & \(b\) & 55 mm \\ \hline \hline \end{tabular}
\end{table}
Table 1: Dimensions of tank and impeller.  
Figure 2: Structure diagram of the impellers. (**a**) PBT, (**b**)PBPT, (**c**) BCBT, (**d**) BCPBT.  
A flat-bottomed cylindrical tank equipped with four baffles that were mounted perpendicular to the tank wall was studied, as shown in Figure 4. The dimensions of the tank are listed in Table 1. The cylindrical tank was placed in a square tank to reduce the optical refractive index effect at the cylindrical surface of the tank. In order to prevent the reflection of the laser from damaging the high-speed camera CCD, the impellers and shaft were painted black. The tank was stirred by the traditional impeller (PBT) and the novel impellers (PBPT, BCBT and BCPBT), as depicted in Figure 2. The properties of the liquid and the solid particles are given in Table 2.  
proposed the kinetic theory of granular flow (KTGF). [PERSON] et al. [33] and [PERSON] et al. [34] investigated solid-liquid mixing systems utilizing E-E and Eulerian-Eulerian methods combined with the kinetic theory of granular flow (EE-KTGF), and found that the EE-KTGF method is available to accurately predict the flow field and particle distribution with high concentrations and large particle sizes. Therefore, the EE-KTGF model was adopted to describe the solid-liquid two-phase flow in the stirred tank in the present work. This model assumed that the solid was a pseudo fluid. Viscosity, solid pressure and stress were solved by the KTGF model. The continuity equation and momentum equation of each phase were solved under the Euler framework, and the coupling between phases was obtained through the pressure and interphase exchange coefficients.