**2. Experimental Methods**

#### *2.1. The measurement of the Fluid Flow in the Ladle Water Model*

A hydraulic model of the ladle was established by the principle of hydraulic similarity. The ratio was 1:2.4 between the water model and the prototype. The dimensions of the argon-stirred ladle in the prototype and water model are shown in Table 1. The angle between the two plugs was 135◦ in the prototype. The fluid velocity in the hydraulic model was measured by particle image velocimetry (PIV) technology. The prototype ladle can contain 25 t of molten steel.

**Table 1.** The dimensions of argon-stirred ladle in prototype and water model.


Where *R* represents the radius, subscript m represents the hydraulic model, and p represents the prototype.

Figure 1 shows the schematic of the velocity measurements in the hydraulic ladle. The plug was placed at 0.6*R*m, and the laser sheet emission was from the right side and passed through the plug. The camera was vertical to the plane where the laser sheet was at. The flow rate was 6 L·min−1, controlled by the valve, and the argon flowed through the tube and out from the plug. The PIV equipment contained: laser (Litron lasers LPY704-100 PIV, Rugby, UK), guiding arm (LaVision Gmbh, Göttingen, Germany), sheet optics, Nikon AF-S 50 mm f/1.4 G lens (Nikon Corporation, Tokyo, Japan), calibration plate (LaVision Gmbh, Germany), camera (LaVision Gmbh, Germany), programmable timing unit X (PTU X), workstation (Intel(R), Xeon(R), CPU E5-2650 v3 @ 2.30 GHz, two processors), laser power equipment, and laser cooling equipment. The measurement and postprocessing were accomplished by the DaVis 8.4.0 (LaVision GmbH, Germany). The seeding particle was vestosint and the seeding particle diameter was 55 μm; it had a good flow following. The laser shutter opened twice in a very short time, and the camera exposed twice following the laser shutter opening. The time interval of the laser shutter opening twice was 0.01428 s, the camera acquisition rate was 70 Hz, and the acquisition time lasted two seconds. During the measurement, the sampling count was 100 and the time-averaged results were calculated by DaVis 8.4.0. The postprocessing was a cross-correlation model, the interrogation window size was 96 × 96 window size, and the interrogation window was decreased to 64 × 64 window size.

**Figure 1.** The schematic of the velocity measurement setup.
