Due to the difficulties and less flexibility of industrial trials, physical modeling and mathematical modeling have been widely used to study the fluid flow phenomena during metallurgical processes, [1][2][3][4] including the multiphase fluid flow, [5][6][7] mass transfer, [8,9] chemical reaction, [10,11] bubbles and inclusions behavior, [12][13][14] and other complex phenomena in the ladle. The Ruhrstahl-Heraeus (RH) is a vital refining process to produce high-quality steel. Circulation rate [15][16][17] and mixing time, [18,19] as two significant parameters, are usually used to evaluate the refining efficiency of RH degasser, such as the melting and mixing of addition alloy. [20] In recent years, investigations on the circulating flow and the mixing phenomena during RH degassing process have been conducted to improve its refining efficiency and service life. [5,21,22] However, several investigations focused on the whole velocity distribution in the RH system using physical models. [21,23] A lot of measurement methods and empirical formulas were reported to predict the circulation rate, including the direct measurement using an intelligent velocity instrument, [24] the overflow method, [25] and the peak value method. [26][27][28] The injection gas flow rate and injection nozzles, [5] the immersion depth of snorkels, [9,[29][30][31] and the pressure in the vacuum chamber [26,32] have great influences on the circulation flow rate. Furthermore, some researchers devoted to the study on the nozzle blockage [27] refractory wear erosion, [33] or the bottom blowing [34,35] to optimize the RH refining process. The stimulus-response experiment was the usual method used to measure mixing time. The tracer was added from the feed inlet port on the vacuum chamber sidewall, and the mixing time was defined as the first time when the conductivity stabilized at AE5%, [21,36] AE3%, [37] or AE1%. [38] As the mixing time is related to the location of monitors and the fluid flow field distribution in the ladle, [6] many researchers have given out the mixing time of several points for different positions and various operation conditions. [23,39,40] However, it is difficult to figure out the mixing time distribution on the whole vertical center section in the ladle. Based on the previously reported work, some equations for calculating the mixing time are shown in Table 1. Many previous investigations indicated that the mixing time has exponential relation with the stirring power, and the range of the index of their relational expression is À0.5 to À0.3. [36,[41][42][43]