## 5 Analysis of Experimental and Simulation Results
### Uniform Water Body Conditions
#### 5.1.3 Case 3 Working Conditions  
For Case 3, the initial velocity of the jet is 0.1 m/s, the water depth is 0.26 m, and there is a temperature difference of 20 \({}^{\circ}\)C with the ambient water body. The temperature difference between the jet and the ambient water body remains at 20 \({}^{\circ}\)C. In comparison to Case 1, the initial temperature difference of the jet has doubled, while both the depth and velocity of the jet remain unchanged. Figure 9 shows the changes in temperature field distribution of the jet discharged in a uniform water environment at 5 s, 10 s, 15 s, 20 s, 25 s, and 30 s under these experimental conditions. From the temperature field of the jet over time, it is observed that at 5 s, the jet temperature begins to rise due to upward diffusion. This is caused by a doubling of the difference in temperature between the jet and the ambient water, as well as an increase in the density difference between the jet and the ambient water at the same depth. According to Formula (2), when the temperature difference between the jet and the ambient water is 10 \({}^{\circ}\)C, there is a density difference of 1.065 kg/m\({}^{3}\), However, when this temperature difference increases to 20 \({}^{\circ}\)C, there is a density difference of 2.89 kg/m\({}^{3}\), approximately 2.7 times higher than before. Within just 5 s of discharge, it is evident that the jet's temperature has already begun to float upwards due to diffusion. In fact, during this  
Figure 8: Simulation calculated results of the thermal jet temperature field. initial stage of movement, there is a significant decrease in horizontal diffusion area for temperatures by around 15 s, with a lateral diffusion distance still within about 20 cm, while upward floating height has reached approximately 20 cm, occurring about six seconds earlier than under Case 1 conditions, and resulting in an increased rate of upward floating by about 47%. When the jet discharge time reaches about 21 s, the jet temperature is diffused to the surface of the water, and the floating rate is increased by 43%. At this time, the lateral diffusion distance of the jet temperature is small, and the jet movement is still dominated by upward floating. At 25 s, the jet temperature diffusion area begins to develop laterally, in the vertical area of 5 cm from the water surface, the jet lateral diffusion area can reach 25 cm, until 30 s, in this vertical area, the jet temperature dissipation phenomenon. When the initial temperature difference of the jet is doubled, the jet undergoes rapid uplift, leading to a 40% increase in the uplift rate. The overall motion of the jet is dominated by uplifting rather than horizontal movement. The time required for the jet temperature to spread to the water surface is significantly reduced, equivalent to 70% of that in Case 1 conditions. However, in the near-surface region, once the jet temperature spreads to the water surface, lateral spreading of the temperature field begins later and extends over a greater distance compared with Case 1, resulting in delayed dissipation of the jet temperature. Based on the experimental conditions, measurements are taken at 5 s, 10 s, 15 s, 20 s, 25 s, and 30 s for analysis of Case 3 simulation calculation results as depicted in Figure 10.  
When the jet is discharged at 5 s, there is a noticeable upward diffusion of temperature, with the jet floating upwards to a height of about 5 cm. Compared to the experiment results, there is an obvious difference in the horizontal diffusion distance of the jet's temperature at this moment. By 10 s, the floating height of the jet's temperature diffusion has nearly doubled, and there is a horizontal diffusion trend in the top temperature of the jet, although the range of diffusion is small. At 20 s after discharge, the jet's temperature diffusion reaches near to the water surface, with a horizontal diffusion distance within 10 cm.