## 4 Results and Discussion
### Simulation and Experimental Results Analysis
#### 4.3.2 Analysis of Richardson Number  
The Richardson number indicates how well the stratification effect performs with the mixing effect. It is the ratio of the levitation effect to the mixing effect.  
The experimental and simulated Ri values for the heat-storage water tank utilizing an elbow-type inlet structure aligned closely, as shown in Figure 14. The data indicated an initial growth pattern, followed by a subsequent decline. The main reason for this trend is that the temperature of the water remains constant in the beginning, and as the hot and cold water flow in and out, they cause changes in the buoyancy and mixing forces. However, the temperature distribution within the water tank became more stratified. This stratification is influenced by buoyancy force, which causes warmer water to rise and colder water to sink. Additionally, mixing forces, such as the turbulence generated by water flow, also play a role in determining the temperature distribution. Towards the end of the experiment and simulation, the Richardson number decreased. This decrease can be attributed to the fact that the water temperature in the tank stabilizes around 26 \({}^{\circ}\)C, resulting in reduced differences in temperature and, consequently, smaller changes in buoyancy and mixing forces. During the experiment, the maximum Richardson number reached 16.03, whereas in the simulation, it peaked at 16.61, at which time the stratification in the tank was the best. When the Richardson number was high, the buoyancy forces dominated, leading to better temperature stratification within the tank. In this case, the peak values of the Richardson number occurred when the tank was approximately half-filled with hot water and an equivalent amount of cold water was introduced. Under these conditions, hot water occupies the upper part of the tank, whereas cold water settles at the bottom. This temperature stratification led to increased buoyancy forces and, consequently, an increase in the Richardson number. The close agreement between the experimental and simulated data validated the accuracy of the simulation model.  
Figure 14: Comparison of experimental and simulation Richardson number using elbow type.  
A comparison of the simulation results for the elbow- and water-distributor-type inlets is shown in Figure 15. The maximum Richardson number by calculation for the water distributor-type inlet is 16.9, while for the elbow-type inlet, it is 16.3. It is evident that the Richardson numbers for both inlet types are nearly identical, indicating a similarity in their fluid dynamic behaviors. When the flow rate remained constant, the water entering through the elbow-type inlet directly impacted the top of the tank and did not disturb its layered structure. Conversely, the water distributor-type inlet regulates the flow rate into the tank by dispersing water through small holes in the wall. Upon passing through the distributor, water flows within the tank primarily because of buoyancy.  
This comparative analysis provides a comparison of the performance characteristics of different inlet types, which can inform the design and optimization of tank systems for various applications.