## 4 Results
### Experimental Validation  
The CFD simulations require validation against relevant experimental data based on the same boundary and initial conditions. The CFD simulations can show how the temperature distribution of the entire flow region changed after the injection. Figure 17 shows the temperature distribution during the injection of colder liquid under the 178.3 GPM flow rate. The figure shows that the temperature field was perturbed by the injection. The closer the temperature sensor is to the injection pipe, the stronger the signal that can be collected. The CFD temperature data at the two sensor locations from the experiment flow loop were collected and compared to the corresponding experimental data. Since the absolute values were slightly different, the relative perturbation in the temperature was the main feature to be compared. Therefore, the percentage of perturbation was calculated and used in the comparison based on the equation below:  
\[T=T_{raw}-T_{steady} \tag{3}\]  
\[\Delta T_{\%}=\frac{T-T_{min}}{T_{max}-T_{min}}\times 100\% \tag{4}\]  
where \(T_{raw}\) is the raw temperature recorded in the experimental loop (or in the CFD simulations) and \(T_{steady}\) is the pre-injection temperature when there is no fluid injection in the flow region. Equation (4) evaluates the temperature perturbation as a percentage of the maximum range. Figures 18-20 show the temperature comparison at the sensor locations under three different flow rates. The temperature data from the CFD model were collected as close to the same locations as possible as those in the experimental flow loop. to quantify the accuracy of the simulations. Table 3 gives the RMSE for TC1 and TC2 under each flow condition. The RMSE values range from 0.0853 to 0.268, further supporting the strong agreement of the CFD simulations with the experimental data. A few observations can also be made: The temperature data from the experiment are quite noisy. One reason for the smoothness of the CFD results is that the average Navier-Stokes k-\(\epsilon\) turbulent model was applied, which resulted in small- and large-scale fluctuations unrelated to the injection being averaged out. Another minor reason is that the physical sensor geometry was not modeled in the CFD model, which did not introduce any local turbulence likely caused by passing the sensor's physical body. Another issue is the timestamp of when the temperature started to change; the figures show that the experimental temperature drop occurred slightly later than the CFD results when the injection happened. The main reason is that the CFD simulations collected the temperature instantaneously (no minimum read time), while the temperature sensor installed in the flow loop had a response time issue, causing the temperature data to delay slightly and exhibiting expected sensor noise. For the lower flow rate, the percentage temperature change was not as large as in the higher-flow-rate cases. One possible reason is that the flow was relatively slow, and the cold injected water had been warmed up before being measured by the temperature sensor. This phenomenon was observed in both the experiments and CFD simulations. It was more obvious for TC2 because TC2 was farther away from the water injection source, resulting in a smaller temperature difference from the main flow. This can also be supported by the temperature distribution shown in Figure 17. One possible solution is to inject a much cooler flow to introduce a relatively more powerful perturbation. Another observation from the comparison figures is that the temperature of TC2 was relatively noisy. The main reason might be that the flow was more perturbed after passing the injection pipe and the first temperature sensor. This was expected because it was further out in the wake of the injected pipe perturbations. Figure 19: Temperature comparison under a medium flow rate (\(\sim\)133 GPM). Figure 18: Temperature comparison under a low flow rate (\(\sim\)40 GPM).