## 4 Results
### Optimal Temperature Sensor Location Investigation  
Figures 21 and 23 suggest that the local velocity depends on how far the sensor tip is from the centerline. The CCF flow estimation measured the local velocity at the sensor locations instead of the bulk flow rate. Since the sensor locations were mainly close to the wall, this resulted in an underestimation of the bulk flow. The discrepancy between the CCF flow estimation and the bulk flow rate increased for larger bulk flows. This section aims to use these CFD simulations to answer questions about the impact of sensor location on flow-rate estimation and to identify the optimal sensor locations for different bulk flow rates. This is accomplished through a brute-force search of potential sensor locations that cover flow regions following the injection pipe. Figure 26 shows all the candidate sensor locations along the flow direction in the CFD simulations. For every cross-section along the flow direction, there are seven candidate locations. These locations are 0.01 m away from each other along the radial direction. These seven candidates form a group at each cross-section, and there are 39 groups uniformly distributed along the horizontal flow direction. Thus, there are a total of 273 locations (39 \(\times\) 7) where the temperature was collected under different flow rates. Two locations were selected for each sensor pair, where the second sensor was restricted to being positioned further from the injection pipe than the first sensor in the flow direction. As a result, there were 36,309 possible sensor pair locations. After collecting the temperature at each of the candidate sensor locations under a prescribed bulk flow and injection pressure, the CCF was applied to each possible pair to investigate the relationship between the pair locations and the performance of CCF flow estimation. For each main flow rate and injection pressure, the top 10 sensor location pairs, in terms of bulk flow estimation accuracy, were selected and plotted on a temperature distribution plot for visualization. We explored optimal sensor pair locations for low, medium, and high flow rates, as well as low and high injection pressures. Figure 27 shows the top ten sensor pairs for CCF flow estimation plotted on the temperature contour of the main cross-section after 0.5 s of water injection at 80 psi. The background contour shows the temperature distribution after the colder water had been injected. Since the injected water was colder than the main flow, the major yellow region shown in the plot represents the cool region. With few exceptions, the distance between the two sensors among these top ten pairs did not vary significantly for a given flow rate, although the distance between sensors tended to increase as the bulk flow rate increased (Table 4). Figure 27 presents the results under the highest injection pressure (with the largest injection flow rate of 0.920 m/s). The highest injection flow rate introduced strong perturbations and diffused over a broader region, especially when the mean flow rate was low (Figure 27a). This is one of the reasons why these top ten pairs were not clearly clustered within the cooler region along the pipe, indicated in yellow in the figure, which had a temperature of approximately 303 K. Additionally, the RANS equ  
Figure 26: Candidate sensor locations. the local eddy motions and only modeled this behavior. The temperature fluctuations might have impacted a larger region due to diffusion and convection. Therefore, some sensor pairs outside the investigated temperature region might produce better CCF flow estimation performance. To further understand the influence of fluid injection on CCF flow estimation performance, the same analysis was performed for injections at a low pressure of 30 psi. Figure 28 shows the results under the same bulk flow-rate conditions with the reduced injection pressure. Comparing Figures 27 and 28, it was observed that the area of the temperature perturbation region depends on the injection pressure.