# Effect of Different Control Strategies on the Heat Transfer Mechanism of Helical Energy Piles
## 3 Results
Figure 8: Heat exchange and temperature variation in energy piles under three different operating strategies as (**a**) cumulative heat exchange in one day (\(Q_{0}\)); (**b**) average temperature of pile foundation (\(\overline{T}_{p}\)); (**c**) average soil temperature (\(\overline{T}_{soil}\)). Figure 7: Temperature gradient distribution of energy pile walls. 25.97% greater if they continue until the 10 th day. Moreover, \(Q_{0,A}<Q_{0,B}\) when \(t\) extends for more than 5 days. Figure 8b illustrates how the energy pile foundation's average temperature (\(\overline{T}p\)) rises quickly with t during continuous operation up until the second day, at which point the temperature progressively stabilizes. This shows that the heat transfer effect substantially diminishes as the pile foundation's heat transfer capacity reaches its limit and the heat transfer between the fluid, pile foundation, and soil approaches the dynamic equilibrium. At the same time, \(\overline{T}p\) is greatly impacted by \(SP\). \(\overline{T}p\) decreases as \(SP\) decreases. For instance, on day nine, the temperature rise \(\Delta\overline{T}_{p,SP=18}\) for the three operation techniques in a single day is 85.4%, 127.36%, and 127.67% higher than the temperature rise \(\Delta\overline{T}_{p,SP=40}\) for the energy piles. Figure 8c illustrates how the increase in soil temperature (\(\Delta\overline{T}_{soil}\)) increases with \(t\) and decreases with \(SP\) when using strategies A, B, and C for 5 days. \(\Delta\overline{T}_{soil}\) for strategy A decreases by 80.96% and 81.43%, respectively, compared with strategy C. The values for t and SP are 0.50 K, 0.19 K, and 0.09 K, and 0.42 K, 0.16 K, and 0.08 K, respectively. The downtimes of daily operation of all five types of spiral-sloped energy piles under operation strategy C are taken into consideration as reference points for the duration of the system's operation. The average change in soil temperature within the 6 m \(\times\) 6 m region centered on the energy piles was then fitted to the data. The average change in soil temperature during intermittent operating conditions can be predicted by fitting the data. Equations (6)-(8) display the respective prediction equations. Global hybrid continuous prediction curves:  
\[T_{(SP,t),1}=291.69117-0.0017 SP+0.01291t+2.062\times 10^{-5}SP^{2}-2.124\times 1 0^{-4}t^{2} \tag{7}\]  
where \(t\) is the number of operating days. Global intermittent forecast curves:  
\[ \begin{array}{ll}T_{(SP,t),2}&=291.66842-0.00134 SP+0.02048t+1.594\times 10^{-5 }SP^{2}-6.615\times 10^{-4}t^{2}\\ &+\left\lfloor t/7\right\rfloor\times 0.0657\\ \end{array}  \tag{8}\]  
Global forecast curves with adjustments:  
\[ \begin{array}{ll}T_{(SP,t)}&=291.66842-0.00134 SP+\varepsilon_{t,week}t+1.594 \times 10^{-5}SP^{2}-6.615\times 10^{-4}t^{2}\\ &+\left\lfloor t/7\right\rfloor\times\Delta T_{week}\varepsilon_{AT,SP}\\ \end{array}  \tag{9}\]  
where  
\[\varepsilon_{t,week}=0.02048-0.0023\times\left\lfloor t/7\right\rfloor+1.25 \times 10^{4}\times\left\lfloor t/7\right\rfloor^{2}\]  
\[\Delta T_{week}=0.0113+0.0703\times\left\lfloor t/7\right\rfloor-0.0062\times \left\lfloor t/7\right\rfloor^{2}\]  
\[\varepsilon_{AT,SP}=3\times 10^{-6}\times SP^{3}-10^{-4}\times SP^{2}-0.0059 \times SP+1.1399\]  
Equations (7)-(9) were used to forecast soil temperature changes in the energy pile with SP = 20 operating at strategy C for 6 weeks. The results of these simulations are compared in Figure 9.  
For predicting the average soil temperature over a 6-week period, Equation (8) (Predictive-3) has a very good goodness of fit with a determination coefficient of 0.986. Equation (7) (Predictive-2) has a high goodness of fit only within 2 weeks, and notably, the amount of dispersion increases when it exceeds 2 weeks, indicating that the temperature increase in a single week is not a linear change over time. It is evident that Equation (6) (Predictive-1) still has a high goodness of fit within 3 weeks with a determination coefficient of 0.70 but drops to 0.47 after 4 weeks.