# Effect of Different Control Strategies on the Heat Transfer Mechanism of Helical Energy Piles
## 3 Results  
Influence Law of Spiral Pitch on Heat Transfer Rate and Temperature in Some Local Positions of Energy Piles  
The numerical simulation of an SGHPs-P energy pile with a radius of 0.2 m, a spiral tube diameter of 25 mm, and five kinds of dimensionless spiral pitches (SP = 18, 24, 28, 36, 40) was carried out. The curves for dimensionless temperature, dimensionless time, and dimensionless temperature gradient are defined by Equations (4)-(6). The dimensionless temperature profiles are displayed in Figure 6 when \(Fo\) is equal to 1.22 (\(t\) = 91 h) along the horizontal line where \(Y\) = 0 and \(Z\) = 0 in the x-direction and \(X\) = 0 and \(Z\) = 0 in the y-direction, and the line is based on the G-function method [14]. \[\theta=k_{g}h_{b}(T_{i}-T_{g})/\Phi_{f} \tag{4}\]  
\[Fo=\alpha\tau/r_{sp}^{2} \tag{5}\]  
\[\partial\theta/\partial R=(\partial T/\partial r_{s})(k_{g}h_{p}r_{s}/\Phi_ {f}) \tag{6}\]  
where \(k\) is thermal conductivity; the subscripts \(b,f,g\), \(tube\), and \(I\) stand for the pile wall, fluid, soil, pipe wall, and temperature at a local point on the line, respectively; and \(\Phi\) is heat transfer quantity. Based on the graph shown in Figure 6a, it can be seen that the temperature distribution of SGHPs-P at the \(Z\) = 0 plane has peaks at \(X\) = \(\pm\)0.5. This occurrence may be due to the accumulation of heat. Additionally, some peaks can also be observed at \(Y\) = \(\pm\)0.25 in Figure 6b due to the significant impact of the straight outlet tube. The dimensionless temperature gradient profiles are displayed in Figure 7 when Fo is equal to 1.22 (\(t\) = 91 h) along the vertical line where \(X\) = 13 and \(Y\) = 0, and the line is based on the G-function method [14]. In addition, the temperature differential of the energy piles in the horizontal direction increases while the temperature in its radial direction rapidly drops toward the exterior. As the helical pipe pitch distribution changes, the temperature gradient at the pile base wall in Figure 7 swings frequently, and the magnitude of the fluctuation diminishes as SP decreases. Figure 6: Temperature distribution of energy piles as (a) horizontal temperature distribution in \(x\)-axis, (b) horizontal temperature distribution in \(z\)-axis. Letting A, B, and C represent three SGHEs-P operating strategies: A represents continuous operation under constant temperature (308 K) at the inlet, B stands for intermittent operation with the same inflow temperature as A, and C indicates intermittent operation in which the inflow temperature data were measured. The changes in cumulative heat transfer (\(Q_{0}\)), average pile foundation temperature (\(\overline{T}p\)), and average soil temperature (\(\overline{T}soil\)) over time for 1 day in 2 weeks for each of the five \(S\)Ps of SGHEs-P under the same inflow rate are shown in Figure 8. The variations in the energy piles' inlet water temperature over time for each of the three operating strategies are summarized in Table 2.  
The cumulative heat transfer (\(Q_{0}\)) of SGHEs-P for a single day is shown to be uniformly affected by t and SP in Figure 8a, meaning that \(Q_{0}\) declines as \(t\) and \(SP\) increase. \(Q_{0,\text{SP}=18}\) is greater than \(Q_{0,\text{SP}=40}\) by 4.14%, 24.89%, and 25.66%, respectively, when the SGHEs-P are operated using strategies A, B, and C for 5 days. The percentages are 2.13%, 24.99%, and \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Time** & **8:00** & **9:00** & **10:00** & **11:00** & **12:00** & **13:00** & **14:00** & **15:00** & **16:00** & **16:30** \\ \hline Operating strategy A & & & & & & 308 (keep all day) & & & & \\ Operating strategy B & 308 & 308 & 308 & 308 & 308 & 308 & 308 & 308 & 308 & 308 \\ Operating strategy C & 300.03 & 299.64 & 300.13 & 298.98 & 299.13 & 298.95 & 300.42 & 299.52 & 301.12 & 300.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Energy pile inflow water temperature (K) parameters.