# Abrasion-Resistant and Temperature Control of
## 3 Numerical Simulation of Temperature Field  
### Model, Parameters and Schemes  
This numerical simulation of the temperature field of sidewall C\({}_{90}\)50 concrete was performed by a 3D finite element method based on ANSYS [32]. The size of surrounding rock in the numerical model was roughly set at three times of the spillway tunnel diameter; the origin of the whole coordinate system was set at the bottom of the spillway tunnel (the direction from the upstream face to the downstream face as \(y\)-axis orientation; the horizontal direction perpendicular to the spillway tunnel axis as \(x\)-axis orientation; the upward vertical direction as \(z\)-axis orientation). The boundary conditions were selected as follows: the top and bottom and four sides of the surrounding rock served as the adiabatic boundaries; the construction placement section of the spillway tunnel played the role of solid-gas boundary, treated as a category-III boundary (the surface heat transfer coefficient between the boundary of the object and the surrounding fluid and the temperature of the surrounding fluid are specified). In mesh generation, hexahedral elements were adopted for surrounding rock and lining concrete, while pentahedral or tetrahedral elements were used locally as transition. The contact elements of zero thickness could be used for transmitting heat, compressive stress, shearing stress and so forth. The numerical model is shown in Figure 8. According to the site construction data and mix proportion optimization design, concrete performance test results at Dagangshan Hydropower Station and reference to similar engineering experience [33; 34; 35], the thermodynamic parameters of the C\({}_{90}\)50 anti-scouring and abrasion-resistant concrete were used as listed in Table 9. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Strength Grade**} & \multirow{2}{*}{**Grade**} & \multirow{2}{*}{**Water-Binder Ratio**} & \multirow{2}{*}{**Sand Ratio/\%**} & \multirow{2}{*}{**Binder Materials Content**} & \multicolumn{4}{c}{**Amount of Material in Each Cubic Meter of Concrete**} & \multirow{2}{*}{**Water Content**} & \multirow{2}{*}{**Air Rendducing Agent of Al-PCA**} \\  & & & & & & & & & & & & & & \\ \hline C\({}_{90}\)50 & Two & 0.33 & 38 & 379 & 125 & 284 & 718 & 1172 & 76 & 19 & 3.411 & 0.015 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Construction mix proportion of spillway tunnel sidewall lining concrete (unit: kg/m\({}^{3}\)). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Strength Grade**} & \multicolumn{2}{c}{**Elastic modulus/CFA**} & \multicolumn{2}{c}{**Compressive Strength/MFA**} & \multicolumn{2}{c}{**Split Tensile Strength/MFA**} & \multicolumn{2}{c}{**Abusive Resistance/high/C\({}_{90}\)7-1**} & \multicolumn{2}{c}{**Volume Skin leakage Rate/(C\({}_{90}\)-9)**} & \multicolumn{2}{c}{**Thermal**} \\  & **Modulus/CFA** & & & & & & & & & & & & & &During casting of the sidewall C\({}_{90}\)50 anti-scouring and abrasion-resistant concrete for the spillway tunnel, a pre-buried HDPE (High density polyethylene) plastic cooling water pipe was used for cooling purposes (inner diameter, 28 mm; wall thickness, 2.0 mm; thermal conductivity coefficient, 1.67 kJ/(mh \({}^{\circ}\)C)); it was laid in a uniform \(S\)-shaped mode, with a vertical laying interval of 1 m. During casting, it was buried inside the concrete (Figure 9). In general, cooling water has a throughput temperature \(T\) in the range of 12-17 \({}^{\circ}\)C, a throughput flow in the range of 1.5-1.8 m\({}^{3}\)/h and a throughput duration of no less than 7 day. The water flow should be continuous.