Improvement and Verification of One-Dimensional Numerical Algorithm for Reservoir Water Temperature at the Front of Dams

Abstract

The deep-water temperature of large reservoirs is low, thus easily leads to the appearance and expansion of cracks on the upstream faces of concrete dams. Therefore, in the design phase of a dam, accurately predicting the water temperature distribution at the front of the dam during the operation period of the reservoir takes on a critical significance in the dam simulation analysis of temperature control and crack prevention design. The vertical one-dimensional numerical algorithm of reservoir water temperature was optimized in accordance with the heat transfer equation and considering certain factors (e.g., water temperature transfer, inflow distribution, slag at the bottom of the reservoir, and solar radiation) to solve the above problem. The Nash–Sutcliffe efficiency coefficient (NSE) was adopted to analyze the simulation error qualitatively and quantitatively, and to verify the applicability of the algorithm. The results validated with temperature data measured in four reservoirs illustrate that the proposed algorithm exhibits a higher prediction accuracy than the empirical equation method for water temperature at the front of dams at different scales under different operation modes. The mean deviations of the proposed algorithm are all below 1 °C, and the Nash–Sutcliffe efficiency coefficients (NSE) are all above 0.85. Moreover, compared with the three-dimensional numerical algorithm, the proposed algorithm not only requires a smaller amount of data, but also is simpler to apply and has a higher efficiency. The twelve-month water temperature calculation for a large reservoir takes less than 1 min. This study further reveals that the slag at the bottom of the reservoir is capable of significantly rising the temperature at the dam heel by 5–6 °C. The program compiled by the proposed algorithm can be seamlessly embedded in the simulation program for concrete dam temperature control; thus, the reliability of the simulation of the temperature can be enhanced for temperature field and stress field on the upstream surface of the dam without affecting the total calculation efficiency.