基于LB方法的河库流-温-质耦合模拟研究

Study on coupled simulation of flow, temperature, and concentration in river reservoirs based on LB method

摘要

【目的】针对山区河库复杂水动力条件，构建基于格子玻尔兹曼方法的三维流-温-质耦合数值模型，用于描述水体流动、温度分层及污染物输移过程。【方法】模型采用多分布函数格式并行求解流场、温度场与浓度场，并通过三维双扩散自然对流算例进行验证，在多组Rayleigh数工况下平均Nusselt数与Sherwood数的相对误差均小于0.8%。在此基础上，将模型应用于西南高原山区典型河库，模拟冷水入汇条件下的水温演化及污染物短时扩散过程。【结果】结果表明，冷水入汇后在库底形成潜流并诱发水温分层；当冷水主流到达坝址后，下泄水温在60 min内由约11.5℃降至约6.5℃。污染物在缓流区发生局部富集，高浓度区尺度可达约150 m,并在主流区表现为以对流为主的纵向输移特征。【结论】研究表明，该耦合模型能够在复杂边界条件下稳定刻画流-温-质多场相互作用，适用于山区河库冷水潜流诱发分层及污染物短历时扩散过程的高分辨率模拟，可为分层取水调度与污染风险分析提供参考。

Abstract

[Objective] To address the complex hydrodynamic conditions in mountainous river reservoir systems, a three-dimensional flow-temperature-concentration coupled numerical model based on the lattice Boltzmann method is developed to describe water flow, thermal stratification, and pollutant transport processes. [Methods] A multi-distribution-function scheme was employed to solve the flow field, temperature field, and concentration field in parallel. The model was validated using three-dimensional double-diffusive natural convection cases, and the relative errors of the averaged Nusselt and Sherwood numbers under multiple Rayleigh number conditions were all less than 0.8%. On this basis, the model was applied to a typical river reservoir in the southwestern plateau to simulate water temperature evolution and short-term pollutant transport under cold-water inflow conditions. [Results] The result showed that after the cold-water inflow, a subsurface undercurrent formed at the reservoir bottom, inducing thermal stratification. When the main cold-water flow reached the dam site, downstream water temperature decreased from approximately 11.5 ℃ to approximately 6.5 ℃ within about 60 minutes. Pollutants accumulated locally in low-velocity zones, with high-concentration regions extending up to approximately 150 m, and were transported longitudinally in the mainstream predominantly by advection. [Conclusion] The coupled model can stably characterize the multi-field interactions of flow, temperature, and concentration under complex boundary conditions. It is applicable to high-resolution simulations of stratification induced by cold-water undercurrents and short-term pollutant transport in mountainous river reservoir systems, providing a reference for stratified water intake scheduling and pollution risk analysis.

关键词

格子玻尔兹曼方法 / 多场耦合 / 河库 / 传热传质 / 对流扩散 / 冷水入汇 / 分层取水 / 污染风险

Key words

lattice Boltzmann method / multi-field coupling / river reservoir / heat and mass transfer / convection-diffusion / cold water inflow / stratified water withdrawal / pollution risk

基金资助

重庆市水利科技项目(CQSLK-2023018)

重庆市水利科技项目(CQSLK-2023001)

国家自然科学基金项目(52479059)