单相受热管动态数学模型的改进
Improvement of dynamic modelling for single-phase heated tubes

为提高多段集总参数模型的仿真精度,用动态方程代替静态方程计算控制体管壁放热量,建立了一种新的单相受热管集总参数动态数学模型.将机理模型中偏微分方程的时空分离,采用集总和解析相结合的方法,推导出管内工质温度分布的解析解,再由传热微元方程积分得到管壁放热量的动态方程式.新模型具备稳定、通用和可显式求解的特点.理论精度分析结果表明:模型的响应初终值不存在静态误差;均分3段时的计算结果明显优于传统多段模型均分5段时的计算结果.对某台超超临界压力锅炉过热器的仿真实验表明:新模型在入口温度阶跃响应方面改进明显;纯延迟时段内模型的计算结果基本与分布参数模型吻合.相比传统的多段模型,在相同条件下新模型可采用更少的分段数,且能更好地反映管内工质的输运延迟特性.
To improve the currently available multi-segment lumped parameter models, a new dynamic mathematic model for single-phase heated tubes is established by employing dynamic equations instead of the traditional static equations for calculating the heat transfer across the control volume’s tube wall. Through separating the temporal and spatial terms of the partial differential equations, and combining both lumped and analytical methods, an analytical solution for the temperature distribution of the steam and water in the tubes is derived. Then, by integrating the elemental volume equations, dynamic equations for the heat release of the tube wall are achieved. The improved model, which can be explicitly solved, is more stable and has much wider applicability. The precision analysis results indicate that no static error exists for the initial and final values; a 3-segment series model can achieve more accurate results than the 5-segment one using traditional models. After applying the improved model to an ultra-supercritical boiler superheater, the results show that the response characteristics for the inlet temperature step change are significantly improved, and the results during the pure delay periods are in accordance with those of the distributed parameter models. Compared with traditional multi-segment models, the improved model can achieve higher precision even with less segments. Besides, the transport delay characteristics of the water or steam within tubes can be analyzed more accurately with the improved model