Performance analysis of three iteration-free numerical methods for fast and accurate simulation of thermal dynamics in district heating pipeline

Abstract

Numerical methods can provide sufficient information for thermal dynamics of district heating (DH) network. However, high computation burden restricts its application, especially for large-scale DH networks. This dilemma can be overcome by establishing fast numerical calculation procedure and properly selecting the calculation steps without reduction of numerical accuracy. The first-order implicit upwind method is an iteration-free numerical approach for fast simulation of DH pipeline thermal dynamics, while the first-order precision restricts its numerical performance. To further improve the simulation performance, two iteration-free numerical methods with high-order precision, the second-order implicit upwind method and third-order semi-implicit QUICK method are developed. Validations of the three numerical methods are conducted with the measured data of a real DH pipeline. Preferred calculation steps of the three methods are studied via comprehensive numerical experiments. Based on the preferred step size, simulation comparisons of the numerical methods are performed. Results show that the outlet temperature fluctuations of DH pipeline can be feasibly predicted by these methods with satisfying accuracy. The second-order implicit upwind method perform best considering least computation burden (0.003 s) within acceptable error. With the application of the second-order implicit upwind method, simulation analyses on DH pipeline under varying flow velocities are performed.