高壓蒸汽分配網路之動態分析

Abstract

本研究旨在探討高壓蒸汽網路之動態。首先，確立所需要使用的控制方程式，包含連續方程式、動量守恆方程式以及能量守恆方程式，用這三條控制方程式來求解流速、壓力以及溫度。在數學解析方法中有顯式法和隱式法兩種，顯式法可使用較小的時間間隔，但受限於穩定性且運算時間會拉長；而在隱式法中可使用較長的時間間隔，運算時間也會縮短，且適合用在長時間的動態分析上面。因此在本研究中採用完全隱式法來探討高壓蒸汽網路的動態，另外在求解非線性方程式則是使用牛頓法。 結合完全隱式法和牛頓法，首先運用在可壓縮與不可壓縮流體的單管系統中，運算結果的穩態結果透過和Aspen Plus比較後，確認此運算方法是可行的，之後針對不同的時間間隔和管段間隔進行探討並選出在此運算方法中較適當的數值。之後，在環狀蒸汽網路系統中，利用修正後的哈迪‧克勞斯法來計算蒸汽網路流量分配，並結合進運算迴圈中，模擬的範例包含樹枝狀系統以及三個環狀網路系統，其中包括雙環路系統、多供應端多需求端系統和大型蒸汽網路系統。在不同網路系統中探討，若流量發生變化時，不同的操作方式，會使的各單元有什麼樣的溫度壓力變化，並提供一個參考依據，有助於提高蒸汽網路系統的操作效益。

The purpose of this study is to investigate the transient response analysis of high pressure steam pipeline system. The mathematical model contain three governing equations, included continuity equation, momentum equation and energy equation. With these three governing equations, we can get flow rate, pressure and temperature. There are two types of mathematical analysis method, one is explicit method and the other is implicit method. For explicit method can use smaller time step but time step is limited by stability and computation time will spend more time. For implicit method can be applied to the long-term transients due to it is stable when using large time step and will reduce computation time. Therefore, we use fully implicit method in this study. And the algorithm to solve the governing equations is based on Newton-Raphson method. Combine fully implicit method and Newton-Raphson method in our calculation loop. In the single pipe system, we simulate two types of fluid, one is compressible fluid and the other is incompressible fluid. Each system is compared with Aspen Plus simulation at steady state. We also discuss different time step and number of sections in order to make a good choice in calculation loop. In the looped steam network, the calculation loop we add modified Hardy Cross method in calculation loop to calculate flow rate distribution. In the case study, start from one special case of looped network: branch network, then we design two-looped network, multi-supply and multi-demand network and larger looped network. In these case studies, transient condition is flow rate change. With different operation, we provide the calculation results of units’ temperature and pressure change. And we hope that we can give them a way to make decision when the transient conditions happen.