1. Introduction
Steam has characteristics of a wide temperature range and pressure changes, high heat-carrying capacity, and low thermal inertia. It is irreplaceable in industrial situations, such as food, chemical, and pharmaceutical industries [
1]. According to the China Urban Construction Statistical Yearbook, China’s steam system supplied 671.13 million GJ of heat, accounting for 15.67% of the total heat supplied in 2022 [
2]. Improving the operational energy efficiency of steam heating systems can realize energy saving, which contributes to sustainable development. Steam needs to be transported by a steam heating pipeline. Due to the multi-heat-source nature of industrial steam heating systems, the load fluctuation of the heat users, and the state change of steam in the flow process, the hydraulic and thermal characteristics of steam heating pipelines are complex and variable [
3,
4,
5].
Establishing an efficient and accurate mathematical model of steam heating pipelines is an important way to study the steam hydraulic–thermal characteristics and to improve the operational energy efficiency of steam heating systems, and several scholars have researched this issue. Hinkelman et al. (2022) [
6] proposed a novel split-medium approach that enables the simultaneous numerical computation of an efficient liquid water model with various water/steam models, which breaks costly algebraic loops and reduces computation time significantly. Hofmann et al. (2018) [
7] developed a new algorithm for fast computation of water/steam properties in the single-phase and two-phase regions, which is useful for solving the steam control equations. It can be applied to real-time calculations and reduces the computation time. Zhuang et al. (2024) [
8] modeled an energy system coupled with electricity and steam and introduced a steam accumulator into the system to compensate for fluctuations in renewable energy sources, and the overall economic efficiency of the system was improved by 11.39%, proving the feasibility of joint operation of the electricity–steam system. Garcia-Gutierrez et al. (2015) [
9] established a hydraulic model of steam transportation based on an existing simulator for a 125 km long steam pipeline network in Mexico, and the average relative error between the calculated pressure and flow rate and the measured values was less than 10%. Zhong et al. (2023) [
10] established a dynamic hydraulic model and a thermal inertia model of a steam system and investigated the feasibility of utilizing the thermal inertia of steam for energy storage to meet the optimal scheduling of energy systems in industrial parks. The results show that it is feasible to simulate a large-scale steam pipeline reliably with numerical simulators [
11].
Due to heat loss from the pipeline to the environment, steam will condense during the flow process, and for long-distance steam pipelines, the impact of condensate on the hydraulic and thermal characteristics of steam cannot be ignored [
12]. Zhou et al. (2023) [
13] proposed an adaptive space-step simulation method for steam networks taking condensate losses into account, where the steam enthalpy is obtained by a quasi-linear fitting method to simplify the calculation. Results show that the method is applicable to pipeline networks containing both superheated and saturated steam. Wang et al. (2017) [
14] proposed a new hydraulic–thermal model for steam heat network transportation that considers the amount of drainage losses, resulting in the acquisition of drainage mass loss and heat loss to more accurately describe the steam flow parameters. Yang et al. (2023) [
15] proposed an improved method to optimize the dynamic operation of the steam thermal network, where the steam pipeline network is modeled by a thermal–electrical analogy model and graph theory. It is assumed that the steam is superheated and there is no phase transition, and when the steam pipeline exceeds 8 km, condensate may appear, thus affecting the dynamic steam transmission. Zhong et al. (2015) [
16] developed a hydraulic computational model to study the flow pattern of steam considering heat dissipation and condensate, where the steam density and the friction coefficient are considered as constant. Chen et al. (2022) [
17] considered condensate loss and heat dissipation and proposed a new simulation method for an electric–steam combined operation system, which improved the accuracy of heat loss calculation, and verified the accuracy of the model through the actual pipeline network. The results show that it is feasible to eliminate steam stagnation by optimizing the heat load of each heating source and it is essential to take condensate into account when calculating the steam state.
In addition, the external environmental temperature, pipeline sizing, and resistance are the key parameters that affect the hydraulic and thermal characteristics of the steam pipeline [
18]. Jie et al. (2020) [
19] developed an optimization model to minimize the environmental impact by optimizing the pressure drop per unit length of the network, which takes into account the heat source, the operation strategy, and the design temperature range. Zhang et al. (2023) [
20] used MATLAB R2020b software to analyze the effect of pipeline diameter and soil depth on the whole life cycle cost of direct buried heating pipeline networks and made an economic evaluation of the thickness of pipeline insulation. The optimum thickness of the insulation layer for different pipeline types is given, which provides a reference for designing and analyzing pipeline insulation. Kruczek et al. (2013) [
21] presented a novel method for determining annual heat loss from pipelines to the external environment for complex steam pipelines. The annual heat loss is predicted by the fluctuation of meteorological parameters throughout the year, and the payback period is calculated to determine the pipeline segments to be retrofitted. Zeng et al. (2016) [
22] optimized the pipeline diameter combination of steam heat network based on a genetic algorithm, established a mathematical model of the annual equivalent cost of a regional heating and cooling pipeline network, and analyzed the impact of electricity price on the economy of the optimal pipeline diameter combination. The study shows that the electricity price has little effect on the economy of the optimal pipe diameter combination, so the method is applicable to pipe networks in all regions.
The above research provides a foundation for the modeling and simulation of steam heating pipelines. However, the current unsteady-state modeling of steam pipelines is usually simplified as steady-state hydraulic modeling coupled with dynamic thermal modeling, which results in the steam hydraulic and thermal calculations being separated and failing to form a unified computational whole and affects the accuracy of the calculations.
In this paper, a coupled hydraulic–thermal unsteady-state model of a steam heating pipeline that considers condensate generation and steam state parameter changes is developed, and the model accuracy is verified by the actual operation data of a branched steam heat network. The effects of heat transfer coefficient and frictional resistance coefficient on the outlet temperature and pressure of the steam pipeline are simulated and analyzed, and the calculation results of the model with and without considering condensate are compared. The effects of key parameters including pipeline length, external environmental temperature, and inlet boundary on the hydraulic and thermal characteristics of steam are analyzed. This study can guide the efficient operation of steam pipeline networks and improve the efficiency of heat energy utilization.
5. Conclusions
In this study, the dynamic coupled hydraulic–thermal model of a steam pipeline is established considering the steam state parameter changes and condensate generation, and the model accuracy is verified by the operating data of the steam pipeline network under typical conditions. The necessity of considering condensate is clarified based on the comparative analysis of the calculation results between the model with and without considering condensate. The effects of the changes in frictional resistance coefficient, heat transfer coefficient, environmental temperature, pipeline inlet temperature, and pipeline inlet pressure on the hydraulic and thermal characteristics of the steam pipeline are simulated and analyzed, and the main conclusions are obtained as follows:
The dynamic coupled hydraulic–thermal model of a steam pipeline is experimentally verified by the operating data of a steam pipeline network, and the average relative error between the calculated and measured values of steam state parameters is only 8%, proving the accuracy of the model.
Considering condensate or not has a small effect on the outlet pressure of the steam pipeline but has a larger effect on the outlet temperature. When the heat transfer coefficient increases by 0.8 W/(m2·K), the effect of condensate on the steam outlet increases the temperature by 11.3 °C.
The effect of environmental temperature on the outlet temperature of the steam pipeline is delayed and attenuated, and the larger the heat transfer coefficient of the steam pipeline, the more significant the effect of environmental temperature.
As the steam pipeline inlet temperature increases, the time required for outlet temperature stabilization increases by 25 s to 30 s for each additional 400 m of pipeline length. As the inlet pressure decreases, the outlet pressure decreases without delay, and the magnitude of the outlet pressure decrease is even greater.
The study of the hydraulic thermal coupling characteristics of steam heating pipelines in this article can establish the relationship between supply and demand of steam heating systems and guide the adjustment and control of actual operating parameters of steam heating systems. By adjusting the pressure and temperature on the steam supply side, while managing the steam supply grade to satisfy the system’s end demand, one can optimize burner combustion efficiency, enhance energy conversion efficiency, and mitigate energy consumption and carbon emissions, ultimately enhancing operational efficiency and fostering sustainable development within the steam heating system.