Abstract: A hot water heating system is a complex network that includes thermal users, heat distribution pipelines, heat sources, and circulation pumps. To ensure the circulation pump operates in an efficient region and meets the required flow without causing severe water and heat imbalance, it's essential to analyze the operational status of single or multiple pumps within the system. The goal is to optimize the system so that the pump can operate as close as possible to its "full load, high efficiency" condition.
Keywords: hot water heating system, circulation pump, performance curve, hydraulic balance, least squares method. A hot water heating system involves various components such as users, heat networks, and pumps. Ensuring the pump runs efficiently while maintaining proper flow is crucial for system performance. This requires careful analysis of the pump’s operating conditions, especially when multiple pumps are involved.
Traditional methods like drawing and difference techniques for determining pump parameters and operating points are often inaccurate and time-consuming. Therefore, using the least squares method for curve fitting of experimental data from heating circulation pumps offers a more accurate approach. This allows for a better understanding of pump performance under different operating conditions.
1. Pump Curve Fitting
In this study, the least squares method is used for polynomial curve fitting to determine the performance curve equations of the circulation pump. The basic idea involves setting up error equations through error analysis, deriving normal equations based on minimal error, and solving them to obtain regression coefficients (least squares estimates). This process helps establish a precise polynomial curve that represents the pump’s performance characteristics.
2. Applied Research
After obtaining the numerical solution of the pump performance curve equation, it becomes easier to predict pump operation. By combining this with the pipeline characteristic equation, we can solve for the working point, calculate the flow and head at that point, and compare it with the actual total flow and resistance of the pipeline. This analysis helps assess the system’s hydraulic conditions and identify solutions for hydraulic imbalances. Several examples are thoroughly discussed in this section.
2.1 System Overview
Consider a heating system covering an area of 90,000 square meters. The estimated heat load is 5.2 MW. The supply water temperature is 95°C, and the return temperature is 70°C. The system has a leakage and dissipation coefficient of 1.05, and a flow adjustment factor of 1.2. The heating radius is 500 meters, with a frictional resistance of 70 Pa/m. The local resistance accounts for 30% of the total length. The heat source internal resistance is 10×10ⴠPa, and the user system resistance is 1×10ⴠPa. A safety margin coefficient of 1.15 is applied.
2.2 System Condition Analysis
Hydraulic imbalances in heating systems, particularly affecting end users, cannot be simply resolved by increasing pump power. If the operating point of a single pump is already in the flat region of the performance curve, increasing the pump will result in limited flow improvement. Adding a second pump in parallel may lead to even smaller increases in total flow. Therefore, the first step in resolving hydraulic imbalances should be adjusting the valves at the user inlets to achieve a more balanced flow distribution. Only if the total flow is insufficient should a pump matching the system or a combination of multiple pumps be considered to ensure efficient operation.
3. Conclusion
(1) As the number of heat users increases over time, the original pump may become too small. Through pump performance analysis, it may be possible to use multiple pumps in parallel. However, in many cases, a single pump's flow and head far exceed actual needs due to network imbalance. To compensate for this, multiple pumps are often added, but the resulting increase in flow is minimal, leading to low pump efficiency.
(2) Severe hydraulic imbalances in the network make it impossible for the pump to meet the needs of end users, even after adding more pumps or replacing them with larger ones. If the pipeline performance remains unchanged, increasing flow will not resolve the imbalance—it will persist at the same level.
(3) Analyzing hydraulic conditions is key to understanding the entire system's operation. Establishing a pump performance curve equation provides great convenience for system design and management. It lays the theoretical foundation for selecting the right pump and supports quantitative control and optimization of the system.
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