Simplifying Hydraulic Calculations with Mathematical Models for District Heating Systems

What is it about?

In the realm of thermal energy systems, the intricate workings of District Heating (DH) systems rely heavily on network hydraulics during both their design and operation phases. Anticipating even greater hydraulic intricacies in the near future, it becomes imperative to develop efficient solutions. This publication introduces a novel mathematical procedure tailored specifically to address the unique characteristics of branched DH networks. By leveraging straightforward input data, such as a pipe-node list, this procedure effectively captures the network layout through detection algorithms for both incidence and loop matrices. Through this matrix-based approach, the solution procedure identifies network flow patterns and pressure distributions. These computations are conducted utilizing either Newton-Raphson or Genetic Algorithm, grounded in principles of mass and energy conservation. A critical aspect of the problem formulation involves rectifying end-user flow rates to ensure energy conservation across the network's closed loops. This adjustment significantly expedites the convergence to a solution.

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Photo by Nastya Dulhiier on Unsplash

Photo by Nastya Dulhiier on Unsplash

Why is it important?

The novelty of this paper lies in several key innovations: Firstly, the modelling approach for District Heating (DH) networks introduces a fundamental shift by focusing on the network structure as a closed-looped parallel configuration. This approach remains independent of the network topological formation, offering a versatile solution applicable across various network layouts. Furthermore, the paper introduces a novel feature in network mapping, emphasizing the simplicity of input required for the modelling process. This simplification enhances accessibility and usability, particularly for practitioners in the field. The utilization of graph theory and customized detection algorithms to characterize the network mathematically represents another notable advancement. By enabling a matrix-based solution domain, this approach accelerates hydraulic simulations, facilitated by a rapid solver. Moreover, the matrix-based solution domain, coupled with the correction of flow rates at the end-user level, marks a departure from conventional models. Instead of adjusting flow corrections throughout the entire branches of the network, the focus shifts to localized corrections at the end-user level within the close-loop formation. This targeted approach not only expedites simulations but also enhances the accuracy and efficiency of the modelling process.