Radiator design optimization to ensure required heat supply to renovated dwellings in district heating networks

This study investigates the optimization of radiator design in renovated dwellings connected to a district heating network to ensure that each dwelling receives the required amount of thermal energy. A one-dimensional, steady-state model of non-isothermal flow is developed for a simplified network consisting of supply and return pipelines, radiators, elbows, T-junctions, and n-way junctions. The governing equations of mass, momentum, and energy conservation are solved using the finite element method, while a gradient-based optimizer, the method of moving asymptotes, adjusts radiator diameters to compensate for temperature drop and flow redistribution along the pipeline. Four operating cases were analyzed, considering combinations of optimized and non-optimized radiator diameters, including or excluding local pressure losses. The novelty of this study lies in optimizing radiator diameters within a district heating network to compensate for temperature drop and flow redistribution in the main pipelines while accounting for local hydraulic pressure losses. A radiative heat transfer analysis is also conducted to assess the effects of thermal radiation on radiator performance and optimized design parameters. In addition, an economic analysis based on life-cycle cost is performed to compare the economic implications of different design configurations, accounting for pipe material costs and pumping energy requirements. The results demonstrate that constant radiator diameters lead to insufficient heating performance in downstream buildings due to temperature reduction and flow redistribution along the pipeline. In contrast, optimized radiator diameters provide a uniform heat supply across all dwellings, achieving the required heating demand throughout the network. Including local resistances significantly raises the required inlet pressure. The optimized continuous diameters are then mapped to commercial pipe sizes. Sensitivity analyses performed for inlet temperatures ranging from 50 to 70 °C show that lower inlet temperatures require substantially larger radiator diameters to maintain the required heating power.