技術論文とプレゼンテーション

Power cables are essential components of modern infrastructure, transmitting electric power over long distances, and supporting the green energy transition. For mechanical protection, when cables are installed underground or beneath the seabed, they are frequently routed through circular ducts. Inevitably, these ducts create unfavorable thermal conditions for the cabling system making this part of the route a potential thermal bottleneck. Therefore, studying heat transfer between the cable and the duct is of great importance. To study heat transfer in air-filled ducts, several approaches have been developed to account for the occurring heat transfer mechanisms, namely convection and radiation. The IEC 60287-2-1 standard provides an analytical formula for the calculation of a combined convective and radiative thermal resistance (T4’) of the unfilled duct [1], depending on the duct and fluid material, average fluid temperature and cable diameter. An applicability range is specified for the cable diameter. This formula is also adopted by CIGRE TB 963 [2], showcasing its application to Finite Element Method (FEM) studies and extending its applicability to larger cable diameters. An analytical formula which defines an effective thermal conductivity of the duct fluid and accounts for convective effects is proposed by [3], along with an applicability range for the Prandtl and Rayleigh numbers. When applicable, surface-to-surface radiation physics is commonly combined with the latter approach ([4], [5]). The analytical approaches of [1], [2], and [3] assume concentric placement of the cable inside the duct and isothermal cable and duct boundaries. In reality, the temperature may vary by 5-10 K along these boundaries, and the cable is typically installed at the bottom of the duct. Additionally, when the surrounding duct is metallic, currents are induced in the duct, generating electromagnetic (E/M) losses. Proper E/M modelling is therefore necessary to accurately account for these induced losses [5]. To account for the actual installation conditions, Computational Fluid Dynamics (CFD) modelling can be applied [4], where the fluid field and heat transfer inside the duct are resolved. However, CFD modelling requires an additional physics module in COMSOL Multiphysics®, thereby increasing the level of required physics understanding, setup complexity, and computational time. This paper presents a practical workflow for the setup, meshing, and execution of models for current-rating studies of ducted cables. The analysis includes detailed guidelines regarding the modelling techniques and the physics involved in ducted cable installations. The expected outcome of this study is to provide guidance on how ducted cables can be modelled in COMSOL Multiphysics by presenting the available modelling options, along with their strengths and challenges, while underlining the significance of proper modelling in current-rating studies for power cables. Specifically, the coupling of heat transfer in solids and fluids with surface-to-surface radiation and, if necessary, magnetic field physics is detailed, enabling the reader to select the most appropriate modelling approach depending on their needs.