On Efficient Numerical Algorithms for Simulation of High Power Electrical Cables - Čiegis, Raimondas; Jankevičiūtė, Gerda; Tumanov, Natalija (Mathematical Modelling and Analysis, 2015)
The new virtual modelling tool is constructed, which is used for optimal design of power transmission lines and cables. The construction of such lines should meet the latest power transmission network technical and economical requirements. The solver is is based on classical and modified mathematical models describing main heat conduction processes: diffusion, convection and radiation in various materials and environments. In basic heat conduction equation, we take into account a linear dependence of the resistance on temperature. Multi-physic and multi-scale models are required to simulate industrial cases of power transmission lines. The velocity of convective transport of the heat in air regions is simulated by solving a coupled thermo-convection problem including the heat conduction problem and the standard Navier-Stokes model of the heat flow in air. Another multi-physic model is used to describe changes of material heat conduction coefficients in soil due to influence of heating. This process is described by by solving a simplified mass balance equation for flows in porous media. The multi-scale and homogenization analysis is required to to formulate simple and accurate mathematical describing heat conduction process is metal region which consists of a bundle of tightly coupled metal wires. The FVM is used to solve the obtained systems of differential equations. Discretization of the domain is done by applying “aCute” mesh generator, which is a modification of the well-known Triangle mesh generator. The discrete schemes are implemented by using the OpenFOAM tool.