This review addresses the modeling approaches for heat transfer processes in oil-immersed transformer. Electromagnetic, thermal, and hydrodynamic thermal fields are identified as the most critical aspects in describing the state of the transformer. The paper compares the implementation complexity, calculation time, and details of the results for different approaches to creating a mathematical model, such as circuit-based models and finite element and finite volume methods. Examples of successful model implementation are provided, along with the features of oil-immersed transformer modeling. In addition, the review considers the strengths and limitations of the considered models in relation to creating a digital twin of a transformer. The review concludes that it is not feasible to create a universal model that accounts for all the features of physical processes in an oil-immersed transformer, operates in real time for a digital twin, and provides the required accuracy at the same time. The conducted research shows that joint modeling of electromagnetic and thermal processes, reducing the dimensionality of models, provides the most comprehensive solution to the problem.

The development of digital twins for power transformers has become increasingly important to predict possible operating modes and reduce the likelihood of faults. The accuracy of these predictions relies heavily on the numerical models used, which must be both simple and computationally efficient. This work focuses on creating a simplified numerical model for a template oil-immersed power transformer (100 MVA, 230/69 KV). The study investigates how the number of elements and the strategies used to set up the mesh in the domain of interest influence the results, aiming to identify the key parameters that affect the outcomes. Furthermore, a significant effect of resolving thermal boundary layers on the accurate identification of hot spots is demonstrated. Two approaches to resolving thermal boundary layers are explored in this work. This study presents a comprehensive analysis of three numerical models for conjugate heat transfer simulations, each with distinct features and computational domain compositions. The results show that the addition of extra calculation domains leads to the emergence of new vortex structures, affecting the velocity profile at the channel inlet and altering the location of hot spots. This study provides valuable insights into the configuration and composition of calculated domains in numerical models of oil-immersed power transformers, essential for the accurate prediction of hot spot temperatures and ensuring reliable operation.

Transient plasma events in fusion devices can make the quasi-static magnetohydrodynamic approximation less reliable. Models at finite magnetic Reynolds number are then often needed. General-purpose CFD tools such as OpenFOAM usually lack accurate electromagnetic boundary conditions for electrically isolated walls. The common pseudo-vacuum treatment is suitable mainly at low magnetic Reynolds number and can shift the flux-expulsion transition. Exact boundary conditions are more accurate, but they are limited to simple geometries and spectral methods.This work presents \texttt{mhdMultiRegionPimpleFoam}, a multi-region OpenFOAM solver. It couples a magnetic vector-potential formulation in the fluid to a Laplace equation in the surrounding non-conducting region. This external-domain treatment, called Real Vacuum Boundary Conditions (RVBC), is tested on the flux-expulsion problem for isolated walls and compared with a semi-analytic Fourier reference. RVBC captures both Hartmann-like and Poiseuille-like regimes around the isolated-wall transition. The agreement is good in the steady Hartmann-like regime. Differences grow near the transition and if the exterior domain is too small.Wall conductivity is shown to control the exit from the low-magnetic-Reynolds-number Hartmann-like state. Weakly conducting walls tend toward a Poiseuille-like regime, while strongly conducting walls remain Hartmann-like. Intermediate wall conductance delays this change. RVBC thus offers a practical way to treat isolated walls at finite magnetic Reynolds number in OpenFOAM.

In this paper the effect of such parameter as a Q-factor on the speed/thrust characteristics and the degree of inductor current asymmetry of the linear induction motor (LIM) is considered. The problem is solved by 2D formulation by the finite element method and magnetic field is calculated on the basis of the Maxwell equations in the A-formulation. The influence of the transverse edge effect is taken into account by the Bolton's coefficient. As a result of the work, conclusions have been made about the degree of influence of Q-factor on the characteristics of the LIM and the correctness of application of Q-factor as an indicator of the economy and performance of the LIM.

This paper explores the application of conceptual hydrological models in optimizing the operation of hydroelectric power plants (HPPs) in steppe regions, a crucial aspect of promoting low-carbon energy solutions. The study aims to identify the most suitable conceptual hydrological model for predicting reservoir inflows from multiple catchments in a steppe region, where spring runoff dominates the annual water volume and requires careful consideration of snowfall. Two well-known conceptual models, HBV and GR6J-CemaNeige, which incorporate snow-melting processes, were evaluated. The research also investigated the best approach to preprocessing historical data to enhance model accuracy. Furthermore, the study emphasizes the importance of accurately defining low-water periods to ensure reliable HPP operation through more accurate inflow forecasting. A hypothesis was proposed to explore the relationship between atmospheric circulation and the definition of low-water periods; however, the findings did not support this hypothesis. Overall, the results suggest that combining the conceptual models under consideration can lead to more accurate forecasts, underscoring the need for integrated approaches in managing HPP reservoirs and promoting sustainable energy production.

Numerical simulation of forced magnetohydrodynamic (MHD) channel flow is performed under conditions where the magnetic Reynolds number is comparable to or significantly exceeds 1. The dimensionless parameters of the problem, used for verification, correspond to flow regimes characterized by the complex MHD interaction between the flow and the magnetic field. The aim of this work is to verify and analyze the performance and accuracy of numerical simulation software packages COMSOL Multiphysics, ANES, OpenFOAM, and Elmer in application to two different formulations of the considered problem: one written in terms of the induced magnetic field, and the other in terms of the magnetic vector potential. The results of the author's calculations are compared with the results from the approximate analytical solution for a one-dimensional formulation and with those from other authors. A comparative analysis indicates the key role of a nonlinear term in the equation of motion, which correctly models the phenomenon of hydraulic resistance crisis during the transition from Hartmann flow to Poiseuille flow. Neglecting this term leads to significant errors in the representation, especially, of unsteady Poiseuille flow. The computational experiments conducted by the authors, as well as those known from literature sources, show that the models of all software packages tested in this work are capable of reproducing the main flow patterns; however, the highest accuracy is achieved with strict adherence to the Courant criterion. The model implemented in OpenFOAM demonstrates values especially close to the published values in the Poiseuille regime. In terms of computational efficiency, the best performance is shown by the OpenFOAM system (open-source) and the freely distributed ANES, both implemented using the finite volume method. The finite element models of COMSOL and Elmer packages are characterized by longer computation time and lower parallelization efficiency. Based on the obtained results, one can select software packages that are best suited for numerical simulation of specific unsteady MHD flows in fusion-related problems.