Eduard V. Usov

Within the framework of linear Maxwell generalized hydrodynamics, explicit expressions for the Green's functions of longitudinal and transverse modes are obtained. Using the fluctuation-dissipation theorem, the spectral densities of individual contributions to the total energy of the fluid are determined. Exact frequency integration by the residue method is performed for the kinetic and potential (elastic) energy. An explicit analytical expression for the total internal energy of the fluid as a function of the gap width in the wave-number spectrum of transverse modes is obtained. An expression for the excitation spectrum in the fluid is constructed. It is shown that the excitation spectrum in the Maxwell model does not generally have a Debye quadratic form. The results are placed in the context of the Maxwell-Frenkel theory of liquids, and comparison with existing numerical simulations is provided.

The article describes the models used in the SAFR severe accident module to calculate the destruction of fuel elements with oxide and nitride fuels. The models used to calculate the melting of fuel elements, the dissociation of nitride fuel, and the eutectic interaction of dissociation products (liquid uranium) with cladding steel are considered. Detailed attention is given to models for calculating the flow and heat transfer of the melt with the surface of the fuel element. The results of validating the model on experimental data, as well as test calculations of the problem of destruction of fuel elements with nitride fuel, are presented.

—An analysis of the relationships for calculating the thermal properties of liquid lead (hereinafter referred to as lead) was carried out, and the method for determining its heat capacity over a wide range of temperatures, including at high values, was chosen. This is especially important for numerical studies to justify the safety of designed reactor installations with liquid metal coolants, such as BREST-OD-300 and BR-1200. Measuring the properties of lead at temperatures close to the boiling point is often difficult due to the lack of reliable methods and materials that can withstand temperatures above 2273 K. At present, theoretical approaches to calculating the properties of simple liquids based on phonon theory are being actively developed. Such approaches can be used to derive semiempirical relations for the heat capacity of liquid lead that would allow physically correct extrapolation of the data to the high-temperature region. In this regard, the aim of this work is to obtain a relationship for calculating the heat capacity of liquid lead from its melting point to its boiling point based on modern theoretical approaches. To achieve the set goal, the following tasks were solved. Firstly, an analysis of the works of various authors was carried out and empirical formulas were selected that make it possible to reliably calculate the heat capacity at a constant volume c_v (isochoric heat capacity) for a lead coolant from the melting point to 1500 K. Secondly, based on them, using phonon theory, an approximating formula was constructed, thanks to which it is possible to physically correctly extrapolate the properties of lead to the boiling point (2022 K).

Models of the severe-accident SAFR module used to calculate the cladding melt relocation along the fuel pin surface during its melting are presented in relation to severe accidents in fast-neutron reactors cooled by liquid metal. The choice of the basic system of equations and closing relations is presented. The models are validated based on experiments on melting and flow of cladding simulator melts. The error of calculating the cladding mass loss due to its melting and flowing along the fuel pin surface is estimated.

In this article, based on the concept of instantaneous normal modes, a simple semiempirical formula for calculating the heat capacity of liquids is proposed. The calculation results were compared with experimental data on the heat capacity of sodium, lead, and bismuth. It is shown that the formulas make it possible to assess properties in the high-temperature region with satisfactory accuracy.

In order to ensure efficient and safe operation of oil and gas fields, a tool is required to design production wells and surface infrastructure. It is important to take into account the physical processes that occur during production, as well as fluid properties and phase transitions. The "d-Flow" software package enables the creation of a comprehensive field model based on geological and field data to calculate hydraulic losses of pipelines and forecast hydrocarbon production. The fluid flow modelling is based on the calculation of multiphase friction with the wall of a well or a pipeline. The article discusses the implementation of four friction models: the Beggs-Brill model, the Gray model and its modification, and the Mukherjee-Brill model. The purpose of this work is to compare the predictions of friction models with the results obtained using commercial realizations of the same models. The results of the Schlumberger PIPESIM hydraulic simulator calculations were used as a benchmark for comparison with the "d-Flow" models. Numerical experiments were conducted to investigate two-phase flow under varying well geometry and flow regimes. The models used were compared, and the results showed that the predicted liquid holdup had an average relative error of 0.06%. In some cases, the error was as low as 0.02%. The predicted cumulative pressure drop in the well did not exceed 0.34% for all considered models. Based on the comparison results, we conclude that the "d-Flow" software package is suitable for calculating pressure drop in wells of different geometry and surface networks.

Application of computation tools resting on contemporary physical and mathematical models for substantiating the design solutions adopted for various heat-transfer equipment components helps save time, manpower, and financial resources of design institutions. The variety of both existing reactors and those being designed, which differ from one another both in design and type of coolants calls for the availability of a versatile thermal hydraulic computer code suited for a wide range of applications. The new-generation HYDRA-IBRAE/LM thermal hydraulic module of the EUCLID integrated code, which has been developed as part of the Proryv (Breakthrough) Project, meets these requirements. The operation of this thermal hydraulic module as part of the integrated code opens the possibility to simulate an essentially wider range of reactor plant operation modes and, as a consequence, those of individual heat-transfer equipment components. The developed thermal hydraulic module, which has been certified at the Scientific and Engineering Center for Nuclear and Radiation Safety (SEC NRS), offers the possibility to analyze the thermal hydraulics of sodium, lead, lead–bismuth, gas, and water coolants in various NPP equipment items. Reactor plant steam generators (SGs) belong to the category of equipment components most complex for modeling since they may contain two types of coolants. The article presents study results demonstrating the code’s abilities to analyze in a correct way the processes in the steam generators of only sodium cooled reactor plants, because these plants exist and are actively operated in Russia and around the world. The data presented in the article allow a conclusion to be drawn that the thermal hydraulic module developed at IBRAE RAS is an efficient tool for numerically analyzing complex heat-transfer processes in reactor plants. By using an extended system of closing correlations implemented in the module, it is possible to perform substantiation of design thermal engineering solutions as applied to individual heat-transfer equipment components.

The paper presents approaches that can be used to analyze the behavior of mixed nitride uranium–plutonium fuel rods during emergency situations accompanied by thermal destruction of fuel rods. The validation results based on currently available data are presented. The calculation error was estimated from the validation results. Based on the validated model, the results of a numerical study of the specific features of the breakdown of mixed nitride uranium–plutonium fuel rods are presented for accident conditions typical of reactor plants with sodium and lead coolants.