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The article presents the results of a numerical study of the flow structure in a two-dimensional flat diffuser. A feature of diffusers is that they have a complex anisotropic turbulent flow, which occurs due to recirculation flows. The turbulent RANS models, which are based on the Boussinesq hypothesis, are not able to describe the flow in diffusers with sufficient accuracy. Because the Boussinesq hypothesis is based on isotropic turbulence. Therefore, to calculate anisotropic turbulent flows, models are used that do not use this hypothesis. One of such directions in turbulence modeling is the methods of Reynolds stresses. These methods are complex and require rather large computational resources. In this work, a relatively recently developed two-fluid turbulence model was used to study the flow in a flat diffuser. This model is developed on the basis of a two-fluid approach to the problem of turbulence. In contrast to the Reynolds approach, the two-fluid approach allows one to obtain a closed system of turbulence equations using the dynamics of two fluids. Consequently, if empirical equations are used in RANS models for closure, then in the two-fluid model the equations used are exact equations of dynamics. One of the main advantages of the two-fluid model is that it is capable of describing complex anisotropic turbulent flows. In this work, the obtained numerical results for the profiles of the longitudinal velocity, turbulent stresses in various sections of the channel, as well as the friction coefficient are compared with the known experimental data. To demonstrate the advantages of the used turbulence model, the numerical results of the Reynolds stress method EARSM are also presented. For the numerical implementation of the systems of equations of the two-fluid model, a non-stationary system of equations was used, the solution of which asymptotically approached the stationary solution. For this purpose, a finite-difference scheme was used, where the viscosity terms were approximated by the central difference implicitly, and for the convective terms, an explicit scheme against the flow of the second order of accuracy was used. The results are obtained for the Reynolds number Re = 20 000. It is shown that the two-fluid model, despite the use of a uniform computational grid without thickening near the walls, is capable of giving a more accurate solution than the rather complex Reynolds stress method with a high resolution of computational grids.

A mathematical model is formulated for the coastal slope erosion of sandy channel, which occurs under the action of a passing flood wave. The moving boundaries of the computational domain — the bottom surface and the free surface of the hydrodynamic flow — are determined from the solution of auxiliary differential equations. A change in the hydrodynamic flow section area for a given law of change in the flow rate requires a change in time of the turbulent viscosity averaged over the section. The bottom surface movement is determined from the Exner equation solution together with the equation of the bottom material avalanche movement. The Exner equation is closed by the original analytical model of traction loads movement. The model takes into account transit, gravitational and pressure mechanisms of bottom material movement and does not contain phenomenological parameters.

Based on the finite element method, a discrete analogue of the formulated problem is obtained and an algorithm for its solution is proposed. An algorithm feature is control of the free surface movement influence of the flow and the flow rate on the process of determining the flow turbulent viscosity. Numerical calculations have been carried out, demonstrating qualitative and quantitative influence of these features on the determining process of the flow turbulent viscosity and the channel bank slope erosion.

Data comparison on bank deformations obtained as a result of numerical calculations with known flume experimental data showed their agreement.

The main feature of a two-dimensional turbulent flow, constantly excited by an external force, is the appearance of an inverse energy cascade. Due to nonlinear effects, the spatial scale of the vortices created by the external force increases until the growth is stopped by the size of the cell. In the latter case, energy is accumulated at these dimensions. Under certain conditions, accumulation leads to the appearance of a system of coherent vortices. The observed vortices are of the order of the box size and, on average, are isotropic. Numerical simulation is an effective way to study such the processes. Of particular interest is the problem of studying the viscous fluid turbulence in a square cell under excitation by short-wave and long-wave static external forces. Numerical modeling was carried out with a weakly compressible fluid in a two-dimensional square cell with zero boundary conditions. The work shows how the flow characteristics are influenced by the spatial frequency of the external force and the magnitude of the viscosity of the fluid itself. An increase in the spatial frequency of the external force leads to stabilization and laminarization of the flow. At the same time, with an increased spatial frequency of the external force, a decrease in viscosity leads to the resumption of the mechanism of energy transfer along the inverse cascade due to a shift in the energy dissipation region to a region of smaller scales compared to the pump scale.

Nowadays, active development of 4th generation nuclear reactors with liquid metal coolants takes place. Therefore, simulation of their elements and units in 3D modelling software are relevant. The thermal-hydraulic analysis of reactor units with liquid metal coolant is recognized as one of the most important directions of the complex of interconnected tasks on reactor unit parameters justification. The complexity of getting necessary information about operating conditions of reactor equipment with liquid-metal coolant on the base of experimental investigations requires the involvement of numerical simulation. The domestic CFD code FlowVision has been used as a research tool. FlowVision software has a certificate of the Scientific and Engineering Centre for Nuclear and Radiation Safety for the nuclear reactor safety simulations. Previously it has been proved that this simulation code had been successfully used for modelling processes in nuclear reactors with sodium coolant. Since at the moment the nuclear industry considers plants with lead-bismuth coolant as promising reactors, it is necessary to justify the FlowVision code suitability also for modeling the flow of such coolant, which is the goal of this work. The paper presents the results of lead-bismuth eutectic flow numerical simulation in the heat exchange tube bundle of NPP steam generator. The convergence studies on a grid and step have been carried out, turbulence model has been selected, hydraulic resistance coefficients of lattices have been determined and simulations with and without $k_\theta^{}$-$e_\theta^{}$ model are compared within the framework of fluid dynamics and heat exchange modeling in the heat-exchange tube bundle. According to the results of the study, it was found that the results of the calculation using the $k_\theta^{}$-$e_\theta^{}$ turbulence model are more precisely consistent with the correlations. A cross-verification with STAR-CCM+ software has been performed as an additional verification on the accuracy of the results, the results obtained are within the error limits of the correlations used for comparison.

The article presented the computational algorithm developed to study chemical processes in the internal flows of a multicomponent gas under the influence of laser radiation. The mathematical model is the gas dynamics’ equations with chemical reactions at low Mach numbers. It takes into account dissipative terms that describe the dynamics of a viscous heat-conducting medium with diffusion, chemical reactions and energy supply by laser radiation. This mathematical model is characterized by the presence of several very different time and spatial scales. The computational algorithm is based on a splitting scheme by physical processes. Each time integration step is divided into the following blocks: solving the equations of chemical kinetics, solving the equation for the radiation intensity, solving the convection-diffusion equations, calculating the dynamic component of pressure and calculating the correction of the velocity vector. The solution of a stiff system of chemical kinetics equations is carried out using a specialized explicit second-order accuracy scheme or a plug-in RADAU5 module. Numerical Rusanov flows and a WENO scheme of an increased order of approximation are used to find convective terms in the equations. The code based on the obtained algorithm has been developed using MPI parallel computing technology. The developed code is used to calculate the pyrolysis of ethane with radical reactions. The superequilibrium concentrations’ formation of radicals in the reactor volume is studied in detail. Numerical simulation of the reaction gas flow in a flat tube with laser radiation supply is carried out, which is in demand for the interpretation of experimental results. It is shown that laser radiation significantly increases the conversion of ethane and yields of target products at short lengths closer to the entrance to the reaction zone. Reducing the effective length of the reaction zone allows us to offer new solutions in the design of ethane conversion reactors into valuable hydrocarbons. The developed algorithm and program will find their application in the creation of new technologies of laser thermochemistry.

The presence of a contact boundary between water and transformer oil greatly reduces the electrical strength of the oil phase. The presence of an electric field leads to varying degrees of polarization at the interface and the appearance of a force acting on a liquid with a higher dielectric constant (water) in the direction of a liquid with a lower dielectric constant (oil). This leads to the contact surface instability development. Instability as a result of its development leads to a stream of water being drawn into oil volume and a violation of the insulating gap. In this work, we experimentally and numerically study electrohydrodynamic instability at the phase boundary between electrically weakly conductive water and transformer oil in a highly inhomogeneous electric field directed perpendicular to the contact boundary. The results of a full-scale and numerical experiment of studying of the electrohydrodynamic instability development in a strong electric field at the interface between water and transformer oil are presented. The system consists of a spherical electrode with a radius of 3.5 mm, placed in water with a conductivity of 5 $\mu S/cm$, and a thin blade electrode 0.1 mm thick, placed in transformer oil of the GK brand. The contact boundary passes at the same distance from the nearest points of the electrodes, equal to 3 mm. The work shows that at a certain electric field strength, the cone-shaped structure of water grows towards the electrode immersed in transformer oil. A numerical correspondence was obtained for both the shape of the resulting water structure (cone) during the entire growth time and the size measured from its top to the level of the initial contact boundary of phase separation. The dynamics of this structure growth has been studied. Both in numerical calculations and in experiment, it was found that the size of the resulting cone along the electrode connection line depends linearly on time.

In this paper, the structure of a shock wave in a binary gas mixture is studied on the basis of direct solution of the Boltzmann kinetic equation. The conservative projection method is used to evaluate the collision integral in the kinetic equation. The applied evaluation formulas and numerical methods are described in detail. The model of hard spheres is used as an interaction potential of molecules. Numerical simulation is performed using the developed simulation environment software, which makes it possible to study both steady and non-steady flows of gas mixtures in various flow regimes and for an arbitrary geometry of the problem. Modeling is performed on a cluster architecture. Due to the use of code parallelization technologies, a significant acceleration of computations is achieved. With a fixed accuracy controlled by the simulation parameters, the distributions of macroscopic characteristics of the mixture components through the shock wave front were obtained. Computations were conducted for various ratios of molecular masses and Mach numbers. The total accuracy of at least 1% for the local values of molecular density and temperature and 3% for the shock front width was achieved. The obtained results were compared with existing computation data. The results presented in this paper are of theoretical significance, and can serve as a test computation, since they are obtained using the exact Boltzmann equation.

In this paper a numerical model for blood flow through a venous bifurcation with an obliterating clot is investigated. We studied propagation of perturbations of blood flow velocity and perturbations of pressure inside the vein. The model is built in acoustic (linear) approximation. Computational results reveal conditions for clot resonance oscillation, which can cause its detachment and thromboembolism.

The aim of research is to develop software system for solving gas dynamic problem in multiply connected integration domains of regular shape by high-performance computing system. Comparison of the various technologies of parallel computing has been done. The program complex is implemented using multithreaded parallel systems to organize both multi-core and massively parallel calculation. The comparison of numerical results with known model problems solutions has been done. Research of performance of different computing platforms has been done.

We consider the two-dimensional mathematical model of wildfire. Numerical solution algorithm based on the method of large particles was developed for this model.