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The work submits new release of the FlowVision software designed for automation of engineering calculations in computational fluid dynamics: FlowVision 3.09.05. The FlowVision software is used for solving different industrial problems. Its popularity is based on the capability to solve complex non-tradition problems involving different physical processes. The paradigm of complete automation of labor-intensive and time-taking processes like grid generation makes FlowVision attractive for many engineers. FlowVision is completely developer-independent software. It includes an advanced graphical interface, the system for specifying a computational project as well as the system for flow visualization on planes, on curvilinear surfaces and in volume by means of different methods: plots, color contours, iso-lines, iso-surfaces, vector fields. Besides that, FlowVision provides tools for calculation of integral characteristics on surfaces and in volumetric regions.

The software is based on the finite-volume approach to approximation of the partial differential equations describing fluid motion and accompanying physical processes. It provides explicit and implicit methods for time integration of these equations. The software includes automated generator of unstructured grid with capability of its local dynamic adaptation. The solver involves two-level parallelism which allows calculations on computers with distributed and shared memory (coexisting in the same hardware). FlowVision incorporates a wide spectrum of physical models: different turbulence models, models for mass transfer accounting for chemical reactions and radioactive decay, several combustion models, a dispersed phase model, an electro-hydrodynamic model, an original VOF model for tracking moving interfaces. It should be noted that turbulence can be simulated within URANS, LES, and ILES approaches. FlowVision simulates fluid motion with velocities corresponding to all possible flow regimes: from incompressible to hypersonic. This is achieved by using an original all-speed velocity-pressure split algorithm for integration of the Navier-Stokes equations.

FlowVision enables solving multi-physic problems with use of different modeling tools. For instance, one can simulate multi-phase flows with use of the VOF method, flows past bodies moving across a stationary grid (within Euler approach), flows in rotary machines with use of the technology of sliding grid. Besides that, the software solves fluid-structure interaction problems using the technology of two-way coupling of FlowVision with finite-element codes. Two examples of solving challenging problems in the FlowVision software are demonstrated in the given article. The first one is splashdown of a spacecraft after deceleration by means of jet engines. This problem is characterized by presence of moving bodies and contact surface between the air and the water in the computational domain. The supersonic jets interact with the air-water interphase. The second problem is simulation of the work of a human heart with artificial and natural valves designed on the basis of tomographic investigations with use of a finite-element model of the heart. This problem is characterized by two-way coupling between the “liquid” computational domain and the finite-element model of the hart muscles.

The study of the physiological and pathophysiological processes in the cardiovascular system is one of the important contemporary issues, which is addressed in many works. In this work, several approaches to the mathematical modelling of the blood flow are considered. They are based on the spatial order reduction and/or use a steady-state approach. Attention is paid to the discussion of the assumptions and suggestions, which are limiting the scope of such models. Some typical mathematical formulations are considered together with the brief review of their numerical implementation. In the first part, we discuss the models, which are based on the full spatial order reduction and/or use a steady-state approach. One of the most popular approaches exploits the analogy between the flow of the viscous fluid in the elastic tubes and the current in the electrical circuit. Such models can be used as an individual tool. They also used for the formulation of the boundary conditions in the models using one dimensional (1D) and three dimensional (3D) spatial coordinates. The use of the dynamical compartment models allows describing haemodynamics over an extended period (by order of tens of cardiac cycles and more). Then, the steady-state models are considered. They may use either total spatial reduction or two dimensional (2D) spatial coordinates. This approach is used for simulation the blood flow in the region of microcirculation. In the second part, we discuss the models, which are based on the spatial order reduction to the 1D coordinate. The models of this type require relatively small computational power relative to the 3D models. Within the scope of this approach, it is also possible to include all large vessels of the organism. The 1D models allow simulation of the haemodynamic parameters in every vessel, which is included in the model network. The structure and the parameters of such a network can be set according to the literature data. It also exists methods of medical data segmentation. The 1D models may be derived from the 3D Navier – Stokes equations either by asymptotic analysis or by integrating them over a volume. The major assumptions are symmetric flow and constant shape of the velocity profile over a cross-section. These assumptions are somewhat restrictive and arguable. Some of the current works paying attention to the 1D model’s validation, to the comparing different 1D models and the comparing 1D models with clinical data. The obtained results reveal acceptable accuracy. It allows concluding, that the 1D approach can be used in medical applications. 1D models allow describing several dynamical processes, such as pulse wave propagation, Korotkov’s tones. Some physiological conditions may be included in the 1D models: gravity force, muscles contraction force, regulation and autoregulation.

In the last decades, universal scenarios of the transition to chaos in dynamic systems have been well studied. The scenario of the transition to chaos is defined as a sequence of bifurcations that occur in the system under the variation one of the governing parameters and lead to a qualitative change in dynamics, starting from the regular mode and ending with chaotic behavior. Typical scenarios include a cascade of period doubling bifurcations (Feigenbaum scenario), the breakup of a low-dimensional torus (Ruelle–Takens scenario), and the transition to chaos through the intermittency (Pomeau–Manneville scenario). In more complicated spatially distributed dynamic systems, the complexity of dynamic behavior growing with a parameter change is closely intertwined with the formation of spatial structures. However, the question of whether the spatial and temporal axes could completely exchange roles in some scenario still remains open. In this paper, for the first time, we propose a mathematical model of convection–diffusion–reaction, in which a spatial transition to chaos through the breakup of the quasi–periodic regime is realized in the framework of the Ruelle–Takens scenario. The physical system under consideration consists of two aqueous solutions of acid (A) and base (B), initially separated in space and placed in a vertically oriented Hele–Shaw cell subject to the gravity field. When the solutions are brought into contact, the frontal neutralization reaction of the second order A + B $\to$ C begins, which is accompanied by the production of salt (C). The process is characterized by a strong dependence of the diffusion coefficients of the reagents on their concentration, which leads to the appearance of two local zones of reduced density, in which chemoconvective fluid motions develop independently. Although the layers, in which convection develops, all the time remain separated by the interlayer of motionless fluid, they can influence each other via a diffusion of reagents through this interlayer. The emerging chemoconvective structure is the modulated standing wave that gradually breaks down over time, repeating the sequence of the bifurcation chain of the Ruelle–Takens scenario. We show that during the evolution of the system one of the spatial axes, directed along the reaction front, plays the role of time, and time itself starts to play the role of a control parameter.

Verification results of supersonic turbulent jets computational characteristics are presented. Numerical simulation of axisymmetric nozzle operating is realized using FlowVision CFD. Open test cases for CFD are used. The test cases include Seiner tests with exit Mach number of 2.0 both fully-expanded and under-expanded $(P/P_0 = 1.47)$. Fully-expanded nozzle investigated with wide range of flow temperature (300…3000 K). The considered studies include simulation downstream from the nozzle exit diameter. Next numerical investigation is presented at an exit Mach number of 2.02 and a free-stream Mach number of 2.2. Geometric model of convergent- divergent nozzle rebuilt from original Putnam experiment. This study is set with nozzle pressure ratio of 8.12 and total temperature of 317 K.

The paper provides a comparison of obtained FlowVision results with experimental data and another current CFD studies. A comparison of the calculated characteristics and experimental data indicates a good agreement. The best coincidence with Seiner's experimental velocity distribution (about 7 % at far field for the first case) obtained using two-equation $k–\varepsilon$ standard turbulence model with Wilcox compressibility correction. Predicted Mach number distribution at $Y/D = 1$ for Putnam nozzle presents accuracy of 3 %.

General guidelines for simulation of supersonic turbulent jets in the FlowVision software are formulated in the given paper. Grid convergence determined the optimal cell rate. In order to calculate the design regime, it is recommended to build a grid, containing not less than 40 cells from the axis of symmetry to the nozzle wall. In order to calculate an off-design regime, it is necessary to resolve the shock waves. For this purpose, not less than 80 cells is required in the radial direction. Investigation of the influence of turbulence model on the flow characteristics has shown that the version of the SST $k–\omega$ turbulence model implemented in the FlowVision software essentially underpredicts the axial velocity. The standard $k–\varepsilon$ model without compressibility correction also underpredicts the axial velocity. These calculations agree well with calculations in other CFD codes using the standard $k–\varepsilon$ model. The in-home $k–\varepsilon$ turbulence model KEFV with compressibility correction a little bit overpredicts the axial velocity. Since, the best results are obtained using the standard $k–\varepsilon$ model combined with the Wilcox compressibility correction, this model is recommended for the problems discussed.

The developed methodology can be regarded as a basis for numerical investigations of more complex nozzle flows.

In present paper we reexamine the properties of CABARET numerical scheme formulated for a weakly compressible fluid flow basing the results of free shear layer modeling. Kelvin–Helmholtz instability and successive generation of two-dimensional turbulence provide a wide field for a scheme analysis including temporal evolution of the integral energy and enstrophy curves, the vorticity patterns and energy spectra, as well as the dispersion relation for the instability increment. The most part of calculations is performed for Reynolds number $\text{Re} = 4 \times 10^5$ for square grids sequentially refined in the range of $128^2-2048^2$ nodes. An attention is paid to the problem of underresolved layers generating a spurious vortex during the vorticity layers roll-up. This phenomenon takes place only on a coarse grid with $128^2$ nodes, while the fully regularized evolution pattern of vorticity appears only when approaching $1024^2$-node grid. We also discuss the vorticity resolution properties of grids used with respect to dimensional estimates for the eddies at the borders of the inertial interval, showing that the available range of grids appears to be sufficient for a good resolution of small–scale vorticity patches. Nevertheless, we claim for the convergence achieved for the domains occupied by large-scale structures.

The generated turbulence evolution is consistent with theoretical concepts imposing the emergence of large vortices, which collect all the kinetic energy of motion, and solitary small-scale eddies. The latter resemble the coherent structures surviving in the filamentation process and almost noninteracting with other scales. The dissipative characteristics of numerical method employed are discussed in terms of kinetic energy dissipation rate calculated directly and basing theoretical laws for incompressible (via enstrophy curves) and compressible (with respect to the strain rate tensor and dilatation) fluid models. The asymptotic behavior of the kinetic energy and enstrophy cascades comply with two-dimensional turbulence laws $E(k) \propto k^{−3}, \omega^2(k) \propto k^{−1}$. Considering the instability increment as a function of dimensionless wave number shows a good agreement with other papers, however, commonly used method of instability growth rate calculation is not always accurate, so some modification is proposed. Thus, the implemented CABARET scheme possessing remarkably small numerical dissipation and good vorticity resolution is quite competitive approach compared to other high-order accuracy methods

Exact solution of the stationary problem of wind-induced flow of two-layered viscous fluid is found for two-dimensional in vertical plane current and for drift current in three-dimensional case. The condition of sliding is set on the bottom of a water body. The condition of nonpassage is set on the lateral surface. Results of some calculations are given in comparison with those obtained using Ekman’s model (which does not take into account horizontal viscosity of the layer).

The reentry vehicle of the transportation spacecraft that is being created by RSC Energia in regular mode makes soft landing on land surface using a parachute system and thruster devices. But in not standard situations the reentry vehicle also is capable of executing a splashdown. In that case, it becomes important to define the hydrodynamics impact on the reentry vehicle at the moment of the first contact with the surface of water and during submersion into water medium, and to study the dynamics of the vehicle behavior at more recent moments of time.

This article presents results of numerical studies of hydrodynamics forces on the conical vehicle during splashdown, done with the FlowVision software. The paper reviews the cases of the splashdown with inactive solid rocket motors on calm sea and the cases with interactions between rocket jets and the water surface. It presents data on the allocation of pressure on the vehicle in the process of the vehicle immersion into water medium and dynamics of the vehicle behavior after splashdown. The paper also shows flow structures in the area of the reentry vehicle at the different moments of time, and integral forces and moments acting on the vehicle.

For simulation process with moving interphases in the FlowVision software realized the model VOF (volume of fluid). Transfer of the phase boundary is described by the equation of volume fraction of this continuous phase in a computational cell. Transfer contact surface is described by the convection equation, and at the surface tension is taken into account by the Laplace pressure. Key features of the method is the splitting surface cells where data is entered the corresponding phase. Equations for both phases (like the equations of continuity, momentum, energy and others) in the surface cells are accounted jointly.

The Richtmyer–Meshkov and the Rayleigh–Taylor instabilities of viscoplastic (or the Bingham) fluids are studied in the three–dimensional formulation of the problem. A numerical modeling of the intermixing of two fluids with different rheology, whose densities differ twice, as a result of instabilities development process has been carried out. The development of the Richtmyer–Meshkov and the Rayleigh–Taylor instabilities of the Bingham fluids is analyzed utilizing the MacCormack and the Volume of Fluid (VOF) methods to reconstruct the interface during the process. Both the results of numerical simulation of the named instabilities of the Bingham liquids and their comparison with theory and the results of the Newtonian fluid simulation are presented. Critical amplitude of the initial perturbation of the contact boundary velocity field at which the development of instabilities begins was estimated. This critical amplitude presents because of the yield stress exists in the Bingham fluids. Results of numerical calculations show that the yield stress of viscoplastic fluids essentially affects the nature of the development of both Rayleigh–Taylor and Richtmyer–Meshkov instabilities. If the amplitude of the initial perturbation is less than the critical value, then the perturbation decays relatively quickly, and no instability develops.When the initial perturbation exceeds the critical amplitude, the nature of the instability development resembles that of the Newtonian fluid. In a case of the Richtmyer–Meshkov instability, the critical amplitudes of the initial perturbation of the contact boundary at different values of the yield stress are estimated. There is a distinction in behavior of the non-Newtonian fluid in a plane case: with the same value of the yield stress in three-dimensional geometry, the range of the amplitude values of the initial perturbation, when fluid starts to transit from rest to motion, is significantly narrower. In addition, it is shown that the critical amplitude of the initial perturbation of the contact boundary for the Rayleigh–Taylor instability is lower than for the Richtmyer–Meshkov instability. This is due to the action of gravity, which helps the instability to develop and counteracts the forces of viscous friction.

The paper describes an analytical study of hydrodynamic processes taking place in the course of coolant flow through a fuel assembly of the core of a fast neutron sodium-cooled reactor. Within the framework of the study, a procedure and an analytical model were developed based on program complex FlowVision of computational fluid dynamics, which, using proved simplifications, permits to obtain a coefficient of rod lifting margin of a fuel assembly and to study hydrodynamic characteristics of processes taking place in the course of simulation of different initial events influencing motion of a reactor core fuel assembly.

For analytical justification a fuel assembly model was developed, which is equivalent by hydraulic resistance values and permits not to simulate explicitly a complicated full-scale fuel assembly design, thus, decreasing a number of computational cells in the model and, as a result, reducing computational and time resources.

Hydraulic parameters of the equivalent fuel assembly model in program complex FlowVision were analyzed in two stages. At the first stage, to determine the minimum rod lifting margin coefficient of a fuel assembly, steady-state analyses were performed, where various flowrate values were assigned at the model inlet and forces acting upon the assembly were analyzed. A series of dynamic mode analyses was performed at the second stage. Jump-like pressure increase being the initial event which could occur hypothetically in the fast neutron sodium cooled reactor plant was assigned in these modes. Hydrodynamic parameters and forces acting upon the fuel assembly were determined.

The results of the first stage of the analytical study proved the minimum coefficient of rod lifting margin of a fuel assembly of the fast neutron reactor justified in reactor plant design documentation. As a result of the second stage of the study, conclusions were made on impossibility for the fuel assembly to move at the initial event associated with jump-like pressure increase in the reactor pressure chamber.

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.