Complete System Of Navier-Stokes Equations Research Articles

Параметрические исследования течений в микросоплах

The work is devoted to parametric investigations of the krypton flow in a conical micronozzle when flowing into a region with low pressure. The features of the flows are studied at various values of the stagnation pressure in the pre-nozzle volume, including the occurrence of a condensed phase in the flow. Mathematical modeling was carried out on the basis of a numerical solution of the complete system of Navier-Stokes equations, supplemented by the equation for the mass fraction of the condensate. The mathematical model takes into account the change in the coefficients of dynamic viscosity and thermal conductivity depending on the gas temperature. The problem was solved by the control volume method on a block-structured regular grid of quadrangular elements using schemes of the second order of accuracy. The equations were integrated with respect to time using the Runge-Kutta method. The calculations were carried out at stagnation pressures of 5, 10, and 15 atm for single-phase and two-phase flows. The distribution fields of temperature and Mach number in the nozzle and in the space behind it are presented. The axial distribution of pressure, temperature, and Mach number has been studied. It is shown that in the case of a single-phase flow, self-similarity of gas flows is observed. The pressure fields were similar, but in a dimensionless form they coincided to each other. In this case, the identity of the velocity and temperature fields was observed at different values of the stagnation pressure. The self-similarity of the flow is violated in the zone of formation of condensed particles. The dimensions of the zones of local temperature increase, as well as the intensity of heat release, depend on the given stagnation pressure, which is reflected in the velocity characteristics of the flow.

Calculation of the speed characteristics of an upward swirling gas flow under conditions of side wind

The paper presents the results of numerical modeling of lateral wind effects on three-dimensional unsteady air flows in an upward swirling stream of an artificially created tornado in a stationary mode of operation. The mathematical model is the complete system of Navier-Stokes equations taking into account the viscosity and thermal conductivity of a moving gas, as well as the action of gravity and Coriolis. Using an explicit difference scheme and an appropriate choice of initial and boundary conditions, solutions are obtained numerically for the complete system of Navier-Stokes equations in the computational domain in the form of a rectangular parallelepiped. All components of the gas flow velocity were calculated at fixed time instants and
 instantaneous streamlines were constructed with constant horizontal wind direction taken into account. The calculations showed that the result of the wind effect on the upward swirling flow is an asymmetric change in peripheral speed, its uneven
 deformation in opposite sections, and the total displacement of the vortex in the direction of the wind. In addition, the displacement and curvature of the vertical part of the vortex in the direction of the wind was established, a “detachment” of some instantaneous streamlines from the vertical rotating part and the appearance in the center of the vortex of an area that is free of streamlines increasing in diameter were recorded. In the studied time variation range, the stability of the air vortex to wind action and the stable operation of the used computational scheme are observed.

Calculation of the speed descrioptions of the upward swirling gas flow in conditions of lateral wind action

The paper presents the results of numerical simulation of lateral wind impact on three-dimensional non-stationary air flows in ascending vortex flow of artificially created tornado in the stationary operating mode. The mathematical model represents a complete system of Navier-Stokes equations taking into account the viscosity and thermal conductivity of the moving gas, as well as the effects of gravity and Coriolis. Using the explicit difference scheme and the corresponding choice of initial and boundary conditions, the solutions of the complete system of Navier-Stokes equations in the computational domain representing a rectangular parallelepiped are numerically obtained. All components of gas flow speed are calculated at fixed time points and instantaneous current lines are built taking into account the constant horizontal wind speed. The calculations showed that the result of the wind action on the ascending vortex flow is an unsymmetrical change in the circumferential velocity, its uneven deformation at opposite sections, and the total displacement of the vortex in the wind direction. Besides, the displacement and the curvature of the vertical vortex part in wind direction are established, the “separation” of some instantaneous current lines from vertical rotating part and the area in the vortex center increasing in diameter, free from current lines is fixed. In the studied time change range, the wind resistance of the air vortex and stable operation of the used computational scheme are observed.

Calculation of the thermodynamic characteristics of an upward swirling gas flow under conditions of side wind

The paper presents the results of numerical modeling of lateral wind effects on three-dimensional unsteady air flows in an upward swirling stream of an artificially created tornado after entering a stationary mode. Under the corresponding initial and boundary conditions, the solutions of the complete system of Navier-Stokes equations in the computational domain in the form of a rectangular parallelepiped are numerically obtained using the explicit difference scheme. At fixed points in time, the gas-dynamic characteristics of air flows are calculated under the action of gravity and Coriolis, as well as taking into account the constant horizontal directional wind speed. Numerical calculations showed that the resulting density, temperature, and pressure gradients lead to significant and asymmetric changes in air flows at different points in time and at different points in the computational domain. The total displacement of the vortex in the direction of the wind, the deformation and increase in the diameter of the vortex, which begin in the bottom part and pass into its vertical part, are established. In the considered range of time changes, the stability of the air vortex under study against wind action and the stable operation of the computational scheme used are noted.

The Human Comfort Level in an Energy-Saving Simulation Model of Office Building

Currently high attention is drawn to the studies of the influence of pulsating flow to the heat transfer. Such unsteady flows can be created artificially or may appear during the operation of the thermal energy equipment. The purpose of this work is to perform numerical studies of the pulsating fluid flow effect supplied to a panel heating radiator on its heat output; and to determine the effect of pulsations of heat output on a human comfort level as well. Numerical modeling was prepared with CAD/CFD/HVAC complex of SolidWorks/FlowSimulation software. Where the complete system of Navier-Stokes equations and the energy equation were solved using the k-ε turbulence model in a non-stationary formulation of the problem. Results of the numerical calculations showed that the periodic pulsating flow of the fluid in the heating radiator during operation, in comparison with the stationary mode, leads to increasing and decreasing in the thermal power of the radiator. But at the same time, with an average estimate, the thermal power with pulsations of the fluid’s flow increases for about 10-15% comparing with a stationary mode. Model of the office room in the considered operating mode is not comfortable; this conclusion is based on such criteria as operating temperature, PMV, PPD, identified in the numerical calculations process.

Calculation of gas velocities in concentrated fire vortices

The article presents the results of numerical modeling of the generation of free fire vortices in laboratory conditions without the use of special swirling devices. The fundamental possibility of physical modeling of the occurrence of concentrated fire vortices is described in a series of experimental studies conducted under the supervision of A. Yu. Varaksin, corresponding member of the RAS. In the model of compressible continuous medium for the complete system of Navier-Stokes equations, an initial-boundary-value problem is proposed that describes complex three-dimensional unsteady flows of viscous compressible heat-conducting gas in ascending swirling heat flows. Using explicit difference schemes and the proposed initial-boundary conditions, approximate solutions of the complete system of Navier-Stokes equations are constructed and the velocity characteristics of three-dimensional unsteady gas flows initiated by local heating of the underlying surface by nineteen heat sources are numerically determined.

Валидация методов расчета горения водорода в сверхзвуковом потоке модельного воздуха по экспериментальным данным Бича — Эванса — Шекснайдера

This paper deals with numerical simulation of combustion of a hydrogen-air mixture in a supersonic flow. The simulation is based on solving the complete system of Navier-Stokes equations with closure using the turbulence model and detailed chemical kinetics. The mixing and combustion of a hydrogen-air fuel mixture is considered in the experimental formulation of Beach-Evans-Schexnayder. The effect of various kinetic mechanisms, turbulence models, TCI models, and boundary conditions on the solution is studied qualitatively and quantitatively. The relative errors of mass concentration of water for control sections are determined, and the methods’ boundaries are shown. Conclusions are drawn on the influence of turbulent mixing mechanisms and chemical kinetics on the combustion of hydrogen.

Numerical simulation of hydrogen combustion in oxidizer supersonic flow in flowpaths of various configurations

The paper deals with the numerical simulation of the combustion of a hydrogen-air mixture in a supersonic flow in channels of various configurations. Axisymmetric and plane type flows are considered. The simulation is based on solving the complete system of Navier-Stokes equations with closure using a turbulence model and detailed chemical kinetics. To validate the results, Beach-Evans-Schexnayder and Burrows-Kurkov experimental data are used. The influence of various kinetic mechanisms, models of turbulence, and boundary conditions on the solution obtained is considered. The boundaries of the methods are shown.

Calculation of thermodynamic characteristics of gas flows in concentrated fire vortices

The article presents the results of numerical simulation of gas flows in free fire vortices. The fundamental possibility of physical modeling of the occurrence of concentrated fire vortices is presented in a series of experimental studies carried out at the Joint Institute for High Temperatures of the Russian Academy of Sciences. In the model of a compressible continuous medium for the complete system of Navier-Stokes equations, an initial-boundary-value problem is proposed that describes complex three-dimensional unsteady flows of viscous compressible heat-conducting gas in ascending swirling heat fluxes. Using explicit difference schemes and the proposed initial-boundary conditions, approximate solutions of the Navier-Stokes system of equations are constructed and the thermodynamic characteristics of three-dimensional unsteady gas flows are numerically determined. The calculation results showed that in the process of formation of fiery vortices, it is formally possible to distinguish several stages. The calculations of the thermodynamic characteristics of gas flows during heating of the underlying surface by several local sources showed that the selected mathematical model under the corresponding initial and boundary conditions allows numerical experiments to describe the arising of complex unsteady three-dimensional flows.

Dependence of energy characteristics of ascending swirling air flow on velocity of vertical blowing

In the model of a compressible continuous medium, for the complete Navier-Stokes system of equations, an initial boundary problem is proposed that corresponds to the conducted and planned experiments and describes complex three-dimensional flows of a viscous compressible heat-conducting gas in ascending swirling flows that are initiated by a vertical cold blowing. Using parallelization methods, three-dimensional nonstationary flows of a polytropic viscous compressible heat-conducting gas are constructed numerically in different scaled ascending swirling flows under the condition when gravity and Coriolis forces act. With the help of explicit difference schemes and the proposed initial boundary conditions, approximate solutions of the complete system of Navier-Stokes equations are constructed as well as the velocity and energy characteristics of three-dimensional nonstationary gas flows in ascending swirling flows are determined.

Numerical Simulation of Fire Vortices with Consideration of Gravity and Coriolis Forces

Numerical simulation of the swirled air flow around a fluently heated vertical cylindrical domain was performed under the influence of gravity and Coriolis forces. Solutions were obtained for the complete system of Navier-Stokes equations with constant coefficients of viscosity and thermal conductivity; together with initial and boundary conditions, they describe complicated nonstationary three-dimensional flows of compressible heat conducting gas. All gasdynamic parameters (density, temperature, and three components of gas velocity for various moments of time at the initial stage of air flow formation) are calculated with explicit-difference schema. Instantaneous streamlines corresponding to trajectories of particles in appearing flow were plotted. A negative swirling of air flow during heating of the vertical cylindrical domain was established.

Gas Flow in the Capillary of the Atmosphere-to-Vacuum Interface of Mass Spectrometers.

Numerical simulations of a gas flow through a capillary being a part of mass spectrometer atmospheric interface were performed using a detailed laminar flow model. The simulated interface consisted of atmospheric and forevacuum volumes connected via a thin capillary. The pressure in the forevacuum volume where the gas was expanding after passing through the capillary was varied in the wide range from 10 to 900 mbar in order to study the volume flow rate as well as the other flow parameters as functions of the pressure drop between the atmospheric and forevacuum volumes. The capillary wall temperature was varied in the range from 24 to 150 °C. Numerical integration of the complete system of Navier-Stokes equations for a viscous compressible gas taking into account the heat transfer was performed using the standard gas dynamic simulation software package ANSYS CFX. The simulation results were compared with experimental measurements of gas flow parameters both performed using our experimental setup and taken from the literature. The simulated volume flow rates through the capillary differed no more than by 10% from the measured ones over the entire pressure and temperatures ranges. A conclusion was drawn that the detailed digital laminar model is able to quantitatively describe the measured gas flow rates through the capillaries under conditions considered. Graphical Abstract ᅟ.

CALCULATION OF THERMODYNAMIC CHARACTERISTICSOF THE ASCENDING SWIRLING FLOW WITH FIVE SOURCES OF HEATING

Calculations of the thermodynamic characteristics of air flows were carried out when several local sources were heated by the underlying surface. The basic mathematical model is the complete system of Navier-Stokes equations with constant coefficients of viscosity and thermal conductivity when gravity and Coriolis are taken into account. Numerical experiments were carried out using an explicit difference scheme with an appropriate choice of the initial and boundary conditions. The varying local pressure differences found during the calculations lead to the corresponding gas flows both in horizontal and vertical planes.

ACCOUNTING INFLUENCE OF CENTRIFUGAL FORCE IN THE NUMERICAL MODELING OF RISING SWIRLED GAS FLOW

In work the consistent inclusion of centrifugal force in the numerical calculations of three-dimensional gas-dynamic characteristics of the unsteady flow of compressible viscous heat-conducting gas in an upward swirling flow caused by the vertical cold blowing. Provides detailed conversion of the complete system of Navier-Stokes equations associated with consistent view of the centrifugal force. Results of thermodynamic calculations and comparisons, speed and power characteristics of emerging upward swirling flows. There was a slight influence of the centrifugal force on the basic parameters of the gas-dynamic study of complex flows of gas.

Modeling of methane steam reforming in a microchannel subject to multicomponent diffusion

Catalytic methane steam reforming in a slot microchannel under external heat supply to the mixture reacting on walls is considered based on numerical simulation of a complete system of Navier-Stokes equations. Three ways of heat supply to channel walls are represented, namely, a uniform heat flux, a heat flux linearly decreasing in channel length, and a heat flux following the reaction rate profile of the main reaction. The thermophysical parameters of the mixture depend on its temperature and composition. Two diffusion models are considered, namely, models with equal and different diffusion coefficients for each mixture component. It is shown that consideration of multicomponent diffusion does not practically affect the concentration of the components and the methane reforming at the outlet. For the above-mentioned ways of heat supply, the methane reforming with a heat flux linearly decreasing in channel length is most significant.

The special features of heat transfer in a supercritical fluid: Mathematical and physical modeling results

The special features of heat transfer in a supercritical fluid were considered for the example of two problems, those of Rayleigh-Benard convection in a horizontal layer heated from below and nonstationary heat transfer in a closed volume with heated boundaries. Isentropic equilibrium of a compressible medium that obeyed the van der Waals equation of state was studied. The calculation results were generalized, and the special features of convective heat transfer in a supercritical fluid beyond the stability threshold of hydrostatic equilibrium were discussed. The results of numerical and experimental studies of the relaxation of density and temperature nonuniformities as the temperature of volume walls changed were presented. The calculations were performed using the complete system of Navier-Stokes equations and the equation of state of an ideal or van der Waals gas.

Direct numerical simulation of the laminar-turbulent transition in a thick spherical layer

The results of a numerical study of the laminar-turbulent transition in unsteady isothermal three-dimensional flows of viscous incompressible fluid in a thick spherical layer between counter-rotating spherical boundaries are presented. The calculations are performed for the governing parameters corresponding to the experimental data [1, 2]. The numerical investigations include both solving the complete system of Navier-Stokes equations and analyzing the linear stability of steady-state axisymmetric flows with respect to three-dimensional disturbances. A stochastic flow regime is calculated for the first time. The limits of existence of different flow regimes and the hysteresis regions are found. The spatial flow patterns and frequency characteristics are obtained, which makes it possible to extend and refine the existing experimental data.

Hypersonic Flow Past the Spherical Nose of a Body in the Presence of a Magnetic Field

The hypersonic flow past the nose of a spherical body containing current sources generating a magnetic field is investigated theoretically and numerically. The magnetohydrodynamic (MHD) flow is analyzed on the basis of the complete system of Navier-Stokes equations containing the force and thermal MHD terms and the electrodynamic equations. Local and integral thermal and aerodynamic characteristics of the body are found. It is shown that the presence of a magnetic field makes it possible to reduce the heat flow to the body in the neighborhood of the stagnation point by several times. However, in this case the total body drag increases.

Theoretical and Numerical Investigation of Gas Lubrication Processes on the Basis of Aerodynamic Equations

The dimensionless parameters of the complete system of Navier-Stokes equations of a compressible gas are estimated with reference to a typical gas bearing. It is found that the three-dimensional compressible boundary layer equations should be used as the determining equations for describing gas lubrication processes. After introducing certain assumptions with respect to the dimensionless parameters in the determining equations, an equation for the pressure, the generalized Reynolds equation, is obtained. Use of the spectral method of analysis makes it possible to transform the generalized Reynolds equation into a system of ordinary differential equations. An analytic solution of the entire boundary value problem is obtained for a journal bearing with fairly small eccentricity. By comparing the numerical results obtained using both the solution of the generalized Reynolds equation and the traditional theory it is possible to estimate the effect of the inertia forces, dissipation processes, and heat transfer.

Comparison of the Calculated Results for Hypersonic Flow Past Blunt Bodies with the OREX Flight Test Data

The physico-chemical hypersonic air flow model is verified for the conditions of the experimental vehicle OREX reentry path over the altitude range H = 84 –105 km. The calculations are performed on the basis of both the viscous shock layer equations and the complete system of Navier-Stokes equations. The temperature and chemical component concentration fields calculated within the framework of the two models are in good agreement for H ≤ 100 km (Re∞ ≥ 300). The numerical results for the heat flux at the stagnation point and the electron concentration agree well with the flight test data over the entire altitude range considered.