Viscous Compressible Gas Research Articles

CFD Analysis of Gas-Dynamic and Heat Transfer Processes in a Propulsion System Using Polymer Fuel

In the presented work, a computer model of thermodynamic and gas-dynamic processes in a rocket engine of a new type, which uses solid polymers as fuel is considered. The design feature is the presence of a central body - a gasification chamber, where solid polymer fuel is decomposed into volatiles. To conduct the research, a preliminary thermodynamic analysis of the combustion of gasification products was carried out. Based on the results of the thermodynamic analysis using the mathematical model of the turbulent flow of viscous compressible gas, the processes of gas dynamics and heat transfer in the chamber and nozzle of the rocket engine were simulated. Analyses are made for the geometry of a real experimental sample of a polymer-fueled rocket engine developed at Oles Honchar Dnipro National University (Ukraine), which has passed the first successful tests. As a result of CFD simulation, dynamic and thermal fields in the combustion chamber and engine nozzle were obtained, and ways of further improvement of the design were determined.

Numerical Studies of the Influence of the Nature of the In-Chamber Flow on the Initial Period of Operation of the Gas Generator

The ignition of a fuel pellet in a gas generator chamber is a time-consuming complex physico-chemical process. During the ignition of the checker, the operating conditions of the device differ significantly from the conditions of its operation in the main area of operation. In particular, an important characteristic of the initial stage is the pattern of flame propagation over the surface of the fuel. A computational algorithm for modeling unsteady turbulent flows of compressible viscous gas based on numerical integration of unsteady equations obtained using physical conservation laws was used to study the vortex flow of gas in the gas generator path and the ignition process of the fuel block. The method used a system of equations written in a cylindrical coordinate system. The computational algorithm is based on a modified flow vector splitting scheme (Steger – Warming scheme). The algorithm has the 2nd order of accuracy in space. The obtained results of numerical simulation of the gas flow in the gas generator allow us to investigate the patterns of development of the ignition process of the fuel block in time, depending on the nature of the gas flow in the combustion chamber.

Modeling Object Motion on Arbitrary Unstructured Grids Using an Invariant Principle of Computational Domain Topology: Key Features

This paper uses a finite volume algorithm to address the numerical modeling of fluid flow around moving bodies. The Navier–Stokes equations, which describe the flow of viscous compressible gas, along with key boundary conditions and discretization schemes, are presented. As the motion of boundaries typically leads to changes in the control volumes, the basic discretization schemes need to be adapted. This paper provides a detailed discussion on the adaptation of the initial system to deforming boundaries while preserving communication topology. The method for calculating the boundary velocity is a crucial element of the numerical scheme. The paper proposes an approach to reconstruct the boundary velocity vector using deformation analysis and the condition of geometric conservation. This approach ensures correct simulation results for arbitrary unstructured computational grids. A comparison of two approaches to reconstructing the boundary velocity vector for characteristic aviation problems in the direct formulation is presented. It is shown that the proposed approach allows for more accurate modeling of object motion on arbitrary grids using the “invariant” principle of the computational domain topology.

NUMERICAL SIMULATION OF THE FLOW AROUND AN AIRFOIL TYPE TRANSPORT VEHICLE NEAR THE GROUND

The problem of modeling the flow around an airfoil type transport vehicle near the ground is considered. The flow around the vehicle is turbulent. Nowadays, the most advanced mathematical models of aerodynamics are based on the physical properties of a viscous compressible gas and are based on the Reynolds-averaged Navier – Stokes equations. Mathematical modeling of turbulent flows remains one of the most challenging problems. Reliable prediction of the characteristics of turbulent flows is an extremely important scientific problem. This is due to the complexity and insufficient study of turbulence as a physical phenomenon. The aim of this work is to build a mathematical model, a numerical method, an algorithm for solving the problem, and to develop software for studying the aerodynamic characteristics of a vehicle of the airfoil type. To close the Reynolds-averaged Navier –Stokes equations, the one-parameter Spalart – Allmaras turbulence model was used. The initial system of differential equations is written in a curved coordinate system. The initial and boundary conditions for the flow parameters are formulated. The methodology, algorithm for solving the problem, and software are developed. The finite-volume method was used for numerical integration of the system of differential equations. The problem was solved in a multi-block formulation. The developed methodology of algorithms and a set of programs were tested on standard aerodynamic problems: the flow around a transversely placed circular cylinder and a ball. Numerical modeling of the flow of compressed gas around a vehicle moving near the ground was performed. All calculations were carried out for the Reynolds number Re=1,0*10^6 and the Mach number M=0,4. Numerical simulations were performed on a curved multi-block grid. The influence of the ground on the characteristics of the flow around the vehicle was investigated. The studies have shown that the presence of a nearby ground has a significant impact on the flow characteristics around the vehicle. Thus, in order to ensure the required parameters of vehicle dynamics near the ground, it is necessary to take into account the influence of the ground on its aerodynamic characteristics.

Point Source-Induced Spherically Symmetric Flow of a Viscous Heat-Conducting Compressible Perfect Gas

Point Source-Induced Spherically Symmetric Flow of a Viscous Heat-Conducting Compressible Perfect Gas

Parameters to Assess the Operation of Thrust Vector Control Systems in Jet Engines

This paper discusses the parameters for evaluating the effectiveness of various methods of controlling the thrust vector of jet engines. An approach to the multi-parametric optimization of the nozzle structure and the parameters of jet injection into the supersonic flow is developed. The approach is based on a numerical model for a turbulent flow of a viscous compressible gas. A classification of parameters is proposed for evaluating methods for controlling the thrust vector of jet engines.

Analysis of an alternative Navier–Stokes system: Weak entropy solutions and a convergent numerical scheme

We consider an alternative Navier–Stokes model for compressible viscous ideal gases, originally proposed in [M. Svärd, A new Eulerian model for viscous and heat conducting compressible flows, Physica A 506 (2018) 350–375.] We derive a priori estimates that are sufficiently strong to support a weak entropy solution of the system. Guided by these estimates, we propose a finite-volume scheme, derive the analogous estimates and demonstrate grid convergence towards a weak entropy solution. Furthermore, this existence proof is valid for “large” initial data and no a priori assumptions on the solution are needed.

RANS-based numerical simulation of shock wave/turbulent boundary layer interaction induced by a blunted fin normal to a flat plate

Results of refined RANS-based numerical simulation of shock wave/turbulent boundary layer interaction induced by a blunted fin mounted on a flat plate are presented. The RANS equations for compressible viscous gas flow closed by a (varied) eddy-viscosity turbulence model were solved using the finite volume method implemented in the unstructured-grid parallelized in-house code SINF/Flag-S developed at the SPbPU. Detailed numerical data concerning time-averaged characteristics of the separation region and the shock wave/turbulent boundary layer interaction are acquired, including identification of the horse-shoe vortices and their influence on the pressure and shear stress distributions on the streamlined surfaces. A thorough comparison with measurements presented in literature were conducted. Methodical data on the influence of grid resolution and turbulence model on the predicted structure of the viscous-inviscid interaction are obtained and recommendations for achieving a high-quality resolution of the viscous effects and the complex shock-wave pattern of the flow are worked out.

Numerical modeling of unsteady subsonic flow over the conical shape body

The article presents the results of a numerical study of the unsteady vortex motion of gas arising over the conical body with a segmental bottom surface for various angles of attack in a subsonic flow regime. The simulation is based on the viscous compressible gas model (Navier–Stokes model). For various attack angles, the patterns of vortex flow around the conical surface of the body, in the area of its conjugation with the segmental bottom surface and in the near wake are presented. Data on non-stationary behavior and the magnitude of pressure in the conjugation area are given. For numerical simulation the method of finite volumes is used. Taking into account phenomena of the flow separation, the computational grids used have condensation to the surface of the body. Numerical calculations were carried out on the basis of parallel algorithms of the method and were realized on multiprocessor computing complexes.

Сопоставление математических моделей динамики электрически заряженных газовзвесей для различных концентраций дисперсной компоненты

This work is devoted to mathematical modeling of the dynamics of inhomogeneous electrically charged media. A dusty environment - solid particles suspended in a gas – was considered as an inhomogeneous medium. The mathematical model implemented a continuous approach to modeling the dynamics of inhomogeneous media. The complete hydrodynamic system of equations was solved for each component. The system of equations for the dynamics of each component included the equations of mass continuity, momentum components, and the energy conservation equation for the mixture component. Intercomponent interaction took into account momentum exchange and intercomponent heat transfer. The carrier medium was described as a viscous compressible heat-conducting gas. The flow was described as a flow with a two- dimensional geometry. The equations of the mathematical model were supplemented with initial and boundary conditions. The mathematical model took into account the wall viscosity in the channel. The system of equations of the mathematical model was integrated by McCormack's explicit finite-difference method. To obtain a monotonic grid function, a nonlinear scheme for correcting the numerical solution was used. The mathematical model was supplemented by the Poisson equation describing the electric field formed by charged dispersed particles. Poisson's equation was integrated by finite-difference methods on a gas-dynamic grid. Such a choice of the computational grid was necessary to calculate the concentration of particles required both for solving the electric field equation and for calculating the physical fields of the dynamics of inhomogeneous media. The reciprocal motion of a gas suspension caused by the movement of dispersed particles under the action of the Coulomb force was numerically investigated. The values of the surface and mass densities are determined, at which the models of the surface and mass densities of charges in the simulation of such a process are the same. It is revealed that the surface and mass models of charges are identical with respect to the volumetric content.

Турбулентные течения газа в каналах различных форм поперечного сечения с массоподводом

The issues of mathematical modeling of turbulent flows in channels with blowing of different cross-sectional shapes are considered. As a result of a series of computational experiments using the OpenFoam tools, the influence of the channel shape on the realized features of flows is investigated. A mathematical model of conjugate heat transfer for the channels under consideration is proposed. Comparison of the results of numerical simulation with the known experimental data has shown the correctness of the proposed models, schemes and algorithms. The topological features of the structure of viscous compressible heat-conducting gas flow in the channels with mass flow of complex shapes have been studied, including the features of the velocity profiles formed in the outlet sections of the channels, the results of calculating the coefficient of non-uniformity of velocity have been described.

Исследование акустических характеристик одиночной сверхзвуковой струи, истекающей в затопленное пространство

In this paper, the acoustic characteristics of a single supersonic jet flowing from a nozzle of a rocket engine into a flooded space at different pressure ratios are studied. A system of the Favre-averaged Navier-Stokes equations is used to describe the unsteady flow of a viscous compressible heat-conducting gas in a supersonic Laval nozzle and an outflowing jet. The system is enclosed by the ideal gas law. The implementation of the physical and mathematical model and the numerical studies are carried out using the OpenFOAM Extended open platform based on the modified dbnsTurbFoam solver. A conical nozzle with an opening angle of 45° at the Mach number of 3 at the nozzle exit is considered in this study. Air is used as the working gas. Amplitude-frequency spectra of acoustic radiation at the point located at a distance from the nozzle outlet are obtained at different pressure ratios of the outflowing supersonic jet. Analysis of the amplitude-frequency characteristics of the jet under study shows that the maxima occur mainly at low frequencies. The maximum oscillation amplitude for the considered jet configurations is revealed at a pressure ratio of 1 on a frequency of 787 Hz. The maximum sound pressure level is 149 dB.

Coupled heat transfer in the cavity of constant volume with pulse-periodical energy supply

The possibilities of organizing a repetitively pulsed process with given frequency characteristics in a cavity of constant volume with an external energy supply to the working gas mixture are considered. Modelling of gas-dynamic and thermal processes is carried out using the numerical solution of the conjugate heat transfer problem. The gas medium is described on the basis of a viscous compressible gas model. To find the temperature field in the walls of the structure, the equation of non-stationary heat conduction is solved. The conjugation of temperature fields in a gas and a solid is carried out using an iterative procedure. In the calculations, the geometrical parameters of the cavity, the density of the energy supply, the initial pressure, and the composition of the working mixture are varied. The results of calculations obtained in the framework of the one-dimensional and two-dimensional formulation of the problem under the action of both a single pulse and a series of pulses are compared. The results obtained demonstrate the possibility of implementing the required frequency characteristics of the process for given geometric and energy parameters. Keywords: pulse-periodical energy process, gas laser, coupled heat transfer, numerical simulation, energy supply, pulse.

Сопряженный теплообмен в области постоянного объема при импульсно-периодическом подводе энергии

The possibilities of organizing a repetitively pulsed process with given frequency characteristics in a cavity of constant volume with an external energy supply to the working gas mixture are considered. Modelling of gas-dynamic and thermal processes is carried out using the numerical solution of the conjugate heat transfer problem. The gas medium is described on the basis of a viscous compressible gas model. To find the temperature field in the walls of the structure, the equation of non-stationary heat conduction is solved. The conjugation of temperature fields in a gas and a solid is carried out using an iterative procedure. In the calculations, the geometrical parameters of the cavity, the density of the energy supply, the initial pressure, and the composition of the working mixture are varied. The results of calculations obtained in the framework of the one-dimensional and two-dimensional formulation of the problem under the action of both a single pulse and a series of pulses are compared. The results obtained demonstrate the possibility of implementing the required frequency characteristics of the process for given geometric and energy parameters.

Nonlinear dynamics for the 3D ideal viscous gas flow over the cylinder

The system of governing equations for the dynamics of the compressible viscous ideal gas is considered in the 3D bounded domain with the inflow and outflow boundary conditions. The cylinder is located in the domain. Such problem is simulated using the high order WENO-scheme for inviscid part of the equations and using 4-th order central approximation for the viscous tensor part with the third order temporal discretization.The method of Proper Orthogonal Decomposition (POD) is applied to the problem at hand in order to extract the most active nodes. Cascades of bifurcations of periodic orbits and invariant tori are found that correspond to the excitation in different POD modes. The approximation of the reduced order model is analyzed and it is shown that one cannot make parameter extrapolations for the reduced order model to capture the same dynamics as is observed in the original full size model.

Global existence and asymptotic behavior of solutions for one‐dimensional infrarelativistic model of a compressible viscous gas with radiation

In this paper, under suitable hypotheses on the transport coefficients, we prove the global existence and asymptotic behavior of solutions in (see below for its definition) for the one‐dimensional infrarelativistic model of a compressible viscous gas with radiation. We have improved the previous results in Qin et al. (2014).

Unsteady flow simulation of compressible turbulent flow in dual-bell nozzle with movement of extendible section from its initial to working position

The use of extendible nozzles in propulsion systems is one of the ways to increase the geometric degree of expansion of the nozzle and the thrust. Numerical simulation of a supersonic turbulent flow of a viscous compressible gas in an extendible nozzle is considered. The simulations performed take into account the movement of the extendible part of the nozzle from the its initial to the working position. The Reynolds-averaged Navier–Stokes equations and the equations of the SST turbulence model discretized on moving meshes are used for numerical calculations. The unsteady flowfield formed when the nozzle is brought to the working position is studied, and the topological features of the flow (separation, mixing, reattachment, secondary flow), and the spatial and temporal distributions of flow quantities are investigated. The distributions of pressure at different times and the axial force applied to the inner walls of the nozzle during the outflow of a supersonic underexpanded jet from the nozzle are discussed. The distributions of flow quantities computed with unsteady and quasi-state formulations of the problem are compared.

Multiparameter Optimization of Thrust Vector Control with Transverse Injection of a Supersonic Underexpanded Gas Jet into a Convergent Divergent Nozzle

The optimal design of the thrust vector control system of solid rocket motors (SRMs) is discussed. The injection of a supersonic underexpanded gas jet into the diverging part of the rocket engine nozzle is considered, and multiparameter optimization of the geometric shape of the injection nozzle and the parameters of jet injection into a supersonic flow is developed. The turbulent flow of viscous compressible gas in the main nozzle and injection system is simulated with the Reynolds-averaged Navier–Stokes (RANS) equations and shear stress transport (SST) turbulence model. An optimization procedure with the automatic generation of a block-structured mesh and conjugate gradient method is applied to find the optimal parameters of the problem of interest. Optimization parameters include the pressure ratio of the injected jet, the angle of inclination of the injection nozzle to the axis of the main nozzle, the distance of the injection nozzle from the throat of the main nozzle and the shape of the outlet section of the injection nozzle. The location of injection nozzle varies from 0.1 to 0.9 with respect to the length of the supersonic part of the nozzle; the angle of injection varies from 30 to 160 degrees; and the shape of the outlet section of the injection nozzle is an ellipse with an aspect ratio that varies from 0.1 to 1. The computed fluid flow in the combustion chamber is compared with experimental and computational results. The dependence of the thrust as a function of the injection parameters is obtained, and conclusions are made about the effects of the input parameters of the problem on the thrust coefficient.

Numerical study of the effect of the dispersed particles properties on the electrically charged polydisperse gas suspension dynamics in a channel with electrodes on the walls

In this article the flow of an electrically charged gas suspension in a channel is numerically simulated. It is assumed that the solid component of the gas suspension has a polydisperse composition. Solid component fractions may differ in particle size and density. For the velocity components of the mixture components on the channel surfaces, the Dirichlet boundary conditions were specified, thereby taking into account the wall viscosity. The dynamics of the carrier medium was described by the system of equations of a viscous compressible heat-conducting gas motion. Potentials of different signs are applied to the lateral surfaces of the channel. It was found that due to the action of an electric field, positively charged particles are deposited onto the channel wall with a negative potential. The article studies the effect of particle parameters on the deposition rate of fractions of an electrically charged solid component of the mixture.

Stability of stationary for inflow problem on the coupled compressible Navier–Stokes/Allen–Cahn system

In this paper, we study the large-time behavior of solutions to the Navier–Stokes/Allen–Cahn system of compressible viscous gases in half space. We prove that the corresponding stationary solutions of the small amplitude to the inflow problem for the Navier–Stokes/Allen–Cahn system are time-asymptotically stable. The proof of asymptotic stability is based on the basic energy method.