Flow Of 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.

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.

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.

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.

Energy exchange in a compressible turbulent mixing layer

Asymptotic methods have been used to study a turbulent flat mixing layer comprising a viscous compressible gas flow descending from the trailing edge of a body and a gas at rest having the same chemical composition but a different temperature. In contrast to the existing methods for analysing turbulent flows using the Reynolds-averaged Navier-Stokes (RANS) equations, with some closure hypotheses, this paper considers the Navier-Stokes equations using known classic assumptions and facts. The characteristic Reynolds number of the flow is considered large, the thickness of the mixing layer is small, and the Mach numbers are limited within the range of ‘0–5’. The method of multiple scales allows a stationary (secondary) flow inside the turbulent mixing layer to be found and investigated as a principal part of the fluctuating solution. It is shown that the self-induced entrainment of gas from the external flow into the mixing layer is the main stationary flow that ensures the supply of kinetic energy from the zone of maximum speed to the turbulence generation area. It is also discovered that heat diffusion and the inflow of high-velocity gas from the external flow together determine the properties of the mixing layer. The Kolmogorov-scale and turbulence generation regions do not influence the stationary solution in the main approximation.

Gas Flow in Microchannels and Nanochannels With Variable Cross Section for All Knudsen and All Mach Number Values

AbstractThe analytical solution for steady viscous pressure-driven compressible isothermal gas flow through micro- and nanochannels with variable cross section for all Knudsen and all Mach number values is presented in this paper. The continuum one-dimensional governing equations are solved using the friction factor that is established in a special way to provide solutions for mass flow rate, pressure, and velocity distribution through the microchannels and nanochannels in the entire rarefaction regime. The friction factor, defined by the general boundary condition and generalized diffusion coefficient proposed by Beskok and Karniadakis (1999, “A Model for Flows in Channels, Pipes, and Ducts at Micro and Nano Scales,” J. Microscale Thermophys. Eng., 3, pp. 43–77), spreads the solution application to all rarefaction regimes from continuum to free molecular flow. The correlation between the product of friction factor and Reynolds number (Poiseuille number) and Knudsen number is established explicitly in the paper. Moreover, the obtained solution includes the inertia effect, which allows the application of the solution to both subsonic and supersonic gas flows, which was not shown earlier. The presented solution confirms the existence of the Knudsen minimum in the diverging, converging, and microchannels and nanochannels with constant cross section. The proposed solution is verified by comparison with experimental, analytical, and numerical results available in literature.

Hyperbolic turbulence models for moment closures

The ten-moment equations of gaskinetic theory provide a first-order hyperbolic model for the treatment of viscous compressible gas flows that is valid both in and out of local thermodynamic equilibrium. Until now, the practical applicability of this model to real-world continuum-regime problems has been limited by the lack of appropriate turbulence models. In this paper, the Reynolds-averaging concept is applied to the ten-moment model. To close the new unknowns generated by this process, a turbulence model is required. However, instead of coupling to traditional RANS models, which require second-order derivatives, a first-order turbulence model is proposed. It is developed by hyperbolizing Prandtl's existing one-equation RANS model. The resulting system is shown to recover the same solution as Prandtl's original model in the appropriate limit. This new first-order turbulence model is in hyperbolic-relaxation form and includes one extra equation per spacial dimension. Unlike the traditional RANS model, this model has the same hyperbolic balance-law form as the ten-moment equations. Solutions of such hyperbolic-relaxation systems exhibit dispersive wave behaviour. To study this, an eigenstructure and dispersion analysis is presented for the new turbulence model coupled to the ten-moment system. The model is then validated by solving a canonical two-dimensional turbulent plane mixing-layer problem. The numerical solution in steady state is compared to experimental measurements at various locations in the flow field.

Limits for Detailed Description of Problems in Continuous Media Mechanics and Numerical Algorithm for Viscous Gas Flow Simulation

A mathematical model for viscous gas flow simulation with time scales bounded by the characteristic time between molecular collisions is considered. This approach is a variant of the quasi-gasdynamic system of equations, which is based on the relationship between the kinetic and macroscopic descriptions of continuous medium motion. Based on the presented model, a numerical algorithm is constructed for modeling viscous compressible gas flows. As an example, the algorithm is used to study some features of inhomogeneous flow around a blunt body.

Self-similar and non self-similar turbulent flow of viscous compressible gas inside a conical diffuser

Self-similar and non self-similar turbulent flow of viscous compressible gas inside a conical diffuser

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.

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 Study of the Supersonic Base Flow around Aircraft Model

This paper deals with a numerical study of the base part of the supersonic flow past an aircraft model. The simulation was carried out using the software developed by the authors for calculating 3D turbulent flow of viscous compressible gas in the framework of the unsteady Reynolds averaged Navier–Stokes equations (URANS) with the Spalart–Allmaras (SA) and Menter’s SST turbulence models. Flight modes with M = 2.5 and angle of attack α = 0°, 3° were considered. A comparison is made of the effect of the choice of the turbulence model on the base flow.

Space-time discontinuous Galerkin method for the numerical simulation of viscous compressible gas flow with the k-omega turbulence model

In this article we deal with the numerical simulation of the non-stationary compressible turbulent flow described by the Reynolds-Averaged Navier-Stokes (RANS) equations. This RANS system is equipped with two-equation k-omega turbulence model. The discretization of these two systems is carried out separately by the space-time discontinuous Galerkin method. This method is based on the piecewise polynomial discontinuous approximation of the sought solution in space and in time. We use the numerical experiments to demonstrate the applicability of the shown approach. All presented results were computed with the own-developed code.

THE SECOND PROJECTION OF THE MOTION EQUATION IN THE CYLINDRICAL COORDINATE SYSTEM

The complex flows of viscous compressible heat-conducting gas arising during heating the vertical field, have a pronounced axial symmetry. Therefore, for the numerical solution of the complete Navier-Stokes equations system to describe such gas flows it is advisable to use a cylindrical coordinate system. This paper describes a transformation of the second projection of the motion equation of the complete Navier-Stokes equations system. The result of this transformation is writing of the second projection of the equation of a continuous medium motion in the cylindrical coordinate system.

Numerical study of a quasi-hydrodynamic system of equations for flow computation at small mach numbers

The applicability of numerical algorithms based on a quasi-hydrodynamic system of equations for computing viscous heat-conducting compressible gas flows at Mach numbers M = 10–2–10–1 is studied numerically. The numerical algorithm is briefly described, and the results obtained for a number of two- and three-dimensional test problems are presented and compared with earlier numerical data.

Preconditioning of gas dynamics equations in compressible gas flow computations at low mach numbers

Features of the simulation of low-velocity inviscid and viscous compressible gas flows are considered, and a finite-volume discretization of gas dynamics equations at low Mach numbers on unstructured meshes is discussed. Preconditioning based on the use of physical variables is used to speed up the convergence of time marching to a steady state and to improve the accuracy of the steady-state solution. The structure of the preconditioning matrix and the diagonalization of the Jacobian of the preconditioned system of equations are discussed. The capabilities of this approach are demonstrated using model gasdynamic simulations ing a wide range of Mach numbers.

Construction of Godunov-Type Difference Schemes in Curvilinear Coordinates and an Application to Spherical Coordinates

A method is proposed for the construction of conservative flow difference schemes for the calculation of compressible viscous gas flows in curvilinear coordinates based on an arbitrary Godunov-type Cartesian scheme. The realization of the scheme in curvilinear coordinates requires minimal additions to the basic Cartesian scheme code. The method is illustrated in application to the case of spherical coordinate. A spherical scheme of second-order spatial approximation is constructed. Results of test calculations are reported.

Simulation of laminar–turbulent transition in compressible Taylor–Green flow basing on quasi-gas dynamic equations

We report the results of numerical simulation of laminar–turbulent transition in the Taylor–Green vortex for viscous compressible gas flow basing on quasi-gas-dynamic (QGD) equations. Here the QGD system is obtained by a temporal averaging of the Navier–Stokes equations. The additional dissipative terms in QGD system serve to model the effects of the unresolved subgrid scales. Comparison with direct numerical simulation and large eddy simulation reference data demonstrates that QGD numerical algorithm provides a uniform and adequate simulation of both laminar and turbulent evolution of the vortex for Reynolds numbers from 100 up to 5000, including transition.

Method for the Construction of Godunov-Type Difference Schemes in Curvilinear Coordinates and its Application to Cylindrical Coordinates

A method is proposed for the construction of conservative flow difference schemes that compute compressible viscous gas flows in curvilinear coordinates based on an arbitrary Cartesian Godunov-type scheme. The method is designed for easy use in the sense that the implementation of the scheme in curvilinear coordinates requires only minimal additions to the program code of the basic Cartesian scheme. The scheme construction procedure is illustrated for the case of cylindrical coordinates. A cylindrical scheme is constructed to second order approximation in space. Results of test calculations are reported.