Viscous Compressible Gas Research Articles

Evaluation of different turbulence models in simulating the subsonic flow through a turbine blade cascade

Numerical simulations of the 2D turbulent flow of a viscous compressible gas through a turbine cascade were carried out. The main objective of this work is to evaluate the capability of different turbulence models in predicting the aerodynamic characteristics of a steady flow. Four turbulence models were considered; Spalart-Allmaras, realizable k-epsilon, k-omega SST, and SST transition model. The numerical results of the profile loss coefficient were compared with the available experimental data. The profile loss coefficient calculated using the SST transition model showed the most accurate agreement with the experimental data.

LARGE EDDY SIMULATION OF ACOUSTIC CHARACTERISTICS OF A SUBSONIC JET OUTFLOWING FROM CONICAL NOZZLE

The calculation of noise generated by a jet of viscous compressible gas flowing out from a conical nozzle is considered. The calculations used the implicit version of the LES (Implicit LES, ILES), in which the role of the subgrid turbulence model performs numerical dissipation used finite-difference scheme. The distributions of the gas-dynamic and acoustic characteristics of the jet upon changing the conditions of its outflow are discussed. The analysis of the modal composition of the received noise is carried out and the correspondence between the features of the received directionality of the noise is determined by its various components and sources. The numerical simulation results are compared with the available experimental and calculated data.

НЕСТАЦИОНАРНОЕ ПОВЕДЕНИЕ ЗАРЯДА ТТ БЕССОПЛОВОГО РДТТ ПОД ДЕЙСТВИЕМ ГАЗОДИНАМИЧЕСКОЙ НАГРУЗКИ

The numerical solution to a conjugate problem of an unsteady flow of combustion products in a flow path of the nozzleless solid rocket motor (SRM) and the oscillation of a solid propellant charge under the action of the forces directed from combustion products is considered. The Navier-Stokes equations for a compressible viscous gas are used to mathematically describe the flow of the combustion products. To model the charge oscillations, the equations of solid mechanics are applied, which take into account the propellant hyperelasticity. Pressure distributions and the propellant burning rate along the charge channel are presented for different models of the propellant burning rate. It is revealed that at the stage of SRM design, the use of the burning rate law, determined by pressure in the head of the combustion chamber, is more preferable in order to assess the internal ballistic characteristics. The solution to the conjugate problem shows that in the nozzleless SRM with the propellant having low Young's modulus, resonance can occur, which causes uncontrolled charge oscillations.

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.

Exact Local Controllability of a Two-Dimensional Viscous Gas Flow

In a two-dimensional bounded domain $$\Omega $$ , we consider the system of Navier–Stokes equations describing the flow of a viscous compressible gas with no allowance for heat exchange with the ambient medium under small variations of density in the equations of motion. We prove the existence of a solution to the problem of exact local controllability of this system by an external force supported in an arbitrary fixed subdomain $$\omega \subset \Omega $$ .

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.

Numerical simulation of a compressible viscous gas flow in solid-fuel rocket engine with a central body

Numerical simulation of a compressible viscous gas flow in solid-fuel rocket engine with a central body

Numerical simulation of the propagation of a shock wave from a neutral and electrically charged dusty medium into a homogeneous gas

In this work, the expansion of a shock wave from a dusty medium into a pure gas is simulated. The carrier medium is described as a viscous compressible and heat-conducting gas. A mathematical model of the dusty medium dynamics allowed for force interaction. Also, the mathematical model took into account inter-component heat transfer. The aim of the work was to study the effect of the electric charge of the dispersed component on the parameters of a shock wave during the passage of a shock wave from an inhomogeneous medium to a homogeneous gas. Differences between processes in neutral and electrically charged dusty media were revealed.

Modeling Thermal Gas Dynamic Processes of the Production of Silicon from Its Halides

A procedure was developed to model the gas-dynamic and thermal conditions of the production of powdered silicon from silicon tetrachloride and tetrafluoride in a high-frequency induction plasma chemical reactor. The model includes a description of the turbulent flow of a mixture of ideal viscous compressible gases while taking into account the induction heating of the gas by conduction, convection, and radiation, as well as taking into account the effect of the electromagnetic force on plasma motion. The powdered particles form according to the results of the thermodynamic calculations, and the particle distribution in the flow is described by the diffusion mechanism. The results of modeling the conversion of volatile silicon chloride and fluoride in a swirl-stabilized high-frequency induction plasmatron are presented.

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.

Weak Solutions for a System Modeling the Movement of a Piston in a Viscous Compressible Gas

We first study the global-in-time existence of strong solutions to a one-dimensional system modeling the movement of a piston in a viscous compressible gas. Moreover, we prove the asymptotic stability of the solution toward a chosen constant state (in the sense that we can impose the final position of the piston, the final densities being fixed by the conservation of mass and the choice of the final position) thanks to a constant force acting in the equation of the point mass whose expression depends explicitly of the chosen final position. The norm of the solution in the function space of the initial data decays exponentially toward this constant state. Then, we prove the existence of weak solutions to this system for initial velocity in the energy state and for the initial density with bounded total variation. The weak solution is unique and also decay exponentially toward the chosen constant state thanks to the same constant force acting on the point mass. We use the result of existence of strong solutions to prove the existence of weak solutions, whereas the result on exponential decay of weak solution is independent of the one for the strong solutions.

The large-time behavior of solutions in the critical Lp framework for compressible viscous and heat-conductive gas flows

The $L^{p}$ theory for non-isentropic Navier-Stokes equations governing compressible viscous and heat-conductive gases is not yet proved completely so far, because the critical regularity cannot control all non linear coupling terms. In this paper, we pose an additional regularity assumption of low frequencies in $\mathbb{R}^d(d\geq 3)$, and then the sharp time-weighted inequality can be established, which leads to the time-decay estimates of global strong solutions in the $L^{p}$ critical Besov spaces. Precisely, we show that if the initial data belong to some Besov space $\dot{B}^{-s_{1}}_{2,\infty}$ with $s_{1}\in (1-\frac{d}{2}, s_0](s_0\triangleq \frac{2d}{p}-\frac{d}{2})$, then the $L^{p}$ norm of the critical global solutions admits the time decay $t^{-\frac{s_{1}}{2}-\frac{d}{2}(\frac{1}{2}-\frac{1}{p})}$ (in particular, $t^{-\frac{d}{2p}}$ if $s_1=s_0$), which coincides with that of heat kernel in the $L^p$ framework. In comparison with \cite{DX2}, the low-frequency regularity $s_1$ can be improved to be \textit{the whole range}.

МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ВЗАИМОДЕЙСТВИЯ СОСТАВНОЙ СВЕРХЗВУКОВОЙ СТРУИ С ПРЕГРАДОЙ

The paper presents the results of the mathematical modeling of a supersonic twin jet interaction with an obstacle for the Mach number of 4.5 specified at the nozzle exit. Mathematical formulation of the problem includes a system of Favre-averaged Navier-Stokes equations and SST turbulence model for a viscous compressible ideal gas. The calculations are carried out using the free software OpenFOAM Extended with the Godunov method employed. The effect of the distance between nozzles on the shock-wave structure of the gas flow and on the force action of the plumes on the obstacle is studied. The distance between the nozzles varied in the range of 0.1−4. It is found that with an increase in the distance from 0.1 to 0.5, the flow structure is significantly rearranged, and two pressure maxima arise, which increase in comparison to the distance of 0.2. A decrease in pressure on the obstacle is observed at the distance over 1.0. For a distance of 4, two pressure maxima occur on the axis of each jet, while the force action of each jet is half as high as the resultant jet force action for a distance of 0.1. The transition from a stationary regime to a self-oscillating one is observed when the distance exceeds the value of 1.5.

Моделирование инфразвукового пистонфона

There are presented the results of numerical simulation of an applied acoustic problem – modeling of gas processes occurring in the measuring chamber of the infrasound pistonphone 3202 at different frequencies of piston oscillation (0.1 – 1000 Hz) and characterized by extremely small Mach numbers (9.1·10-7÷9.1·10-3). The simulation was performed using quasi-gas-dynamic (QGD) and quasi-hydrodynamic (QHD) equations of a viscous compressible heat-conducting gas with the use of a time-explicit difference scheme, all spatial derivatives was approximated by central differences. It is shown that QGD and QHD models can be used for a simulation of applied acoustics and, in particular, to the simulation of infrasonic pistonphone: the stability limits of the QGD and QHD algorithms in this problem were determined, the dependence of sound pressure on the tuning parameter α is investigated and it is shown that this dependence is quite small. The spectra of sound pressure at the control point calculated by QGD and QHD are given, their dependence on the tuning parameter α is shown, both models equally predict the value of the sound pressure amplitude at the fundamental frequency oscillations. At the end of the article, the sound pressure at the control point at the fundamental frequency oscillations obtained by using QGD and QHD is compared with the values calculated by using semi-empirical formula of sound pressure at closed volume for a case of small oscillations using the polytropic index obtained by Henry Gerber instead of the adiabatic coefficient.

Численное исследование скоростного скольжения несущей и дисперсной фазы при взаимодействии ударной волны с электрически заряженной газовзвесью

In this paper, we consider the propagation of a shock wave from a pure gas into a heterogeneous mixture con-sisting of solid particles suspended in a gas and having an electric charge. The applied mathematical model takes into account the speed and thermal interaction of the carrier and dispersed components of the mixture. The mathematical model assumed a monodisperse composition of the solid component of the mixture, that is, it was assumed that all particles have the same linear size, shape and consist of one material. The force interaction of particles and gas included the Stokes force, the strength of the attached masses, as well as the dynamic force of Archimedes. The carrier medium was described as a viscous compressible heat-conducting gas. The equations of the mathematical model were solved by the explicit finite-difference method of the second order of accuracy, using the non-linear correction of the grid function. The system of equations of the mathematical model was supplemented by boundary and initial conditions for the desired functions: at the boundaries of the computational domain, the Dirichlet boundary conditions were set for the velocity components of the carrier and dispersed phase for the remaining dynamic functions Neumann conditions were set. For the Poisson equation describing the distribution of the internal electric field of a charged gas suspension, homogeneous Dirichlet boundary conditions were specified. As a result of numerical calculations, differences were revealed in the velocity slip of the carrier and dispersed phases, in cases where the shock wave propagates into a neutral and electrically charged dusty medium. It was also revealed the effect of particle size on the speed of sliding of the carrier and dispersed components of a heterogeneous mixture during the propagation of a shock wave into a neutral and electrically charged gas suspension.

Interaction Dynamics Problem of a Layer, Being Squeezed, of Viscous Compressible Gas with Elastic Plate

Interaction Dynamics Problem of a Layer, Being Squeezed, of Viscous Compressible Gas with Elastic Plate

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 flow rates in concentrated fire vortices

The article presents the results of numerical simulation of the generation of free fire vortices in the laboratory without the use of special twisting devices. A. Yu. Varaksin, the corresponding member of the Russian Academy of Sciences, in his experimental studies has described the principal possibility of physical modeling of the occurrence of concentrated fire vortices. In the model of a compressible continuous medium for the complete system of Navier — Stokes equations, an initial-boundary value problem has been proposed that describes complex three-dimensional unsteady flows of a viscous compressible heat-conducting gas in ascending swirling heat flows. We has constructed approximate solutions of the complete Navier — Stokes system of equations and has determined velocity characteristics of threedimensional unsteady gas flows initiated by local heating of the underlying surface by nineteen heat sources, using explicit difference schemes and the proposed initial-boundary conditions.

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.