Numerical study of unsteady rarefied diatomic gas flows in a plane microchannel

The numerical solution of a kinetic equation for a diatomic gas (nitrogen) is used to study two-dimensional unsteady gas flows in a plane microchannel caused by discontinuous in the initial distributions of macroscopic gas parameters. The plane discontinuity fronts are perpendicular to the walls of the channel. The arising flows are model ones for gas flows in a shock tube and a microchannel. The reflection of an incident shock wave from a flat end face is studied. It is found that the gas piles up at the cold wall, which slows down the shock wave detachment. The numerical results are in qualitative agreement with experimental data.     

Simulation of stochastic pulsating flows with instabilities using minimum-stencil difference schemes

Pulsating flows with contact discontinuity instabilities and generated regions of turbulent-like gas parameter fluctuations were numerically simulated. The flows were driven by the interaction of an infinite heated rarefied channel with a shock layer. Pulsating flow regimes were analyzed for an energy source located symmetrically or asymmetrically relative to the body. Averaged steady flows characterized by stagnation point oscillations about a new position at the end face were examined, and steady-state flow structures with gas parameter nonmonotonicities near the body end face were studied. The simulation was based on minimum-stencil modified schemes.     

Conditions for shockless state of the vortex flow in two-dimensional laval nozzles : PMM vol. 37, n6, 1973, pp. 1040–1043

Conditions given in [1, 2] for the absence of shocks in the flow in the vicinity of the center of a nozzle for two-dimensional vortex-free flows of an ideal gas are generalized to the case of rotational flows. Both continuous flows and flows with shock waves are constructed.     

Unidirectional flows of viscoelastic fluids and their gasdynamic counterparts

We have shown that unidirectional flows of viscoelastic fluids are mathematically equivalent to plane potential flows of a fictitious gas. The classification of type and some exact solutions of the equations describing fictitious gas flows are presented. The Prandtl-Mayer flow and its viscoelastic counterpart is discussed in more details in connection with the Sternberg-Koiter paradox.     

Kinetic model of the Boltzmann equation for a power-law intermolecular interaction potential

A model kinetic equation approximating the Boltzmann equation with a linearized collision integral is constructed to describe rarefied gas flows at moderate and low Knudsen numbers. The kinetic model describes gas flows with a power-law intermolecular interaction potential and involves five relaxation parameters. The structure of a shock wave is computed, and the results are compared with an experiment for argon.     

Nonlinear nonequilibrium kinetic model of the boltzmann equation for monatomic gases

A model kinetic equation approximating the Boltzmann equation in a wide range of nonequilibrium gas states was constructed to describe rarefied gas flows. The kinetic model was based on a distribution function depending on the absolute velocity of the gas particles. Highly efficient in numerical computations, the model kinetic equation was used to compute a shock wave structure. The numerical results were compared with experimental data for argon.     

Implicit multiblock method for solving a kinetic equation on unstructured meshes

A parallel multiblock implementation of a second-order accurate implicit numerical method based on solving a model kinetic equation is proposed for analyzing three-dimensional rarefied gas flows. The performance of the method is illustrated by computing test examples of gas flows in a circular pipe in a wide range of Knudsen numbers. The convergence rate and scalability of the method are analyzed depending on the number of blocks in the spatial grid.     

Modeling of flow separation of assist gas as applied to laser cutting of thick sheet metal

The present paper describes the results of mathematical modeling of supersonic flows of a viscous compressible gas, obtained by numerically solving three-dimensional full Navier–Stokes equations, and also the results of experiments with visualization of gas jet flows in channels geometrically similar to the laser cut. Separation of the gas flow from the cut front is predicted numerically and then validated by experiments on a model setup. The gas flow structure arising in a narrow channel behind a sonic (conical) or supersonic nozzle is described. Specific features of originating in the flow separation on a smooth surface in a narrow channel are examined, and mechanisms controlling the separation are proposed. Flow separation directly affects the changes in the shape and structure of striations and is the one of main reason for the worse quality of the laser cut surface. It is shown that the changes in the structures of striations over the thickness of the sheet being cut are closely related to aerodynamic features of jet flows of the assisting gas in the cut channel.     

Kinetic model of the Boltzmann equation for a diatomic gas with rotational degrees of freedom

A system of model kinetic equations is proposed to describe flows of a diatomic rarefied gas (nitrogen). A conservative numerical method is developed for its solution. A shock wave structure in nitrogen is computed, and the results are compared with experimental data in a wide range of Mach numbers. The system of model kinetic equations is intended to compute complex-geometry three-dimensional flows of a diatomic gas with rotational degrees of freedom.     

Subsonic non‐isentropic ideal gas with large vorticity in nozzles

This paper investigates the steady subsonic inviscid flows with large vorticities through two‐dimensional infinitely long nozzles. We establish the existence and uniqueness of the smooth subsonic ideal flows, which are governed by a two‐dimensional complete Euler system. More precisely, given the horizontal velocity with possible large oscillation and the entropy of the incoming flows at the entrance of the nozzles, it was shown that there exists a critical value; if the mass flux of the incoming flows is larger than the critical one, then there exists a unique smooth subsonic polytropic gas through the given smooth infinitely long nozzles. Furthermore, the maximal speed of the flows approaches to the sonic speed, as the mass flux goes to the critical value. The results improve the previous work for steady subsonic flows with small vorticities and for subsonic irrotational flows and indicate that the large vorticity is admissible for the smooth subsonic ideal flows in nozzles. This paper gives a rigorous proof to the well posedness of the smooth subsonic problem first posed back in the basic survey of Lipman Bers for inviscid flows with large vorticities. John Wiley & Sons, Ltd.     

Implicit numerical method for computing three-dimensional rarefied gas flows on unstructured meshes

The method based on the numerical solution of a model kinetic equation is proposed for analyzing three-dimensional rarefied gas flows. The basic idea behind the method is the use of a second-order accurate TVD scheme on hybrid unstructured meshes in physical space and a fast implicit time discretization method without iterations at the upper level. The performance of the method is illustrated by computing test examples of three-dimensional rarefied gas flows in variously shaped channels in a wide range of Knudsen numbers.     

Time averaging as an approximate technique for constructing quasi-gasdynamic and quasi-hydrodynamic equations

Quasi-gasdynamic and quasi-hydrodynamic equations for compressible gas flows and viscous incompressible fluid flows are constructed by averaging the corresponding Navier-Stokes equations over time with the use of certain approximations.     

带激波的一维非定常两相流动的数值模拟

本文将处理带激波的单相气体非定常流动问题的两种高分辨数值方法(随机取样法和二阶GRP有限差分法)推广应用于气固悬浮体(亦称含灰气体)两相情况,计算了含灰气体激波管中两相激波特性、波后流场结构及气固两相流动参数随时间的变化.数值结果表明:这两种方法均能给出带有尖锐间断阵面的两相激波松弛结构.二阶GRP方法在计算精度和机时耗用等方面优于随机取样法.     

The non-stationary invariant solution of the equations of gas dynamics describing the spreading of a gas into a vacuum

An invariant solution of the equations of gas dynamics, constructed on a one-dimensional subgroup (according to the classification in /1/) which is only allowed in the case of a polytropic gas with a special adiabatic index, is considered. The gas spreads out into a vacuum after a finite time. New solutions are constructed which describe one-dimensional flows from a source into a vacuum and the focussing of the gas within a sphere or a cylinder with shock waves. The spreading of a concentration of the gas with an arbitrary boundary when there is a contact discontinuity is also considered.

One-dimensional flows have been treated in detail in /2, 3/, mainly in the case of extended subgroups.     

On the complexity of instationary gas flows

We study a simplistic model of instationary gas flows consisting of a sequence of $k$ stationary gas flows. We present efficiently solvable cases and NP-hardness results, establishing complexity gaps between stationary and instationary gas flows (already for $k=2$) as well as between instationary gas $s$-$t$-flows and instationary gas $b$-flows.     

The problem of obtaining prescribed distributions of gas parameters

Using one-dimensional cylindrically and spherically symmetric flows as examples, the following problem is investigated in which a prescribed density distribution in a gas is obtained: given a known gas flow (background flow), it is required to continuously attach another, unknown gas flow whose density distribution at a fixed instant of time is described by some previously given function. It is shown that this problem is a characteristic Cauchy problem of standard type for which there is a valid analogue of the Kovalevskaya theorem, provided that the input data are analytic. Other problems of the same type are considered: to ensure that the unknown flow will have a prescribed gas velocity distribution and the prescribed density of the gas in the unknown flow is strictly greater than that of the gas in the background flow (flow with discontinuity). On the assumption that the input data to these problems are analytic, the existence and uniqueness of solutions are proved, in fact—of piecewise analytic solutions. The theorems proved are extended to the case of non-one-dimensional flows.     

Mathematical modeling of shock-wave processes under gas solid boundary interaction

The results of numerical simulations are presented for planar air flows in a bounded volume of square cross section diminishing due to a uniform motion of the walls, for a flow of a propane-air mixture under sinusoidal variation of the size of the square domain, and for three-dimensional supersonic air and propane-air flows in channels of variable square cross section. Specific features of shock-wave processes that are associated with the piston effect and cumulation are established. The hypersonic analogy between planar and spatial flows is confirmed, which allows one to use two-dimensional solutions in estimating three-dimensional flows. The equations of a multicomponent ideal perfect gas and one-stage kinetics of chemical reactions are used to describe the flows. The method of numerical simulations is based on S.K. Godunov’s scheme and implemented within an original software package.     

On Some Finite Difference Scheme for Gas Dynamics Equations

A conservative difference scheme with linear dependence of the pressure on the density of gas is proposed for gas dynamics equations. The scheme allows us to simulate 1-D flows inside a cylindrical domain with time-variable cross-sections and guarantees the positive sign of the density function.     

A minimum-stencil difference scheme for computing two-dimensional axisymmetric gas flows: Examples of pulsating flows with instabilities

A minimum-stencil difference scheme for computing two-dimensional axisymmetric gas flows is described. The scheme is explicit, conservative, and second-order accurate in space and time. The numerical results obtained for pulsating flows and contact discontinuity instabilities are discussed. The mechanisms of flow pulsation and instability generation are described.