Stability of one-dimensional gas flows in expanding regions

The stability of gas flows produced by the motion of a flat piston or the decay of an arbitrary discontinuity is considered. The boundaries of the region (or regions) in which the development of perturbations is considered are planes (shock wave, contact discontinuity, piston, etc.) which move away from each other.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 112–119, March–April, 1981.     

Stability of plane flows with permeable boundaries

A passive method of flow stability control is proposed. Control is achieved exclusively by varying the boundary conditions for the disturbance on the permeable wall. This passive method is shown to be quite effective for the boundary layer on a flat plate and for Poiseuille flow. In both cases, depending on the structure of the permeable wall, both stabilization and significant destabilization of the flow are possible.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 60–68, September–October, 1992.     

Two-dimensional self-similar flows generated by the interaction between a shock and low-density gas regions

A plane time-dependent flow generated by the interaction between a normal shock and a low-density gas region occupying a quarter of the plane is theoretically investigated. Numerical simulation is performed on the basis of the Euler equations. It is established that after the shock has come in contact with the low-density region two-dimensional self-similar flows of different type can develop. On regular interaction the original shock is refracted on the low-density region with the matching of the accelerated and original shock and the refracted contact discontinuity at a common point. On irregular interaction a complicated flow occurs; it includes curved and oblique shocks, a contact discontinuity with points of inflection, multiple matching points, a high-pressure jet, and a layered vortex. The jet and vortex structures are investigated in detail. The tendency of the gasdynamic structure development with variation in the control parameters of the problem is determined. A simplified, near-analytical technique for estimating the slopes of the main shocks and the gas parameters behind them is proposed.     

Stability of rarefied dusty gas and suspension flows in a plane channel

The stability of two-dimensional dispersed Poiseuille flow is analyzed within the framework of the linear theory. A numerical solution of the corresponding Orr-Sommerfeld equation is constructed. The effect of the particle mass concentration, dimensions, and relaxation time on the flow stability is considered.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 79–85, September–October, 1995.     

Two dimensional self-similar expanding crack problems in elastic half-space

The application of the property of dynamic similarity is useful to the solution which admits a self-similarity or homogeneous form. One independent variable has been dropped in the present equivalent set of the governing equations. The displacement discontinuity on the crack face and also the displacement field on the surface due to an in-plane shear model over an expanding zone of slippage of arbitrary dip have been obtained. The moving slip edge extends towards the surface with a constant velocity. Cagniard De-Hoop technique has been used here to obtain the two dimensional exact transient response due to the slip in the vertical mode via body force equivalent. The results of the present paper are valid at least up to the time when the diffracted waves from the crack edge have not reached the receiving station. The spectral behavior of the source time function has also been discussed.     

Critical time for asymptotic waves in self-similar flows

The problem of shock wave formation within a self-similar flow is studied through the asymptotic wave methodology.The conditions for the breakdown of the perturbations are discussed in terms of the adiabatic index.     

Some self-similar viscous gas flows in a channel

We consider the class of self-similar axisymmetric and two-dimensional laminar flows of a viscous gas in a long channel with smooth contour, in which the longitudinal component of the velocity and the gas temperature are functions of a single dimensionless transverse coordinate. Such flows correspond to exponential (axisymmetric flow) or linear (two-dimensional flow) increase of the radius or height of the channel and corresponding exponential or hyperbolic decrease of the static pressure along the channel.     

Stability of arbitrary plane shear flows of viscoelastic fluids with fading memory

By appropriate choosing the time scale, any fluid within a class described by Coleman and Noll [6] will have rapidly fading memory. For this class of fluids equations are derived which govern the perturbations of arbitrary plane shear flows. These equations contain the equations of Becker [3] as a special case. On the basis of them it is shown that for large enough shear rate the local stress power generated by the perturbations is non-positive. Results relating to the stress power obtained by Akbay and Sponagel [2] on the basis of Becker's [3] equations are placed in context.     

One class of self-similar flows of a radiating gas

This article discusses self-similar statements of the problem of the motion of a completely radiating and absorbing gas. The field of radiation is assumed to be quasi-steady-state, and the contribution of the radiation to the internal energy, as well as the pressure and the viscosity of the medium, are not taken into account. The presence of local thermodynamic equilibrium is assumed. The absorption coefficient is approximated by a power function of the pressure and the density. Scattering of the radiation is not taken into account. Under these assumptions, there exist self-similar statements of the problem for one-dimensional unsteady-state flows (a strong detonation, the problem of plug-flow, motion under the effect of a radiation source, and others) and two-dimensional steady-state flows (flow in a diffuser, supersonic flow around a wedge or a cone). It is shown that there exists a non steady-state spherically symmetrical flow depending on four parameters; this flow is adiabatic in spite of the presence of radiation. This article is made up of seven sections. It is shown in the first section that the presence of radiation leads to the appearance of new dimensional constants, entering into the equations of the problem. The second section is devoted to self-similar nonsteady-state one-dimensional flows. The third section contains a detailed study of one class of such flows. In a partial case, adiabatic flows of a radiating gas are obtained. In the fourth and fifth sections, a detailed analysis is made of the initial and boundary conditions from the point of view of dimensionality. The sixth section describes self-similar two-dimensional steady-state flows of a radiating-absorbing gas. The seventh section consists of remarks with respect to approximations of the transfer equation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 8–22, July–August, 1970.     

Instability of self-similar ideal gas flows with shock waves

The results of the numerical simulation of three problems of ideal gas flow with shock waves, which admit self-similar solutions, are presented. These problems are the double Mach-type reflection of a shock from a wedge, the breakdown of a combined discontinuity on a 90° sharp corner, and the outflow of a supersonic jet from an expanding slot. It is shown that for certain input data the self-similar solution may become unstable and is replaced by a fluctuating flow. The reasons for the generation of these fluctuations and their mechanism are discussed. Volgograd. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 166–175, July–August, 1998.     

Stability of self-similar pipe flow with suction

The stability of self-similar flows with various boundary conditions at the wall is investigated. In the region of nonexistence of self-similar solutions an oscillatory regime is detected. The problem of stability with respect to disturbances of general form is studied. The dependence of the critical values of the axial Reynolds number and the Strouhal number on Re is calculated for various suction rates.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 18–25, September–October, 1991.     

Instability of elastoplastic plane flows

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 152–156, May–June, 1991.     

Viscoelastic properties in plane squeeze-film flows

In this paper, we consider the problem of plane squeeze-film flows in a kinematics based on the formalism of convected (moving and deforming) coordinates. The flows discussed are treated as instantaneous motions with proportional stretch histories (cf. [16]). Certain simplifications in the constitutive equations of an incompressible simple fluid (cf. [10]) have been achieved for moderately low Deborah numbers.Approximate solutions of plane flows are obtained either for slightly viscoelastic fluids or in a form valid in the vicinity of any arbitrarily chosen instant of time. The conditions of improved lubrication, leading to inequalities imposed on material constants or kinematic quantities, are discussed in detail. Also, the necessary conditions are discussed under which the time-dependent distance between the plates may decrease non-monotonically, showing some “bounces”.     

Aspects of self-similar diffraction gas flows and their numerical simulation

A large number of papers has been devoted to the investigation of the interaction of a plane shock wave with bodies of various geometric shapes, and they have been generalized and classified for a stationary body in [1, 2]. Separate results of experimental and theoretical investigations of the interaction of a shock wave with a wedge, cone, sphere, and cylinder moving with supersonic velocities are contained in [3–9]. Analysis of the available results shows that the features of the unsteady gas flows formed in this case largely depend on the nature of the boundary-value problem that arises for the system of differential gas dynamic equations. The question of the wave structure of the unsteady gas flow and the accuracy of the obtained solution is central to the numerical investigation of the present class of problems. The most characteristic types of unsteady self-similar gas flows that arise on the interaction of a plane shock wave with bodies of a wedge or convex corner type are calculated on the basis of an explicit numerical continuous calculation method of the second order of accuracy. The accuracy of the numerical solutions is discussed on the basis of a comparison with the experimental data. The case of the interaction of a shock wave with the rarefaction wave that arises in a supersonic flow past a convex corner is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 146–152, July–August, 1986.     

Hodograph relativistic equations of plane flows

Summary Various forms of hodograph equations for relativistic irrotational steady plane flows are worked out. The transformation from the hodograph to the physical plane is studied. Elementary solutions of these equations are found. An approximate hodograph equation for relativistic transonic flows is determined.

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Sommario Si ricavano, in diverse forme, le equazioni odografiche per le correnti relativistiche irrotazionali stazionarie piane. Si esamina il passaggio dal piano odografico al piano fisico. Si trovano alcune soluzioni elementari delle dette equazioni. Si determina un'equazione odografica approssimata per le correnti transoniche relativistiche.

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This work was done in the sphere of activity of the C.N.R. groups for mathematical research.     

On steady plane flows in classical elasticity

A new class of boundary-value problems in mathematical elasticity is proposed, wherein the medium flows steadily relative to a non-embedded surface over which tractions or velocities are prescribed. Such flows are seen in metal forming operations where purely elastic streams enter and leave the working zone. The deformations are assumed here to be plane and isochoric. A general solution is formulated in terms of two complex potentials. Residual stress is accounted for in detail and a uniqueness theorem is proved. Some simple flows are examined, but it remains to develop a systematic procedure for matching the general solution to arbitrary boundary data.     

Stability of colliding flows

The stability of the flow in the interaction region of colliding streams is investigated in the framework of linear theory. To simplify the analysis, the treatment is restricted to the case of an ideal fluid and an irrotational main flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti Gaza, No. 5, pp. 143–147, September–October, 1981.     

Stability of Hartmann flows

The stability of Hartmann flows for arbitrary magnetic Reynolds numbers is investigated in the framework of linear theory. The initial three-dimensional problem reduces to the equivalent two-dimensional problem. Perturbation theory is used to find asymptotic expressions for the eigenvalues. Distinguishing two types of disturbances — magnetic and hydrodynamic — is shown to be advantageous in a number of cases. Simple features of the stability are considered for particular cases. The well-know Lundquist result is generalized. An energy approach is applied to the problem of stability. The results of simulations involving the solution of the linear stability problem are described. A distinctive picture of stability is developed. There are several types of instability and they can develop simultaneously. The hydrodynamic and magnetic phenomena interact with each other in a very complex fashion. The magnetic field can either enhance flow stability or reduce it.Novosibirsk. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 6, pp. 17–31, November–December, 1972.     

Small-perturbation theory of steady plane relativistic flows

Summary Small-perturbation theory for relativistic irrotational steady flows past profiles is developed. Subsonic or supersonic approximation, as well as transonic, is determined. Similarity rules, in both cases, are established.

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Sommario Viene sviluppata la teoria delle piccole perturbazioni per le correnti relativistiche irrotazionali stazionarie che lambiscono profili sottili. Vengono esaminate le approssimazioni valide nel caso subsonico o supersonico, e nel caso transonico. Vengono stabilite le regole di similitudine che sussistono per le correnti subsoniche o supersoniche, e la regola che vige in condizioni transoniche.

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This work was done in the sphere of activity of the C.N.R. groups for mathematical research.