A. P. Likhachev

Numerical modeling of shock-wave instability in thermodynamically nonideal media

A numerical analysis of the nonlinear instability of shock waves is presented for solid deuterium and for a model medium described by a properly constructed equation of state. The splitting of an unstable shock wave into an absolutely stable shock and a shock that emits acoustic waves is simulated for the first time.

On the Neutral Stability of a Shock Wave in Real Media

The results of the theoretical analysis and computer simulation of the behavior of neutrally stable shock waves with real (van der Waals gas, magnesium) equations of state are presented. An approach is developed in which the region of the neutral stability of a shock wave for each pressure value in front of the wave is determined from the analysis of the equation of state. A simple algorithm is developed to determine the cause of acoustic perturbations (a shock front or an external source) immediately from the flow pattern. In contrast to the predictions of the linear theory, the amplitude of the perturbations of the neutrally stable shock wave decreases with time, although this process is noticeably slower than in the case of an absolutely stable shock wave.

Stability and Ambiguous Representation of Shock Wave Discontinuity in Thermodynamically Nonideal Media

The nonlinear analysis of the behavior of a shock wave on a Hugoniot curve fragment that allows for the ambiguous representation of shock wave discontinuity has been performed. The fragment under consideration includes a section where the condition L > 1 + 2M is satisfied, which is a linear criterion of the instability of the shock wave in media with an arbitrary equation of state. The calculations in the model of a viscous heat-conductive gas show that solutions with an instable shock wave are not implemented. In the one-dimensional model, the shock wave decays into two shock waves or a shock wave and a rarefaction wave, which propagate in opposite directions, or can remain in the initial state. The choice of the solution depends on the parameters of the shock wave (position on the Hugoniot curve), as well as on the form and intensity of its perturbation. In the two-dimensional and three-dimensional calculations with a periodic perturbation of the shock wave, a “cellular” structure is formed on the shock front with a finite amplitude of perturbations that does not decrease and increase in time. Such behavior of the shock wave is attributed to the appearance of the triple configurations in the inclined sections of the perturbed shock wave, which interact with each other in the process of propagation along its front.

Interaction between a Composite Compression Wave and a Vortex in a Thermodynamically Nonideal Medium

A numerical analysis is presented of two-dimensional interaction between a transverse vortex and a composite compression wave that can exist in a thermodynamically nonideal medium. It is shown that the interaction of a composite wave involving a “neutrally stable” shock with a vortex generates weakly damped outgoing acoustic waves; i.e., the shock is a source of sound. This phenomenon increases the post-shock acoustic noise level in an initially turbulent flow.

Pulse Gas Injection in Separation Zone of Hypersonic MHD Flow Over Rotation Body

The hypersonic MHD flow over rotation body with imbedded magnetic dipole is usually characterized by formation of extensive separation zones with practically motionless medium. The position of these zones at the body surface and their size strongly depend on and are controlled by the direction and value of the dipole magnetic moment. The gasdynamic streamlines bypass the separation zone following close to the magnetic lines of force. The surface heat flux inside this zone is markedly reduced. It is of interest to consider the possibilities of additional heat protection of the body surface by a cold gas pulse injection to the separation zones, which look quite stable with regard to external impacts. This is the problem considered in the present paper by means of the numerical modeling. The calculations have been performed in the framework of the complete MHD model taking into account viscosity, thermal conductivity, induced magnetic field, and real-air thermodynamic properties. It has been revealed that the pulse injection of cold gas into the separation zone leads to cooling of this zone and the corresponding decrease of the total heat flux. The effect persists for a long time after the injection termination. It is also noted that this effect does not depend on the separation zone location but manifests itself more intensively in the case of the injection into the separation zone in the shock layer.

Behavior of relativistic shock waves in nuclear matter

An equation of state of nuclear matter describing the quark–hadron phase transition is derived within a variant of the MIT bag model. This equation of state is analyzed in order to test the criteria of instability and neutral stability of relativistic shock waves. It is shown that Taub adiabats passing through the phase transition region contain segments with an ambiguous representation of the shock-wave discontinuity, which means the possibility of splitting a shock wave with the formation of a combined compression wave. Isentropes passing through the mixed phase region have bends and are not completely convex (in the p–T plane, where T is the generalized specific volume); as a result, shock and combined rarefaction waves can appear. Numerical simulation has confirmed the appearance of these singularities of wave processes in nuclear matter in the region of the phase transition from the hadronic state to the quark–gluon plasma.

Mechanism of the appearance of the cellular structure of a shock wave in the region of its ambiguous representation

The mechanism of the formation of the cellular structure for a planar shock wave in an equilibrium medium, which arises due to its ambiguous representation characterized by the fulfillment of the condition L > 1 + 2M, i.e., one of the linear criteria of the instability of the shock wave in media with arbitrary thermodynamic properties, has been considered. It has been shown that this process is based on “switching” between different types of the possible decay configurations, which occurs during the motion and interaction of the transverse waves moving along the shock wave front.

Stability and ambiguous representation of shock wave discontinuity in media with arbitrary thermodynamic properties

The non‐linear analysis of the plane shock wave stability in media with arbitrary equation of state has been carried out in a systematic way. The one and multi‐dimensional computations have been conducted in the inviscid and viscous formulations. The real and properly constructed model equations of state have been used. The behavior of shocks in the regions of their ambiguous representation overlapping the Hugoniot segments that meet the linear criteria of the shock wave instability has been studied. The evolution of shock waves being neutrally stable in keeping with the results of the linear analysis has been also simulated. The results obtained indicate basic distinctions from the linear theory predictions.

MHD-EFFECTS IN OVERFLOW OF MAGNETIC DIPOLE BY HIGHLY CONDUCTING PLASMA IN PRESENCE OF EXTERNAL MAGNETIC FIELD

Plasma flow over linear magnetic dipole is numerically studied. 2D solution of the problem has been obtained. The linear magnetic dipole is imbedded in the body. The body is a long bar moving at constant velocity in the highly conducting plasma and uniform external magnetic field. The axis of the body is normal to the computational plane in which the magnetic field lines are situated. The dipole magnetic moment is parallel to the external magnetic field and is perpendicular to the direction of the motion. The approximation of perfect non-radiating compressible gas is supposed to be valid. The stationary gasdynamic and electromagnetic structures featured by the presence of MHD shock wave, two X-points of reconnection of magnetic field, MHD vortices and jets and current layers are examined. The local relation between the gradient of gasdynamic pressure and the electromagnetic body force in the regions of each X-point has been analyzed. The role of the magnetic pressure gradient and the force of tension of magnetic field lines being components of the electromagnetic body force in the formation of plasma structures in the vicinity of the X-points is determined and analyzed.