A. V. Konyukhov

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.

Simulation of sub- & supersonic flows in inductive plasmatrons

Simulation of sub- and supersonic thermochemical equilibrium flows in plasmatrons is considered. A physicochemical model, numerical method, and computation results for equilibrium inductive coupled plasma flows in a plasmatron are given. An effective preconditioning technique along with an implicit total-variation-diminishing scheme is used to solve the Navier‐Stokes equations in both subsonic and supersonic regimes. The governing equations include source terms corresponding to the electromagnetic field influence: the Lorentz force components (so-called magnetic pressure) and Joule heat production. The necessary transport coefficients were calculated in advance for equilibrium air plasma as the functions of pressure and temperature. Transport properties were calculated by the precise formulas of the Chapman‐Enskog method in the temperature range 300 < ‐ T < 15,000 K. Calculations of equilibrium air plasma flows for the IPG-4 (Institute for Problems in Mechanics, Russian Academy of Science) discharge channel geometry with the channel radius Rc = 0.04 m and length Zc = 0.40 m were performed. Creation of both underexpanded and overexpanded jets exhausted from the plasmatron channel is considered. A comparison with experimental results is given.

Structurization of chaos

Vortex cascades of instabilities forming a core are studied. Large-scale linear waves in a fluctuating medium are described.

Upscaling of an immiscible non-equilibrium two-phase flow in double porosity media

We study an immiscible incompressible two-phase, such as water–oil flow through a -periodic double porosity media. The mesoscopic model consists of equations derived from the mass conservation laws of both fluids, along with a generalized Darcy law in the framework of Kondaurov’s non-equilibrium flow model. The mobility functions as well as the capillary pressure function for each component of the porous medium are the functions of the saturation and an additional non-equilibrium parameter, which satisfies a kinetic equation coming from the definition of the Helmholtz free energy. The fractured medium consists of periodically repeating homogeneous blocks and fractures, where the permeability ratio of matrix blocks to fracture planes is of order . Using the method of two-scale asymptotic expansions, we derive the macroscopic model of the flow which is written in terms of the homogenized phase pressures, saturation, and the non-equilibrium parameter. For small relaxation times, we compare our model with the global models obtained earlier by H. Salimi and J. Bruining. We show the novelty of our macroscopic double porosity flow model.

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.

New non-equilibrium matrix imbibition equation for double porosity model

Abstract The paper deals with the global Kondaurov double porosity model describing a non-equilibrium two-phase immiscible flow in fractured-porous reservoirs when non-equilibrium phenomena occur in the matrix blocks, only. In a mathematically rigorous way, we show that the homogenized model can be represented by usual equations of two-phase incompressible immiscible flow, except for the addition of two source terms calculated by a solution to a local problem being a boundary value problem for a non-equilibrium imbibition equation given in terms of the real saturation and a non-equilibrium parameter.

On the theory of countercurrent flow in a rotating viscous heat-conducting gas

The countercurrent flow in a gas centrifuge is simulated. Mechanical and thermal methods for its excitation are discussed; thermal restructuring, the thermal control of the velocity field, and a shift in the inversion point are analyzed; and the formation of overtone flows in the rarefaction zone is studied.

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.

Numerical stability analysis of the Taylor-Couette flow in the two-dimensional case

The stability of the laminar flow between two rotating cylinders (Taylor-Couette flow) is numerically studied. The simulation is based on the equations of motion of an inviscid fluid (Euler equations). The influence exerted on the flow stability by physical parameters of the problem (such as the gap width between the cylinders, the initial perturbation, and the velocity difference between the cylinders) is analyzed. It is shown that the onset of turbulence is accompanied by the formation of large vortices. The results are analyzed and compared with those of similar studies.