Self-similar solution of the Navier-Stokes equations for a completely ionized hydrogen plasma (the plane piston problem)

The self-similar motion of a completely ionized hydrogen plasma is considered in the two-temperature hydrodynamic approximation, i.e., we consider the plane piston problem and the problem on energy release at a fixed wall. Results obtained by numerical integration of the relevant system of ordinary differential equations are quoted.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 10, No. 3, pp. 34–39, May–June, 1969.     

Parametric instability in a weakly ionized magnetoactive plasma

The stability of a weakly ionized homogeneous plasma, situated in a weak superhigh frequency (shf) electric field and a constant magnetic field, is studied. Expressions are obtained for longitudinal wave deviation increments in the plasma, and for the threshold values of the external shf field, at which the system begins to develop instability. It is shown that the presence of the external magnetic field produces either a stabilizing or a destabilizing effect on the system, dependent on the orientation of the shf field. In particular, when the direction of the magnetic field B is perpendicular to the electric fieldE and the Langmuir electron frequency _Le= (4n_ee_e ²/m_e)^1/2 is less than the cyclotron electron frequency _e = e_eB/m_ec, the threshold value of shf electric field intensity in (Le/)³ is lower than the corresponding value for an isotropic plasma.Translated from Zhumal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 12–16, September–October, 1971.In conclusion, the author thanks A. A. Rukhadze for his interest in the study.     

Large eddy simulations of a turbulent thermal plume

Large eddy simulations of a three-dimensional turbulent thermal plume in an open environment have been carried out using a self-developed parallel computational fluid dynamics code SMAFS (smoke movement and flame spread) to study the thermal plume’s dynamics including its puffing, self-preserving and air entrainment. In the simulation, the sub-grid stress was modeled using both the standard Smagorinsky and the buoyancy modified Smagorinsky models, which were compared. The sub-grid scale (SGS) scalar flux in the filtered enthalpy transport equation was modeled based on a simple gradient transport hypothesis with constant SGS Prandtl number. The effect of the Smagorinsky model constant and the SGS Prandtl number were examined. The computation results were compared with experimental measurements, thermal plume theory and empirical correlations, showing good agreement. It is found that both the buoyancy modification and the SGS turbulent Prandtl number have little influence on simulation. However, the SGS model constant C _s has a significant effect on the prediction of plume spreading, although it does not affect much the prediction of puffing.     

Electrode region of a weakly ionized plasma in chemical equilibrium

The paper is devoted to an analysis of the wall (electrode) region of disturbance of the electric parameters of a weakly ionized plasma, i.e., the region in which the concentrations of the charged particles and the values of the electric field change from the distributions corresponding to the conditions in the undisturbed plasma to the values determined by the boundary conditions on the wall.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 142–153, January–February, 1982.I thank G. A. Lyubimov and G. A. Tirskii for interest in the work and valuable discussions.     

Shock wave structure for a fully ionized plasma

We study planar shock wave structure in a two-temperature model of a fully ionized plasma that includes electron heat conduction and energy exchange between electrons and ions. For steady flow in a reference frame moving with the shock, the model reduces to an autonomous system of ordinary differential equations which can be numerically integrated. A phase space analysis of the differential equations provides an additional insight into the structure of the solutions. For example, below a threshold Mach number, the model produces continuous solutions, while above another threshold Mach number, the solutions contain embedded hydrodynamic shocks. Between the threshold values, the appearance of embedded shocks depends on the electron diffusivity and the electron–ion coupling term. We also find that the ion temperature may achieve a maximum value between the upstream and downstream states and away from the embedded shock. We summarize the methodology for solving for two-temperature shocks and show results for several values of shock strength and plasma parameters in order to quantify the shock structure and explore the range of possible solutions. Such solutions may be used to verify hydrodynamic codes that use similar plasma physics models.     

The boundary layers of a fully ionized two-temperature plasma with given component temperatures at an electrode

The flow of a plasma with different component temperatures in the boundary layers at the electrodes of an MHD channel is investigated without any assumptions as to self-similarity. For the calculation of the electron temperature, the full energy equation for an electron gas [1] is solved with allowance for the estimates given in [2]. In contrast to [3, 4], the calculation includes the change in temperature of electrons and ions along the channel caused by the collective transport of energy, the work done by the partial pressure forces, and the Joule heating and the energy exchange between the components. The problem of the boundary layers in the flow of a two-temperature, partially ionized plasma past an electrode is solved in simplified form by the local similarity method in [5–7]. In these papers, either the Kerrebrock equation is used [5, 6] or the collective terms are omitted from the electron energy equation [7].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 3–10, September–October, 1972.The author thanks V. V. Gogosov and A. E. Yakubenko for interest in this work.     

Stationary efflux into a vacuum by a dual-temperature fully ionized plasma

It is shown that the macroscopic process of plasma discharge from an expanding nozzle is determined, when the thermal conductivity of electrons and heat transfer between the components are taken into account, by a unique dimensionless parameter: the adiabaticity parameter characterizing the transition from adiabatic flow of a dense plasma to the flow of comparatively rarefied plasma when the free path length of the particles is commensurate with the characteristic dimension of the nozzle. A numerical method is used to find the distribution of gas-dynamic and electrical parameters of the plasma stream, and the relationship between the generalized output parameters. It is shown that the energy associated with the ions at infinity, in the latter case, can be tens of times greater than the energy in adiabatic efflux, because of the high thermal conductivity with respect to electrons, but unrealistically large expansion of the nozzle is needed in order to attain it. Singular flow patterns occurring when stationary discharge of plasma at infinity is calculated are also discussed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 10–20, November–December, 1971.In conclusion, the author thanks I. K. Fetisov for helpful discussion.