A nonlinear theory for the motion of hydrodynamic discontinuity surfaces

The complete system of hydrodynamic equations that describe the free surface of an inviscid fluid, a tangential discontinuity, and the development of the hydrodynamic instability of a reaction front is reduced to a closed system of surface equations using Lagrangian variables, special integrals of motion, and their analogues. The vorticity is shown to play a fundamental role in the pattern of motion of hydrodynamic discontinuities, imparting a differential form to the equations. In the isentropic approximation, it is demonstrated how to take into account the fluid density oscillations caused by this motion. The derived system of equations is consistent with the previously known analytical solutions obtained in special cases.     

Free surface and flow problem for a viscous liquid

An exact closed system of equations is proposed for describing the shape of the free surface of a viscous steady-state liquid in the 2D case in terms of the surface itself. A method that lowers the dimensionality in the Navier-Stokes equation is demonstrated, and its application in problems of steady-state flow past solids is considered.     

Numerical investigation of hydrodynamics behaviour of melt layer during laser cutting of steel

Understanding of the melt layer hydrodynamic behaviour during laser-cutting process under gas jet assistance is of high importance for cut quality control. In the present work, a numerical model is developed to calculate the three-dimensional behaviour of the melt flow on the kerf front, while an inert gas jet interacts with the melt film. Fluent CFD code is used to solve the governing hydrodynamic equations by finite volume method. The results show that the melt flow on the kerf front reveals a strong instability, which depends on the cutting speed and on the gas jet velocity. Global flow behaviour (gas and molten metal flows) computed using a laminar model, reveals oscillations of the gas–metal liquid interface, which is assimilated to Kelvin–Helmholtz instability. The origin of this instability is discussed in terms of instabilities in thermal dynamics and hydrodynamics. Instability in thermal dynamics is related to the localized melting, while the instability in hydrodynamics is governed by forces balance between gas and resistant surface tension.     

A study on the inclusion of body forces in the lattice Boltzmann BGK equation to recover steady-state hydrodynamics

When the lattice Boltzmann (LB) method is used to solve hydrodynamic problems containing a body force term varying in space and/or time, its modelling at the mesoscopic scale must be verified in terms of consistency in order to avoid the appearance of non-hydrodynamic error terms at the macroscopic scale. In the present work it is shown that the modelling of spatially varying steady body force terms in the LB equation must be different from the time-dependent case, when a steady-state flow solution is sought. For that, the Chapman-Enskog analysis is used to derive the LB body force model for the LB BGK equations in a steady-state flow problem. The theoretical findings are supported by numerical tests performed on two different 2D steady-state laminar flows driven by spatially varying body forces with known analytical solutions.     

On the influence of a magnetic field with circular field lines on the gravity flow of a magnetic fluid film down a thin cylinder

The gravity-induced flow of a magnetic fluid film down a vertical thin current-carrying cylindrical conductor is considered. The relative thickness of the film is small. A nonlinear equation is derived from a system of ferrohydrodynamic equations that describes the time evolution of the axisymmetric shape of the free film surface, which is set at the zero time. Using this equation, the development of disturbances of the hydrodynamic field is studied in the linear statement. The hydrodynamic field corresponds to the steady flow of the magnetic fluid in the form of a cylindrical film. It is found that such a flow is stable if the current passing through the conductor is sufficiently high.     

Laminar flame and acoustic waves in two-dimensional flow

The complete system of fluid dynamics equations describing the development of instability of a reaction front in a two-dimensional flow in reversed time are reduced to a closed system of equations of front dynamics by using Lagrangian variables and integrals of motion. The system can be used to analyze processes behind the front without solving the complete system of fluid dynamics and chemical kinetics equations. It is demonstrated how the gas density disturbances induced by the moving front can be described in the adiabatic approximation.     

Temperature field of dielectric films under continuous ion-beam irradiation

In the present study, we theoretically examine the formation process of the steady-state temperature field in dielectrics under irradiation with a continuous ion beam in air with allowance for the temperature dependence of thermophysical quantities. Analytical expressions for the temperature field were obtained. An interconnected system of nonlinear algebraic equations for the steady-state temperatures at the front (irradiated) and rear surfaces of the sample, and the steady-state temperature at the interface between the ion-damaged and non-damaged region was obtained; by numerical solution of this system, a nonlinear dependence of the mentioned temperatures on the characteristics of incident ion flux was revealed.     

Free surface instability in a confined suspension jet

A suspension confined between two close parallel plates is studied in the Stokesian regime. The use of boundary integral equations and the lubrication approximation allows to compute the hydrodynamic forces acting on the particles. The forces are long ranged and depend on the orientation of the relative position and velocity of particles. This tensorial character predicts an “antidrag” that is observed in experiments. The effect of the computed hydrodynamic forces is studied in the dynamics of a jet of particles falling by a gravitational field, which shows a surface instability similar to the Kelvin–Helmholtz one. A theoretical model, based on hydrodynamic-like equations, is able to predict the instability that is produced by the interaction of the long-range forces and the free surface.     

Plasma expansion and current flow in a vacuum arc with a smallanode

A low-density plasma flow in a vacuum arc with a small anode, which intercepts only part of the cathodic plasma jet, was studied theoretically using a two-dimensional approximation. The plasma expansion was modeled using the sourceless steady-state hydrodynamic equations, where the free boundary of the plasma was determined by a self-consistent solution of the gasdynamic and electrical current equations. Magnetic forces from the azimuthal self-magnetic field were taken into account. The influence of the ratio of the anode radius to initial plasma jet radius on the plasma density, velocity, current distribution, and anode sheath potential drop is analyzed. It is shown that the mass and current flow in a 500 A arc are compressed near the axis. This leads to an increase in the plasma density by a factor of two and in the axial current density by a factor of 1.5     

脉冲电子束对材料破坏效应的数值研究

利用ＭｏｎｔｅＣａｒｌｏ方法计算了电子束的能量沉积，用流体动力学方程计算了热击波的传播，所用物态方程为ＧＲＡＹ三相物态方程。全部计算均由程序ＤＲＡＭ１Ｄ完成。讨论了波的传播规律，并给出了铝材迎光面反冲速度峰值及比质量亏损与电子束的入射通量和能量之间的关系。     

SELF-CONSISTENT TREATMENT OF PLASMA EXPANSION IN THE PRESENCE OF ELECTRON PLASMA WAVE

The hydrodynamic modification of an expanding plasma near the reflection point of an electron plasma wave is investigated by simultaneously solving the wave equation together with the steady-state hydrodynamic equations.The electric field and electron density fluctuation of the plasma wave are derived in a self-consistently steepened density profile. while the density jump and its dependence on the wave amplitude are also determined.     

Diffraction of a two-shock configuration by a convex cylindrical surface

The subject of this work is numerical investigation into the diffraction of a shock-wave configuration by a convex cylindrical surface. The diffraction is a stage of interaction of a shock wave with a two-dimensional body. It is preceded by the stage of shock wave reflection from the front surface of the body, the back surface of which has a convex cylindrical shape. The two-or three-shock configuration formed on the front surface diffracts by the back cylindrical surface. The emphasis is on studying the diffraction of the two-shock wave configuration with the diffraction angle varying continuously. The object under study a wedge with an inclined front surface and convex cylindrical back surface. The results of numerical investigation are obtained by integrating the Euler equations. Flow features associated with the simultaneous diffraction of the incident and reflected shock waves are revealed. The evolution of the gasdynamic system (stagnation wave + TU layer) arising inside the diffraction area is studied. Breakaway and vorticity initiation are considered. It is shown that the positions of the line of separation and TU layer change in the course of diffraction. They merge together at the stage of steady flow. Comparison is made between the flow formed upon diffraction of the two-shock configuration by the cylindrical surface and the flow generated upon diffraction by horizontal and vertical surfaces.     

Hydrodynamic instability of premixed flame propagating in narrow planar channel in the presence of gas flow

The paper analyses the hydrodynamic instability of a flame propagating in the space between two parallel plates in the presence of gas flow. The linear analysis was performed in the framework of a two-dimensional model that describes the averaged gas flow in the space between the plates and the perturbations development of two-dimensional combustion wave. The model includes the parametric dependences of the flame front propagation velocity on its local curvature and on the combustible gas velocity averaged along the height of the channel. It is assumed that the viscous gas flow changes the surface area of the flame front and thereby affects the propagation velocity of the two-dimensional combustion wave. In the absence of the influence of the channel walls on the gas flow, the model transforms into the Darrieus–Landau model of flame hydrodynamic instability. The dependences of the instability growth rate on the wave vector of disturbances, the velocity of the unperturbed gas flow, the viscous friction coefficients and other parameters of the problem are obtained. It is shown that the viscous gas flow in the channel can lead, in some cases, to a significant increase in instability compared with a flame propagating in free space. In particular, the instability increment depends on the direction of the gas flow with respect direction of the flame propagation. In the case when the gas flow moves in the opposite direction to the direction of the flame propagation, the pulsating instability can appear.     

Theoretical investigation of hydrodynamic surface mode in a lined duct with sheared flow and comparison with experiment

A spectral collocation method is used to solve the linearized Euler equations in a duct with shear flow and lined walls in order to identify a possible hydrodynamic instability observed in published experiments. This method is first checked against a reference test case in a cylindrical duct. Then a theoretical test case in a plane bi-dimensional duct with no-slip flow is considered: the Briggs-Bers stability criterion is proved to be valid and it shows that the hydrodynamic instability does correspond to a right-running amplified wave. Eigenmode analyses are then performed on the experimental configuration. An unstable hydrodynamic surface mode is found, with an axial wavenumber and velocity eigenfunctions which are in good agreement with the experimental ones. Acoustic energy calculations show that the hydrodynamic instability paradoxically carries noticeable levels of acoustic energy in the upstream direction. Finally, the influence of Mach number and frequency is investigated.     

General Navier–Stokes-like momentum and mass-energy equations

A new system of general Navier–Stokes-like equations is proposed to model electromagnetic flow utilizing analogues of hydrodynamic conservation equations. Such equations are intended to provide a different perspective and, potentially, a better understanding of electromagnetic mass, energy and momentum behaviour. Under such a new framework additional insights into electromagnetism could be gained. To that end, we propose a system of momentum and mass-energy conservation equations coupled through both momentum density and velocity vectors.     

Supersonic flows with small perturbations in the presence of external effects in the flow. Part 1: “Thin body of revolution”

Axisymmetric supersonic flow about a thin body of revolution with an external energy supply and an external force localized near the body surface is considered in the linear approximation. An analytic theory is constructed for calculating spatial fields of flow parameters in this case for an arbitrary dependence of external effects on the longitudinal coordinate. Formulas are derived for the pressure ratio on the surface of the thin body of revolution. The results of calculations based on the analytic theory are in good agreement with numerical data obtained from the solution of hydrodynamic equations in the Euler approximation.