In this series of talks, I will discuss the fluid-dynamic-type equations that is derived from the Boltzmann equation as its the asymptotic behavior for small mean free path. The study of the relation of the two systems describing the behavior of a gas, the fluid-dynamic system and the Boltzmann system, has a long history and many works have been done. The Hilbert expansion and the Chapman–Enskog expansion are well-known among them. The behavior of a gas in the continuum limit, however, is not so simple as is widely discussed by superficial understanding of these solutions. The correct behavior has to be investigated by classifying the physical situations. The results are largely different depending on the situations. There is an important class of problems for which neither the Euler equations nor the Navier–Stokes give the correct answer. In these two expansions themselves, an initialor boundaryvalue problem is not taken into account. We will discuss the fluid-dynamic-type equations together with the boundary conditions that describe the behavior of the gas in the continuum limit by appropriately classifying the physical situations and taking the boundary condition into account. Here the result for the time-independent case is summarized. The time-dependent case will also be mentioned in the talk. The velocity distribution function approaches a Maxwellian fe, whose parameters depend on the position in the gas, in the continuum limit. The fluid-dynamictype equations that determine the macroscopic variables in the limit differ considerably depending on the character of the Maxwellian. The systems are classified by the size of |fe− fe0|/fe0, where fe0 is the stationary Maxwellian with the representative density and temperature in the gas. (1) |fe − fe0|/fe0 = O(Kn) (Kn : Knudsen number, i.e., Kn = `/L; ` : the reference mean free path. L : the reference length of the system) : S system (the incompressible Navier–Stokes set with the energy equation modified). (1a) |fe − fe0|/fe0 = o(Kn) : Linear system (the Stokes set). (2) |fe − fe0|/fe0 = O(1) with | ∫ ξifedξ|/ ∫ |ξi|fedξ = O(Kn) (ξi : the molecular velocity) : SB system [the temperature T and density ρ in the continuum limit are determined together with the flow velocity vi of the first order of Kn amplified by 1/Kn (the ghost effect), and the thermal stress of the order of (Kn) must be retained in the equations (non-Navier–Stokes effect). The thermal creep[1] in the boundary condition must be taken into account. (3) |fe − fe0|/fe0 = O(1) with | ∫ ξifedξ|/ ∫ |ξi|fedξ = O(1) : E+VB system (the Euler and viscous boundary-layer sets). E system (Euler set) in the case where the boundary is an interface of the gas and its condensed phase. The fluid-dynamic systems are classified in terms of the macroscopic parameters that appear in the boundary condition. Let Tw and δTw be, respectively, the characteristic values of the temperature and its variation of the boundary. Then, the fluid-dynamic systems mentioned above are classified with the nondimensional temperature variation δTw/Tw and Reynolds number Re as shown in Fig. 1. In the region SB, the classical gas dynamics is inapplicable, that is, neither the Euler

Kinetic Theory and Fluid Dynamics

Hydrodynamic and hydromagnetic stability

Plasma waste treatment has over the past decade become a more prominent technology because of the increasing problems with waste disposal and because of the realization of opportunities to generate valuable co-products. Plasma vitrification of hazardous slags has been a commercial technology for several years, and volume reduction of hazardous wastes using plasma processes is increasingly being used. Plasma gasification of wastes with low negative values has attracted interest as a source of energy and spawned process developments for treatment of even municipal solid wastes. Numerous technologies and approaches exist for plasma treatment of wastes. This review summarizes the approaches that have been developed, presents some of the basic physical principles, provides details of some specific processes and considers the advantages and disadvantages of thermal plasmas in waste treatment applications.

http://iopscience.iop.org/article/10.1088/0022-3727/41/5/053001/pdf

Thermal plasma waste treatment

Considerable progress has been made over the last decades in thermal spray technologies, practices and applications. However, like other technologies, they have to continuously evolve to meet new problems and market requirements. This article aims to identify the current challenges limiting the evolution of these technologies and to propose research directions and priorities to meet these challenges. It was prepared on the basis of a collection of short articles written by experts in thermal spray who were asked to present a snapshot of the current state of their specific field, give their views on current challenges faced by the field and provide some guidance as to the R&D required to meet these challenges. The article is divided in three sections that deal with the emerging thermal spray processes, coating properties and function, and biomedical, electronic, aerospace and energy generation applications.

https://link.springer.com/content/pdf/10.1007%2Fs11666-016-0473-x.pdf

The 2016 Thermal Spray Roadmap

M Mitchner and Charles H Kruger Jr Chichester: J Wiley 1973 pp 518 price £13.95 Sandy Brown of MIT and his publishers (Wiley) have been encouraged by the enormous success of Basic Data of Plasma Physics to embark upon the Wiley Series in plasma physics which has now reached the dozen mark. In Partially Ionized Gases the Stanford authors, Mitchner and Kruger, deal with the theory of real plasma properties in a clear and comprehensive manner.

https://iopscience.iop.org/article/10.1088/0031-9112/26/1/026/pdf

Partially Ionized Gases

A complete classification of shock waves in a van der Waals fluid is undertaken. This is in order to gain a theoretical understanding of those shock-related phenomena as observed in real fluids which cannot be accounted for by the ideal gas model. These relate to admissibility of rarefaction shock waves, shock-splitting phenomena, and shock-induced phase transitions. The crucial role played by the nature of the gaseous state before the shock (the unperturbed state), and how it affects the features of the shock wave are elucidated. A full description is given of the characteristics of shock waves propagating in a van der Waals fluid. The strength of these shock waves may range from weak to strong. The study is carried out by means of the theory of hyperbolic systems supported by numerical calculations.

/pdf/admissible-shock-waves-and-shock-induced-phase-transitions-2hysa8e9dj.pdf

Admissible shock waves and shock-induced phase transitions in a van der Waals fluid

Molecular extended thermodynamics of rarefied polyatomic gases and wave velocities for increasing number of moments

A 3D model for the simulation of inductively coupled plasma torches (ICPTs) working at atmospheric pressure is presented, using a customized version of the computational fluid dynamics (CFD) commercial code FLUENT®. The induction coil is taken into account in its actual 3D shape, showing the effects on the plasma discharge of removing the axisymmetric hypothesis of simplification, which characterizes 2D approaches. Steady flow and energy equations are solved for optically thin argon plasmas under the assumptions of local thermodynamic equilibrium (LTE) and laminar flow. The electromagnetic field equations are solved on an extended grid in the vector potential form. In order to evaluate the importance of various 3D effects on calculated plasma temperature and velocity fields, comparisons of our new results with the ones obtainable from 2D models and from an improved 2D model that includes 3D coil effects are presented. 3D results are shown for torches working under various geometric and operating conditions and with different coil shapes, including conventional helicoidal, as well as planar, elliptical, and double-stage configurations.

Three-dimensional modeling of inductively coupled plasma torches

A 3D model for the simulation of inductively coupled plasma torches (ICPTs) working at atmospheric pressure is presented, using a customized version of the computa- tional fluid dynamics (CFD) commercial code FLUENT ® . The induction coil is taken into account in its actual 3D shape, showing the effects on the plasma discharge of removing the axisymmetric hypothesis of simplification, which characterizes 2D approaches. Steady flow and energy equations are solved for optically thin argon plasmas under the assumptions of local thermodynamic equilibrium (LTE) and laminar flow. The electromagnetic field equa- tions are solved on an extended grid in the vector potential form. In order to evaluate the im- portance of various 3D effects on calculated plasma temperature and velocity fields, com- parisons of our new results with the ones obtainable from 2D models and from an improved 2D model that includes 3D coil effects are presented. 3D results are shown for torches work- ing under various geometric and operating conditions and with different coil shapes, includ- ing conventional helicoidal, as well as planar, elliptical, and double-stage configurations.

https://old.iupac.org/publications/pac/2005/pdf/7702x0359.pdf

Three-dimensional modelling of inductively coupled plasma torches

A new technique for using the CFD commercial code FLUENT\(^{\copyright}\) to simulate inductively coupled plasma torches by means of two-dimensional axisymmetric models is presented. The method is based on an external user-defined function (UDF) which fully solves the electromagnetic field equations, letting the FLUENT\(^{\copyright}\) built-in module calculate only the plasma temperature and velocity fields inside the torch region. In this framework, computations have been carried out for LTE, optica lly thin argon plasmas at atmospheric pressure, using extended grid models with either magnetic dipole or vanishing vector potential boundary conditions for the electromagnetic field. It is shown that our newly developed technique is up to 60% faster on each iteration than that using user-defined scalars (UDS) previously proposed in the literature, as the need of solving flow field equations also outside the plasma zone is eliminated. Calculations are also performed using exact integral boundary conditions for the vector potential, as given by the standard electromagnetic field approach, taking into account the effects of both exciting and induced currents. The corresponding results are compared with the approximate ones obtained by employing extended grid models, showing that for small radial dimensions of the electromagnetic field domain, the magnetic dipole boundary conditions give more realistic solutions than those assuming a vanish ing vector potential.

Andrea Mentrelli

Papers

Admissible shock waves and shock-induced phase transitions in a van der Waals fluid

Molecular extended thermodynamics of rarefied polyatomic gases and wave velocities for increasing number of moments

Three-dimensional modeling of inductively coupled plasma torches

Three-dimensional modelling of inductively coupled plasma torches

Comparison of different techniques for the FLUENT©-based treatment of the electromagnetic field in inductively coupled plasma torches