Melting Powder Particles in a Low-Pressure Plasma Jet

1987 ◽  
Vol 109 (4) ◽  
pp. 971-976 ◽  
Author(s):  
D. Y. C. Wei ◽  
B. Farouk ◽  
D. Apelian
Keyword(s):  
Stokes Equations ◽  
Plasma Jet ◽  
Low Pressure ◽  
Velocity Fields ◽  
Temperature History ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
History Of ◽  
Powder Particles ◽  
Temperature And Velocity Fields

A numerical model has been developed to predict the temperature history of metal particles injected in a low-pressure (supersonic) d-c plasma jet. The temperature and velocity fields of the plasma jet are predicted by solving the parabolized compressible Navier–Stokes equations using a spatial marching scheme. Particle trajectories and heat transfer characteristics are calculated using the predicted plasma jet temperature and velocity fields. Correction factors have been introduced to take into account the noncontinuum effects encountered in the low-pressure environment. The plasma jet profiles as well as the particle/plasma interactions under different jet pressure ratios (from underexpanded to overexpanded cases) have been investigated.

Numerical Study of the Temperature History of Thermally Protected Blunt Nose during Flight

2014 ◽  
Vol 598 ◽  
pp. 294-297 ◽  
Author(s):  
Amir Mahdi Tahsini ◽  
Seyed Amir Hosseini
Keyword(s):  
Stokes Equations ◽  
Thermal Protection ◽  
Numerical Study ◽  
Temperature History ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Numerical Predictions ◽  
History Of ◽  
Protection Coating ◽  
Blunt Nose

In the present work, the surface temperature history of a metal shell of the blunt nose of supersonic launch vehicle which is covered by a thermal protection coating is numerically predicted and compared with experimental data. The full Navier-Stokes equations are used to estimate the aerodynamic heat flux during flight, coupled with the governing equations for the thermal protection system to study the erosion rate and temperature variations. The results show the importance of the properties of the coating on accuracy of the numerical predictions.

A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Low Pressure ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

scholarly journals About Universality and Thermodynamics of Turbulence

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 326 ◽  
Author(s):  
Damien Geneste ◽  
Hugues Faller ◽  
Florian Nguyen ◽  
Vishwanath Shukla ◽  
Jean-Philippe Laval ◽  
...  
Keyword(s):  
Phase Transition ◽  
Velocity Structure ◽  
Stokes Equations ◽  
Structure Functions ◽  
Velocity Fields ◽  
Stereoscopic Particle Image Velocimetry ◽  
Navier Stokes ◽  
Universal Curve ◽  
Navier Stokes Equations ◽  
Hölder Exponents

This paper investigates the universality of the Eulerian velocity structure functions using velocity fields obtained from the stereoscopic particle image velocimetry (SPIV) technique in experiments and direct numerical simulations (DNS) of the Navier-Stokes equations. It shows that the numerical and experimental velocity structure functions up to order 9 follow a log-universality (Castaing et al. Phys. D Nonlinear Phenom. 1993); this leads to a collapse on a universal curve, when units including a logarithmic dependence on the Reynolds number are used. This paper then investigates the meaning and consequences of such log-universality, and shows that it is connected with the properties of a “multifractal free energy”, based on an analogy between multifractal and thermodynamics. It shows that in such a framework, the existence of a fluctuating dissipation scale is associated with a phase transition describing the relaminarisation of rough velocity fields with different Hölder exponents. Such a phase transition has been already observed using the Lagrangian velocity structure functions, but was so far believed to be out of reach for the Eulerian data.

scholarly journals A DISPERSIVE APPROACH TO THE ARTIFICIAL COMPRESSIBILITY APPROXIMATIONS OF THE NAVIER–STOKES EQUATIONS IN 3D

2006 ◽  
Vol 03 (03) ◽  
pp. 575-588 ◽  
Author(s):  
DONATELLA DONATELLI ◽  
PIERANGELO MARCATI
Keyword(s):  
Weak Solution ◽  
Stokes Equations ◽  
Velocity Fields ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Artificial Compressibility ◽  
Artificial Compressibility Method ◽  
Dispersive Approach ◽  
Incompressible Navier Stokes Equation

In this paper we study how to approximate the Leray weak solutions of the incompressible Navier–Stokes equations. In particular we describe an hyperbolic version of the so-called artificial compressibility method investigated by J. L. Lions and Temam. By exploiting the wave equation structure of the pressure of the approximating system we achieve the convergence of the approximating sequences by means of dispersive estimates of Strichartz type. We prove that the projection of the approximating velocity fields on the divergence free vectors is relatively compact and converges to a Leray weak solution of the incompressible Navier–Stokes equation.

scholarly journals Sir George Gabriel Stokes, Bart (1819–1903): his impact on science and scientists

2020 ◽  
Vol 378 (2174) ◽  
pp. 20190524
Author(s):  
Paul Ranford
Keyword(s):  
Royal Society ◽  
Large Scale ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Victorian Era ◽  
Wide Range ◽  
History Of ◽  
And Mathematics ◽  
Lord Kelvin

Lucasian Professor Sir George Gabriel Stokes was appointed joint-Secretary of the Royal Society in 1854, a post he held for the unprecedented period of 31 years, relinquishing the role when he succeeded T.H. Huxley as President in 1885. An eminent scientist of the Victorian era, Stokes explained fluorescence (he also coined the word) and his hydrodynamical formulae (the ‘Navier–Stokes equations’) remain ubiquitous today in the physics of any phenomenon involving fluid flows, from pipelines to glaciers to large-scale atmospheric perturbations. He also made seminal advances in optics and mathematics, and formulae that bear his name remain widely used today. The historiography however appears to understate Stokes's significant impact on science as unacknowledged collaborator on a wide range of scientific developments. His scientific peers regarded him as a mentor, advisor, designer of crucial experiments and, as editor of the Royal Society's scientific journals, arbiter of the standards of excellence in scientific communication to be attained before publication would be considered. Three brief case studies on Stokes's correspondence with Lord Kelvin, Sir William Crookes and the chemist Arthur Smithells exemplify how his impact was conveyed through the work of other scientists. This paper also begins consideration of why the character and worldview of Stokes led him to eschew personal reputation and profit for the sake of science and the Royal Society, and of how the development of the discipline of history of science has impacted on historiography relating to Stokes and others. This article is part of the theme issue ‘Stokes at 200 (Part 1)’.

Melting of Powder Particles in a Low Pressure Plasma Jet

1983 ◽  
Vol 30 ◽  
Author(s):  
D. Wei ◽  
D. Apelian ◽  
S. M. Correa ◽  
M. Paliwal
Keyword(s):  
Plasma Jet ◽  
Low Pressure ◽  
Navier Stokes ◽  
Temperature Dependent ◽  
Navier Stokes Equation ◽  
Free Jet ◽  
Binary Model ◽  
Proposed Model ◽  
Powder Particles ◽  
Heat And Momentum Transfer

ABSTRACTA numerical model has been developed to predict the temperature profile of particles injected in a D.C. plasma jet. The equations governing particle melting were applied to spherical powders of binary model alloys. Thermophysical properties of the gas and the powder material have been taken to be temperature dependent. In the proposed model, the latent heat of melting was taken into account by introducing apparent enthalpy as a function of the fraction of liquid formed which can be derived from equations describing non-equilibrium melting. The temperature and velocity profiles of the plasma jet used in this analysis are for a free jet (without target interference) and were calculated using the parabolic Navier-Stokes equation with a K-E turbulence model. Correction factors have been introduced to take into account non-continuum effects encountered in the low pressure environment and the results show that both heat and momentum transfer between the plasma gas and the injected particles are reduced.

On the direct initiation of a plane detonation wave

1986 ◽  
Vol 408 (1834) ◽  
pp. 129-148 ◽  
Keyword(s):  
Shock Wave ◽  
Detonation Wave ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Combustible Gas ◽  
Direct Initiation ◽  
Time Domains ◽  
History Of ◽  
Plane Detonation

It is assumed that energy is transferred at a rapid rate through a plane wall into a spatially uniform and initially stagnant combustible gas mixture. This action generates a shock wave, just as it does in an inert mixture, and also switches on a significant rate of chemical reaction. The Navier-Stokes equations for plane unsteady flow are integrated numerically in order to reveal the subsequent history of events. Four principal time domains are identified, namely ‘early’, ‘transitional’, ‘formation’ and ‘ZND’. The first contains a conduction-dominated explosion and formation of a shock wave; in the second interval the shock wave is responsible for the acceleration of chemical activity, which becomes intense during the ‘formation’ period. Finally a wave whose structure is in essence that of a ZND detonation wave emerges.

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