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Some perspectives on the modeling of plasma jets

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Abstract

A mathematical representation is developed describing the temperature and the velocity profiles and mixing in a plasma jet discharging into ambient air. In the model, realistic allowance is made for turbulent behavior, the temperature-dependent property values, and also for the boundary conditions, including entrainment. The more precise definition of the boundary conditions, mixing, and entrainment are thought to be important novel features of this work. The theoretical predictions were found to be in good agreement with measurements reported by Vardelle regarding the behavior of a nitrogen plasma, but the agreement was less satisfactory for an argon plasma jet. Possible reasons for the discrepancy are discussed.

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Abbreviations

C 1,C 2,C D :

constants inK-ε turbulence model

h :

enthalpy

H 1 :

length of integration region

H 2 :

width of integration region

K :

turbulent kinetic energy per unit mass

m :

mass concentration of plasma

Q f :

mass flow rate of plasma gas for flat inlet profiles

Q P :

mass flow rate of plasma gas for parabolic inlet profiles

P w :

torch power

r :

radial coordinate

R 0 :

internal radius of torch exit

S Φ :

source term for dependent variable Φ

S R :

radiation loss per unit volume of plasma

T a :

ambient temperature

T m :

maximum temperature

T t :

torch tip temperature

u :

velocity inz-direction

u C 1 :

velocity at and in the direction of the symmetry axis of the flow

u m :

velocity of plasma atr=0 andz=0 (maximum velocity)

Δu :

axial direction velocity difference across the width of the mixing region

v :

velocity in r direction

Y :

radial width of the mixing region

z :

axial coordinate

ρ:

density

μ, μe, μt :

molecular, effective, and turbulent viscosities, respectively

ε:

dissipation rate of turbulence energy

η:

thermal efficiency of plasma torch

σ:

Prandtl/Schmidt number forh, K, ε, andm

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Author notes

  1. J. Szekely (Professor of Materials Engineering)

    Present address: Department of Materials Science and Engineering, Massachusetts Institute of Technology, 02139, Cambridge, Massachusetts

Authors and Affiliations

  1. Department of Materials Science and Engineering, Massachusetts Institute of Technology, 02139, Cambridge, Massachusetts

    A. H. Dilawari

Authors
  1. A. H. Dilawari
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  2. J. Szekely
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Visiting Fulbright Scholar and Associate Professor of Chemical Engineering, on leave from the Institute of Chemical Engineering and Technology, Punjab University, Lahore-20, Pakistan.

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Dilawari, A.H., Szekely, J. Some perspectives on the modeling of plasma jets. Plasma Chem Plasma Process 7, 317–339 (1987). https://doi.org/10.1007/BF01016520

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  • DOI: https://doi.org/10.1007/BF01016520

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