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A two-fluid model of turbulence for a thermal plasma jet

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Abstract

In this paper, a turbulent argon plasma jet issuing into a stagnant argon environment at 1 ATM is .studied by applying a two-fluid turbulence model, in order to advance our understanding of thermal plasma jets. The mathematical model has some similarities to the models of two-phase flows, so that the turbulent plasma jet is treated as a two-phase mixture. The governing equations include the transport equations far mass, momentum, and energy far two different fluid parcels (in-moving parcels and out-moving parcels). Auxiliary relations that govern the physical phenomena of the interfluid mass, momentum, and energy exchange are preserved together with a description of the mechanisms that control the growth or diminution of the fragment size. The results are presented with conditional- and unconditional-averaged forms and compared with experimental results from enthalpy-probe measurements. A well-known nondimensional farm (a Gaussian error function) can represent the radial distributions of the measured- and predicted-unconditional mean axial velocity and temperature in consecutive sections (20–45 mm from the nozzle exit). Further insight into the behavior of turbulent plasma jets can be gained by looking at the conditional fluid properties. The results show that this model can predict phenomena that escape more conventional models, e.g., the uninixing phenomenon.

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Abbreviations

C a ,C b :

constants in the fragment-size equation

C f :

interfluid friction constant

C m :

interfluid mass-transfer constant

C ν :

shear-source constant

C μ :

turbulent-viscosity constant

c p :

specific heat at constant pressure of fluidi

d :

nozzle diameter

f ii :

interfluid friction

h :

mean specific enthalpy

h i :

mean specific enthalpy of fluidi

I :

arc current

k :

turbulent kinetic energy

l :

effective length scale

l i :

fragment size of fluidi

l p :

Prandtl mixing length

m ii :

interfluid mass-transfer rate

Pri :

turbulent Prandtl numberp pressure

O :

net power input to the plasma jet

r :

spatial coordinate (normally radial)

r i :

volume fraction of fluidi

S R i :

radiation loss of fluidi (+)

S ν :

shear-induced source of momentum

T :

mean temperature ath, whereh=(r 1 ρ 1 h1 +r2ρ2h2)/ρ

T i :

mean temperature of fluidi

t :

time coordinate

U :

average ofU 1 andU 2 : U = (r1ρ1U1 + r2ρ2U2)/ρ

U i :

velocity component of fluidi in thex direction

V i :

velocity component of fluidi in ther directionV volt arc voltage

V t :

velocity vector of fluidi

x :

spatial coordinate (normally axial)

δ Θ :

half-width of the thermal jet, the value ofr for which Θ=Θν/2

δ U :

half-width of the momentum jet, the value ofr for whichU=U ν /2

ε :

dissipation rate of turbulent kinetic energy

Γ h i :

energy-dlffuslon-exchange coefficient of fluidi

γ :

intermittent factor

η :

thermal efficiency of the torch

η Θ :

dimensionless coordinate,r/δ Θ

η ν :

dimension less coordinate,r/δ ν

κ l :

thermal conductivity of fluidi

μ l :

effective dynamic viscosity of fluidi

μ l i :

laminar dynamic viscosity of fluidi

μ l :

turbulent dynamic viscosity

Θ:

excess mean temperature (T−T a )

ρ :

average density:ρ=r 1 ρ1 + r2ρ2

ρ i :

density of fluidi

a :

ambient environment

c :

property corresponding to centerline

i :

fluidi

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Authors and Affiliations

  1. ERC for Plasma-Aided Manufacturing, Department of Mechanical Engineering, University of Minnesota Minneapolis, 55455, Minnesota

    P. C. Huang, J. Hebeylein & E. Pfender

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  1. P. C. Huang
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  2. J. Hebeylein
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  3. E. Pfender
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Huang, P.C., Hebeylein, J. & Pfender, E. A two-fluid model of turbulence for a thermal plasma jet. Plasma Chem Plasma Process 15, 25–46 (1995). https://doi.org/10.1007/BF01596680

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