Plasma jets are used as directed sources of energy, momentum and excited species fluxes in diverse technologies, such as spray coating, chemical synthesis, waste treatment and pyrolysis. The fluid, thermal and electromagnetic dynamics from the jet produced by a direct-current non-transferred arc plasma torch are explored using time-dependent three-dimensional simulations encompassing the dynamics of the arc inside the torch, the development of the jet through the outside environment, and the later impingement of the jet over a substrate. The plasma flow is described mathematically by a chemical equilibrium and thermodynamic nonequilibrium (two-temperature) model and numerically by a coupled fluid-electromagnetic transport model and a Variational Multiscale Finite Element Method. Simulation results uncover various aspects of the flow dynamics, including the jet forcing due to the movement of the arc, the prevalence of deviations between heavy-species and electron temperatures in the plasma fringes, the development of shear flow instabilities around the jet, the occurrence of localized regions with high electric fields far from the arc, the fluctuating expansion of the gas ejected from the torch, and the formation and evolution of coherent flow structures.

Abstract

1. Introduction

References 1)  J. P. Trelles, “Computational Study of Flow Dynamics from a DC Arc Plasma Jet”, Journal

of Physics D: Applied Physics (2013) Vol. 46, No. 25, 255201. 2)  J. P. Trelles, C. Chazelas, A. Vardelle and J. V. R. Heberlein, “Arc Plasma Torch Modeling”,

Journal of Thermal Spray Technology (2009) Vol. 18, No. 5/6, pp. 728-752.

Department of Mechanical Engineering and Energy Engineering Graduate Program University of Massachusetts Lowell

Juan Pablo Trelles

Flow Dynamics from a Nonequilibrium Atmospheric-Pressure Arc Discharge Jet

Fig. 1. (left) schematic of the plasma inside a dc non-transferred arc torch and (right) optical high-speed image of the plasma jet.

Kevin-Helmholtz instability

4.2. Nonreflecting Boundary Conditions

3. Numerical Model 3.1. Variational Multiscale Finite Element Method

5. Flow Dynamics From a DC Plasma Jet

5.2. Thermodynamic, electrical & fluid relaxation

6. Conclusions

5.4. Instabilities Development

2. Mathematical Model

Table 1. Set of fluid – electromagnetic evolution equations for the arc discharge plasma flow; for each equation:

Transient + Advective – Diffusive – Reactive = 0.

Fig. 2. Computational domain for the flow from an arc plasma torch: (A) Spatial domain Ω, boundary surfaces (cathode, anode, inflow, outflow, substrate, and end face) and characteristic dimensions; (B) detail of the cathode region and

depiction of the current path; and (C) numerical domain of the sponge zone Ωs used to mitigate wave reflection from the outflow boundary.

4.1. Computational Domain

τ ≈ L−1 = (A0∂t + (Ai∂i )−∂i (Kij∂ j )−S1)−1

3.2. Solution Approach §  Time stepping: Predictor multi-corrector alpha method – fully implicit,

second order, control of resolved frequencies. §  Nonlinear solver: Globalized Inexact Newton-Krylov – robust & efficient. §  Linear Solver: Preconditioned GMRES.

4. Model Set-Up

R (Y) = −σY (Y−Y∞ )

§  Thermodynamic nonequilibrium (NLTE): dissimilar distribution functions for electrons and heavy-species (Th ≠ Te).

§  Optically thin radiative transport. §  Fully-coupled: Compressible, reactive, electromagnetic fluid.

5.1. Arc Reattachment and Flow Dynamics

Fig. 3. Flow dynamics during an arc reattachment event: Sequence of snapshots of Th distribution. The arrows indicate the location of the initial (old) and formed

(new) arc anode attachments. The total voltage drop is: (A) 32.6, (B) 34.2, (C) 35.6, (D) 32.5, (E) 31.5, (F) 29.8, (G) 31.2, and (H) 32.3 [V].

5.3. Thermodynamic Nonequilibrium

* Van Dyke, An Album of Fluid Motion

HOT  plasma  

COLD  gas  

Th Te

[K]

Optical emission

Smooth  and  sharp  

Smooth  but  diffuse  

Sharp  but  non-­‐smooth  

Anode phenomena

Cathode phenomena

Balance drag – Lorentz forces

Arc attachment

MHD instabilities

Fluid instabilities

Radiative transfer

Cold flow entrainment

Turbulence Chemical non-equilibrium

Thermodynamic non-equilibrium

Electrode erosion

§  Variational form: 0YWYW ==Ω⋅∫Ω ))(,()( RR d

§  Large scales: resolved §  Small scales: modeled

0YWYW =+ ∗ )',())(,( LR

) (' YτY R−=

large = f(small)

small = f(large)

' and ' WWWYYY +=+=

total = large + small

§  Scale decomposition:

“Standard” Finite Element

Methods

§  DC Arc Plasma Torches: Essential components of diverse industrial technologies, e.g. plasma spraying, metallurgy, gasification.

§  Flow in plasma torches controlled by diverse & complex phenomena …

approx. inverse of transport operator

§  Domains: Torch inside (arc dynamics), torch outside (jet dynamics), substrate region (impingement), “sponge zone” (nonreflecting outflow).

§  Discretization: Hexahedra Finite Elements (second order accurate); refined solid boundaries to capture sharp gradients.

Fig. 4. (Top) thermodynamic nonequilibrium parameter θ = Te/Th, (center) magnitude of effective electric field ||Ep||, and (bottom) magnitude of vorticity

during an arc reattachment event. The arrows indicate the location of arc anode attachments.

||ω ||=||∇×u ||

Fig. 6. Formation and development of shear flow instabilities: Sequence of snapshots of Th distribution in the region encompassing the cathode tip and the torch discharge. The arrows indicate the location where an instability develops.

5.5. Fluid Dynamics and Coherent Structures

Fig. 5. Instantaneous snapshots of: (Left) experimental optical emission, (center) electron temperature Te, and (right) heavy-species temperature Th.

Optical emission between

Te and Th fields

Fig. 7. Evolution of Q-criterion coherent structures. Three-dimensional, x-z and y-z views of the structures;

arrows point to a single lobular structure.

§  Outflow boundaries: “Reflected” information (i.e. pressure, vorticity, entropy, Alfven waves) can contaminate solution.

§  Sponge zone: Artificial zone for gradual damping of outgoing information – robust & computationally efficient.

§  Flow dynamics from an arc discharge plasma jet: Fully-coupled nonequilibirum simulations – capture from optical emission to instabilities.

§  Comprehensive (consistent & complete) turbulence model not yet included.

§  Flow structures: large-scale flow features that can be unambiguously identified.

§  Q-criterion: Symmetric (Ω) & anti-symmetric (S) parts of

Q0 reference value

QQ0

= 12 ((Ω :Ω)− (S :S))

∇u

Modification of plasma flow model in sponge zone Ωs:

σY = diag([ 1 0 0 1 1 0 0 0 0 0 ]T )

Y∞ = [ p∞ 0 0 0 T∞ T∞ 0 0 0 0 ]T

Damping parameters: Efficient +

minimal flow perturbation

High local electric

field

Vorticity layers