# Generation of Long Laminar Plasma Jets: Experimental and Numerical Analyses

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## Abstract

A novel direct current non-transferred arc plasma torch that can generate silent, stable and super-long laminar plasma jets in atmospheric air is investigated. The results showed that laminar plasma jets of length ranging from 100 to 720 mm in length can be generated by controlling the gas input rate ranging from 8.5 to 15 L min^{−1} and the output power from 8.5 to 28 kW. The length of the plasma jets generally increased with the output power and gas flow rate. Observations of temporal evolution of the plasma jet appearance and the voltage demonstrated that the jet is highly stable in the atmospheric environment. The fluid dynamic properties of the laminar plasma jet were studied using a numerical simulation incorporating a laminar flow model and an RNG turbulent flow model. Simulation results show the expansion of a high temperature region close to the torch nozzle exit, corresponding to a bright region observed in experiments.

## Keywords

Laminar plasma jet Voltage current characteristics Voltage vibration Numerical simulation## List of Symbols

*C*_{p}Specific heat at constant pressure (J kg

^{−1}K^{−1})*E*Electric field (V m

^{−1})*T*Temperature (K)

*W*Power (W)

*I*Current (A)

*Q*Gas flow rate (kg s

^{−1})*k*Turbulent kinetic energy (m

^{2}s^{−2})

## Greek Symbols

*ε*Dissipation rate of turbulent kinetic energy (m

^{2}s^{−3})*ε*_{r}Net emission coefficient (W m

^{−3}sr^{−1})*κ*Thermal conductivity (W m

^{−1}K^{−1})*μ*Dynamic viscosity (kg m

^{−1}s^{−1})*μ*_{t}Turbulent viscosity (kg m

^{−1}s^{−1})*μ*_{eff}Effective viscosity (kg m

^{−1}s^{−1})*σ*Electrical conductivity (S m

^{−1})*ρ*Density (kg m

^{−3})*ϕ*Electric potential (V)

## Abbreviations

- LTE
Local thermodynamic equilibrium

- RNG
Renormalization group methods

- MHD
Magnetohydrodynamic model

- NEC
Net emission coefficient

## Introduction

Thermal plasmas are characterized by heavy-particle and electron temperatures of order 10^{4} K, and typically operate at or near atmospheric pressure. They can be generated by electric arcs, which have high current densities, and can be transferred to the workpiece (as, for example, in arc welding, plasma cutting and other applications) or non- transferred (as, for example, in plasma spraying) [1]. In the non-transferred arc plasma torch, high temperature is achieved through a direct current (dc) arc induced between a conical cathode and an anode nozzle [2]. The arc properties depend on the internal-channel design of the torch, the type of working gas and its flow rate, the arc current and other operating parameters. The arc generates the high-temperature plasma through continuous energy dissipation of the current flowing through the gas. The plasma jet exits the torch from the anode nozzle, subsequently experiencing deceleration and cooling due to its interaction with the cold gas from the discharge environment. As a representative example, at an axial position of 100 mm from the nozzle exit, a pure argon plasma jet consists of about 80% air in an atmospheric environment [3]. The length of plasma jet in an atmospheric environment is usually less than 200 mm. Non-transferred arc plasma jets are used in deposition, gasification, waste conversion, metallurgy, some welding and cutting processes, and plasma spraying.

Arc plasma torches generally operate at high output power (25–150 kW) and high gas flow rate (usually ≥ 30 slpm) [2, 3], and generate high levels of noise to the surrounding environment (≥ 120 dB). In the atmospheric plasma spraying process, the fluid dynamics of the plasma jet lead to the development of turbulence associated with strong entrainment of ambient gas into the plasma jet, lowering the controllability and reproducibility during the plasma spraying process [4, 5]. The fluctuation behavior of the plasma jet and the internal arc instabilities also significantly affect both torch performance and coating quality [6, 7].

An alternative type of plasma jet is the laminar plasma jet, which operates at a relatively low Reynolds number at the nozzle exit and reduces turbulent cold gas entrainment and the axial attenuation of the jet temperature and velocity. During the past three decades, several groups around the world have researched direct-current non-transferred arc plasma torches that can generate stable, long, quasi-laminar or totally laminar plasma jets. Zhukov and coworkers took the lead in designing a powerful high-enthalpy direct current plasma torch that was applied to plasma chemical technologies [1, 8]. Their design featured several linear interelectrode inserts between the cathode and the anode to extend the arc column [9].

Subsequently, a plasma torch with a much larger nozzle outlet and a jet length up to 600 mm was developed by Hamatanis of the Nippon Steel Corporation in 1999. This torch used an optimized interelectrode geometry and was used in metallic pipe butt welding and the synthesis of fine powders [10, 11].

At almost the same time, W. X. Pan and C. K. Wu from the Chinese Academy of Science designed an argon- nitrogen direct- current plasma torch that can generate a long, silent and stable plasma plume within a wide range of working parameters in either the ambient environment or in a low-pressure environment [12, 14]. The laminar plasma jet had a length up to 45 times its diameter and was applied to depositing thermal sprayed coatings and for strengthening metallic surfaces by remelting [12, 13]. Since then, researchers from Pan’s group and Chen Xi’s group studied the flow characteristics of this laminar plasma torch and jet using experimental and numerical simulation methods. These works included the studies of torch geometry and the voltage–current characteristics [14, 15, 16], experimental measurement of the jet flow field [17, 18] and the heat flux density of the plasma plume [19]. They performed experimental and numerical investigations of the laminar plasma jet impinging on a substrate [20, 21, 22, 23, 24], observations of the arc root motion in the cylindrical channel of the plasma torch [25] and two and three-dimensional modelling of laminar plasma jets with or without the entrainment of ambient air and a cylindrical shield [26, 27, 28, 29]. These results explored the effects of natural convection and lateral particle injection on the laminar plasma jet [30, 31] and compared the performances of turbulent and laminar plasma jet using experimental and numerical analyses [28, 32]. These fundamental studies and practical achievements made huge contributions to the field of laminar plasma torch research.

In the thermal spraying research area, the huge entrainment of surrounding gas and turbulent transport in the plasma plume always occurred in atmospheric environment. The coating quality is significantly affected from the jet instabilities of the plasma torch [33]. This newly developed laminar plasma torch has significant potential for application in advanced thermal spraying processes [12, 34, 35] and other materials processing technologies [9, 11, 13].

In this work, a novel direct-current non-transferred arc plasma torch with a unique inside channel structure is presented. This torch can also generate long, silent and stable laminar plasma plumes in atmospheric environment at different gas flow rates and output powers. The fluid dynamic properties of the laminar plasma jet have been studied by a combination of experiments and numerical simulation. Experiments have been conducted to study the voltage–current and plasma jet flow characteristics under various working parameters, including the jet lengths variation, time-resolved of arc voltage fluctuation and jet plume. The numerical simulation was modelled in two-dimensional calculation domain by using Laminar model and RNG turbulent transport model.

## Characteristics of Plasma Jet, Power Supply and Working Parameters

### Properties of the Laminar Plasma Jets

^{−1}or higher than 15 L min

^{−1}, the plasma jets become uniformly short (about 80 mm) and extremely noisy (about 110 dB) because of intense entrainment of ambient air, just as in the case of conventional direct-current non-transferred arc plasma jets.

^{−1}(Fig. 5). The maximum length of the laminar plasma jet reaches 720 mm at a current of 160 A and a gas flow rate of 8.5 L min

^{−1}; this is longer than the values obtained in other published studies [9, 11, 14]. At the high gas flow rate of 15 L min

^{−1}and a current of 160 A, a stable laminar plasma jet with a length greater than 200 mm is also generated (Fig. 3b). As shown in Fig. 4, the length of the laminar plasma jet decreased approximately monotonically with increasing gas flow rate at a given current. The laminar plasma jets at a current of 160 A (Fig. 4b) were all longer than those at a working current of 100 A (Fig. 4a) for every gas flow rate investigated, suggesting that the higher output power associated with the higher current increases the nozzle exit temperature and velocity.

### Arc Voltage–Current Characteristics Under Various Conditions

#### Arc Voltage Current Characteristics in Different Gas Mixtures

#### Arc Voltage–Current Characteristics for Different Gas Flow Rates

Initially, at a relatively low current (from around 60 to 70 A), the arc voltage decreases slightly with increasing current. This is because the arc temperature increases and the arc expands rapidly, so the electrical conductivity averaged over a radial cross-section of the arc increases. As the current increases further, the arc diameter remains approximately constant, and the electric conductivity increases less rapidly than the current. The voltage is approximately constant for a small range of currents, and then increases as the current continues to increase from about 80 A to 165 A. The voltage–current curve has an approximate U-shape over a large portion of its range. This behaviour is opposite to that of conventional direct current non-transferred arc plasma torches with a linear channel structure, such as the Sulzer PTF4 Gun, 3 MB Gun and Praxair SG-100 Gun, which exhibit voltage–current curves with a drooping shape at the same level of output power [4, 5]. Moreover, the rising voltage–current characteristic enables the power supply to maintain an electrical efficiency close to unity. It is worth noting that the same rising voltage–current characteristics can be obtained in other laminar plasma torches that with very different inner channel structures: those of Osaki et al. [38], Pan et al. [14], M. F. Zhukov et al. (2003) [8, 39], Vilotijevic et al. [40] and Wang et al. [41].

## Modelling of the Long Laminar Plasma Jet

Computational fluid dynamics modelling was performed to obtain greater understanding of the flow and heat transfer characteristics of the laminar plasma jet. A two-dimensional axisymmetric steady-state modelling approach was applied in this study. The model is constituted by the governing equations of conservation of mass, momentum and energy, and is implemented in the commercial software package ANSYS-Fluent v16.0. The simulations used was the pressure-based solver, the SIMPLE algorithm, and second order upwind differencing. The model assumes that the plasma is in Local Thermodynamic Equilibrium (LTE).

In these equations, *u* and *v* are the axial (*x*) and radial (*r*) velocity components; *ρ*, *μ*, *k*, *C*_{p}, and *4πε*_{r} are the plasma density, viscosity, thermal conductivity, specific heat at constant pressure, and radiated power per unit volume of plasma, respectively.

The Renormalization Group *k*-*ε* Model (RNG) was used for modelling turbulent viscosity in this study [42]. The RNG theory provides an analytically-derived differential formula for effective viscosity that accounts for low Reynolds-number effects, and an analytical formula for turbulent Prandtl numbers, while the standard *k*-*ε* model uses user-specified constant values. These features make the RNG *k*-*ε* model more accurate and reliable for a wide class of flows than the standard *k*-*ε* model, especially in the case of the laminar plasma jet considered here.

*G*

_{k}represents the generation of turbulent kinetic energy due to the mean velocity gradients, and

*Y*

_{M}represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate [42]. The quantities

*α*

_{k}and

*α*

_{ε}, respectively the inverse effective Prandtl numbers for

*k*and

*ε*are both set equal to 1.393.

*C*

_{1ε}and

*C*

_{2ε}are set equal to 1.42 and 1.68 respectively. The main difference between the RNG and the standard

*k*-

*ε*model lies in the additional term of the turbulent dissipation equation given by:

*η*

_{0}= 4.38,

*β*= 0.012,

*C*

_{μ}= 0.0845. The effective viscosity is given by:

For the case of laminar flow simulations, Eqs. (1) to (4) were used by setting the turbulent viscosity µ_{t} equal to 0 and Eqs. (5) and (6) were removed from the model. The effective viscosity option in the RNG Model was used in the simulation. This allows modelling of the effective turbulent transport variation with the effective Reynolds number (or eddy scale), allowing the model to better handle low- Reynolds- number and near- wall flows [42].

Actually, authors have tried Standard k-ε Model, k-omega Model, Reynolds Stress Model and Spalart–Allmaras Model to simulate this plasma jet. These results list in the supplement files. However, these results are all far away from the experiment observations.

^{−1}. The maximum velocity and temperature at the inlet are respectively 2024 m/s and 16 870 K. The boundary BC is the water-cooled wall of the torch nozzle, for which the thermal boundary conditions is specified by a heat transfer coefficient (

*h*

_{w}) of 1.0 × 10

^{5}W m

^{−2}K

^{−1}and reference cooling water temperature (

*T*

_{w}) of 500 K.

_{2}mixtures used in the model and air for the characteristics of the plasma jet (i.e. temperature < 14,000 K).

^{−1}is about 100 mm. The high temperature jet expands rapidly as it is ejected out of the nozzle exit. The temperature distribution showed a high-temperature vortex region at over 10,000 K very close to the nozzle exit before narrowing to form a uniform and slowly expanding jet. This is consistent with the experimental observation shown in Figs. 3a and 15 of the presence of a bright region close to the nozzle exit.

## Conclusions

This article presented the experimental and numerical study of a novel direct current non-transferred arc plasma torch that can generate different lengths of long laminar plasma jets in ambient air. The results showed that the long laminar plasma jets can be conveniently controlled through the gas flow rate and output power of the equipment. The experimental observations of the plasma jet indicated a high stability in the atmospheric environment. The maximum jet length can reach about 720 mm in air. An increasing voltage current characteristic was obtained under a gas flow rate of 8.5–15 L min^{−1} and a working current of 60–165 A, for operation with a mixture of 70% nitrogen and 30% argon by volume.

The flow characteristics of the long laminar plasma jet were studied using two-dimensional computational fluid dynamics model that makes use of nozzle data produced by a coupled electromagnetic and fluid dynamic model of the plasma inside the body of the torch. A bright region near the nozzle exit that was observed in the experiments corresponds to a region predicted to be at the temperature of over 10,000 K; the temperature was predicted to rapidly decrease downstream of the bright region. The attenuation of velocity along the torch axis was smaller than that of temperature. The turbulent kinetic energy and intensity were predicted to be highest near the nozzle exit. This is in contrast to conventional plasma torches, in which they are largest in the regions at the interface between the expanding plasma jet and the atmosphere.

## Notes

### Acknowledgements

The authors are grateful to Prof. Ren-zhong Huang from the Department of New Materials of Guangzhou Non-Ferrous Metal Research Institute for his selfless help with the computer programming. This work was supported by the Natural Key R&D Program of China (Basic Research Project, Grant No. 2017YFB0306104), the Ph.D. Short-term Academic Visiting Program of Graduate School of Xi’an Jiaotong University and National Ph.D. Degree Program of the China Scholarship Council.

## Supplementary material

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