Thermal plasmas have a great variety of applications in many industries, including arc welding, surface treating, ultrafine  particle synthesis, carbon nanotubes production, etc.^{[1– 5]} Owing to the advantages in high concentrated energy flux, high chemical reactivity, and high temperature, more and more attention has been paid to the plasma conversion of fossil resources and biomass to produce syngas or acetylene.^{[6, 7]}

Due to the steep temperature gradient and non-uniformity inside the plasma jet, it is difficult to achieve good mixing between processing materials and the plasma jet.^[1] A larger volume of homogeneous plasma could be obtained when an external magnetic field is applied.^[8] Also the magnetically driving plasma arc will spread the heat load on the anode surface, reduce erosion of the electrode and increase the mixing efficiency, which has been used in the 1-MW plasma torch of AVCO^[9] and the 9-MW plasma torch of DuPont.^[10]

The current– voltage (I– V) characteristic is one of the major characteristics of the plasma torch.^[11] This characteristic depends on both the geometry of the torch and operating parameters such as anode size, gas flow rate, working gas, etc. Shashkov and Yas’ Ko^[12] introduced similarity theory to characterize the DC plasma around the 1970s, and many relevant dimensionless numbers were established. Similarity theory^{[12, 13]} has been successfully used to study plasma characteristics. It provides a reasonable way to construct the relationship between experimental data and mathematical formula. Then the experimental workload could be reduced, and the corresponding plasma characteristics can be predicted. The similarity theory was used in DC vortex plasma torches, which included the button and well-type cathode by Brilhac et al.^{[14, 15]} and Zhang et al.^[16] reported the characteristics of a DC dual-jet plasma generator. Paingankar et al.^[17] used the dynamic similarity to characterize a non-transferred plasma spray torch.

Therefore, it is of theoretical and practical significance to study the current– voltage (I– V) characteristic of the plasma torch for designing and operating the torch.

In the present work, two sets of plasma torches are designed and built. The corresponding powers are 50  kW (smaller one) and 1  MW (larger one), respectively; they are designed similarly in geometry as shown in Fig.  1. Both the plasma torches are conducted under a constant current power supply. The circuit voltages for the 50-kW torch and the 1-MW torch are 500  V and 2000  V, respectively. Atmospheric hydrogen plasmas are produced at different anode sizes, gas flow rates, and magnetic flux density (Table  1).

Fig.  1.

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	Fig.  1. Schematic diagram of the experimental set-up. 1: cathode; 2: anode; 3: cooling water inlet; 4: quenching water inlet; 5: gas outlet; 6: quenching chamber; 7: anode chamber; 8: magnetic coil; 9: cooling water outlet; 10: gas entrance.

Table 1.

Table 1.

Table 1. Experimental conditions. Parameters 50-kW torch 1-MW torch Anode inner diameter D/mm 25, 30, 35 100, 130 Anode length/mm 180 400 Current/A 80– 200 250– 650 Gas flow rate G/(Nm3/h) 4– 19 94– 319 Magnetic flux density B/T 0.01– 0.17 0.01– 0.12

Table 1. Experimental conditions.

The anode chamber can be reassembled with anodes of different sizes. Three anodes with different inner diameters are adopted in the 50-kW torch: 25  mm, 30  mm, and 35  mm, respectively. The corresponding diameters of the cathodes are 6  mm (50  kW) and 20  mm (1  MW), respectively.

For the 1-MW plasma torch, anodes with 100  mm and 130  mm are used. Cooling water continuously flows to the anode and the cathode to ensure the temperature of the plasma torch is kept at a reasonable limit level. All the experimental data are collected by a computer system.

The similarity theory provides a feasible way to generate a relationship between experimental data and mathematical formula, and then the corresponding plasma characteristics can be predicted.

According to Shashkov’ s theory, ^[12] considering thermal conductivity, electric field, and enthalpy as the major physical parameters, the relevant dimensionless numbers can be derived as follows:

Here, variables with subscript “ 0” refer to the reference values, G is the gas flow rate, μ the viscosity, L the difference in radius between anode and cathode, σ the electrical conductivity, h the specific enthalpy, λ the thermal conductivity, T the temperature, I the arc current, and U the arc voltage.

In this case, an additional external magnetic field is used in the plasma torch, so it should be taken into consideration. The dimensionless quantity about magnetic pressure is

Here, v₀ is the initial gas inlet velocity, and B is the magnetic flux density. The Reynolds number associated with the magnetic field strength could be changed into

Then, the five dimensionless quantities involved can be obtained as

According to the five dimensionless quantities, the similarity formula can be written as

According to the power law approximation, ^[17] equation  (12) could be expressed as

Physical properties of hydrogen under a certain reference temperature^[13] are chosen as the reference values (Table  2) used in the formula above.

Table 2.

Table 2.

Table 2. Reference values of H2 plasma.[13] Physical variables Reference values of H2 plasma Temperature T0/K 1.23× 104 Electrical conductivity σ 0/(S/m) 4.54× 103 Viscosity μ 0/Pa· s 5.89× 10− 5 Thermal conductivity λ 0/(W/(m· K)) 5.31 Enthalpy h0/(J/kg) 6.01× 108 Density ρ 0 (kg/Nm3) 9× 10− 4

Table 2. Reference values of H2 plasma.[13]

Three anodes with different inner diameters for the 50-kW plasma torch are used: 25  mm, 30  mm, and 35  mm. For the arc current in a range between 80  A and 200  A, the arc voltage decreases with the increase of arc current. When the gas flow rate increases, the arc voltage increases. The same positive trend can be found when the magnetic flux density changes.

The negative current– voltage characteristics are found to be the same in the case of the 1-MW plasma torch with two anodes (inner diameters are 100  mm and 130  mm). The similarity theory is applicable to the characterization of the magnetically rotating DC plasma, and the formula which is satisfied by the experimental data of different torches is found to be reasonably appropriate. The linear fitting result shows that the Pearson correlation coefficient is 0.9958.