## 2 Experimental Approach  
The experimental system is shown in Figure 1. An air compressor was used as the gas source. The volume of the gas storage tank was 1 cubic meter, the power was 15 kilowatts, and the maximum realizable steady air supply flow was 2400 SLPM. The air flow rate was monitored by a hot air flowmeter with a full range of 500 SLPM and a precision of 1.0%-1.5%. In the experiment, the AC power supply (CTD-1000Z, Nanjing Corona Lab) was used to supply the discharge tube, allowing a maximum voltage of 20 kV and rated power of 2000 W. The output high voltage of the power supply was connected to the outer side of the high voltage electrode flange of the discharge tube, and the convergent nozzle was grounded to realize the arc discharge between the discharge cone and the nozzle. The discharge parameters were measured using a P6015A high voltage probe and TCP0030A current probe and the data were collected with a MDO3024 digital oscilloscope. A Phantom-v2512 high-speed camera captured the discharge details. When the maximum resolution was 1024 \(\times\) 1024, the maximum shooting speed was 20,000 frames per second. When the minimum resolution was used, the maximum shooting speed was 670,000 frames per second. As shown in Figure 2, when air was supplied to the discharge chamber, it passed through a double-loop swirler first, which made the air flow rotate clockwise, seen from back to front. The external diameter of the swirler was 50 mm, and there were two circles of 3 mm diameter holes on the circumference of 28 mm and 38 mm in diameter. The number of holes in each circle was 12. The angle between the center axis of the hole at inner ring and the axis of the discharge tube was 35.94 degrees, and the angle between the center axis of the hole at the outer ring and the axis of the discharge tube was 44.52 degrees. Therefore, the degree of air swirl in the outer oblique hole was more severe than that in the inner oblique hole. The high-voltage electrode was arranged in the downstream direction 90 mm from the axial distance of the swirler. The high-voltage electrode was similar to a flange shape. The discharge cone was fixed on the central axis of the discharge tube through four fixed ribs with a width of 3 mm on the inside of the flange. The discharge cone can be replaced by a threaded connection. A diversion cone was set on the upstream side of the high-voltage electrode to minimize the influence of the presence of the high-voltage electrode on the flow field and pressure loss. The high voltage electrode flange was connected to a flange made of Teflon (PTFE) to realize the insulation of the grounding electrode and the swirler. The grounding electrode was a convergent  
Figure 1: Schematic diagram of gliding arc discharge experimental system. nozzle with a minimum inner diameter of 15 mm. The discharge structure can be assembled to satisfy that the minimum cross section of the discharge cone end and convergent nozzle is on the same plane. Six discharge cones with diameters of 5 mm to 10 mm and an interval of 1 mm were selected and numbered from small to large as No. 1 to No. 6. The discharge gap could be 5 mm, 4.5 mm, 4 mm, 3.5 mm, 3 mm, and 2.5 mm with the change of the size of the discharge cone. The total length of the extension tube used in the experiment was 100 mm (the condition of adding an extension tube is expressed in A, and the condition of not adding an extension tube is expressed in B). In the case of the 250 SLPM air flow, the arc evolution process of six kinds of discharge cones with and without extension tubes was photographed from the front and side, respectively. The influence of the extension tubes on arc length, arc rotation frequency, and regeneration frequency was studied. The effects of air flow rate (100-400 SLPM) on arc length, arc rotation frequency, and regeneration frequency were studied when the extension tube was added and the No. 5 discharge cone used.