A new electromagnetic probe array diagnostic for analyzing electrostatic and magnetic fluctuations in EAST plasmas

1.   Introduction

Ultra-high voltage (UHV) hybrid DC power transmission is an essential technical means to implement the national strategy of 'carbon peaking and carbon neutral' and to achieve long-distance and high-capacity transmission of clean energy [1, 2]. When a fault occurs in the receiving AC system, the fault quickly develops and creates a large power surplus on the flexible bus, resulting in an overvoltage and a serious threat to the safety of the converter manifold. It urgently requires a quick energy relief device on the flexible bus to control the switching equipment with an action time <1 ms and a rated voltage of up to 100 kV to achieve a rapid release of surplus energy, reduce overvoltage and achieve the purpose of safe protection of the transmission system [3–7]. The gas gap switch based on pulse power technology is extended by a high-voltage pulse discharge to generate an arc along the surface, which ablates the insulating gas-producing material inside the trigger cavity and generates a large amount of plasma, which is rapidly jetted to the main gap under the action of high-pressure to achieve sub-millisecond conduction [8, 9]. This is important to enhance the safe and stable operation of the UHV hybrid DC transmission system.

The plasma jet is an important conduction medium in the process of gas gap switch-induced breakdown, its development process and the change of characteristic parameters directly affect the success or failure to conduct. Scholars have carried out studies related to the development process of plasma jets from both numerical calculations and experimental tests, respectively.

In terms of numerical calculations, scholars are currently focusing on the expansion characteristics of the plasma jet. Zhang et al [10] used FLUENT to simulate the plasma jet development process at small discharge energy (100 J). It is concluded that the pressure in the flow field gradually decreases in magnitude with time, and the mixing effect continues to intensify. Kim et al [11] established a two-dimensional unsteady mathematical model. It is assumed that the plasma is an ideal gas, and the structural characteristics after ejecting into the atmosphere are calculated by the arc Joule heat equation. Plasma jets are imperfectly expanded in the atmosphere, accompanied by Mach disks and spherical shock waves. Sharikov et al [12] recorded the position of the Mach disk on the jet axis through numerical calculation and gave the relationship between the axial distance from the jet outlet to the Mach disk and the pressure in the capillary and the ambient pressure. It is found that the structure of the plasma jet is similar to that of the stable highly incomplete expansion jet. Shao et al [13] concluded that with the increase of trigger energy, the electron temperature and electron density of the plasma jet increased, and the initial velocity of the jet accelerated, forming a high-temperature and high-speed jet in the calculation region. At the nozzle, a periodic shock wave effect is generated due to the strong interaction of the plasma jet with the ambient medium. The head of the plasma jet has a high-pressure value, which is a compression wave. The middle part of the plasma has a relatively low-pressure value, which is an expansion wave. Wang et al [14], Mazouffre et al [15] and Pei et al [16] suggested that the higher the discharge energy, the faster the plasma jet flow and the wider the flow field distribution. Increasing the deposition energy, reducing the diameter of the jet nozzle, and increasing the diameter-to-height ratio for the same trigger cavity volume can also produce high-velocity airflow.

In terms of experimental studies, a large number of studies have been carried out on the spatial and temporal evolution of the plasma jet process and the propagation mechanism. Dong et al [17] and Tie et al [18] used a high-speed camera to observe the plasma jet process, and the experiments showed that the plasma was approximately axisymmetrically distributed. The energy of the applied pulse was increased, and the transition of the plasma jet from 'bullet' to 'surge' propulsion was accelerated. This accelerates its axial and radial motion and effectively reduces the discharge delay and jitter. Dong et al [19] studied the development of plasma jet motion in different environmental media. As the ambient medium cools and the plasma jet appears to be strongly coiled and turbulent, the plasma gradually dissipates. The suppression effect of the strongly electronegative gas SF₆ accelerates the dissipation rate and leads to intermittent phenomena at the end of the plasma jet development. Huang et al [20] conducted a series of experiments on the temporal and spatial distributions of plasma parameters such as temperature, pressure, density, and the velocity of the plasma jet. It was found that when the plasma jet left the capillary and was injected into the atmosphere, its temperature, pressure, and density all decayed rapidly. The velocity of the plasma jet at the nozzle of the trigger chamber was about 1.3 km·s^-1. Dong et al [21] used pseudo-color image processing methods to highlight the inherent characteristics of the plasma images and extracted the plasma characteristic regions by using an adaptive double-threshold algorithm for fine segmentation of the images to obtain the characteristic parameters characterizing its evolution process. However, during the development of the plasma jet, its brightness changed in real-time, making it difficult to accurately extract its characteristic parameters using a grey-scale threshold. Pavlenko et al [22] studied the pressure propagation law of shock waves generated by capillary electrical explosions using ceramic piezoelectric sensors and pointed out that the shock waves generated by wire explosions contain two components, which are generated during the phase change of the wire from liquid to gas, and during the breakdown of the wire vapor. A shock wave measurement is widely used in the field of wire electrical explosion, but in the field of gas gap switches there is still little research.

In summary, there have been more experimental studies of the plasma jet process. However, the existing simulations mainly study the expansion characteristics of the plasma jet in the atmosphere without combining with the experiment, ignoring the changes in the key characteristic parameters of the plasma jet, and the relevant experimental studies mainly focus on the parameters such as electron temperature, density, and velocity of the plasma jet, without considering the plasma jet shock wave effect. Moreover, the plasma jet applied to the fast energy release device has large trigger energy and high velocity, and its jet process and characteristic parameter changes are more complicated. Therefore, it is necessary to perform numerical calculations to investigate the development of the plasma jet process of the gas gap switch. In view of this, this work establishes a two-dimensional transient fluid calculation model of the gas gap switch plasma jet process based on the renormalization-group (RNG) k-ε turbulence equation, investigates the spatial and temporal distribution of its characteristic parameters (pressure, velocity, etc), explores the jet motion process and the distribution of flow field parameters for different trigger voltages and gas media, and verifies them experimentally.

2.   Numerical calculation model of plasma jet process of gas gap switch

2.1   Basic assumptions of two-dimensional flow field of plasma jet

The gas switch trigger cavity studied in this paper is a two-stage along-face trigger structure. The process of plasma jet generation and its injection is as follows. The first cavity generates a small amount of plasma through high-voltage pulse surface discharge. As the plasma moves into the second cavity, the middle electrode and ground electrode are shortened by the plasma jet. The electric arc ablates the inner wall of the trigger cavity, generating a large amount of plasma consisting of neutral molecules, atoms, electrons, positive and negative ions, and other mixed matter in an aggregated state. The pressure inside the trigger cavity increases significantly due to the Joule heating effect of the arc current. The gas in the cavity is expanded by heat and ejected from the nozzle, forming a high-temperature, high-velocity plasma jet that strongly interacts with the ambient medium. To simplify the computational analysis, the plasma is considered an ideal gas in this paper, and the influences of the plasma composition and its own complex electrochemical reactions on the plasma jet properties are ignored. Meanwhile, after the plasma is jetted out of the cavity, the influence of the external electric field can be ignored due to the large distance of the external gap, so only the aerodynamic effect is studied.

The working mechanism of the plasma generated by the ablation of the trigger cavity is based on the Joule heating effect of the electric arc, so from an image-only point of view, the detailed physicochemical processes of the plasma can be ignored and only equated to the effect of an applied heat source. In this work, we established a numerical model of the finite element flow field and the following assumptions are made for the plasma jet process in combination with experimental conditions as follows [23–26].

(1) The thermal performance and motion development characteristics of plasma are determined by temperature and nozzle pressure, which are in local thermal equilibrium without considering space radiation.

(2) The plasma jet is regarded as an ideal compressible gas, and the jet process mainly considers fluid properties.

(3) The plasma forms a free jet in the atmospheric environment, ignoring the chemical reaction between the plasma and the surrounding gas medium components.

(4) The plasma viscosity, electromagnetic force, mass force, volume force and other secondary factors are ignored.

2.2   Mathematical equation of two-dimensional flow field of plasma jet

According to the gas dynamics theory, the process of a plasma jet changing with velocity is divided into three fluid state modes: laminar flow, transition state, and turbulence state. The Reynolds number is used to judge the plasma fluid state simply:

where $\rho$is the plasma density, ξ is the fluid viscosity, respectively taking 1 kg·m^-3 and 1.785×10^-5 m²·s^-1 [27], d is the diameter of the trigger cavity nozzle, taking 2×10^-3 m, $\nu$ is the plasma jet velocity, taking 0.4–1.0 km·s^-1. When $\nu$ is small, i.e. $Re$<2000, the plasma jet is in the laminar low, when 2000≤$Re$<4000, it is in the transition state, when $Re$ ≥4000, it is in the turbulent state. By calculation, the value of $Re$ in the plasma jet process of the gas gap switch is 0.4×10⁵–1.3×10⁵, so its jet development process belongs to a turbulence state.

To analyze the development process and flow field distribution rule of the plasma jet, COMSOL Multiphysics simulation is used, and the RNG k-ε turbulence model is established and solved. The governing equations of numerical simulation mainly include: mass conservation equation, momentum conservation equation, energy conservation equation, kinetic energy conservation equation, turbulence basic equation and gas state equation [28–30].

(1) The mass conservation equation

(2) The momentum conservation equation

where $S_u$ and $S_v$ are, respectively:

(3) The energy conservation equation

where $S$ is the energy source term.

(4) The RNG k-$\epsilon$turbulence equation

where: $G_k$ is turbulent kinetic energy caused by average velocity gradient, $G_{\mathrm{b}}$ is buoyancy induced turbulent kinetic energy, $Y_{\mathrm{M}}$ is the effect of compressible turbulent energy on total dissipation rate, ${\alpha }_k,$${\alpha }_{\epsilon }$ are the inverse of the effective turbulent Planck number for the turbulent kinetic energy k and the dissipation rate ε, respectively. $G_{1\epsilon }$ and $G_{2\epsilon }$ are constants of 1.42 and 1.68, respectively. The turbulent viscosity coefficient ${\mu }_{\mathrm{e}}=\rho C_{\mu }{\displaystyle \frac{k^2}{\epsilon }}.$ C_μ takes the value of 0.09. ${\alpha }_k,$${\alpha }_{\epsilon }$ take the value of 1.393.

(5) General state equation

According to thermodynamic theory, the equation of state of plasma mixture expressed by particle number density and thermodynamic temperature can be written:

In the actual calculation process, the plasma is considered an ideal gas and the density distribution of each component is not considered. $n_{\mathrm{e}}+{\displaystyle {\sum }_{i=0}^{i_{\max }}{n}_i}=\rho ,$ where p is gas pressure, $\rho$ is gas density, T is gas temperature.

2.3   Division of the calculation region of plasma jet

Referring to the test conditions of the gas gap switch, the plasma develops upward along the middle region, and the regions on both sides are large enough. The two-dimensional simulation profile model of the gas gap switch jet plasma flow field is shown in figure 1. The contact surface between the trigger cavity and the computational domain is defined as the initial boundary (entrance boundary). In order to eliminate the influence of the boundary setting on the calculation results, the radius of the external calculated flow field is set to 15 mm and the height of the top boundary from the jet inlet is 50 mm. The two sides and the top are defined as the export boundary conditions, whose pressure and temperature are the external ambient atmospheric pressure and temperature, respectively. The bottom boundary is defined as the no-slip condition of the object's surface. The trigger cavity boundary is defined as the fluid-solid coupling surface, and the material is polytetra-fluoroethylene (thermal conductivity is 0.24 W (m^-1·K^-1)).

Figure  1.  The plasma jet numerical calculation area of gas gap switch.

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The calculation area size is 30 mm×50 mm. In order to investigate the influence of grid division on the development of a plasma jet, a finer meshing of 0.012 mm and an ultra-fine meshing of 0.0045 were used. The results show that the ultra-fine meshing agrees well with the experimental results, but the computation time is longer, and the convergence speed is slower. Moreover, the plasma jet is concentrated and does not spread to the whole calculation domain. Therefore, in order to accurately calculate the velocity field distribution above the nozzle while considering the calculated velocity, the central part of the profile is more intensive. The complete grid contains 17 465 domain cells and 514 boundary elements.

The outlet boundary condition in the calculation is the pressure boundary, which suppresses the backflow. The inlet boundary is set to inlet pressure, normal flow, and backflow suppression. The energy source term S is added to the trigger cavity region, the ambient gas in the computational domain is set to air, the initial temperature is 300 K at room temperature, and the initial pressure is 1 atm. The computational time step is 2 μs, and 20 iterations are performed in each time step. The absolute tolerance factor is 0.05, and the normalized error of all variable iterations is less than 10^-6.

3.   Numerical calculation results and analysis

3.1   Characteristics of velocity distribution

The parameters of the pressure inlet are set according to the measured plasma blast wave at the nozzle. The fitting formula is $P=5000000{\mathrm{e}}^{-0.12t}+20,$t is time (μs), P is pressure (Pa).

Figure 2 shows the evolution sequence of the plasma jet. The jet height and the velocity are shown in figure 3. Analyses of figures 2 and 3 show that the plasma is jetted from the nozzle into the ambient medium, it forms an olive-like jet head with an initial velocity up to 1.0 km·s^-1, which develops in the radial and axial directions, and the jet gradually changes to a slender plasma column. The plasma is stretched and dragged due to the viscous effect of the air, resulting in severe friction, collisions, and exchange of energy and momentum between the two phases of the plasma jet and the air. The plasma jet head produces a strong entrainment phenomenon to the surrounding static air, and continuously takes away the surrounding gas to reduce the surrounding air pressure. Combined with the Coandǎ effect of the free jet, the plasma head tends to deviate from its axis and bend due to the unbalanced pressure on both sides. At this stage (45–50 μs), the overall manifestation of the plasma jet is a slow forward expansion, the spatial and temporal distributions of the plasma are relatively consistent. The change rate of jet height and velocity is less than 5%. At about 60 μs, the jet intensity and velocity decrease due to the friction and coiled suction of the plasma jet with the surrounding stationary gas, which gradually dissipates and produces a strong turbulent mixing effect between the two-phase fluid, leading to the gradual deformation and fracture of the plasma jet head and the dispersion phenomenon. As the plasma jet continues to expand, the two-phase mixing effect and the dispersion zone increase continually, the development of the plasma jet will decrease, and the main body of the plasma jet itself will gradually become thinner, fragment, and gradually dissipate.

Figure  2.  Sequence diagram of plasma jet evolution.

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Figure  3.  Variation law of plasma jet velocity and height.

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Figure 4 shows that the plasma jet velocity fluctuates apparently along the axial height, which decreases first, then rises slowly, and finally decreases rapidly with the height increases. The jet velocity at 20 μs is about 0.95 km·s^-1, and gradually decays along the axial height, reaching a minimum of 0.7 km·s^-1 at 10 mm. However, the velocity rises to 0.75 km·s^-1 at 15 mm. This point corresponds to the center of the plasma head, which is the maximum jet velocity at the axial height (figure 4 shows the region of maximum velocity). During the initial phase of the plasma jet, due to the accumulation of a large amount of plasma in the trigger cavity, the generated shock wave pressure is large and the plasma jet at the nozzle will form a plasma cloud with high velocity. However, the pressure inside the trigger cavity decreases dramatically, and the jet velocity decreases significantly as the plasma jet develops. The collision between the particles in the plasma jet head and the ambient gas medium causes a high kinetic energy loss of the ion body jet, resulting in an asymptotic decrease of the jet velocity at the axial height. However, the jet velocity at the plasma head position at the axial height increases, so the jet velocity near the plasma head is the smallest (figure 4 shows the region of minimum velocity). The maximum and minimum values of jet velocity move backward and gradually decay, and the plasma jet overall shows a rapid decay trend.

Figure  4.  Axial variation trend of plasma jet velocity.

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3.2   Characteristics of pressure distribution

Figure 5 shows the pressure cloud diagram during the development of the plasma jet. The red region is the high-pressure region during the development process, where the charged particles are dense and expanding. Blue is the low-pressure zone where the plasma jet forms a vortex.

Figure  5.  Pressure cloud diagram of plasma jet development.

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During the development stage of the plasma jet, the gas molecules at the interface between the high-pressure plasma cloud and the air are rapidly compressed. The plasma jet and the surrounding air medium squeeze against each other, and a pressure expansion wave is formed. The wave surface continues to move forward, gradually contracting until it disappears. During the jetting process, a high-pressure zone is formed at the head of the plasma jet. Due to the high velocity of the plasma jet head, the flow surface will become suddenly larger after being injected into air. The plasma jet head will be taking away a large number of ambient gas molecules, and the pressure in the middle of the plasma jet will quickly drop below the atmospheric pressure, and even a negative pressure region will form. Turbulent mixing effects between ambient gas and plasma become more and more pronounced as the plasma jet continues to develop. Meanwhile, the plasma viscosity causes friction between the side of the jet and the air, causing the plasma jet to continuously diffuse into the surrounding environment and lose energy, so that the pressure peak of the shock wave gradually decreases. Moreover, the plasma jet head tends to deviate from its main axis under the influence of the Coandǎ effect.

After the plasma is jetted into the ambient medium, the pressure inside the trigger cavity drops by about 80% within 20 μs, and the plasma jet velocity decreases rapidly, and the peak jet pressure drops by about 60%. The plasma jet shock wave not only affects the distribution of the spatial flow field, but also acts as a carrier of plasma and promotes the continuous development of the plasma jet. The wavelength of the shock wave generated by the plasma jet is at the centimeter level [24–26], which is considerably larger than the diameter of the nozzle of the trigger cavity by 2 mm. Therefore, the shock wave will form diffraction at the nozzle and spread around. The wavelength of the plasma jet shock wave is calculated by equation(11) to 5.6 cm. In addition, the plasma jet will diffuse freely in the radial direction, and the combined effect will cause the radial size of the plasma jet head to be larger than the root

where v represents the jet velocity, t_d is the duration of the shock wave pressure.

3.3   Experimental verification of plasma jet characteristics

In order to verify the accuracy of the numerical model calculation, a test platform for plasma jet characteristics of gas gap switch is established in this work. The loop parameters, observation methods and data processing methods are referred to [21]. As shown in figure 6, the test platform is mainly composed of a trigger discharge circuit, integrated observation system, trigger control module, and environmental test chamber. The test instruments mainly include a high-speed camera, high-voltage probe, Rogowski coil, oscilloscope, and so on. Compared with the numerical results, it is found that the distribution of the plasma flow field is consistent with the experimental results. The comparison results of jet velocity, jet height, and shock wave pressure are shown in figure 7.

Figure  6.  Test platform.

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Figure  7.  Variation trend of jet characteristics with time. (a) Plasma jet pressure change, (b) variations of plasma jet height and velocity.

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The measured initial jet velocity is about 1.1 km·s^-1, and the maximum jet height is 52 mm, which is in good agreement with the calculated results (deviation <10%). However, with the development of the plasma jet, the deviation of jet velocity increases gradually, and the deviation at 60 μs is about 15%. The reason is that the movement of plasma particles and optical radiation makeit difficult to effectively determine the edge of the plasma jet. Meanwhile, the plasma head displacement velocity is used to characterize the plasma jet velocity in the test, which cannot accurately represent the plasma motion state. For example, when the development time >80 μs, its plasma jet length starts to decrease. At this time, the plasma jet velocity obtained by using plasma image processing technology is negative, which is inconsistent with the actual situation. Therefore, it is more reasonable to use simulation methods to characterize the plasma jet velocity.

The variation of plasma shock wave pressure at the nozzle of the trigger cavity with time is consistent with the calculated result. When the plasma jet development time is less than 10 μs, the test value of the plasma shock wave pressure is larger than the simulation value. Because the pressure sensor needs a certain response time (3 μs) to test the impact pressure value, the test time accumulates longer, so the experimental results are larger than the simulation results in the shorter plasma jet time. When the development time is greater than 10 μs, the test value is slightly smaller than the simulated calculated value, but the maximum deviation is less than 10%. The main reason is that the development process of plasma jet is complex during the test, the effects of plasma viscosity, heat conduction, thermal radiation, and other factors have not been considered in the numerical calculation, and the factors such as plasma mass force, volume force and so on have been ignored, resulting in the test results being slightly lower than the calculated values.

4.   Influence law of plasma jet characteristics

4.1   The action characteristics of trigger voltage

By increasing the trigger voltage, the amount of plasma generated by arc ablation along the trigger cavity of the gas switch increases, the pressure value and jet velocity increase significantly, resulting in significant differences in the plasma jet morphology. The trigger voltage is positively correlated with the pressure value of the plasma jet exit cavity, so the characteristics of the plasma jet at different trigger voltages in the test are simulated by varying the inlet pressure value in the simulated conditions. Referring to the measured shock wave pressure values at different charging voltages in the previous tests, the inlet pressure values of the numerical model were set. The 5 MPa corresponds to a charging voltage of 500 V, 12 MPa corresponds to 750 V, and 20 MPa corresponds to 1000 V. The plasma flow field at 40 μs is shown in figure 8.

Figure  8.  Plasma jet flow field under different voltages.

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The higher the jet inlet pressure, the greater the energy obtained by the plasma jet, the larger the volume of the jet ejected from the nozzle at the beginning of the expansion, and the larger itsradial and axial dimensions during expansion, but the overall expansion pattern is similar. The initial velocity of the plasma is 1.0 km·s^-1 at 5 MPa, and up to 1.4 km·s^-1 at 20 MPa, and the head offset effect is significantly larger, with an offset of about 17.6° from the main axis, compared to only 12.4° at 12 MPa. This is mainly because the larger the set inlet pressure value, the faster the plasma jet velocity, the roll absorption effect is obvious, resulting in the deepening of the pressure imbalance of the ambient gas medium, the plasma is shifted toward the side with lower pressure, thus causing a larger shift angle, which in turn produces the Coandǎ effect.

Figure 9 shows the variation of the plasma jet velocity and pressure at the nozzle. At different trigger voltages (different inlet pressure values), the variation laws of the jet velocity and the pressure at the nozzle are basically the same. The velocity of the plasma jet and the pressure at the nozzle decay gradually. The faster the initial velocity of the jet, the larger the velocity decay rate. The main reason is that the higher the injected energy (the larger the inlet pressure value set in the simulation), the greater the initial velocity of the plasma high-speed jet process, the more obvious the turbulent dissipation phenomenon caused, the more serious the front end of the jet is broken, resulting in an increase in the decay rate of the plasma jet velocity. Meanwhile, the higher the jet velocity, the stronger the shock wave effect. The calculated results show that the plasma jet velocity decreases to 0.5–0.6 km·s^-1 at 80 μs.

Figure  9.  Comparison of plasma jet characteristic parameters. (a) Variation of plasma jet velocity, (b) pressure changes at nozzle of trigger cavity.

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4.2   The action characteristics of trigger medium

In this part, numerical calculations and experimental comparisons are made to study the characteristics of the influence of the atmospheric medium (air, SF₆) on the development process of the plasma jet. The trigger voltage is 1000 V, i.e. the pressure inlet is set to 20 MPa, and a comparison of the test and simulation results of the plasma jet development process in different environmental media is shown in figure 10.

Figure  10.  Simulation comparison chart of plasma jet in air and SF₆.

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The jet boundary photographed by the high-speed camera is the optical boundary according to the brightness of the plasma jet, which is somewhat different from the real gas-phase boundary of the plasma. Therefore, the experimental results differ slightly from the jet distributions obtained by simulation calculations. But the plasma jet development process in different environmental media can all be divided into three stages. The evolution of the plasma jet morphology in SF₆ lags behind that in air, and the corresponding parameters of the plasma jet are all smaller.

(a) Jet development stage (0–50 μs). After the plasma jet is ejected from the trigger cavity, a rapidly developing plasma column is formed, which develops rapidly along the radial and axial directions. The jet height increases by nearly four times, and the jet diameter increases by nearly 1 time within 20 μs, the axial velocity is considerably greater than the radial development velocity. The jet height in SF₆ increases nearly 2 times, and the evolution rate of the plasma formation lags significantly behind that in air. The morphology of the plasma jet obtained from the test is consistent with the morphology of the plasma flow field distribution obtained from the simulation calculation, which can verify the accuracy of the numerical simulation model calculation.

(b) Jet stabilization stage (50–65 μs). The jet appears to be coiled and sucked into the surrounding air, and ear-shaped jet clusters are formed on both sides of the jet column. Due to the limitation of optical imaging, the experimental images precisely show the ear-shaped jet formed by air entrainment, but there is a clear tendency of coiled suction. The SF₆ viscous effect is stronger, its corresponding morphology evolves more slowly, and the coiled accretion effect is weaker. At this stage, the plasma jet develops slowly, the variation of the plasma jet morphology is small, and the change rate of the jet height and diameter is within 5%.

(c) Jet dispersion stage (65–90 μs). Due to the collision between plasma jet and ambient gas molecules and the strong turbulent mixing, the flow energy of plasma jet is seriously lost, it cannot continue to move forward and maintain the jet shape. Therefore, the main body of the jet gradually becomes thinner, broken, until dissipated. The image sequence of the experimental results also has the same phenomenon of gradual thinning and fracturing of the jet body and turbulent mixing with the air in both phases. The relative molecular mass of SF₆ is larger, and its viscous force to plasma particles is greater than its inertial force during movement. When the plasma diffuses to the surrounding, the small change of the edge velocity is easy to form a disordered and irregular turbulent flow field, which causes the turbulent dissipation to be more obvious. Therefore, the morphological changes of the plasma jet are more suppressed in SF₆ and a more serious breakup of the plasma plume head.

Figure 11 shows the comparison of the variation of the plasma jet characteristic volume. The pressure value at the nozzle and the jet velocity vary with time in a consistent manner, and both decay asymptotically. Compared with air, the plasma characteristic parameters in SF₆ are lower, and the decay rate is significantly higher than that in air. The maximum height of the plasma jet under air is 55.3 mm, while under SF₆ it is only 37.4 mm, but the tendency to move away from the main axis is weaker. This is mainly because the molecular density and relative molecular mass of SF₆ under the same pressure are significantly greater than those under air, the collision probability between the plasma jet and gas molecules is significantly increased, and the energy loss of its head particles is increased, resulting in faster speed loss in the subsequent development process. For example, at 80 μs, the plasma jet velocity in SF₆ is about 0.36 km·s^-1, which is only 60% of that in air. At this time, the velocity of the plasma head is low, and it cannot continue to develop upwards. Due to the cooling effect of the environmental medium and the suppression effect of SF₆ on the evolution of plasma morphology, there is no obvious head shift phenomenon during the development of the plasma jet, and it dissipates rapidly in SF₆. Its development process is significantly shorter than that in air.

Figure  11.  Comparison of plasma jet characteristic changes. (a) Pressure changes at nozzle of trigger cavity, (b) variation of plasma jet height, (c) variation of plasma jet velocity, (d) variation of plasma jet velocity (experiment).

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The initial plasma jet velocity in different environmental media is the same, about 1.4 km·s^-1. However, under the experimental conditions, the initial velocities under air and SF₆ are 1.44 km·s^-1 and 1.15 km·s^-1, respectively. The main reasons for these phenomena are that under the experimental conditions, the average velocity calculated by the displacement distance of the plasma head for a period of time is used as the initial velocity of the plasma jet. Under the simulation conditions, the plasma jet velocity fluctuates along the axial height, and the fluctuation peaks of each velocity curve are connected to obtain the initial velocity of the jet. In the two cases, the average velocity and instantaneous velocity are used as the initial velocity of the plasma jet, resulting in differences. The trend of plasma jet censoring is basically the same for both conditions, with a rapid decay within a few tens of microseconds, and then entering a short stabilization period.

5.   Conclusions

(1) The plasma jet develops as a long strip, with an initial velocity of up to 1.0 km·s^-1, and develops at a high speed along the axial directions, and there is strong turbulent mixing between the plasma jet and air, the jet velocity fluctuates obviously along the axial height, and the plasma jet gradually begins to dissipate. The measured values of the initial velocity and height of the plasma jet are well inagreement with the calculated results. But the deviation of jet velocity gradually increases with the development of plasma jet.

(2) After the plasma is ejected from the trigger cavity, the internal pressure of the trigger cavity drops by 80%, resulting in a rapid drop in jet velocity. Due to the mutual extrusion of the plasma jet and air molecules, a high-pressure zone is formed at its head. The pressure peak value decreases gradually with the height increase, and the jet head deviates from the main axis. The measured value of plasma shock wave pressure is consistent with the calculated value, slightly smaller than the calculated value.

(3) With the increase of the inlet pressure value, the shock wave effect at the plasma jet inlet becomes more pronounced, and the initial velocity of the plasma jet increases. The coiling effect between the plasma jet and the ambient medium is also more pronounced, leading to an increased degree of pressure imbalance in the ambient gas, and the plasma will shift toward the side with lower shock wave pressure. The greater the initial jet velocity, the greater the degree of deflection caused, and the Coandǎ effect is more obvious.

(4) The process of plasma jet development in different environmental medium can be divided into three stages: development stage, stabilization stage, and dissipation stage. The variation laws of the jet velocity and the pressure value of the plasma jet shock wave with time are also relatively consistent, and both are asymptotically attenuated. At the same pressure, the density and viscosity coefficient of SF₆ gas molecules are greater than those of air. The drag and pull effects of plasma jet development are more obvious. Its morphological evolution lags behind that of air, and the corresponding characteristic parameters are smaller. The computational model can well simulate the morphological changes of the plasma jet.