| Citation: |
Wei XIE, Zhenbing LUO, Yan ZHOU, Qiang LIU, Xiong DENG, Yinxin ZHU. Experimental and numerical study on double wedge shock/shock interaction controlled by a single-pulse plasma synthetic jet[J]. Plasma Science and Technology, 2025, 27(4): 044004. DOI: 10.1088/2058-6272/ad91e9
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The phenomenon of shock/shock interaction (SSI) is widely observed in high-speed flow, and the double wedge SSI represents one of the typical problems encountered. The control effect of single-pulse plasma synthetic jet (PSJ) on double wedge type-VI and type-V SSI was investigated experimentally and numerically, and the influence of discharge energy was also explored. The findings indicate that the interaction between PSJ and the high-speed freestream results in the formation of a plasma layer and a jet shock, which collectively governs the control of SSI. The control mechanism of single-pulse PSJ on SSI lies in its capacity to attenuate both shock and SSI. For type-VI SSI, the original second-wedge oblique shock is eliminated under the control of PSJ, resulting in a new type-VI SSI formed by the jet shock and the first-wedge oblique shock. For type-V SSI, the presence of PSJ effectively mitigates the intensity of Mach stem, supersonic jet, and reflected shocks, thereby facilitating its transition into type-VI SSI. The numerical results indicate that the peak pressure can be reduced by approximately 32.26% at maximum. Furthermore, the development of PSJ also extends in the Z direction. The pressure decreases in the area affected by both PSJ and jet shock due to the attenuation of the SSI zone. With increasing discharge energy, the control effect of PSJ on SSI is gradually enhanced.
The occurrence of complex shock/shock interaction (SSI) phenomena is common in the internal and external flows of high-speed vehicles, resulting in potential detrimental effects such as increased aerodynamic drag, elevated pressure and thermal loads, as well as low-frequency unsteady oscillations [1–4]. The typical SSI of an oblique shock interacting with a bow shock was initially investigated by Edney and was classified into six types based on the variation in incident oblique shock location and SSI structure [5]. Subsequently, a multitude of researchers have conducted experiments and numerical simulations to provide valuable references for the design of high-speed vehicle [6–11].
The double wedge configuration is also a typical arrangement commonly employed for the investigation of SSI. It consists of two compression planes aligned in the same direction, which typically results in the interaction between oblique shocks or between an oblique shock and a detached bow shock. The occurrence of such phenomena is common in the practical vehicle design process. Olejniczak et al [12] conducted the pioneering investigation on double wedge SSI, wherein they classified four types of SSI in high-speed inviscid double wedge flow: type-IV, type-V, and type-VI, which correspond to Edney’s classification. Additionally, they made a novel discovery of a subtype within type-IV denoted as type-IVr. The presence of a separation zone, a separation shock and vortical structures significantly complicates the double wedge SSI flow in the actual viscous flow, rendering the effects of three-dimensionality non-negligible. The impact of the double wedge angle on viscous SSI flows was investigated by Durna and Celik [13]. The findings suggested that the effects of three-dimensionality are negligible when the second-wedge angle is below 50°. However, once the angle exceeds 50°, vortical structures aligned in the streamwise direction begin to emerge, thereby disrupting symmetry within the flow. The simulations of Reinert et al [14] and Davide et al [15] also suggested that the double wedge SSI flow is three dimensional, asymmetric, and unsteady under various stagnation enthalpies. There are also scholars who have conducted more comprehensive simulations. The linear instability mechanisms of the double wedge SSI were investigated by Sawant et al [16] utilizing the particle-based DSMC method. It was discovered that the amplification of the most unstable three-dimensional flow perturbations results in synchronized low-frequency unsteadiness of the triple point, characterized by a Strouhal number approximately equal to 0.028. The direct numerical simulations conducted by Tong et al [17] revealed that an increase in the length of the first wedge results in a significant reduction in the size of the separation bubble, a complex shock system, a decrease in spanwise width, and an enhancement of spanwise coherency of counter-rotating streamwise vortices. The aforementioned studies progressively enhance the investigation of double wedge SSI, while also demonstrating the complexity of SSI flow field and the necessity of flow control.
The field of plasma flow control technology has gained considerable attention in recent years [18–22]. Various plasma flow control methods have been preliminarily employed to control the double wedge SSI problem, aiming to alleviate its detrimental effects. Tang et al [23] and Kong et al [24] employed low-frequency array surface arc discharge actuators for double wedge type-VI SSI control. The findings demonstrated that the array plasma discharge modifies the structure of the complex shock system induced by the double wedge through inducing a virtual profile, thereby potentially mitigating the pressure and heat flux amplification effect caused by the second wedge-induced shock. The study conducted by Yang et al [25] utilized a 30-channel high-energy surface arc discharge array to control type-V SSI. The experimental results demonstrated that the shock array induced by the high-energy surface arc discharge array successfully eliminates or intermittently disrupts the SSI structure. The experiments carried out by Zhang et al [26] involved the utilization of a high-frequency surface arc discharge array to control shock wave/boundary layer interaction (SWBLI) on a double wedge geometry. The findings revealed two distinct types of control effects: manipulation of the shock structure and modification of the low-frequency unsteadiness of the shock. Furthermore, it was observed that employing a 20 kHz actuation yielded superior results compared to using a 10 kHz actuation in terms of reducing the intensity of the shock. The aforementioned studies demonstrate an abundance of research on the control of double wedge SSI by surface arc discharge, encompassing a wide discharge frequency from low to high and spanning both single-channel and multi-channel approaches. In addition, Surzhikov [27] proposed a method that combines glow discharge and magnetic field for the control of double wedge SSI, which has also demonstrated remarkable efficacy in achieving effective control.
The plasma synthetic jet (PSJ) actuator (PSJA), also referred to pulsed plasma jet or SparkJet actuator, was developed by Grossman et al [28] in 2003 and holds great promise as a highly efficient plasma actuator. PSJA is capable of generating a high-velocity pulsed plasma jet (up to 833 m/s [29]) without requiring an external air source, thereby exhibiting exceptional control effectiveness over high-speed flows. The ability of PSJA to control SSI is considerably superior to that of the aforementioned surface arc discharge and glow discharge. It is worth noting that some scholars have also embraced the implementation of steady jet control for SSI, yielding commendable control efficacy. Nevertheless, this method necessitates a substantial air source, resulting in significant payload and spatial occupancy challenges, thereby impeding its practical application in vehicles [30]. A typical PSJA consists of two electrodes and a discharge cavity with an exit. The operation stages are typically categorized as energy deposition, jet ejection and suction recovery. The flow control function of PSJA is achieved through the generation of high-temperature and high-speed pulsed PSJ by the arc discharge in the compact discharge cavity [31–33]. The primary applications of PSJ in high-speed flow include the control of shock waves [34], SWBLI [35], supersonic separation [36], mixing [37], and SSI [29]. For example, the drag reduction potential of a single-pulse opposing PSJ on a hemisphere was experimentally and numerically validated in the study conducted by Xie et al [38, 39], achieving a maximum average drag reduction of 25.82%. Li et al [40] investigated the impact of nanosecond pulse PSJ on the aerodynamic performance of a high-speed airfoil. The results indicated that the continuous-pulse PSJ can reduce the airfoil drag coefficient by generating diffracted waves to shift the leading-edge shock. The aforementioned research primarily focused on the control of bow shock waves. Due to the robust control capability of PSJ, researchers are gradually considering its application in complex SSI flow fields, which present a more complex challenge encountered by actual vehicles. The preliminary simulations and wind tunnel experiments conducted by Xie et al [29] aimed to achieve initial qualitative control effects on the double wedge SSI. However, only the type-VI SSI was investigated, and no quantitative control effect of the double wedge SSI was provided. In this study, experiments on the double wedge type-VI and type-V SSI controlled by single-pulse PSJ were conducted in conventional high-speed wind tunnel. The flow evolution was obtained through high-speed schlieren, and the influence of discharge energy on the control effect was investigated. A quantitative and mechanism analysis was performed by the shock polar theory and three-dimensional numerical simulation.
The wind-tunnel experiments were carried out in the Ф = 0.5 m (Ф represents diameter) high-speed wind tunnel of Nanjing University of Aeronautics and Astronautics, featuring a freestream Mach number of 8, a total pressure of 0.91 MPa, a total temperature of 500 K, and a unit Reynolds number of 3.83×106 m−1. The duration of each wind-tunnel experiment was 7–10 s.
The study employed two experimental models: the type-VI SSI model and the type-V SSI model. The first wedge of both models has an angle of 30°, while the second wedges have angles of 45° and 60°, respectively. The type-V SSI model is utilized as an exemplar to illustrate the experimental setup. The double wedge, as depicted in figure 1(a), has a width of 60 mm. The first wedge measures l1 = 169.9 mm in length, while the second wedge measures l2 = 89.7 mm in length. A jet exit with a diameter of 4 mm and a length of 5 mm is arranged on the first wedge. The jet exit is positioned perpendicular to the surface of the first wedge, with its center located at 24 mm away from the junction between the first and second wedges. The discharge cavity, depicted in figure 1(b), is positioned below the jet exit and has a diameter of 9 mm and a height of 23 mm. The calculated volume of the cavity amounts to approximately 1463 mm3. Two tungsten electrodes are inserted on both sides of the cavity, each having a diameter of 1 mm, and the electrode spacing is 7 mm. In contrast, the type-VI SSI model features a 10 mm distance between the center of the jet exit and the junction between the first and second wedges. The width of the second wedge is 20 mm, the volume of the discharge cavity is around 980 mm3, and the electrode spacing is 11.2 mm. All other settings remain consistent with those of the type-V SSI model.
The discharge and measurement circuit are depicted in figure 2(a). The power supply utilized in this experiment is a high-voltage capacitive pulsed power supply based on magnetic compression technology developed by the High Voltage Laboratory of Xi’an Jiaotong University. The power supply is capable of applying a high voltage of up to 10 kV to the anode and cathode, inducing breakdown of air in the cavity and generating PSJ. The PSJA was equipped with parallel-connected ultra-high voltage film capacitor at both ends, allowing for adjustable input discharge energy by varying the capacitance C of the capacitor. Moreover, the capacitor possesses the ability to swiftly discharge accumulated energy. The discharge frequency was 6 Hz during the experiment.
The breakdown voltage during discharge was measured using a high-voltage probe and recorded with an oscilloscope. The high-voltage probe was the P6015A passive high-voltage probe manufactured by Tektronix company, featuring a measurement range of 0–20 kV and a bandwidth of 75 MHz. It was connected in parallel to both ends of the PSJA during the experiment. The voltage measurement entails an uncertainty of 0.4 kV, which encompasses both the measurement error and ten sets of data collected under identical conditions. The oscilloscope adopted a DPO4000 four-channel oscilloscope, which has a bandwidth of 350 MHz and a single sampling rate of 5 GSa/s. The typical voltage curve measured is depicted in figure 2(b). Once the spark discharge initiates, the voltage undergoes oscillations and decay due to an approximately underdamped RLC (resistance, inductor, and capacitor) oscillation circuit formed by the capacitor, connecting wires, and PSJA. The breakdown voltage U of the discharge shown in figure 2(b) is about 1.4 kV. The duration of the discharge is around 100 μs as there is minimal voltage fluctuation beyond this time point. More details can be found in references [29, 39].
The side wall of the wind tunnel test section is equipped with an optical glass window featuring a light aperture of 400 mm for optical observation. The interaction process of PSJ and SSI was captured by high-speed schlieren. The schlieren system comprised of a light source, two concave mirrors, two flat mirrors, a knife edge and a high-speed camera arranged in a typical Z-shape configuration. The camera in use was a high-speed Phantom v2640 camera. The camera exposure time remained at 1 μs and the shooting frame rates for type-V and type-VI SSI models were 40,000 fps and 75,000 fps respectively. As a result, the image time intervals for the models were 25 μs and 13.3 μs respectively. There is an uncertainty of around ±0.1 mm in the flow structures measured from the schlieren images [29].
The detailed parameter settings of the experimental cases are presented in table 1, wherein cases 1–3 correspond to type-VI SSI control experiments, and cases 4–6 pertain to type-V SSI control experiments. The discharge energy for each case was calculated based on the measured breakdown voltage U using the formula E = 1/2CU2 and was presented in the table for comparison purposes. By varying the discharge capacitance in cases 1–3 and 4–6, the impact of discharge energy on control effectiveness was investigated. Specifically, cases 1–3 exhibited a breakdown voltage of approximately 1.9 kV, while cases 4–6 had a breakdown voltage of around 1.4 kV.
| Cases | Angle of the second wedge | C (μF) | E (J) |
| 1 | 45° | 0.32 | 0.58 |
| 2 | 45° | 0.64 | 1.16 |
| 3 | 45° | 1.6 | 2.89 |
| 4 | 60° | 0.64 | 0.63 |
| 5 | 60° | 2.24 | 2.20 |
| 6 | 60° | 4.6 | 4.51 |
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Due to the limitations of experimental conditions and the influence of electromagnetic interference from discharges, wind tunnel experiments have limited capabilities in measuring data. The utilization of numerical methods can facilitate the acquisition of more comprehensive data, which is crucial for analyzing flow mechanisms. The numerical simulation settings were established based on the experimental conditions described in case 6. The computational domains and grids were illustrated in figure 3. The grid of walls, corner areas, and PSJA were locally encrypted. The grid spacing of the first layer of the wall was set to 1.3×10−6 to ensure a y+ value below 1, thereby ensuring accurate resolution of the boundary layer. The estimated overall mesh size was approximately 13 million. The computational domain was simulated only in half considering its axisymmetric nature, aiming to minimize the computational cost. The symmetry plane of the z = 0 mm section was omitted in figure 3 to enhance the visibility of the grid. The walls of both the double wedge and PSJA were set to have an adiabatic boundary condition, representing a static non-slip wall surface.
The phenomenological energy source term model has been utilized in previous studies to simulate a PSJ. The fundamental concept involved solving the Navier–Stokes equations for a compressible viscous flow with an energy source term ˙q, which was determined as ˙q = ηE/Vinτ, here η represents the heating efficiency of the PSJA, Vin denotes the volume of the PSJA discharge area and τ signifies the duration of the discharge. The discharge area was situated in the central zone of the PSJA and had a height of 1 mm. The values for η and τ were determined to be 0.35 and 5 μs, respectively. Therefore, the energy source term input in the simulation was calculated to be approximately 8.45×1012 J/(m3 s). The discharge in the PSJA has been verified to be in a state of local thermodynamic equilibrium [41]. The thermodynamic and transport properties of the plasma in a state of local thermodynamic equilibrium are determined by its pressure and temperature. The viscosity coefficient, thermal conductivity, and specific heat for various pressures and temperatures were computed using the empirical equation proposed by Capitelli et al [42]. The SST k-ω model was used as the turbulence model, an implicit formulation was utilized in the solution methods, and the Roe-FDS flux type was implemented. A second-order upwind method was employed for spatial discretization, while a first-order implicit method was utilized for the unsteady formulation. The time step was 2×10−8 s. The maximum number of iterations per time step was set to 20. In our previous work, we conducted numerical verification and grid independence verification for the aforementioned method [39]. In addition, the obtained simulation results are further compared with experimental data on the subsequent page.
The interaction between a single-pulse PSJ and the double wedge type-VI SSI in case 3 is illustrated in figure 4. The schematic diagram of the flow before control is shown in figure 5(a). The oblique shock IP generated by the first wedge interacts with the oblique shock BP produced by the second wedge, resulting in the formation of a reflected shock PW. Due to the discrepancy between the pressure of the post-oblique shock BP and the post-transmitted shock PW, an expansion wave PE is also generated. A slip line PC exists between PW and PE, with consistent flow direction and pressure on both sides. By employing the shock polar, a comprehensive display of pressure distribution in each zone of the flow is conducted, as depicted in figure 6(a). The shock polar is denoted by equations (1) and (2), where the subscripts 1 and 2 indicate the parameters before and after the shock wave, respectively. For example, P1 indicates the pressure before shock BP in figure 5(a). θ and β represent airflow deflection angle and shock wave angle, respectively. The Mach number Ma2 after the shock is determined by equation (3). The freestream enters zone (2) after passing through the oblique shock IP and oblique shock BP in succession, where a pressure augmentation of 74.9 times compared with the freestream is observed. As the deflection angle of the second wedge (45°) exceeds the maximum value of an attached oblique shock under Ma = 8, it can be inferred that the reflected shock PW will take on a curved shape, and the longitudinal coordinate of point (2) in the shock polar consistently surpasses any point on the shock polar of Ma = 8, indicating that the pressure in zone (2) is always greater than that in zone (4). Therefore, it can be determined that the PE generated between zone (2) and zone (3) manifests as an expansion wave, ensuring pressure equilibrium between zone (3) and zone (4).
| P2P1=2γγ+1Ma21sin2β−γ−1γ+1, | (1) |
| tanθ=2cotβMa21sin2β−1Ma21(γ+cos2β)+2, | (2) |
| Ma22=Ma21+2γ−12γγ−1Ma21sin2β−1+Ma21cos2βγ−12Ma21sin2β+1. | (3) |
The discharge process of PSJA initiates the formation of PSJ. At 0 μs, the PSJ emerges from the exit, giving rise to the formation of a jet shock upstream of it. Subsequently, the PSJ and the jet shock expand, encompassing a larger spatial extent, leading to the gradual downstream evolution of the PSJ into a plasma layer characterized by prominent large-scale vortex. The original second-wedge oblique shock BP is gradually eliminated from 26.6 μs onwards, as the plasma layer and the jet shock exert control, with the optimal control effect achieved at 66.6 μs. The flow after PSJ control is analyzed in detail, using the example of the optimal control effect moment. The schematic diagram after PSJ control is depicted in figure 5(b). Under the control of PSJ, the jet shock JP interacts with the first-wedge oblique shock IP to form a new type-VI SSI. The bow jet shock near the wall is approximately considered to be an oblique shock, with a shock angle of about 73.6° (at 66.6 μs), which is greater than the shock angle of the original second-wedge oblique shock BP. Figure 6(b) depicts the corresponding shock polar. At this point, it is evident that the ratio between the pressure in the zone (2) after the jet shock and the freestream has escalated to 105, thereby leading to an increase in pressure on the adjacent area after the jet shock JP. The phenomenon can indeed be interpreted as the plasma layer forming a virtual wedge with an angle of 51.4°, thereby generating a larger angle virtual wedge shock. However, due to the elimination of the original second-wedge shock BP and the influence of the plasma layer, there will be a reduction in wall pressure on the second-wedge surface. Wang et al conducted similar analyses in the study of SWBLI control and validated this decrease in wedge surface pressure through experimental measurements [20]. After 66.6 μs, the PSJ and jet shock experience a gradual attenuation, while the corresponding second-wedge oblique shock BP gradually regains its strength. By 426.6 μs, the flow returns to its reference state, making the conclusion of the single-pulse control period.
The flow comparison of the optimal control effect in cases 1–3 is illustrated in figure 7, where the discharge energy increases progressively from case 1 to case 3, as indicated in table 1. The previous analysis reveals that the elimination of the second-wedge oblique shock and the influence of plasma layer plays a crucial role in decreasing the wall pressure distribution on the second wedge. It is observed that higher energy levels are associated with larger jet shock angles and increased thickness of the plasma layer. From the perspective of shock intensity, coverage area of PSJ and jet shock and the elimination degree of the second-wedge oblique shock, the control effect of double wedge type-VI SSI gradually strengthens with increasing discharge energy. In cases 1 and 2, the presence of the second-wedge oblique shock is still evident, whereas it is eliminated in case 3, resulting in a relatively enhanced control effect.
The interaction between a single-pulse PSJ and the double wedge type-V SSI in case 6 is illustrated in figure 8. The schematic diagram of the flow before control is shown in figure 9(a). The oblique shock IP generated by the first wedge interacts with the bow shock PW produced by the second wedge, resulting in the formation of a transmitted shock PT, a Mach stem TQ and a supersonic jet surrounded by slip lines C1 and C2. The aforementioned structures represent common flow patterns observed in shock reflection and SSI flows. Notably, the Mach stem is a structure that closely resembles a normal shock wave and, along with the three-wave point, serves as a crucial flow feature distinguishing regular reflection from Mach reflection [1]. Additionally, a separation zone is formed between the first and the second wedges, where the separation shock SO ends up striking the transmitted shock PT at point O. Downstream of the separation region, the reattached shock BQ is connected to the Mach stem TQ. The three-wave point Q emits a slip line C3, which wraps around the supersonic flow downstream, and QR represents one of the reflected shock systems [12]. The shock polar is also utilized to illustrate the pressure distribution in each zone of the flow, as depicted in figure 10(a). The Mach number after the first-wedge oblique shock IP is Ma1 = 2.58, and the flow enters zone (1) from (∞). The Mach number after the separation shock SO is Ma2 = 2.41, and the flow enters zone (2) from zone (1). The Mach number after the transmitted shock PT wave is Ma3 = 1.98, and the flow enters zone (3) from zone (2). The function of the transmitted shock PT is to further increase the pressure in zone (2) to achieve pressure matching between zone (3) and zone (4). The Mach number after the reflected shock QB is Ma7 = 1.25, and the flow parameters jump from zone (2) to zone (7). In addition, the pressure in zone (8) locates at the intersection of the shock polars between zone (2) and zone (7). As shown in figure 10(a), the pressure in zones (7) and (8) increases by 165.6 times and 245.8 times respectively, compared with the freestream, surpassing the peak pressure of type-VI SSI by a significant margin.
At 0 μs, the discharge initiates. At 25 μs, the PSJ emerges from the exit, giving rise to the formation of a jet shock upstream of it. Due to the blocking effect of PSJ and the jet shock, the separation point and separation shock move upstream. After 75 μs, as the PSJ and jet shock continue to evolve, the jet shock gradually envelops the entire SSI zone, while the PSJ forms a plasma layer that directly impacts on the SSI zone. The supersonic jet and Mach stem experience significant attenuation under the influence of the jet shock and plasma layer, with optimal control effectiveness achieved at 250 μs. During this time, both the supersonic jet and Mach stem become nearly imperceptible. The schematic diagram illustrates the flow after control, specifically referring to the schlieren result at the moment of optimal control effect, as depicted in figure 9(b). The current flow structure exhibits a resemblance to the post-control flow of type-VI SSI, as depicted in figure 5(b). The corresponding shock polar is depicted in figure 10(b). The pressure amplification in zone (2) after control is reduced to 43.3, indicating a significant decrease. Therefore, the mechanism of double wedge type-V SSI control is to mitigate the intensity of the supersonic jet, Mach stem and reflected shock through PSJ and jet shock, thereby converting the more intense type-V SSI into a less severe type-VI SSI. The SSI in zone (5) is relatively weak at the moment of optimal control effect. However, it still maintains a certain intensity in this zone at other times, leading to an increase in downstream pressure and a decrease in control effectiveness. Especially after 250 μs, as the PSJ and jet shock gradually attenuate, the SSI gradually strengthens, and the flow field gradually reverts to type-V SSI. As a result, the second-wedge wall pressure theoretically decreases initially and subsequently increases.
The flow comparison of the optimal control effect in cases 4–6 is illustrated in figure 11, where the discharge energy increases progressively from case 4 to case 6, as indicated in table 1. The previous analysis reveals that the attenuation of the supersonic jet, Mach stem and reflected shock (or the attenuation of SSI) plays a crucial role in decreasing the pressure. From the perspective of shock intensity, coverage area of the PSJ and jet shock and the attenuation of SSI, the control effect of double wedge type-V SSI gradually strengthens with increasing discharge energy. In cases 4 and 5, the presence of the type-V SSI remains apparent, albeit with a diminished intensity in case 6, resulting in a relatively enhanced control effect.
Due to the significant impact of electromagnetic interference during the discharge process, obtaining quantitative data in the aforementioned experiments becomes challenging. Therefore, this section further validates and analyzes the above conclusions by integrating 3D numerical simulation. The baseline flow field obtained through numerical simulation is presented in figure 12(a). It is worth noting that, for better visualization of the flow field, a coordinate ratio of X:Z = 1:2.5 is applied to all three-dimensional flow field diagrams throughout this paper. In figure 12(a), the wall surface shows the pressure cloud image, and the section plane shows the density gradient magnitude cloud image. The three sections correspond to z = 0 mm, z = 15 mm and z = 30 mm respectively. The high-pressure zone observed in the numerical simulation is situated within the vicinity of the reflected shock QR, as depicted in figure 9, specifically in the SSI zone. The three-dimensional effect also exerts a discernible influence on the flow field of SSI due to the narrowness of the model, primarily manifested by the gradual contraction of the separation zone from center to periphery, accompanied by downstream movement of corresponding separation shocks. However, it is evident that there is no significant modification in the SSI zone, as indicated by the high-pressure zone. In order to compare with the experimental schlieren results, it is imperative to consider the aforementioned three-dimensional effect. Therefore, the numerical results are conducted based on the principle of schlieren spanwise integration [43], as shown in figure 12(b). The comparison between the numerical and experimental results (figure 8: baseline) demonstrates a close agreement, thereby further substantiating the precision of the numerical results.
A few typical interaction moments between PSJ and type-V SSI are depicted in figure 13, exhibiting a consistent evolutionary process with the experimental observations shown in figure 8. Initially, the ejection of PSJ results in the formation of a jet shock and a novel separation zone upstream. After 75 μs, the jet shock gradually envelops the entire SSI zone, while the PSJ forms a plasma layer that directly impacts the SSI zone. The supersonic jet and Mach stem experience significant attenuation under the influence of the jet shock and plasma layer. As a result, the intense type-V SSI is transformed into less severe type-VI SSI. The numerical results indicate that the reflected wave system generated by the new SSI zone is entirely confined to the plasma layer and does not intersect with the wall. The wall pressure is correspondingly reduced to a significant extent, as depicted in figure 14(a), with the optimal outcome achieved at 125 μs, resulting in a maximum reduction of approximately 32.26% in peak pressure. The reduction observed is of great significance, as previous studies have not yielded quantitative results. Additionally, the attenuation of the SSI zone using PSJ is notably more pronounced compared to similar findings reported in existing literature [23–27]. Then the pressure increases gradually as the PSJ and jet shock weaken. The pressure reduction differs from that indicated by the aforementioned shock polar, as the inviscid analysis of the experimental results does not account for the influence of PSJ and boundary layer. The displayed inviscid result represents the pressure after the corresponding shock. But actually, the plasma layer covers part of the second wedge wall, exerting non-ignorable pressure on it, resulting in a higher pressure than the inviscid analysis.
Additionally, the development of PSJ also extends in the Z direction. For instance, at 50 μs, the separation shock of the z = 15 mm section is gradually elevated and the shock angle increases. Nevertheless, the plasma layer does not impact the SSI zone of the z = 15 mm section. Hence, there is a slight enhancement in intensity within SSI zone, resulting in a minor increase in peak pressure, as depicted in figure 14(b). The z = 30 mm section, however, exhibits negligible influence from PSJ and jet shock, resulting in a consistent pressure throughout this section at every moment. In summary, the influence range of PSJ and jet shock is limited. PSJ can affect the flow within a zone approximately located at z = 10 mm, while the jet shock can impact the flow within a zone approximately located at z = 15 mm. The pressure decreases in the area affected by both PSJ and jet shock due to the attenuation of the SSI zone. However, in the zone where PSJ has no influence but the jet shock does, there is a slight enhancement of the SSI zone, leading to an increase in pressure.
In this study, the control effect of a single-pulse PSJ on double wedge type-VI and type-V SSI was investigated through wind tunnel experiments and numerical simulations, and the influence of discharge energy was also explored. The main findings are as follows:
(1) The interaction between PSJ and the high-speed freestream results in the formation of a plasma layer and a jet shock, which collectively governs the control of SSI. From the perspective of shock intensity, coverage area of the PSJ and jet shock, as well as the attenuation of SSI, the control effect of PSJ on SSI is gradually enhanced with increasing discharge energy.
(2) The control mechanism of single-pulse PSJ on SSI lies in its ability to attenuate shock and SSI. For type-VI SSI, under the control of PSJ, the original second-wedge oblique shock is eliminated, resulting in a new type-VI SSI formed by the jet shock and the first-wedge oblique shock. For type-V SSI, under the control of PSJ, Mach stem, supersonic jet and the reflected shocks are significantly attenuated, resulting in a transformation from type-V SSI into type-VI SSI. The numerical results indicate that there is an approximate reduction of 32.26% in peak pressure.
(3) The development of PSJ also extends in the Z direction, however, the influence range of PSJ and jet shock is limited. The pressure decreases in the area affected by both PSJ and jet shock due to the attenuation of the SSI zone. However, in zones where PSJ has no influence but the jet shock does, there is a slight enhancement of the SSI zone, leading to an increase in pressure.
The aerodynamic components, such as the flanks, flaps and inlet lips of high-speed vehicles, are susceptible to SSI, which may result in potential detrimental effects. The findings of this study demonstrate that the single-pulse PSJ can effectively mitigate wall pressure by attenuating SSI, thereby offering potential applications in controlling local pressure loads or achieving overall drag reduction of high-speed vehicles. The excessive local pressure load induced by SSI may lead to structural damage, therefore, reducing the local pressure load is of utmost importance for enhancing aircraft safety. In addition, the integral of pressure corresponds to the drag of the vehicle. Consequently, decreasing the pressure can effectively achieve a certain level of vehicle drag reduction.
This work was supported by the Independent Innovation Science Fund of National University of Defense Technology (No. 24-ZZCX-BC-05), National Natural Science Foundation of China (Nos. 92271110 and 12202488), the Major National Science and Technology Project (No. J2019-Ⅲ-0010-0054), the National Postdoctoral Researcher Program of China (No. GZB20230985), and the Natural Science Program of National University of Defense Technology (No. ZK22-30).
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Figures(14) / Tables(1)
Supported by: Beijing Renhe Information Technology Co., Ltd. 
| Cases | Angle of the second wedge | C (μF) | E (J) |
| 1 | 45° | 0.32 | 0.58 |
| 2 | 45° | 0.64 | 1.16 |
| 3 | 45° | 1.6 | 2.89 |
| 4 | 60° | 0.64 | 0.63 |
| 5 | 60° | 2.24 | 2.20 |
| 6 | 60° | 4.6 | 4.51 |
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