3.1.1. Computational Stiffness and Equation Singularity

The modeling of high-enthalpy, high Mach number airflow under hypersonic conditions was established by the von Karman Institute [64]. They proposed a novel quasiequilibrium flow effective asymptotic model. Through comparison with the results of chemical nonequilibrium (CNEQ) flow calculations, they verified the effectiveness of this model. A comprehensive assessment of chemical kinetics and energy exchange models for thermochemical nonequilibrium flows was performed. Regarding chemical kinetics, the most reliable dataset for reaction rate constants is the Park dataset. However, concerning vibration/chemistry coupling, Park’s model is correlation-based, making it effective under certain conditions but potentially failing under others. Direct numerical simulations of hypersonic flat-plate turbulent boundary layers under both thermal equilibrium and chemically nonequilibrium conditions using the high-speed Navier–Stokes equations were conducted [65, 66]. The results indicated that the high-enthalpy turbulent boundary layer can directly employ transformations such as Van Driest’s velocity and Morkovin’s scaling theory, based on fully gas conditions. Pan and others studied hypersonic chemically nonequilibrium MHD flow, employing a simplified 5-species 17-reaction model for chemical kinetics [67]. Jiang et al. [11] investigated turbulent flows considering high-temperature gas effects under the influence of an external electromagnetic field. This study also considered high-temperature gas effects and turbulence in hypersonic shock–boundary layer interactions. It utilized the Gupta 11-species 20-reaction chemical reaction model, thermochemical nonequilibrium gas model, and two-temperature model, resulting in improved accuracy of the computational results. However, in this research, the influence of turbulence on the species production rate in the component equations was not considered. The chemical reactions were modeled using a finite-rate reaction model, and the mean quantities were directly used when calculating reaction rates. Therefore, the coupling model for the chemical reaction rates in high-enthalpy turbulence remains an unresolved issue [47, 67].

Currently, the methods used in research often involve making certain assumptions or simplifications in thermodynamic or gas models. However, such computational results often exhibit significant discrepancies when compared to real-world scenarios.

3.1.2. Turbulence Model-Related Issues

3.1.2.2. Turbulence Model Modifications

In recent years, there has been a growing trend to introduce data-driven and machine learning methods for modifying turbulence models in Reynolds-averaged Navier–Stokes (RANS) turbulence simulations [26, 68]. These methods are collectively referred to as data-driven modeling approaches. Parish et al. [69] and Singh et al. [70] used flow field inversion to obtain modifications for turbulence models and then employed neural networks to establish the mapping relationship between flow field features and the modifications, resulting in embedded turbulence models. The reconstructed turbulence models provided results that closely matched experimental data. Ling et al. [29] utilized computational results from DNS and LES to develop machine learning–enhanced RANS turbulence models. They compared different machine learning methods such as support vector machines, decision trees, and random forests in predicting flow field uncertainties. The results demonstrated that these methods accurately captured flow characteristics even in cases differing from the training samples. Xiao et al. [71] applied Bayesian methods to quantify the uncertainty in model forms for RANS calculations and incorporated empirical knowledge constraints. The method effectively utilized sparse prior data to capture errors in baseline models and achieve more accurate posterior mean velocity distributions. Wang et al. [72] highlighted the importance of Reynolds stress prediction in determining RANS calculation accuracy. They developed a random forest machine learning reconstruction method based on the Reynolds stress tensor and applied it to turbulence modeling for flows in square ducts and typical separated flows. Wu et al. [31] adopted a similar approach to construct random forest models and provided prior estimates of confidence for RANS calculations. Zhu et al. [73] constructed radial basis neural networks for different regions in the near-wall and wake regions of airfoils. They modeled the Reynolds stress contributions in high Reynolds number turbulent boundary layers and introduced them in real time into the flow field solution process, improving the calculation accuracy. This approach demonstrated a certain degree of generality for various airfoil shapes and flow conditions. In the field of turbulence simulations, data-driven machine learning methods based on large datasets hold great promise, as reviewed in Reference [28], although data-driven turbulence modeling methods based on physical knowledge constraints for RANS turbulence simulations have not been identified.

Zhang et al. [34], while investigating the decomposition of turbulent friction drag using DNS data, identified a consistent scaling relationship for the decomposition terms within the inner layer of the turbulent boundary layer. Building upon this physical insight, they conducted data-driven modeling and modification of the S-A turbulence model, incorporating physical knowledge constraints during modeling.

They compared the impact of modifications with and without physical knowledge constraints on the accuracy of predicting turbulent friction drag in channel flows. The study employed a discrete adjoint method for the optimization of turbulence models, and the optimization process is outlined in Figure 11.

3.1.3. Electromagnetic Model-Related Issues

5.1.1. Arc Wind Tunnels

Arc wind tunnels such as NASA’s AHSTF [152] offer test durations of up to several tens of seconds. Wind tunnel simulations can achieve a total enthalpy of up to 100 MJ/kg, generating a test flow with relatively high ionization and noticeable EMFC effects. As a result of these characteristics, the spatial magnetic field not only affects the high-temperature conductive airflow downstream of the shock but also influences the charged particles ahead of the shock. This introduces some differences compared to real flight conditions. Additionally, as a result of structural strength limitations, the total temperature and pressure capabilities of such wind tunnels are insufficient. Furthermore, there are contamination components in the test medium, rendering it impossible to simulate conditions for supersonic combustion (Ma ≥ 8). Furthermore, long-duration down-blow transient-type equipment such as wind tunnels commonly faces significant challenges in terms of thermal protection.

5.1.2. Plasma Wind Tunnels

Bityurin [153] studied the effects of EMFC phenomena using Russia’s large-scale high-frequency plasma (HFP) wind tunnel. Their research findings indicated that Lorentz body force effects could alter turbulent structures, suppress flow separation, redistribute pressure and heat flux on an aircraft’s surface, optimize the operational efficiency of scramjet/ramjet engines, control ignition, improve combustion in scramjet engine combustion chambers, and generate onboard power and control boundary layers. However, an HFP wind tunnel requires a substantial amount of energy to generate high-density plasma (200 kW).

To provide higher energy, Macheret [122] from Princeton University conducted theoretical and experimental research on EMFC boundary layer acceleration using sliding arc discharges. Their results demonstrated that the magnetic field could accelerate the plasma columns, affecting the flow near the wall and accelerating and controlling the boundary layer flow. Unfortunately, their research used DC power sources and could not provide sufficient high-frequency power for experiments involving oblique shock wave control.

5.1.3. Cryogenic Wind Tunnels

Changbing et al. [144] conducted experimental research on EMFC around oblique shocks in a cryogenic wind tunnel. The objective of their experiments was to weaken the intensity of oblique shocks by utilizing MHD interactions and altering the boundary flow characteristics around the slope. Pulsed DC discharges were employed to generate high-density plasma columns, and the magnetic sources were neodymium—NdFeB rare-earth permanent magnets. The Lorentz body force effects on plasma-induced airflow velocities were validated through particle image velocimetry (PIV) measurements. The experimental results revealed that plasma could impact neutral gas molecules, transferring momentum and accelerating the flow around the slope. Consequently, the plasma columns exhibited significantly higher velocities in the presence of a magnetic field compared to the case when no magnetic field was applied. Under the influence of Lorentz body forces, the oblique shock in front of the slope moved upstream. The flow field characteristics were examined by varying four parameters, namely, the magnetic field direction, distance between electrodes, slope angle, and pulsed DC electric intensity. The graphical results in Figure 21 confirmed that EMFC could substantially alter the flow characteristics around the slope. When the slope angle was 20°, the Pitot pressure ratio after oblique shock decreased by 19.66%.

In this study, the influence of EMFC acceleration and deceleration on flow characteristics was measured using Pitot pressure and Schlieren imaging; the results were depicted in Figure 22.

Furthermore, because a cryogenic supersonic wind tunnel can operate stably for more than 10 s, the reliability of the results can be determined.

5.1.4. Shock Wave Wind Tunnels

Shock wave wind tunnels are crucial in the realm of hypersonic aerodynamics based on their high enthalpy, high total temperature, and extended test durations. Wind tunnels are essential tools for conducting aerodynamic and aerothermodynamic research at high Mach numbers. High-enthalpy shock wave wind tunnels can replicate the conditions of highly hypersonic flight environments, facilitating experiments not only in aerodynamics and aerothermodynamics under conditions with elevated real gas effects but also in areas such as ignition in scramjet engines, stage separation, and electromagnetic scattering. Representative high-enthalpy wind tunnel facilities include the LENS wind tunnel in the United States [139, 154], HYPULSE wind tunnel [155], Caltech’s T5 wind tunnel [141], Oxford University’s T6 [156, 157], University of Queensland’s T4 [158, 159] and X3 [160], Marseille University’s TCM2 [161], DLR’s HEG [162], HIEST wind tunnel in Japan [163], HEG wind tunnel in Germany, and China’s detonation-driven high-enthalpy shock wave wind tunnels JF-10, JF-12 [164–166], FD-21 [166, 167], and newly established JF-22. High-enthalpy shock wave wind tunnels require relatively low investment, operate with air as the test gas, achieve extremely high levels of simulated flow enthalpy and total pressure (expansion tube facilities can reach enthalpies of up to 100 MJ/kg and total pressures in the gigapascal range), and have relatively low operational costs, rendering thermal protection concerns almost negligible. These facilities have been extensively utilized in foreign research on scramjet/ramjet engines. High-enthalpy shock wave wind tunnels are transient wind tunnels capable of generating extremely high temperatures and pressures. Although their effective test durations are limited to milliseconds, the successful application of advanced testing instruments has enabled the study of the complex gas dynamics, aerodynamic optics, and aerodynamic acoustics of aircraft operating at high hypersonic speeds within this brief window [140]. The low free-stream ionization level in high-enthalpy shock wave wind tunnels is similar to that in the magnetic control environments experienced during actual flight. However, this low-ionization level imposes higher demands on the simulation speed and magnetic field strength of equipment.

For high-enthalpy shock wave wind tunnels, Shen et al. [168] systematically introduced tunnel drive technology [141], flow field detection technology, standard testing technology, and specialized test technologies such as supercombustion ramjet engine testing technology, stage separation testing technology, and electromagnetic scattering testing technology. To achieve enhanced drive efficiency, high-performance drive technology typically combines variable cross-section driving with the heating of lightweight gases. Determining free-stream parameters requires a combination of traditional measurement methods and the development of optical testing technologies integrated with computational fluid dynamics. Flow field diagnostic technologies primarily include planar laser–induced fluorescence, tunable diode laser absorption spectroscopy, and coherent anti-Stokes Raman spectroscopy.

The main steps for determining the free-stream parameters in high-enthalpy shock wave wind tunnels are presented in Figure 23.

In high-enthalpy shock wave wind tunnels, when the driving gas passes through the bifurcation region formed near the wall by an incident shock wave, early contamination of the test gas can occur, as shown in Figure 24. Therefore, it is necessary to develop techniques to delay the contamination of test gases.

The California Institute of Technology’s T5 wind tunnel added a sleeve at the end of the shock tube and testing results indicated that this sleeve effectively slowed the early contamination of the driving gas [170].

Lu et al. [171] summarized the experimental capabilities of free-piston high-enthalpy pulse wind tunnels, including free-stream parameter calibration techniques, aerothermal and pressure measurements, aerodynamic force measurements, scramjet engine testing technology, hypersonic boundary layer transition, free-flight experiments, aerodynamic optics research, electromagnetic radiation technology research, and flow field diagnostics using spectral techniques. Table 3 summarizes the equipment parameters of major high-enthalpy shock wave wind tunnels worldwide.

Udagawa et al. [172] conducted experimental research on EMFC using a shock wave wind tunnel with a testing duration of approximately 1 ms. The results indicated that EMFC effect can alter the upstream boundary layer flow and impact the oblique shock wave ahead. Wu et al. [173] studied the effects of electrohydrodynamics (EHD) in shock tubes considering electric field forces, but not magnetic field forces. Han et al. [174] conducted experimental research on EMFC effects on the flow around a cylinder in a shock wave wind tunnel.

5.2.1. Power Extraction

To satisfy increasing power demands, power extraction technologies can be developed by utilizing MHD generators to extract surface energy. This approach can provide electrical power for hypersonic flights and enable energy redistribution through direct MHD interactions by extracting power from the surrounding airflow [75].

Bityurin [153] conducted experiments in his MHD research to maximize power extraction using pulsed DC discharges to generate high-density plasmas and reduce energy consumption based on voltage–current curves. The results indicated that the extracted power level was a small percentage of the total enthalpy flux. Additionally, proximity to electrodes may play a dominant role in power extraction levels. It is noteworthy that the Hall effect has a significant impact and places higher demands on MHD generator configurations.

The reason for employing pulsed DC discharges is that as the pressure increases, DC discharges are less prone to diffusion and high-voltage pulsed discharges can withstand higher applied electric fields [175], making them more efficient for ionization compared to stable DC discharges with the same potential difference. This characteristic facilitates greater power transmission during the pulse, thereby increasing the conductivity. Additionally, DC power sources ensure the continuity of applied Lorentz forces [176].

5.2.2. Enhancing Conductivity

There are three main ways to increase gas conductivity.

Development of ionized gas technology: Thermal ionization, although being replaced gradually as a result of higher power demands compared to low-temperature plasmas, can still be induced through methods such as high-voltage electric fields, laser beams, directed microwaves, and radiation sources [125, 126].

The development of discharge technology has led to two common types: glow discharge [125, 126] and DBD, both exhibiting similar physical properties. DBD is a self-limiting plasma discharge that requires high power and can sustain continuous discharge at atmospheric pressure. To maximize the efficiency of high-speed flow control, the gap between the anode and cathode regions is extremely small, and they are separated by a very thin dielectric layer. Some studies have attempted to improve DBD efficiency by limiting electrostatic shielding. However, overall, DBD is not practical for high-speed flow control. Compared to DBD, most glow discharge studies have been conducted at relatively low pressures with wider gaps between the anode and cathode regions, which are more suitable for high-speed flow environments. The effect of glow discharge mainly originates from the Joule heating effect, which can change the local Mach number, reduce local sound speed, and affect the geometry of resistance and shock waves [177].

Increasing magnetic field strength: Electromagnetic actuators can be installed in flat plates or airfoils, but power consumption and encapsulation are two critical issues that must be addressed, necessitating the careful selection of magnets. Compared to electromagnets, permanent magnets do not consume power, have higher strength, and are lighter. Rare-earth permanent magnets are suitable for placement on thin control surfaces [178]. However, they have notable drawbacks. The high-temperature aerodynamic environments experienced during hypersonic flight significantly weakens magnetic field strength at the surface of permanent magnets and even cause demagnetization at the Curie point [179]. Even with complex active cooling systems, the use of permanent magnets in high-temperature environments remains challenging. The neodymium magnets can only operate below 400 K, whereas some samarium–cobalt alloy magnets can be used at temperatures above 800 K, rendering them more suitable for high-temperature and high-speed environments. However, they produce a smaller overall magnetic field strength than neodymium magnets [180]. Therefore, magnet development should focus on broadening operating temperature ranges. Currently, as a result of temperature limitations, permanent magnets can only be used on slender control surfaces of hypersonic aircraft to a certain extent. Second, regardless of whether samarium–cobalt alloy magnets or neodymium magnets are used, their maximum surface magnetic field strengths do not exceed 0.5 T.

5.3.1. Magnetofluiddynamic Flow Acceleration Technology

MHD accelerators, commonly referred to as cross-field accelerators, generate plasma by applying an external power source to overcome the self-inductive current and reverse its direction. This process generates Lorentz forces in the flow direction that accelerates the fluid. MHD acceleration can be applied in hypersonic propulsion systems, such as MHD-assisted scramjet engines. However, when the acceleration current is applied, the gas temperature and pressure increase significantly, whereas the velocity changes only slightly. This is because the electrical input power must be converted into the kinetic energy and/or enthalpy of the working gas. Therefore, increasing the energy conversion efficiency or gas enthalpy is advantageous for applications in advanced propulsion systems.

To design more efficient operating conditions for pulsed MHD accelerators, Takai et al. [181] conducted principal verification experiments using MHD accelerators and model rocket engines. They studied the influence of the electrode cross-sectional shape on the thrust efficiency by providing preionization through a pulsed discharge to generate stronger Lorentz forces. The experimental setup consisted of a pulsed power supply system, MHD acceleration channel, model rocket engine, permanent magnets, and diagnostic system, as shown in Figure 25.

Figure 26 illustrates the linear MHD accelerator employed in this experiment.

The results indicated that the thrust efficiency of the pulsed MHD accelerator increased as the electrode cross-sectional area decreased. This effect was attributed to a stronger EMFC effect generated with the same current density, resulting in a higher gas velocity and thrust. Conversely, as the electrode area increased, the Joule heating effect dominated, diminishing the contribution of the MHD effect. In such cases, increasing the plasma conductivity and magnetic field strength can further enhance the performance of MHD accelerators.

Nishihara et al. [182] conducted experiments to control airflow acceleration and deceleration under conditions of a magnetic field strength of 2 T and Mach numbers of 3–4. The results showed that the pressure changes were greater during deceleration than during acceleration. This effect was attributed to the Joule heating effect synergistically increasing the pressure during deceleration, whereas it had an opposite effect during acceleration. The magnitude of the pressure increase depended on the polarity of the Lorentz force, indicating that the Mach number and pressure in the test section were influenced by electromagnetic forces, as shown in Figure 27.

Li et al. [183] conducted experimental research on flow acceleration and deceleration using nonequilibrium ionized EMFC with a capacitively coupled radio frequency discharge. The results indicated that under the influence of acceleration and deceleration Lorentz forces, the static pressure increased and the Mach numbers decreased. The magnitudes of the numerical changes during deceleration were slightly greater than those during acceleration.

5.3.2. Magnetohydrodynamic Shock Wave Control Technology

EMFC technology can control the interaction between oblique shock waves and the lip of an inlet. This technique involves altering the position of shock waves in the inlet under off-design Mach numbers using EMFC. It generates large-volume plasma using balanced or unbalanced ionization techniques. By applying an external load to produce directional currents and utilizing the Lorentz force within the magnetic field, the airflow is accelerated or decelerated, thereby redirecting the shock waves at the inlet to interact with the lip, as depicted in Figure 28.

Researchers at the Russian Institute of Physics, led by Bobashev et al. [184], were among the first to conduct experiments on the EMFC inlet shock wave in shock tunnels. They used rare gas krypton with a relatively long electron–ion recombination time as the test medium. The test conditions included a supersonic total temperature of 9800 K and theoretical electrical conductivity of 3200 S/m. This experiment initially demonstrated the feasibility of using a magnetic fluid to control oblique shock waves in the inlets. However, achieving equilibrium ionization at the required temperatures for realistic flight environments requires the Mach numbers to exceed 12. Even with artificially introduced seed ions, Mach numbers of 8 or higher are required for equilibrium ionization to occur. Therefore, subsequent research on MHD flow control in inlets primarily employed nonequilibrium ionization techniques, such as gas discharge.

Macheret et al. [18] and Shneider et al. [19] proposed a method for EMFC inlet shock wave by injecting high-energy electron beams along the magnetic field lines into the channel. This method achieved EMFC inlet shock waves at off-design Mach numbers. This study involved both a theoretical analysis and experimental research on the control effectiveness of the nonviscous MHD model based on electron beam ionization, as depicted in Figure 29, at off-design Mach numbers.

The results showed that when Ma > Ma_d, reasonable control parameters could increase air capture and reduce the total pressure losses. However, for Ma < Ma_d, Joule heating led to reduced air capture and increased total pressure loss.

Lineberry and Bityurin [185] simplified the inlet configuration to wedge-shaped structures and conducted experiments on the control effects of magnetic fields and velocity vectors orthogonal to three basic two-dimensional wedge structures. These three two-dimensional wedge structures were as follows: Type I with symmetrical single-angle wedges featuring surfaces made of metal or ceramics, Type II with double-angle wedges, and Type III with single-angle wedges with relatively symmetrical shield plates. Type I was the first model structure used. Type II was used to simulate double-slope inlets, whereas Type III was based on the first two types and aimed to simulate the lip effects of typical inlet structures. This usage was intended to demonstrate the ability of EMFC to change the shock wave angle. The experimental setup for Type III is shown in Figure 30. Compared to Type I single-angle wedge structures, Type III wedge models had two changes: (1) extending a certain distance downstream to prevent wake-induced separation and (2) installing a plate parallel to the inflow direction above the wedge, positioning based on experimental results to simulate the lip effects of typical inlet structures.

Table 5 provides a chronological summary of the experimental studies based on the aforementioned three wedge models.

Experiments were conducted in a high-speed wind tunnel driven by an MHD accelerator. Figure 31 shows the bottom of the device and test section [153]. The wedge models were designed with embedded electromagnetic coils and surface electrodes to observe the disturbance of flow structures around the wedge, which was caused by magnetic fluid interactions, and to measure the electromagnetic force induction.

Figure 32 illustrates the numerical simulations and experimental results of the flow field with and without the MHD effects for the Type III model. The upper part of the figure shows the supersonic flow unaffected by the MHD interactions, whereas the lower part shows the subsonic flow influenced by the MHD interactions.

The experimental results confirmed that MHD interactions significantly affected the flow structures around the wedge, causing a significant change in the oblique shock wave angle. When operating under off-design conditions, the MHD interactions can be used to adjust the position of the oblique shock wave to interact with the lip. With the addition of an external magnetic field, the main oblique shock wave under the inlet moves upward to interact with the lip under the design conditions. Additionally, in regions with stronger magnetic field intensity, secondary oblique shock waves are formed near the upstream edge.

Merriman et al. [186] placed a diffusion plasma source at the tip of a wedge and conducted glow-discharge EMFC experiments using a mixed flow of nitrogen and helium with a Mach number of 2. The results showed a significant change in the oblique shock wave angle, and because of the plasma heating characteristics, the Mach number decreased from 2 to 1.8. Based on this plasma source design concept, Gnemmi et al. [198] placed a plasma source at the cone tip of the aircraft for discharge experiments, raising free-stream conditions to a Mach number of 4.57 and a static pressure of 54 kPa, achieving favorable results.

Falempin et al. [199], in collaboration with the European Missile Group, conducted an experimental study on flow control in the inlet of supersonic air ducts using surface plasma aerodynamic excitation. Li et al. [9] provided a review of their work. The experiments were conducted in the T-313 supersonic wind tunnel in the UK, using a Mach 2.0 inlet model. The flow control effects were investigated under Mach numbers 2.5 and 3.0, with an excitation power of 6.5 kW. Figure 33 shows Schlieren images of the shock wave structures with and without plasma excitation.

The principle verification experiments successfully demonstrated plane-induced oblique shock waves, forward movement of oblique shock wave positions, and flow separation control at the rear wall step and cavity using plasma aerodynamic excitation.

Macheret et al. [125, 126] introduced the concept of a virtual inlet cowl based on the heating performance of the plasma. It was shown that plasma heating can alter the upstream flow field to reduce lip spillage in the inlet design. However, this requires a considerable amount of power and can only be used during the acceleration process to reach the design Mach number typically in a short duration, as confirmed by preliminary experiments conducted by McAndrew et al. [200].

5.3.3. Magnetofluiddynamic Thermal Protection Technology

The velocities of space reentry vehicles and planetary explorers returning to Earth can exceed 6 km/s. At these simulated speeds, the heat flux exceeds 300 MW/m² [141]. Sustaining continuous equipment operation under such conditions poses a significant challenge, and high-temperature effects cannot be replicated in conventional “cold-state” hypersonic ground equipment. In a hypersonic low-pressure airflow (M > 10), the conductivity behind the bow shock waves may be sufficient to generate strong magnetofluiddynamic interactions under the influence of magnetic fields on the order of 1 T. Therefore, electromagnetic interactions are highly suitable for controlling the shock wave standoff distances and reducing the surface heat flux [201–203].

Table 6 provides an overview of the research on shock wave standoff distance control in high-enthalpy aerodynamic facilities using EMFC models.

The theoretical research model for the MHD interactions is depicted in Figure 34, which illustrates the formation of a shock layer after a shock wave. Its flow characteristics can be roughly estimated using shock wave relations.

Regarding the primary mechanisms of magnetofluiddynamic shock wave control, some early studies believed that magnetofluiddynamic effects were the primary cause [205, 206]. However, it is widely accepted that plasma heating is the predominant factor [207]. This conclusion was validated using calculations conducted by Poggie [208].

There are two types of experimental conclusions in the field of EMFC shock wave standoff distance and heat reduction. The first type consists of “conventional” experimental conclusions that validate existing theories, while the second type comprises “unconventional” experimental conclusions where experimental results deviate from conventional theoretical results.

5.3.3.1. Conventional Findings: Magnetofluiddynamic Thermal Control Achievements

Through the application of a magnetic field to generate Lorentz forces, the shock wave standoff distance can be increased for thermal protection. This concept was initially proposed by Ziemer and Bush [187, 188]. They conducted calculations and experiments to study the influence of an applied magnetic field on the shock wave standoff distance in ionized air, where ionized air flowed at Ma 4.5, through a hemispherical cylinder positioned within a shock tube. The results revealed a substantial increase in the shock wave standoff distance by a factor of 7.5 when a pulsed current of 4-T external magnetic induction field was generated near the stagnation point in the coaxial coil. In addition, the surface heat flux of the model decreased. Figure 35 presents representative experimental observations of the standoff distance in magnetically controlled shock waves.

Baccarella et al. [189] conducted experimental research on magnetic control shock wave standoff distances in two high-enthalpy arc-heated wind tunnels, HEAT and “Scirocco.” The experimental model used the conical body model shown in Figure 36.

Wilkinson [190] studied the heat transfer characteristics of ionized flows under the influence of electromagnetic fields by analyzing the changes in the stagnation point heat flux of blunt cones. This experiment employed thermocouples to measure heat flux and permanent magnets to enhance the applied magnetic induction field. With the increase in magnetic induction intensity (squared), the stagnation heat flux decreased by nearly 30%. However, owing to the short operating time of thermocouples, the magnetic induction polarity caused discrete electromotive forces, resulting in pseudotemperature readings, thus compromising the accuracy of the heat flow measurements. Furthermore, this study suggests the importance of considering transport characteristics as essential similarity parameters for magnetic interactions.

In the late 1960s, Cambel et al. [191, 192] conducted a series of experiments on magnetofluiddynamics and aerodynamics, including heat transfer studies. Li et al. [92] conducted fundamental experimental research on magnetically controlled thermal protection in high-temperature thermochemical nonequilibrium flow fields. Boron nitride was chosen as the ceramic outer shell material, and permanent magnets were utilized to generate a magnetic field in conjunction with water cooling. This experiment marked the pioneering international demonstration of the effectiveness of magnetically controlled thermal protection systems under high-temperature air inflow conditions.

Ali [193] conducted experimental research on reducing the heat flux in high-enthalpy ionized argon flows using an externally applied magnetic induction field in the L2K arc-heated wind tunnel. The test models were axisymmetric blunt-body models with integrated magnetic coils named C2 and C3, where C2 was a hemispherical cylinder, and C3 was a similarly sized cylinder, as shown in Figure 37. An electromagnetic field is generated by the coils within the models.

The main flow parameters of the tests are listed in Table 7.

Table 7. Flow parameters in the reservoir [193].

Parameters	Values
Gas mass flow rate, kg/s	0.020 ± 0.0002
Reservoir pressure, kPa	37.5 ± 0.75
Specific enthalpy, MJ/kg	2.02 ± 0.12
Total temperature, K	3886 ± 224

The change in the flow field was monitored by light emitted from argon-excited atoms or ions, and the magnetic control effect of the C3 model is shown in Figure 38.

After applying the magnetic induction field, the colors of the airflow changed significantly before and after the shock waves, and a bright green spot was observed in the stagnation region. However, the shock wave standoff distance changed minimally, with only slight variations in the shock wave curvature near the central axis.

Figures 39 and 40 are the IR images of the surfaces of the C2 and C3 models with and without an externally applied magnetic induction field, obtained using the IR thermophotometer method.

The temperature at the stagnation point of C3 model significantly decreased after the magnetic field was applied. The size of the cooling region is closely related to the green bright spot observed earlier in Figure 38.

Figures 41 and 42 depict the measured surface temperatures and calculated heat flux distributions for models C2 and C3, with and without the externally applied magnetic induction field.

The experimental results indicated that after applying the magnetic field, both the shock wave standoff distance and resistance increased, the pressure increased, the Hall voltage increased, the surface temperature decreased (by 16% for the C2 model and by 44% for the C3 model), and the heat flux decreased (by 46% for the C2 model and by 85% for the C3 model). Owing to the geometric constraints at the nose of the C2 blunt-body model, the magnetic induction intensity in the stagnation region was relatively low, resulting in less noticeable heat flow control effects and delayed heat flux reduction. In contrast, for the C3 model, the electromagnetic field had an immediate impact on the surface temperature and heat flux rate, resulting in better heat reduction effects.

5.3.3.2. Unconventional Findings in Magnetofluiddynamic Thermal Protection

Lineberry and Bityurin [185] conducted magnetic control experiments using a cylindrical model at the TsAGI MHD WT test facility. However, the expected increase in shock standoff distance, redistribution of heat flux, and significant reduction did not occur. The test results before and during the MHD acceleration are presented in Figure 43.

The experimental results indicated that the natural ionization level in the flow field was very low, with the Hall effect playing a dominant role. The MHD effect was minimal in this experiment, and the MHD interaction parameter was irrelevant to the magnetic field size because the square of the Hall parameter far exceeded 1. To observe more pronounced MHD effects under low-pressure conditions, the characteristic size of the MHD interaction region must be 1.0 m or larger, and the required ionization level must exceed 1%. Achieving this condition requires increasing the external ionization (which deviates further from the actual flight conditions) and significant energy consumption. Therefore, this study suggested that onboard MHD systems must consider mitigating the adverse effects of the Hall effect on MHD interactions for better flow control efficiency. Subsequent research results [197] have also indicated that the flow around a magnetically controlled cylinder is primary influenced by two factors: the magnetic field distribution and the Hall effect. The Hall effect depends on the Hall coefficient and the gas properties. A strong Hall effect can lead to decreased conductivity and altered Lorentz forces and energy distribution.

Nowak and Yuen [195] conducted experiments with ionized argon flowing at Ma 4.6 over a hemispherical cylinder model. They measured the magnetically controlled heat reduction effects using both conductive and insulating fluids, with and without an externally applied magnetic field. This study revealed an unexpected result: When an external magnetic field was applied, the stagnation point heat flux increased. In cases where there was no external magnetic field but the fluid was conductive, the empirical formulas by Lees [210] and Fay and Riddell [211] became inadequate because they could not predict changes in the heat flux distribution. The tip of the cone was equipped with a tip electrode, and a ring electrode was placed at the base based on transverse Seebeck effects [212]. The authors measured the heat flux at two points in the model. The study found that when current passed through, the heat flux increased, mirroring the results of Nowak and Yuen [195]. This experiment again posed a challenge to numerical simulations of flow solutions, indicating that the electromagnetic boundary conditions for nonconductive fluids have not been correctly implemented and the boundary conditions for conductive fluids became even more complex, potentially surpassing the conventional physical understanding. Kkn and Reddy [213] conducted magnetic-aerodynamic interaction experiments in two different hypersonic shock tunnel facilities: HST2 and HST3. HST2 simulated low-enthalpy flow conditions, whereas HST3 simulated high-enthalpy flow conditions with a free-stream Mach number of 11 and a total enthalpy of approximately 6 MJ/kg. A rectangular block was used as the model. The results indicated that an external magnetic field increased the total drag and heat flux.

Shang et al. [196] conducted experimental and numerical simulation studies on the bluff body and cone configurations in weakly ionized hypersonic flows. The experimental results indicated that in low-conductivity environments, owing to the rapid decay of the magnetic field from the pole to the bow shock, the magnetic interaction parameter was much less than 1, leading to no significant magnetic-aerodynamic interactions or visible changes in the shock standoff distance. The external magnetic field had minimal impact on the drag of the bluff body in this scenario. To address this problem, it is necessary to enhance the strength and conductivity of the magnetic field. This enhancement can be achieved by increasing the number of coils to shorten the distance between the magnetic poles and the blunt body, thereby enhancing magnetic field strength [145, 214, 215]. By installing tip electrodes at the stagnation point, the breakdown capability in the high-pressure region can be increased to generate a locally higher electron number density and increase the conductivity. As a result of these improvements, the field strength at the stagnation point increased by 1.333 times compared with the previous test results. At the same conductivity, the magnetic interaction parameter nearly doubled. Notably, this experiment confirmed the presence of electrostatic interactions. The charge release creates a structure resembling a boil on a bow shock (bow shock deformation). Therefore, in EMFC experiments, significant electromagnetic effects can be obtained with a lower density plasma flow combined with an external magnetic field, such as using a low-density plasma wind tunnel.

5.3.4. Magnetofluiddynamic Drag Reduction Control Technology

Zhou et al. [197] conducted research on the electromagnetic force-controlled boundary layer drag reduction around a cylinder. The experiments used a two-dimensional laminar flow model with a plasma current (Faraday current) induced by the MHD fluid flowing along the cylinder axis, as shown in Figure 44.

Figure 45 illustrates the experimental setup of the electromagnetic force fluid control used in this experiment.

By shielding part of the surface electromagnetic field to alter the spatiotemporal characteristics of the electromagnetic force, the separation point around the cylinder can vary between the front and rear stagnation points, producing different control effects. The results indicated that the electromagnetic forces on the fluid boundary layer could continuously control the flow around the cylinder and the formation of wake vortex streets. Positive electromagnetic forces reduced vortices, dampened oscillations, and decreased drag. Conversely, negative electromagnetic forces had a pronounced vortex-enhancing effect, disrupting the symmetry and stability of the vortex distribution on the surface of the cylinder and exerting a braking effect.

5.3.5. Boundary Layer EMFC

A boundary layer can amplify fluid dynamic disturbances, particularly in the case of high-speed, inviscid hypersonic flows, where the plasma conductivity is relatively low, speeds are high, and interaction parameters are low. This makes EMFC boundary layer more feasible [175]. An external magnetic field has several advantages when applied to plasma control in the boundary layers of high-speed nonequilibrium hypersonic flows. These advantages include not requiring the ionization of large gas volumes, lower flow velocities and density within the boundary layer, and maximum magnetic field strength near the wall, resulting in highly efficient boundary layer flow control. By employing simple surface DC discharge electrodes or generating uniform plasma at the bottom region of the boundary layer through DBD or sliding arc discharge, control over boundary layer flow separation can be achieved. Many researchers have used glow discharges [216] and corona discharges [217, 218] to delay subsonic boundary layer separation on flat plates and enhance wing lift [219–222]. Wilkinson [223] explored the use of spanwise oscillating discharge to reduce Reynolds stresses and surface friction in turbulent boundary layers. Kimmel et al. [224] generated longitudinal DC electric fields between surface electrodes on a flat plate using the discharge effect to increase the surface pressure through boundary layer heating and viscous interactions, effectively controlling boundary layer separation. Macheret et al. [122, 124] also conducted theoretical and experimental research on surface discharge for high-speed boundary layer control, demonstrating that magnetically accelerated plasma columns can influence the flow near the wall and serve as an effective means to accelerate boundary layer flow. Figure 46 illustrates the experimental model of EMFC separation control using plasma discharge and magnetic field control.

For the second case, Figure 47 illustrates the flat-plate EMFC actuator designed by Macheret et al. [124]. It consists of five surface electrodes separated by a dielectric material. There are four adjustable NdFeB magnets. The Lorentz force is primarily concentrated on the electrodes, particularly at their edges. The magnitude of the Lorentz force generated by the NdFeB magnet section significantly decreases with decreasing height, but still exerts control over the boundary layer.

In such an axial arrangement of electrodes, it is important to keep the external electrodes grounded to prevent the generation of reactive forces at the edges of the actuator. Consequently, the distribution of Lorentz forces on the actuator is uneven, which is unavoidable. The effect of making the Lorentz force uniform can be approximated by matching the maximum magnetic field strength with the minimum electric field strength field point and vice versa. Early research indicated that the geometric shape of the segmented electrodes has a significant impact on the electric field distribution [228], enabling adjustments in the electrode geometry when designing MHD actuators. Additionally, as the MHD load coefficient decreases, the location of the maximum Lorentz force gradually shifts from the electrode surface to the magnetic pole.

For the third case, Braun [229] incorporated three components, as shown in the diagram below, and experiments were conducted in a low-speed wind tunnel at atmospheric pressure.

The structure of the Lorentz force actuator includes a row of embedded surface electrodes alternating with NdFeB magnets oriented perpendicular to the flow direction. The conductive particle seeding system and ionization actuator operate by seeding low-ionization-energy potassium carbonate particles into the airflow, which are then ionized by a high-voltage field before entering the active EMFC actuator.

The ionization actuator is responsible for generating the glow discharge. However, PIV imaging revealed that the changes occurring in the boundary layer under the influence of the glow discharge were primarily caused by the Joule heating effect, rather than Lorentz forces.

As can be seen from Figure 48, the conductive particle seeding system employs potassium carbonate seeds as ionizing seeds. Although high-voltage fields can ionize air and produce glow discharge, potassium carbonate seeds are essentially unaffected. Therefore, it is suggested that potassium carbonate seeds should be thermally decomposed or vaporized using high-voltage and high-current pulses.

Figure 49 illustrates the results of an EMFC experiment using saltwater, where the EMFC control effect is visualized by the addition of a blue dye. Magnets were placed beneath the surface between the electrodes and upon the activation of the power source, a significant portion of the liquid layer instantly moved forward. Figures 49a, 49b, 49c, and 49d illustrate the time-evolving process of the Lorentz force actuator’s driving effect.

This study suggested that the optimal application for utilizing onboard EMFC may lie in enhancing the control of high-speed missiles. Figure 50 depicts the future development of missile control envisioned in this context. Segmented electrodes are arranged around the missile diameter, enabling control initiation from various positions around the missile to manipulate its direction. Bookey et al. [230] conducted experimental research involving the excitation of plasma discharge at the tips of low-altitude supersonic projectiles to alter aircraft orientation. By providing a discharge between two electrodes via a high-voltage generator, disturbances were induced between the aircraft’s surface and the shock waves at the tip of the conical body. The intensity of these disturbances caused the shock waves to twist and deform, resulting in changes in aerothermodynamic variables and generating lateral forces and pitch moments that redirected the projectile.

Braun [229] summarized information related to EMFC and relevant experiments, introducing the application of artificially added conductive seed particles to boundary layer flow control. This information is presented in Table 8.

Gallitis and Lielausis [231] designed an electromagnetic field activation plate with alternating strip electrodes and magnetic poles, immersed it in a weak electrolyte solution, and for the first time, experimentally confirmed that the Lorentz force could alter the boundary layer structure of a flow field with a certain level of conductivity. Udagawa et al. [172] conducted experiments on EMFC boundary layer in a supersonic flow with a Mach number of 1.5. Their experimental system consisted of two types of components: a supersonic wind tunnel driven by a shock tube and sensors, as shown in Figure 51.

Their experiments involved an analysis of the pressure distribution, wall pressure distribution, and effect of the electromotive force on DC discharge in the boundary layer. The control effect on the boundary layer was altered by changing the position of the oblique shock wave.

Bityurin et al. [194, 232] conducted EMFC and MHD power extraction experiments in an HFP wind tunnel in Russia. The results of these experiments demonstrated that the Lorentz force can control boundary layer separation, alter turbulence, and redistribute pressure and heat flux on the surface of an aircraft. This optimization enhances the operational efficiency of ramjet and scramjet engines, controls ignition, improves combustion in the combustion chamber, and generates onboard electrical power.

Figure 52 illustrates the EMFC separation device developed by Minton [169]. A shock wave generator is placed in the airflow in the wind tunnel at an angle of attack α to generate oblique shock waves. At high angles of attack, the intensity of the shock waves causes airflow separation downstream of the shock wave point. The electrode used for plasma discharge is located upstream of the shock wave point. Electromagnetic coils are positioned in the flow field, creating a magnetic field perpendicular to the flow and discharge current directions.

The surface of the model generates a magnetic field of approximately 2 T in its vicinity. The visualized flow pattern of the measured MHD interaction region is shown in Figure 53, where the angle of attack of the airflow is approximately 2.0°. Strong magnetic fluid interactions can be observed on the underside of the plate.

The excitation generator kept the positions of the reflected excitation waves roughly constant and independent of the angle of attack α, which determined the EMFC separation performance based on the specific parameters presented in Figure 54.

It can be seen that for a Mach number of 4, flow separation is expected to occur at α = 10.1^∘.

This formula yields the pressure increase across a reflected shock wave. Beyond this pressure, the boundary layer separates. After continuously increasing the Mach number using a rotating shock wave generator, at Mach 5, the pressure rise across the reflected shock wave reached the critical pressure that induced boundary layer separation. At this point, the separation region was sufficiently large, and the EMFC separation system was activated. This accelerated the flow ahead of the reflection point to a level that allowed the boundary layer to pass through a significant adverse pressure gradient without separation. The performance characteristics of this flow control system can be studied by adjusting the magnetic field intensity and input power of the discharge.

Figure 55 depicts the experimental results of the surface pressure variation over time under the influence of discharge. Plasma discharge was initiated at 20 s and terminated at 40 s.

When a magnetic field is applied perpendicular or parallel to the surface of the weakly ionized plasma generated in the boundary layer, it affects the plasma distribution in the magnetic field, thereby altering the flow field morphology. Therefore, this study was extended by applying a transverse magnetic field parallel to the surface of the plate and perpendicular to the direction of the free-stream velocity. The magnetic field was varied from 0 to 1 T, and the total current was varied from 0.025 to 0.3 amp. After applying an external magnetic field, the Lorentz force vector directed toward the plate surface suppressed the increase in the surface pressure. However, the results indicated that the primary effect influencing the flow was the Joule heating effect in the boundary layer fluid, rather than the Lorentz force effect. Macheret et al. [124] also noted that the EHD effect could alter the velocity at low densities in combination with the Joule heating effect. Studies related to surface microwave discharge [234] have suggested that local heating in a flow generated by Joule heating effects is accompanied by an increase in pressure and boundary layer displacement.

Menart et al. [145] observed that in the absence of an external magnetic field, a continuous surface DC discharge at Mach 5 led to a localized increase in the static pressure on a flat plate. The discharge, which was oriented in the flow direction on the plate, triggered a Joule heating effect in the fluid, which was the primary cause of the increased boundary layer thickness and pressure, rather than the Lorentz force effect introduced by an external magnetic field. Subsequent measurements performed by Kimmel et al. [235] confirmed this trend. Kimmel et al. [224] further summarized and expanded the findings. Specifically, the influence of an external magnetic field on the pressure distribution, applied voltage, and glow discharge was analyzed. The results indicated that without an external magnetic field, surface discharge could control the pressure field around the flat plate with the pressure increment caused by the discharge roughly following a linear relationship with the discharge power. Notably, as a result of the nonuniformity of the discharge near the cathode, the effect of the constriction discharge was more pronounced near the cathode and less significant downstream. Under an external magnetic field, when the current was less than 100 mA and the magnetic field was less than approximately 0.2 T, the discharge tended to diffuse. As the current and magnetic field intensities increased, the discharge range narrowed. Furthermore, when the Lorentz force vector pushed the discharge downward, the pressure increased, and this effect became more pronounced as the distance along the plate increased. However, considering the three-dimensional nature of discharge, its dependence on the magnetic field, and Joule heating effect in the boundary layer, it is unclear whether these effects were solely caused by Joule heating. When the Lorentz force vector pointed upward, the discharge was pushed away from the flat plate, leading to a decrease in pressure, as shown in Figure 56.

Miles et al. [236] and the Princeton University Applied Physics Group led by Zaidi et al. [237] explored the control of boundary layers using “sliding arc” magnetically driven nonequilibrium surface discharge. In experimental studies, surface arc discharges occurred between two nearly parallel (conical, forming plasma columns upstream) linear electrodes spaced at a certain distance. The electrodes were positioned on the surface and along the flow direction (as shown in Figure 57). The graphical results in Figure 58 indicate that when a high voltage was applied between the electrodes, a contracting plasma column was formed at the minimum separation point (the plasma column was generated by a DC breakdown between the two surface electrodes). This position moved upstream when gradually reducing the gap between the electrodes. According to the results in Figure 59, subsequently, the plasma column was convected by the airflow and flowed downstream at the end of the electrodes. At this point, another plasma column was formed upstream, and this process was repeated. As a result of the fast flow velocity, the discharge appeared approximately uniform to the naked eye. However, when imaged with a high-speed camera, plasma columns could be observed.

These results indicate that when a magnetic field orthogonal to both the plasma column and flow is applied, MHD forces accelerate the plasma column and transfer momentum to the neutral gas, accelerating the flow after surface discharge from electrodes is added compared to the average local flow velocity after the application of a moderate-strength magnetic field (B = 0.5 ~ 3.0 T).

Kalra et al. found that EMFC boundary layer experiments was precisely determined by the momentum transfer of a plasma column generated after the addition of electrodes. The plasma column formed a periodic structure with frequencies ranging from to 1 to 10 kHz between the electrodes and the frequency depended on the current and magnetic field strength. Macheret’s [122] experimental results suggested that a plasma column can act as a unidirectional porous piston for flow control. Under the influence of a magnetic field, the ions in a plasma column flow rapidly downstream and collide with neutral particles, transferring momentum to the boundary layer. In Kalra et al.’s [119] subsequent study, investigations were conducted on the magnetic control effect of an additional electromagnetic field. The results indicate that although the combined action of electric and magnetic fields can provide greater momentum to the flow, simply increasing the current does not necessarily improve the MHD effect. When a shock-induced separation bubble moves downstream, Joule heating occurs. Beyond a certain point, an increase in the current begins to have an inhibitory effect as a result of Joule heating.

Kalra et al. [121] further studied the impact of magnetically driven surface plasma columns on separation caused by shock–boundary layer interactions and introduced the concept of the “snowplow arc.” Surface plasma columns manifest as lateral “arcs” between two bifurcated electrodes that are driven by Lorentz forces to sweep over the gas near the surface either downstream or upstream. In Kalra et al.’s experiments, the wind tunnel had a Mach number of 2.8, and a 10° wedge was used to generate oblique shock waves that impinged on the plane where the plasma actuator was located.

A schematic of the experimental setup is presented in Figure 60. A uniform magnetic field was applied vertically throughout the apparatus, and the plasma column generated between the electrodes was subjected to forces produced by magnetic field B and current J in the upstream or downstream direction.

Figure 61 presents the shadowgraph results of the experiment. The shock wave caused a gradual increase in the static pressure near the wall, leading to separation. A reflected shock wave appeared after the incident shock wave interacted with the boundary layer.

The experimental results indicated that the coupling between the plasma column and SWBLI region led to a shift in the location of the shock wave–induced boundary layer separation point. When the Lorentz force acted upstream, the separation point also moved upstream. When the Lorentz force acted downstream, the separation point was largely unaffected. This study quantitatively highlighted the reasons for the undisturbed downstream behavior by calculating the ratio of the plasma column scale to the boundary layer thickness.

This study also evaluated the effects of electromagnetic field location, magnetic field line angle, and electrode placement using four different testing configurations, as represented in Figure 62. In Case 1, boundary layer driving was performed using surface-embedded copper electrodes, and the electrodes were powered by a DC power source upstream. The magnetic field was perpendicular to both the direction of the current and flow direction, generating Lorentz forces that caused upstream flow of the plasma column. Under these control conditions, the intensity of the separation bubbles increased. In Case 2, the electrode configuration was the same as in Case 1, but the electrode positions shifted from upstream to downstream. The Lorentz forces generated by the magnetic field caused the plasma column to move downstream. Under these control conditions, flow separation was eliminated or separation bubble intensity decreased. In Case 3, the electrode setup was the same as that in Case 1, but the magnetic field lines were bent at a small angle, causing the plasma column to move from the wall into the incoming flow, forcing a high-momentum incoming flow into the separated boundary layer, thereby reducing separation. In strong interactions, separation can be eliminated. In Case 4, there were two concentric electrodes, and after applying a magnetic field perpendicular to the electrode plane, the plasma column rotated, leading to the formation of vortices in the subsonic boundary layer.

The results indicated that compared to the baseline condition (Case 1), when Case 3 increased the applied magnetic field angle from 0° to 10°, the separation decreased. However, further increasing the angle to 20° did not reduce the separation.

In an experimental study on controlling shock wave–induced separation using MHD effects, Thibault and Rossi [238] conducted flat-plate tests with saltwater flow and obtained a boundary layer velocity distribution, as shown in Figure 63, which aligns with the conditions of Case 2 in the aforementioned study by Kalra et al. [121].

Kalra et al. [121] further analyzed the impact of wedge angles and compared the results of tests with 10° and 14° oblique wedges. The 10° oblique wedge corresponded to a lower shock wave intensity, and as the higher downstream pressure gradually penetrated the subsonic region of the boundary layer along the upstream side of the shock wave point, it did not induce recirculation bubbles or separation without plasma driving. However, when the oblique wedge angle increased from 10° to 14°, the oblique shock wave collided with the turbulent boundary layer, leading to bubble separation. At this point, driving the plasma downstream in the direction of the reverse separation bubble altered the geometry of the disturbance region. Additionally, applying a magnetic field at a certain angle allowed the plasma column to enter the boundary layer, increase the momentum of the boundary layer, and prevent separation.

Bookey et al. [230] revalidated the EMFC results for 10° and 14° oblique wedges. The results indicated that compared to the 10° oblique wedge, the reflected shock wave in the flow field of the 14° oblique wedge occurred before the incident oblique shock wave interacted with the boundary layer. When separation occurred, the increased thickness of the boundary layer led to the observation of a reflected shock wave before it collided with the boundary layer. A shadowgraph of the disturbance region is presented in Figure 64.

Furthermore, as shown in Figure 65, the wall pressure exhibits a plateau in the middle, indicating that the interaction described above resulted in separation.

Kalra experimentally investigated the interaction between magnetically forced discharge and boundary layer flow. Images of the plasma columns within the flow field are demonstrated in Figure 66. Instantaneous images of the plasma columns revealed an approximate diameter of 1 mm. With extended exposure times, as shown in the image of the plasma columns progressing along the electrodes in part (a), it becomes evident that the plasma columns move toward the end of the electrode. Based on the limited length of the electrodes, the plasma columns were eventually extinguished and reignited at the shortest distance between the two electrodes. When oblique shock waves are not generated, there is no separation zone. However, as shown in part (b), the oblique wedge generates shock waves, causing boundary layer separation. In this image, the plasma columns do not reach the end of the electrode. This is because as the local flow separated and moved upstream, the plasma columns could not be dragged to the end of the electrodes in the absence of a magnetic field.

The findings demonstrated in Figure 67 present the flow field Schlieren patterns corresponding to the presence or absence of a magnetic field under a constant plasma power input.

The length “l” represents the distance covered after the first compression wave interaction when the incident oblique shock wave separated from the boundary layer. One can see that this distance increases when an external magnetic field is applied.

Scaling of the effect of the Lorentz forces on the local interaction parameters within the boundary layer can be achieved by varying the mean values. Experimental studies on MHD effect conducted on compressible and incompressible [117] flows in the boundary layer have indicated that the interaction parameters significantly influenced the effectiveness of EMFC. Therefore, these interaction parameters can be considered indicators of magnetic control effects.

In Lineberry and Bityurin’s [185] research on EMFC inlets, the MHD interaction parameter “Su” was defined as follows: Su ∝ σu²B²L, where s represents the conductivity, u is the velocity, B denotes the magnetic field strength, and L signifies the length. They determined that maximizing both the conductivity and magnetic field strength is necessary to achieve a sufficient MHD interaction. For moderate magnetic field intensities (0.1–0.5 T), the characteristic scale of the corresponding MHD interaction region must be at least 1 m, and the required ionization level must exceed 1%. The former necessitates a large-scale testing rig, and the latter is challenging to achieve, even with external ionization sources, because energy consumption exceeds expectations.

In the analysis of Henoch and Stace’s [117] experiments on turbulent electrolytes and flat-plate boundary layer EMFC, it was suggested that friction velocity can serve as an improved interaction parameter for measuring velocity scales. This was also acknowledged by Macheret et al. [124] in subsequent research. For laminar flat-plate boundary layers, the surface friction is inversely proportional to the square root of the Reynolds number, and the ratio of the velocity thickness to the flow length is inversely proportional to the square root of the Reynolds number (i.e., c_f = C₁Re^−1/2). Therefore, based on the friction velocity, the interaction was determined to be $$. The values of C₁ and C₂ can be derived based on experimental conditions to obtain similar solutions for laminar boundary layers and subsequently deduce their values.