# Computational and Experimental Modeling in Magnetoplasma Aerodynamics and High-Speed Gas and Plasma Flows (A Review)

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- Controlling the flow and surface flow of the AA with volumetric ponderomotive forces. It is worth noting that controlling the flow near AA with the magnetoplasma effect is based on controlling the main flow as well as the boundary layer;
- Controlling plasma-stimulated combustion in high-speed gas and plasma flows.

## 2. Methods for Controlling the Flow around the External and Internal Surfaces of AA

#### 2.1. Methods Description

- Dynamic influence based on Lorentz force and electrostatic force (in the presence of uncompensated charges in the environment);
- Thermal influence.

^{−10}to 10

^{−2}s occur in a plasma flow with chemical reactions and electric charge relaxation as well as translational, rotary, and oscillating relaxations. Minimum time scale is determined by the establishment of electroneutrality in a plasma flux and has a value of the order 10

^{−11}to 10

^{−9}s. Maximum characteristic time varying from 10

^{−3}to 10

^{−1}corresponds to the time spent in a gas-plasma environment near (or within) AA.

#### 2.2. Pulsed Plasma Dynamic Surface Discharges

_{0}(capacitor bank) into the energy of discharge plasma ${E}_{pl}\left(t\right)$, which can be defined as the transformation efficiency factor $\eta \left(t\right)={E}_{pl}\left(t\right)/{W}_{0}$ for arbitrary time $t$.

_{0}

^{®}Q

_{J}

^{®}E

_{int}+ E

_{kin}+ E

_{pl}) occurring in these modes are further considered with two energy-power options of LSSD: “explosive” mode—${P}_{el}\approx 10\raisebox{1ex}{$\mathrm{MW}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{cm}$}\right.$ (${U}_{0}$ = 50 kV, L = 50 cm), “magnetogasdynamic” mode—${P}_{el}\approx 100\raisebox{1ex}{$\mathrm{MW}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{cm}$}\right.$ (${U}_{0}$ = 100 kV, L = 25 cm). Based on the results presented in the article [16], during the first half-period of discharge current, $J$ lateral expansion of an LSSD discharge channel has an approximately constant velocity ($~2\mathrm{km}/\mathrm{s}$, ${P}_{el}\approx 10\raisebox{1ex}{$\mathrm{MW}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{cm}$}\right.;$ $~4\mathrm{km}/\mathrm{s}$,${P}_{el}\approx 100\raisebox{1ex}{$\mathrm{MW}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{cm}$}\right.$). If ${P}_{el}\ge 40\raisebox{1ex}{$\mathrm{MW}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{cm}$}\right.$, the spatial size of a LSSD discharge channel along the Z-axis is larger than along the Y-axis. There is radiation and magnetogasdynamic change of the parameters in the rupture area; the outer boundary of the discharge is a GD-rupture with parameters different from the parameters of a strong UW (e.g., ${\rho}_{1}/{\rho}_{0}<\left(\gamma +1\right)/\left(\gamma -1\right)$). This effect is most prominent in the direction of the Y-axis due to a “stiff” non-deformable limiter in the form of DIE along the Z-axis and its absence in the direction of the Y-axis.

- -
- -
- LSSD Brightness temperatures reach maximum in moments of time close to maximum energy input power (maximum current) (at ${P}_{el}$ ≈ 10 MW/cm—T
_{br2,3}~ 30 kK; for ${P}_{el}$ ≈ 100 MW/cm—T_{br,2}~ 30 kK, in argon T_{br,3}~ 40 kK and in the air T_{br,2,3}~ 40 kK) and significantly fall for the second and third spectral intervals in the second (16 kK—MW/cm; 25 kK—${P}_{el}$ ≈ 100 MW/cm) and the third half-periods of full current (13 kK—${P}_{el}$ ≈ 10 MW/cm; 20 kK—${P}_{el}$ ≈ 100 MW/cm) [17,18]; - -

#### 2.3. Pulsed Nanosecond Surface Discharges

**V**, $P$—density, velocity vector, flow pressure; $\overrightarrow{E}$, $\overrightarrow{H}$, $\overrightarrow{j}$—vector of electric, magnetic and current density strength, ${\rho}^{\ast}=e{\displaystyle \sum _{k}{Z}_{k}{n}_{k}}$—space charge, $v$—kinematic viscosity, $\overrightarrow{g}$—acceleration of gravity. Here we note that the part $\left|\frac{1}{\rho}\nabla {\rho}^{\ast}\times \overrightarrow{E}\right|$ also the part $\left|\frac{1}{\rho}\nabla \rho \times \overrightarrow{E}\right|$ may be neglected. Then the equation for vorticity $\overrightarrow{\Omega}$ = rot($\overrightarrow{V}$) will take a simpler look:

^{3}) have been analyzed in the work [44]. It is shown that in flow with vortex zones, «sliding» surface discharge develops in the form of a channel width of 1–3 mm, located in the area of reduced density at a distance (5.5–9.0) ± 2 mm from the bottom of the wedge. The electron concentration in the discharge channel, which is significantly (10–20 times) higher than the electron concentration at discharge initiation in a homogeneous medium, has been found.

^{3}rectangular block. The long part of the obstacle was perpendicular to the glass (walls) of the shock tube. Quasi-static current field (installed for ~200 μs) contained an angled shock wave that interacted with the boundary layer on the top wall of the shock tube.

^{3}. The temperature of the near-surface layer of the gas increases by 600–1000 K. It has also been established that the initiation of a «sliding» surface discharge leads to an increase in the mean pressure at the channel wall in the flow behind the shock wave by 6–18% (at flow Mach numbers 1.1–1.6 and densities 0.06–0.20 kg/m

^{3}).

^{6}and a maximum free flow rate of 60 m/s.

#### 2.4. Pulse Nanosecond «Barrier» Surface Discharges

^{2}) using DBD discharge in subsonic flow with Reynolds numbers Re = (0.35–0.875) × 10

^{6}by chord. Surface pressure measurements and flow visualization showed that plasma actuators can significantly reduce or eliminate the flow separation from the wing, which results in a reduction of the negative pressure peak near the front edge on the top surface of the profile. Data were obtained from a wide range of attack angles, flow velocities, plasma excitation frequencies and input power. In works [67,68,69], the possibility of using different voltage pulses was also discussed, including microsecond and nanosecond pulses. As in [66], it has been shown that the efficiency of the actuator is highly dependent on the discharge frequency.

#### 2.5. Surface Glow DC Discharge between Sectioned Electrodes

#### 2.6. Pulse-Periodic Nanosecond (Volumetric) Discharge

_{2}(a1Δg), O

_{2}(b1Σg), and vibrationally excited molecules are preferentially accumulated. The presence of electronically and vibrationally excited molecules significantly increases the rate of chain reactions involving them and allows for the possibility of igniting fuel mixtures at relatively low initial temperatures. This is significant for increasing the completeness of fuel combustion in gas streams with sharply non-homogeneous temperature profiles (when there are regions of relatively cold gas), analyzing the possibility of using lean fuel mixtures, etc.

_{2}H

_{2}mixture were observed at P = 1 atm and T0 = 300 K. Based on the 2D discharge calculations and estimates of ignition in [79], it was concluded that it is possible to ignite the fuel mixture in the cathode region of this discharge with a single nanosecond pulse.

_{0}~ 1500 K, according to calculations [79]. The initial concentration of O atoms in the layer, [O]

_{0}= 1.5 × 10

^{18}cm

^{−3}, was taken from [79] in the hot zone near the edge of the electrode. The goal of the modeling was to determine the conditions under which the mixture ignites and a combustion wave forms before the layer cools due to heat transfer to the metal electrode. One-dimensional numerical modeling is based on solving the Navier–Stokes equation together with mass conservation equations for each component [80]. A kinetic equation system was written for 103 components and 700 reactions. The results of testing the system and the main reactions are presented in [81]. The calculations show that even during the discharge stage (40 ns), fuel conversion begins in the mixture, resulting in the formation of CO and H

_{2}. The hot region with partially converted fuel expands, and ignition begins at 4 microseconds. The temperature increases, including due to the combustion of CO and H

_{2}. At first, the flame front moves towards the electrode, then the temperature drops due to cooling, the flame front changes direction, and then it all repeats; overall, the region expands. Ignition occurs only in the hot layer (T = 1500–2100 K), without taking into account oxygen atoms accumulated during the discharge. Overall, work [81] has shown that thanks to nanosecond discharge actions, a decrease in the initial ignition temperature by 250° and the induction time by 100 times can be achieved.

#### 2.7. Magnetoplasmic Control in High-Speed Gas and Plasma Flows

^{−4}and below is clearly insufficient to provide an acceptable level of electrical conductivity of about 10

^{3}Siemen/m. At the same time, attention was drawn to the fact that the value of the induced electric field $\left[\overrightarrow{V}\times \overrightarrow{B}\right]$ can reach hundreds of Townsend in the area of interest for the MHD parachute and/or onboard generator.

_{2}, N, N

_{2}+, N+, and electron mixtures. In addition to this, the kinetic scheme contains ionization reactions of N

_{2}and N by electron impact, dissociation reactions of N

_{2}by electron impact, and corresponding reverse reactions of recombination and association. It is assumed that the rates of forward reactions are determined by the value of the reduced electric field, E/N

_{0}(E—the magnitude of the field intensity, N

_{0}—gas number density). The rate constants of the reverse reactions are considered to be functions of the electron temperature. When calculating the transport properties of the mixture, it is assumed that the collision frequencies of processes involving electrons are determined by the electron temperature. The electron temperature is found through the solution of the electron energy transport equation, taking into account the tensor nature of electron thermal conductivity, the inflow of energy from the electromagnetic field, and elastic and inelastic losses. The latter includes losses due to ionization and dissociation in electron impact reactions, as well as losses from the excitation of vibrational and electronic states of neutral components. The field kinetics model and inelastic loss model were developed based on works [86,87,88,89].

#### 2.8. The Possibility of Controlling the High-Speed Flow of Gas and Plasma Using Pulsed Optical Discharge or Microwave Discharge

^{−3}cm at a specific energy contribution of about 7 eV per particle with a peak electron density Ne ≅ 5 × 10

^{16}cm

^{−3}. The work [97] showed that the energy efficiency of the microwave method of reducing stagnation pressure at the leading critical point is directly proportional to the ratio D/d, where D and d are the diameters of the blunt body and the heated region, respectively. The universality of this relationship was confirmed in works [98,99] (for model diameters from 8 to 30 mm). These same results confirm the important conclusion about the increase in efficiency (reduction of aerodynamic drag with a decrease in the thickness of the heated layer) when the microwave discharge interacts with the boundary layer.

## 3. Methods for Controlling Plasma-Stimulated Combustion in High-Speed Gas and Plasma Flows

#### 3.1. The Fuel and Air Components

#### 3.2. Initiation of Combustion of the Fuel-Air Mixture by an Electron Beam

#### 3.3. Initiation of a Detonation Wave by Laser Radiation

^{3}–10

^{4}Pa. temperature 400–700 K, and Mach number 4–6) is too large (10 m) even for the hydrogen–oxygen mixture [111]. Therefore, the search for methods to intensify the processes of detonation wave formation in such geometry is an extremely important task.

_{2}/O

_{2}(air) and CH

_{4}/O

_{2}(air) mixtures behind an inclined shock-wave front can be achieved by exciting O

_{2}molecules to an electronic state ${b}^{1}{\sum}_{g}^{+}$. For example, this can be performed by laser radiation with a wavelength $\lambda $ = 762 nm generated by a diode laser, even at low values of energy irradiated to the gas (${E}_{a}\approx {10}^{-3}$ J/cm

^{3}).

_{2}O increases by approximately 20 times (compared to the stagnant gas medium) in the interaction region. Overall, the following parameters of laser radiation are required to create laser plasma in LPP channels: laser beam intensity <1.5 × 10

^{9}W/cm

^{2}, pulse energy of several mJ, duration of laser radiation of hundreds of ns, and a pulse spacing of >5 Hz.

_{2}/O

_{2}was considered. Laser radiation with a wavelength $\lambda $ = 762 nm and uniform intensity throughout the affected area, is applied to the flow in a certain region before the wedge nose, with a length along the flow of ${l}_{p}$ and a height of ${Y}_{e}$. The frequency of this radiation, v, is resonant with the frequency of the bound-electron electronic transition, $m({X}^{3}{\sum}_{g}^{-},$${V}^{\prime}=0,{J}^{\prime}=9,{K}^{\prime}=8)\to $$n({b}^{1}{\sum}_{g}^{+},{V}^{\u2033}=0,{J}^{\u2033}=8,{K}^{\u2033}=8)$ of the molecule ${O}_{2}$, where ${V}^{\prime}$ and ${V}^{\u2033}$— vibrational, and ${J}^{\prime},{K}^{\prime}$ and ${J}^{\u2033},{K}^{\u2033}$—rotational quantum numbers in the states ${X}^{3}{\sum}_{g}^{-}$ and ${b}^{1}{\sum}_{g}^{+}$-e, respectively. Given ${J}^{\prime},{K}^{\prime}$ and ${J}^{\u2033},{K}^{\u2033}$ the absorption coefficient for the considered electronic–vibrational transition is maximal at a gas temperature of T = 300 K. Parameters of the supersonic flow ahead of the affected area: ${P}_{0}$ = 10

^{4}Pa, ${T}_{0}$ = 500–600 K, ${M}_{0}$ = 6.

#### 3.4. Ignition of a Combustible Mixture by a Laser Torch Formed near a Condensed Barrier

_{2}—laser is 10

^{9}W/cm

^{2}, and for Nd—laser is 10

^{11}W/cm

^{2}. However, the presence of a metallic barrier significantly reduces (by several orders of magnitude compared to an unbounded gas medium) the required density of the radiation flux for gas breakdown ${q}_{\u043f}$. This phenomenon is explained by the high-temperature ionized layer (usually consisting of easily ionizable vapor of the obstacle) that forms on the surface of the target under certain critical conditions and which intensely absorbs the incident laser irradiation. The breakdown occurs in the focus region of the laser beam, where there are strong spatial-temporal inhomogeneities of the electric field. The breakdown is possible if so-called seed electrons (for example, by the thermoelectron emission mechanism) enter the breakdown region and if the probability of electrons escaping from the focal spot volume is low (the probability of this process is determined by the electron diffusion coefficient).

^{2}).

#### 3.5. Photoplasmodynamic Method of Combustion Initiation

#### 3.6. Capillary Discharge and Ignition of the Combustible Mixture

## 4. Discussion and Conclusions

^{−3}(at a typical specific energy input of 0.05–0.5 eV per molecule in electronic degrees of gas freedom) with less cooling time (for example, due to gas-dynamic expansion) in the plasma region.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**A system of electrodes with a predominant tangential (

**a**) and normal (

**b**) component of the electric field.

**Figure 2.**Conventional scheme of a nanosecond “sliding” or “barrier” surface discharge: ${R}_{1},{C}_{1}$ are the resistance and capacitance of a solid dielectric; R

_{2}, C

_{2}are the resistance and capacitance of solid air in the interelectrode gap.

**Figure 4.**Interaction of streamers with the surface, various mechanisms: 1—through a dustable surface charge, 2—through surface conductivity, 3—through dielectric polarization, 4—through photoemission and thermoemission (in the case of a spark), 5—dielectric.

**Figure 5.**The difference between the streamer and sparks on the surface with electric field lines (

**a**) and without (

**b**): 1—initial electric field lines, 2—electric field lines perturbed by surface charge, 3—metal, and 4—dielectric.

**Figure 6.**Configuration of electrodes for sliding surface discharge: 1—anode; 2—cathode; 3—interelectrode dielectric insert; 4—additional electrode.

**Figure 7.**Thermal and plasma formation of vortices: 1—open electrode; 2—closed electrode; 3—plasma; 4—dielectric.

**Figure 8.**Schematic representation of gas flow near the wedge and distributed sliding surface discharge: 1—flow; 2—discharge area; 3—discharge channel; 4—wedge.

**Figure 9.**Structure of the plasma gas flow in the discharge chamber with a barrier on the bottom wall: 1—discharge area; 2—research area; 3—flow; 4—obstacle; 5—oblique shock wave; 6—shock wave.

**Figure 10.**Schemes of interaction of the oblique shock of the seal with the boundary layer: (

**a**) continuous interaction; (

**b**) interaction with the formation of flow separation: 1—subsonic layer (

**a**) or separation area (

**b**); 2—incident shock wave; 3—reflected shock wave; 4—compression waves; 5—rarefaction waves; 6—sound line.

**Figure 11.**SDBD bit gap diagram: 1—high-voltage electrode; 2—low-voltage (grounded) electrode; 3—plasma layer.

**Figure 12.**Scheme of the problem of flow around a sharp plate by a supersonic flow of compressible gas, on the surface of which a DC glow discharge burns in an external magnetic field: 1—cathode; 2—anode; 3—dielectric.

**Figure 13.**Geometry of the spatial region in the case of magnetoplasma control of the motion of the descent spacecraft. 1—magnetic field source (electromagnetic coil).

**Figure 15.**Plasma-dynamic discharge (magnetoplasma compressor-MPC) of an erosive type in a gaseous medium: 1—discharge electrodes; 2—plasma of gas and (or) erosion products of the structural elements of the electrode system; 3—interelectrode dielectric insert (MID); 4—shock-compressed gas region; 5—undisturbed gas medium; 6—external radiative magnetogasdynamic discontinuity.

**Figure 16.**Gas-dynamic structure of the region of shock deceleration of the plasma flow of the MPC-discharge on a dense gaseous medium.

**Figure 17.**Capillary plasmatron structure. 1—anode, 2—puck of organic glass, 3—cathode, 4—body of insulation material.

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Kuzenov, V.V.; Ryzhkov, S.V.; Varaksin, A.Y.
Computational and Experimental Modeling in Magnetoplasma Aerodynamics and High-Speed Gas and Plasma Flows (A Review). *Aerospace* **2023**, *10*, 662.
https://doi.org/10.3390/aerospace10080662

**AMA Style**

Kuzenov VV, Ryzhkov SV, Varaksin AY.
Computational and Experimental Modeling in Magnetoplasma Aerodynamics and High-Speed Gas and Plasma Flows (A Review). *Aerospace*. 2023; 10(8):662.
https://doi.org/10.3390/aerospace10080662

**Chicago/Turabian Style**

Kuzenov, Victor V., Sergei V. Ryzhkov, and Aleksey Yu. Varaksin.
2023. "Computational and Experimental Modeling in Magnetoplasma Aerodynamics and High-Speed Gas and Plasma Flows (A Review)" *Aerospace* 10, no. 8: 662.
https://doi.org/10.3390/aerospace10080662