1. Introduction
Effective compression of the air at the engine inlet is one of the most significant engineering issues in the design of a vehicle propelled by an air-breathing engine during hypersonic flight. The ideal compression includes a minimum loss of total pressure on external compression surfaces as well as in the internal flowpath. An ideally designed system might be mechanically complex, so such a case is rarely realized due to weight, materials and control constraints. Practical design always involves trade-offs between functionality and multiple other factors, such as tolerance to incoming flow variation or modulation of external conditions over the trajectory [
1,
2]. In inlet and isolator, a series of weak SW enables a lower pressure loss when compared with a few strong SWs, which is a common concept of multi-SW compression [
3,
4]. Shock train geometry is affected by incoming airflow, BL conditions, gas pressure downstream (combustor), and other factors interfering with each other. The shock train configuration is usually unstable and poorly controllable, resulting in the transformation of oblique SWs into direct SWs (nearly perpendicular to flow velocity vector) and resulting pressure/engine performance losses [
5,
6].
Except for exotic magnetohydrodynamic acceleration techniques, all methods of shock train and inlet control function by decelerating the gas locally in its internal flowpath. Typical examples include mechanical obstacles, wall gas jets, or long isolators to reduce shock train sensitivity to combustor counterpressure [
7,
8,
9,
10]. The methods listed above are effective for stabilizing the shock train, but adversely affect the engine performance. A better technical solution is to use a temporal mode when the controller’s actuation prevents the system from shifting to an undesirable operational mode and does not affect cruise mode. A timely prevention of failure is twice as beneficial because of the hysteresis effect, when, after the duct choking, system restore to original state is challenging. Unfortunately, mechanical controllers have an inertial response time that is significantly longer than typical gasdynamic time in hypersonic/supersonic flow,
ms. Another complication is caused by the essentially three-dimensional structure of the shock train and the inlet flowfield in many cases. A smart, highly adaptive control system is therefore preferred [
11].
Contrary to the slow mechanical methods, the energy deposition inflow is one of the most promising rapid methods of controlling SW structures. In simplest terms, the electrical discharge or beamed energy deposition, such as laser or microwaves, heats gas flowing through it with subsequent pressure jumps and volumetric expansions. It creates a new SW, similar to solid obstacles, but much faster than any mechanical element. In an advanced approach [
12,
13,
14], a spatial modulation of gas temperature is credited with redistributing pressure in the flowfield. High gas temperatures result in higher sonic velocity in the plasma zone, resulting in faster propagation of pressure disturbances or even the appearance of subsonic channels within supersonic flows. Several computational works have investigated the interaction mechanism and consequences for SW propagation in a temperature-stratified medium, see References [
15,
16,
17] for example. In the presence of a single heated longitudinal zone, due to a higher sonic velocity in the heated zone with significant pressure redistribution, the SW propagates much farther upstream in a heated zone than it would in a cold gas, as shown schematically in
Figure 1a. As one of the most popular gasdynamic tricks, the bow SW moves upstream when a heated zone is directly placed in front of a blunt body [
15,
18]. For a “thermally stratified” media, the SW structure looks different with the SWs forming a quasi-front of the propagating pressure jump, as it is shown in
Figure 1b [
17]. For a predefined control effect, the second, advanced, mechanism sounds more beneficial in terms of energy requirements: it declares a triggering effect on a SW position instead of a formation of a high pressure zone in result or the gas heating. A straightforward and the most effective method for a fast gas heating is electrical discharge generated inflow. It is, however, challenging to realize a volumetric, thermally stratified plasma zone—a near-surface implementation would be more realistic.
It has been described numerous times in the literature that a stationary or transient SW appears at the generation of electrical and laser discharges in supersonic flows [
12,
19,
20,
21]. The effects of near-surface filamentary plasmas on SWs position at plane wall and at compression surface arrangements were discussed in several serial works [
14,
22,
23,
24,
25,
26]. It was found that a near-surface stratified gas layer, consisting of lengthwise zones of supersonic and subsonic flow, modifies the SWBLI pattern when impinged by an external SW. The plasma method of SW triggering has been explored in recent publications [
14,
27,
28] where schlieren visualization, pressure sensitive paint methods, and pressure sensing are used to demonstrate fast response with high actuation authority. However, for the SW pattern visualization, a three-dimensional technique is required for the detailed inside.
Apart from a 3D PIV technique, which is problematic in supersonic flow due to particle seeding issues, cross-flow 2D density/pressure maps can be used to reconstruct 3D SW structures. Measurements by planar techniques, such as PLIF and Rayleigh/Mie scattering, can be accomplished by seeding the flow with tracer gas, illuminating by laser sheet, and then observing the flow features. As a result of the seed gas condensation taking place naturally with a proper choice of secondary gas, the Mie scattering method is highly advantageous for the visualization in a supersonic flow since the scattered signal intensity is rather high [
29,
30,
31]. With decreasing static temperature, the secondary gas condenses, forming uniformly distributed nano/micro-sized droplets. Considering that droplets can be of different sizes, Mie scattering theory is used to simulate scattering of light, which in the limit of small droplets approximates Rayleigh scattering. This method delivers a high-resolution instant image identifying the most flowfield features since droplets reevaporate at higher gas temperatures when they are in specific zones such as flow separation and boundary layer.
This study investigates the rapid control of shock train location and pressure redistribution in result of one or three quasi-DC plasma filaments generation near the wall of supersonic duct. In this paper, the key finding is a Mie-scattering visualization of a semi-conical SW that appeared in supersonic flow at BL-SW-plasma interaction.
2. Experimental Arrangement
In this study, testing was performed at the SBR-50 direct-connect supersonic blowdown wind tunnel at the University of Notre Dame [
32]. This facility can operate at a variety of conditions thanks to swappable nozzle blocks and Ohmic heaters installed in the plenum section. For the tests described in this manuscript, the facility was operated with flow Mach number M = 4, ambient stagnation temperatures, stagnation pressures
= 2.6–4 bar,
, and steady-state run time
s. The facility uses a 2D nozzle paired to a rectangular cross section test section. The test section has dimensions 3 × 3 in at the nozzle exit with a 1° expansion on the top and bottom walls to maintain a roughly constant dimension core flow despite growth of the turbulent boundary layer. By installing a 17° spanwise uniform wedge on the top wall, a planar shock wave is generated that impinges on the bottom wall in the region that plasma is generated. The exact position of this SW impingement can be adjusted by moving the wedge between three available mounting positions as shown in
Figure 2a. Plasma was generated from three high voltage electrodes using a quasi-DC (Q-DC) electric discharge. These electrodes were embedded in a ceramic bottom wall insert and spaced 19 mm apart from each other in a row 149 mm downstream from the nozzle exit. Two copper grounding rails were designed to provide initial breakdown and allow the filaments to elongate downstream over the rails. These rails are 2.6 mm wide with a distance of 19.05 mm between them.
Figure 2b provides a schematic overview of this plasma generating insert. To generate the Q-DC discharge, a capacitor-based custom power supply with fast solid-state switch provides a current stabilized operation with breakdown voltages in a range of
= 4–5 kV. This facility also benefits from excellent optical access through quartz side windows spanning from top to bottom walls.
The test instrumentation for this work includes schlieren imaging, static pressure measurements, electrical measurements, high speed imaging of plasma, and optical spectroscopic observations. Static pressure was measured throughout the test section with a 64-channel pressure scanner (Scanivalve MPS4264) at an 800 Hz acquisition rate. The particular interest of this work is in pressure measurements taken along crossflow span within the region where plasma filaments are generated. To accomplish this, two rows of taps were placed at 165.5 mm and 180.7 mm downstream from the nozzle exit as shown in
Figure 2b. The pressure dynamics were studied using 80 kHz Kulite pressure sensors installed in key locations such as the plasma region and area of reflected shock impingement.
The schlieren imaging setup follows a traditional refractive scheme comprised of two telescopes and a high current pulsed white LED light source (100 ns pulse duration) as the illuminator. Images were recorded with a Phantom v2512 high speed camera operating with a frame-rate of 1 kHz and exposure of 1.25 s. Plasma power deposition was computed by recording gap voltages with high voltage electrical probes. High speed imaging of the plasma filaments was also collected using a Photron Nova S9 FastCam recording with a 20 kHz frame-rate and an exposure of 12.5 s. Each plasma filament has the following characteristic parameters: gap voltage = 0.1–0.3 kV, electric current I = 2–4.5 A and plasma power = 0.5–1.0 kW. Gas temperature due to plasma heating was measured through an optical emission spectroscopy technique in which luminescence from the plasma was collected by fiber optics from about a 5 mm diameter spot and then analyzed by a 300–400 nm Ocean Optics spectrometer. Spectra were fitted to the second positive system of molecular nitrogen as simulated by SpecAir software.
In addition to flow visualization by the schlieren imaging method, flow visualization of the SW structure in the zone of plasma was also performed by imaging planar Mie scattering. This technique was previously applied to Mach 2 flow using acetone vapor flow seeding [
33] and repeated at Mach 4 using carbon dioxide gas seeding. In both cases, the flow was seeded by increasing the percentage of seeding gas and maintaining a constant stagnation temperature until the seeded gas condensation through the nozzle forms a sufficient density of nano/micro-droplets to maximize signal-to-noise ratio. Bulk CO
2 seeding is performed by mixing pressurized carbon dioxide gas to the input air and measuring the added percentage of CO
2 using a GasLab CM-40531 0–20% CO
2 sensor at both input and by venting off of the plenum prior to tunnel run. The airflow was seeded with carbon dioxide so that the total concentration after mixing with air was 6–7% by volume. Seed gas concentration is largely specific to a given facility and simply affects the amount of condensation and thus total brightness of Mie scattering. Flow conditions used for Mie Scattering tests are summarized for convenience in
Table 1.
Illumination is performed using a ns-pulsed Nd:YAG laser (Solar Laser Systems LQ 629–100) with a 100Hz repetition rate, frequency doubled from its fundamental wavelength of 1064 nm to produced a 532 nm beam. The laser pulse energy was measured by a thermopile power meter (Ophir 50A-PF-DIF-18) and is approximately 70 mJ/pulse. To image planar Mie scattering, the laser beam was formed into a sheet using a f = −50 mm cylindrical plano-concave lens and a 3-inch diameter f = 500 mm spherical plano-convex lens. The final sheet is aligned in the crossflow direction within the test section and is approximately 3 in tall and 200
m thick its waist. Images are acquired using a 4 MP Phantom v1840 camera with an exposure of 1
s synced so that the q-switch of the laser falls within the center of the exposure. By using an 85 mm, f/2.8 tilt-shift lens, the entire angled imaging plane could be kept in focus. The laser sheet position was also adjusted in 1 cm increments between tunnel runs to provide a 3D understanding of the flow features as shown in
Figure 3.
4. Discussion
In accordance with the model of interaction and the data acquired for a single plasma filament, theory and simulation [
23] predict a semi-cone shape of plasma-induced SW with a zone of augmented pressure within the cone and a significantly lower pressure outside. With multifilamentary plasma arrays, individual SWs interfere with each other, resulting in almost planar plasma-induced SW, which is equivalent to shifting the entire shock train upstream. By analyzing cross-flow pressure distributions for single and triple plasma filament configurations as well as observing carbon dioxide Mie scattering, the predicted effect is now experimentally demonstrated at
. For various conditions [
12,
13,
14,
23], including supersonic flows with
and
, filamentary plasma authority has been well demonstrated. This essentially thermal interaction mechanism is illustrated in
Figure 11: with a high local gas temperature, the multifilamentary plasma zone presents an array of longitudinal subsonic jets enclosed in a supersonic flow. A volumetrically expanded zone produces a long cone of subsonic flow in which the gas speed is similar to that of the supersonic core flow [
13]. Side flow-wise vortices, similar to those generated over the mechanical obstacles or wall-injected jets, push the plasma filament up to the core flow while warm zones beneath the plasma filaments include areas with a reversal in the direction of the gas flow. Gas pressure is significantly redistributed due to such an unusual gasdynamic structure. A pressure bump caused by an impinging SW is mitigated and moves upstream until reaching electrode locations. The negative x-gradient of pressure is reduced significantly due to a presence of flow reversal. The redistribution of gas pressure in this way causes the reflected SW to be mitigated and appears as if a new SW is originating from the electrodes. This mechanism is illustrated in
Figure 11.
Based on the mechanism of SW-BL-plasma interaction, a simplified criterion of effective SW position control can be proposed assuming the following conditions: constant
,
, where
is subsonic Mach number in plasma filaments and immediately surrounded area; and
—that is, the physical gas velocity inside the plasma filament is about that of the external flow velocity [
15]. With such speculations, the gas temperature
in plasma channel should satisfy the following expression:
where
is stagnation gas temperature in external flow with Mach number M. For example, for
the temperature
; for
,
. The criterion is shown graphically in
Figure 12; the curve coming to a
limit at high Mach number. The criterion is well-achievable at low T0 but could be challenging at higher temperatures,
kK for example.
5. Conclusions
This paper discusses the experimental results of a filamentary plasma effect on a shock-dominated supersonic flow in a rectangular duct. Based on schlieren visualization, pressure measurements, and Mie scattering visualization, the major findings of this work are new details of a SW—plasma array/single filament interaction including the shape of the plasma-induced semi-conical SW and the dynamics of the plasma-induced SW. In schlieren images, the wall reflection of SW originating from the ramp appears to be reduced in magnitude or even vanishes, along with the emergence of new oblique SWs at electrode locations. Consequently, a new SW train forms within the test duct, shifting upstream from the previous pattern. Pressure sensor measurements indicate that a delay of approximately 2 ms occurs after plasma activation, followed by a similar delay during the return to baseline flow following plasma switching off.
Through analysis of experimental data, a thermal mechanism of interaction can be formulated as well as a simplified criterion for effective control of SW position. Based on this, the critical plasma temperature for the triggering effect to work is a rising function of the flow Mach number. It is also concluded that the method might be especially effective for cold external flow.
It is a paradigm-shifting concept to use plasma as an active trigger action for SW position control. In supersonic or hypersonic flows, narrow subsonic channels are opened to allow pressure to drain into an upstream area, creating a significant pressure redistribution despite a very small energy deposition relative to the flow total enthalpy.