High-speed Schlieren Visualization Research Articles

Determining pressure from velocity via physics-informed neural network

This paper describes a physics-informed neural network (PINN) for determining pressure from velocity where the Navier-Stokes (NS) equations are incorporated as a physical constraint, but the boundary condition is not explicitly imposed. The exact solution of the NS equations for the oblique Hiemenz flow is utilized to evaluate the accuracy of the PINN and the effects of the relevant factors including the boundary condition, data noise, number of collocation points, Reynolds number and impingement angle. In addition, the PINN is evaluated in the two-dimensional flow over a NACA0012 airfoil based on computational fluid dynamics (CFD) simulation. Further, the PINN is applied to the velocity data of a flying hawkmoth (Manduca) obtained in high-speed schlieren visualizations, revealing some interesting pressure features associated with the vortex structures generated by the flapping wings. Overall, the PINN offers an alternative solution for the problem of pressure from velocity with the reasonable accuracy and robustness.

Effects of doors on an open cavity flow at Mach number 6

Open cavities with different door-opening angles are investigated using high-speed schlieren visualization and dynamic pressure measurements in hypersonic flow with a freestream Mach number of 6. With the help of numerical simulations, the shear layer deformation and pressure increase in the cavities due to the impingement of the door-leading-edge shocks are identified via comparison with those in the cavity without doors. As the door-opening angle decreases from 90°, the shear layer above the forepart of the cavity is gradually raised by the high pressure in the cavity. When the door-opening angle decreases to 30°and 15°, the boundary layer on the upstream flat plate of the cavity separates, and separation shock is observed. The doors enhance the instability of the cavity flow and increase the pressure fluctuations in the cavities. A new oscillation pattern, referred to as coupled oscillation, is observed in the cases with separation on the upstream flat plate, in which the separation shock oscillates at the same dominant frequency as the flow inside the cavity. Compared with the cavity without doors, this coupled oscillation causes a lower oscillation frequency and a larger overall sound pressure level. Cross-correlation analyses between pressure signals indicate that the disturbances generated at the trailing edge of the cavity can propagate to the separation on the upstream flat plate and cause coupled oscillation of the separation shock. The fundamental frequencies of the coupled oscillations can be normalized to approximately the same Strouhal number as that of the cavity without doors. These findings support that the oscillation mechanisms of hypersonic cavities without and with doors are primarily dominated by acoustic feedback.

Initiation process of non-premixed continuous rotating detonation wave through Schlieren visualization

High-speed schlieren visualization on the initiation process of non-premixed air and hydrogen continuous rotating detonation (CRD) is carried out in a well-designed rounded-rectangle hollow combustor in this study. The CRD initiation processes of pre-detonator ignition and spark plug ignition are comprehensively revealed by synchronous high-speed schlieren images and high-frequency dynamic pressure results. The results show that the CRD undergoes three processes after ignition, including initiation process, adjustment process and stable propagation process. The CRD initiation process of pre-detonator ignition involves the upstream-propagation phase of leading shock wave and reaction zone and the coupling phase of circumferentially-propagating shock wave and reaction zone, while that of spark plug ignition includes the upstream-propagation phase of reaction zone, and the coupling phase of circumferentially-propagating pressure wave and reaction zone. The formation of deflagration combustion flowfield and re-establishment of combustible mixture layer after ignition are important prerequisites for CRD initiation. The strong interaction between circumferentially-propagating shock wave and post-shock wave reaction conduces to the rapid initiation of CRD by pre-detonator ignition, while the pressure wave gradually interacts with reaction leading to the detonation initiation by spark plug ignition. The CRD initiation time and adjustment time of pre-detonator ignition are shorter than those of spark plug ignition. This study provides detailed insight into the physics of CRD initiation process of pre-detonator and spark plug ignition, which can deepen the understanding of the initiation mechanism and provide practical guidance for the optimal design of CRDE ignitor.

Supersonic Flow Separation in Front of a Forward-Facing Step

A detailed experimental study has been done to understand the Shock Wave-Boundary Layer Interaction (SWBLI) over a Forward-Facing Step (FFS) of height (h) in a Mach 2.5 flow using Particle Image Velocimetry (PIV). In addition to PIV, unsteady wall pressure measurements, high-speed schlieren and surface oil flow visualization have been studied. Flow separation using surface oil flow visualization was observed around 4.1 step heights upstream of the step face. Shock motions extracted from the schlieren image sequence shows a peak frequency of approximately 1000 Hz, which corresponds to the dominant (low) frequency at which the shock oscillates; this being two orders in magnitude smaller than the characteristics frequency of the incoming boundary layer. Also, spectra of the unsteady wall pressure data shows that the shock oscillates with a peak frequency of approximately 1000 Hz. The effect of shock location (xs) from instantaneous velocity PIV fields in the cross-stream plane due to an upstream influence parameter (line-averaged boundary layer streamwise velocity, ul) and a downstream parameter (separation bubble or recirculation region area, A) is studied. Instantaneous cross-stream PIV measurements show significant variations of the separation shock location, incoming boundary layer velocity fluctuations and recirculation region. Besides, conditionally averaged velocity field based on incoming boundary layer streamwise velocity fluctuations and separation bubble area in the cross-stream plane shows that the shock location (xs) is correlated to the size of the separation bubble and not to boundary layer velocity fluctuations.

The influence of cryogenic temperature on the shock structure of impinging under-expanded flow over a convex surface

This study comprehensively investigates the effect of cryogenic nozzle inlet temperature on the flow structure and interactions of an under-expanded supersonic jet with a spherical solid surface. A combined experimental and numerical approach was employed to achieve this goal, utilizing high-speed Z-type schlieren visualization and Reynolds-averaged Navier–Stokes simulations with a Redlich–Kwong real gas equation of state. This study is significant as it addresses a relatively unexplored area of research on the flow structure of the cryogenic under-expanded supersonic jet. The study examines the shock pattern and interaction region through varying static inlet temperature (Tin = 178–290 K) and nozzle pressure ratio (NPR 5–14). Additionally, parameters including nozzle exit-to-throat area ratio (A/A* = 1.277), the distance between the sphere and the nozzle (1.5 cm), and the diameter of the sphere (d = 1.5 cm) were considered fixed. The results show that the supersonic jet exhibits a change in shock patterns in the first shock cell concerning the location and width of the Mach disk, accompanied by a shift in the location of the last shock crossing point and the shock plate. The simulation provides a more detailed insight into the flow, indicating a temperature drop to 105 K in the case of the cryogenic nozzle inlet. At such a low temperature, the compressibility factor exhibits a 5% reduction from unity, while in the case of the ambient nozzle inlet, the minimum temperature at the nozzle exit reached 170 K, leading to only a 1% drop in the compressibility factor, which is negligible. It triggers different flow structures concerning the nozzle inlet temperature. These findings can contribute to the complex flow structures of supersonic jets seen in different industrial and scientific fields.

Experimental and numerical simulation of shock train characteristics in an isolator with incident shocks

To better comprehend the steady-state structure and dynamic characteristics of shock train flow fields under interactions with incident shocks, wind tunnel experiments investigating the shock train flow fields in a supersonic isolator with incident shocks were conducted. High-speed schlieren visualization with multiple knife edges, surface tuft visualization, and high-frequency wall pressure measurements were used to analyze the shock train flow fields in the primary and corner regions. The understanding of the flow mechanism was enhanced based on additional three-dimensional steady numerical simulations. Flow field asymmetry was observed when the shock train interacted with parallel incident shocks. The shock train leading edge comprised a longer shock, which traversed the entire channel, and a shorter shock, with flow separation extending downstream of the longer shock. The flow downstream of the shorter shock passed through a small separation bubble before reattachment. The flow field was symmetrical when the shock train interacted with crossed incident shocks. Stronger oscillations were observed in the symmetric shock train owing to the adverse pressure gradient created by the incident shock and the inconsistent flow parameters downstream of the shock. The downstream propagation of the pressure fluctuation caused by the oscillation of the shock train leading edge was revealed based on coherence and phase analyses. The flow separation initiated further upstream in the corner region than in the primary region of the shock train flow field, and the separation flow covered a larger proportion of the flow field. These differences were enhanced by increasing the incoming Mach number.

Particle image velocimetry for velocity measurement of muzzle flow: Detailed experimental study

A deep understanding of muzzle flow fields is essential for optimizing muzzle devices and projectile design. This flow characterization has been heretofore limited to local and intrusive measurement techniques such as pressure measurements using pencil probes. Consequently, the quantitative experimental data are limited, so are the number of numerical codes validated in this field. The objective of the present work is to demonstrate the applicability of the Particle Image Velocimetry (PIV) technique to provide accurate velocity measurements in the challenging environment of the propellant flow of a .300 blackout weapon. During this work, we have studied the feasibility of PIV on the muzzle flow using: (i) the naturally existing particles in the combustion gas as tracers, (ii) two different solid tracers; namely TiO2 and ZrO2 particles with a nominal size of 100 nm, seeded using two different methods. The first method implies coating the propellant grains with the tracer powder, in the second one the tracer is added directly inside the cartridge case. The experiments aim to demonstrate in particular: (i) the capability of PIV to resolve the main structures of the flow, (ii) the assessment of particle response across the Mach disk, and (iii) the non-alteration of the weapon's ballistics. To achieve this goal, an experimental setup with five different measurements was installed: (i) PIV system, (ii) classical high-speed schlieren visualization, (iii) optical particle counter, (vi) pressure transducer in the combustion chamber, and (v) projectile velocity measurement. The experimental results demonstrated (i) the ability of PIV to accurately resolve the main features of the flow as well as the instantaneous velocity field; (ii) that the combustion products contain sub-micrometric particles which can follow with high fidelity the gas flow; (iii) that solid ZrO2 particles, when coated on the propellant grains, are suitable as tracers presenting a good flow fidelity and that the seeding of these inert particles is recommended in subsonic conditions (or whenever there is a lack of unburned particles); and (iv) that the TiO2 particles intended to act as tracers, surprisingly not only melted but also functioned as a combustion accelerator and decreased the number of particles in the propellant gas.

Flow Characteristics of Dielectric Barrier Discharge Plasma Actuator Array in Burst Mode

To understand the fundamental physics of dielectric barrier discharge (DBD) actuator array for flow control, the flowfield induced by two successive DBD actuators is investigated under burst-mode actuation. The vortical structures generated by the actuators are revealed using particle image velocimetry (PIV) and high-speed schlieren visualization, allowing their interactions to be explored. Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are used to analyze the plasma-induced flow. Both POD and DMD modes indicate staggered vortical structures, whose dynamic features are associated with the burst frequency of the DBD actuation and its harmonics. The POD–DMD coherence indicates that the most relevant dynamic structure is also the most energetic. Spatial DMD analysis reveals an increase in the convection speeds of the flow structures from the upstream DBD actuator to the downstream DBD actuator. The effects of duty cycle and burst frequency on the coherent structures are explored. For different duty cycle cases, the most energetic mode structures evolve in a similar fashion. As the burst frequency increases, the size of the coherent structures decreases, but their number increases. Both POD and DMD analyses reveal that the burst frequency has a greater effect on the coherent structures than the duty cycle.

Schlieren visualization of the interaction of jet in crossflow and deflagrated flame in hydrogen-air mixture

The objective of this study is to investigate the interaction of a jet-in-crossflow (JICF) and a deflagrated flame in a stoichiometric hydrogen-air mixture. The JICF is introduced prior the arrival of a deflagrated flame, therefore the JICF has a certain time to disturb the flow. By adjusting the time delay before the flame contacting the jet (td) and the pressure ratio (pJ/p0), the interaction between JICF and deflagrated flame and the subsequent flame evolution are recorded by a high-speed Schlieren visualization apparatus. The results show that the deflagrated flame without the perturbation of JICF has a quasi-parabolic shape, which is due to the flame suffering strong shear stress from wall boundaries. At higher initial pressure, the propagation velocity is faster. By introducing JICF, the flame speed is promoted, this is because JICF establishes pressure differential regions in the two sides of the jet, forming pressure gradients and flow instabilities, and increasing the turbulent transport between reactant and product, which accelerates the flame propagation. At relative low and medium pressure ratio (i.e., pJ/p0 = 10 and 20), shorter td has a better performance on enhancing the flame speed, nevertheless, at higher pressure ratio (pJ/p0 = 30), longer td conversely better promotes the deflagrated flame speed. This is because, at the condition of weak pressure ratio and long td, the abruptly burst of N2 JICF results in a prominent effect because of its dilution attribute, which prohibits the chemical reaction and the further development of a deflagrated flame. However, as the jet pressure tends to stronger, the corresponding turbulence is greater; the recirculation effect induced by robust JICF overcomes its dilution effect and gradually plays a more dominant role in the flame acceleration.

Formation and characteristics of composite reaction – Shock clusters in narrow channels

High-speed schlieren visualizations show that a composite reaction-shock cluster structure is formed in the last flame acceleration stage prior to detonation transition for ethylene/oxygen mixture in a narrow channel. The composite structure is bounded by a normal shock at the leading edge of the structure, and series of parallel oblique shocks interweave with reaction front on the other end in the cluster. Propagating velocity of the reaction front at the inception of the cluster is ∼ 45–50% of Chapman-Jouguet detonation velocity of the mixture. Reaction front accelerates rapidly after the formation of the reaction-shock cluster, and run into detonation in tens of microseconds except for very lean mixtures. The angle between the parallel oblique shocks in the cluster and the side wall, defined as ω-angle, is found to be constant for a specific mixture as the reaction wave propagates. Dependence of ω-angle on mixture equivalence ratio and channel size are investigated in the study. Analysis shows that DDT distance is linearly proportional to ω-angle, and an empirical correlation is derived.

Effect of Argon Concentration on Laminar Burning Velocity and Flame Speed of Hydrogen Mixtures in a Constant Volume Combustion Chamber

Abstract Hydrogen combustion, coupled with the use of argon as a working fluid, is a promising approach to delivering clean and efficient energy from internal combustion (IC) engines. The use of hydrogen-oxygen-argon (H2/O2/Ar) mixtures in combustion aids in mitigating harmful environmental pollutants and enables a highly efficient energy conversion process. The use of argon as a working fluid decreases the NOx emissions and increases the thermal efficiency of internal combustion engines due to the high specific heat ratio of noble gases. In this study, premixed hydrogen combustion was investigated with the purpose of examining the effect of the full or partial substitution of argon for nitrogen in air on laminar burning velocity (LBV), flame speed, flame morphology, and instability. The experimental approach uses an optically accessible constant volume combustion chamber (CVCC) with central ignition; the spherical flame development was studied using a high-speed Z-type Schlieren visualization system. Moreover, a numerical model was developed to convert the experimental dynamic pressure rise data to laminar burning velocity. Coupling the model to a chemical equilibrium code aids in determining the burned gas properties. Additionally, an image processing technique has been suggested to compute the flame propagation speed. The experimental and numerical investigations indicate that increasing the concentration of argon as the working fluid in the mixture increases the laminar burning velocity and flame speed while extending the lean flammability limit.

An experimentally verified three-dimensional non-stationary fluid model of unloaded atmospheric pressure inductively coupled plasmas

A three-dimensional non-stationary numerical model of spectrochemical and technological inductively coupled plasma (ICP) systems is presented in the paper. The model considers the ICP as a gaseous media (with temperature-dependent electric conductivity) interacting with electromagnetic field generated by inductive coil. The model is based on simultaneous solution of the Maxwell’s and gas flow equations together with the energy equation coupled-together by corresponding source terms and material properties to take into account inductive current forming within the carrier gas and subsequent Joule heating, the Lorentz force and how does it affect the gas flow pattern. It allows calculation of temporal evolution of three-dimensional distributions of electromagnetic fields, pressure, gas velocity and temperature within a plasma torch and a condensation chamber used for powder processing. The model is applicable for simulation of atmospheric pressure electrodeless plasmas under local thermodynamic equilibrium that consist of pure gases and their mixtures. Such operating conditions are typical for ICPs that are used for elemental analysis and technological powder processing. Special attention is paid to experimental verification of the model. The simulation results are cross-verified for both types of ICPs (spectrochemical and technological one) using high-speed optical and schlieren visualization of gas flows. The discrepancy between calculations and experimental data does not exceed 10%.

Laser-Induced Plasma Ignition Experiments in a Direct-Connect Supersonic Combustor at Mach 3

A new direct-connect supersonic combustor has been designed and tested for the study of plasma-assisted combustion in the ACT-II supersonic combustion tunnel. Laser-induced plasma ignition was investigated in an ethylene-fueled cavity flame holder at Mach 3. Combustor design, geometry, and flow characteristics are discussed in the first part of the paper. The supersonic combustor includes a cavity flame holder, where ethylene fuel is injected, mixed with entrained air, and ignited. Two injector configurations are included, one horizontal and one vertical, which were designed in such a way as to enhance the cavity flow recirculation. Two different plasma ignition mechanisms were considered: 1) a laser-induced plasma located at the center of the cavity, and 2) a spark plug placed on the bottom surface of the cavity. The diagnostics tools tested to characterize the flow include time-resolved pressure measurements, high-speed schlieren visualization and chemiluminescence visualization, and instantaneous planar laser-induced fluorescence of the CH radical. The second part of the paper discusses the results of the comparison between horizontal and vertical fuel injection. The larger backpressurization of the isolator and a more uniform distribution within the cavity suggest a greater heat release and combustion efficiency when the horizontal jet is used.

Entrainment studies in inverse jet flame port burner

The present investigation aims to investigate the fundamental understanding of entrainment characteristics of a Circumferentially Arranged Fuel Port Inverse Jet Flame Burner (CAFP IJF). The high-speed flame Schlieren visualization is carried out experimentally for 8, 18 and 32 port CAFP IJF burner for varying air–fuel operating conditions to visualize the entrainment characteristics. The region of fuel entrainment is found to occur within the base region whereas intense mixing and combustion is observed in transition and main flame region respectively. The 32 port CAFP IJF burner exhibits enhanced entrainment characteristics and augmented ambient air–jet interactions for similar operating conditions as compared to a lesser number of circumferential fuel ports. The jet breakup length is employed to identify the interaction of ambient air with the combustion driven vorticial structures. The steady laminar flamelet model is used to investigate the entrainment characteristics of a 32 port CAFP IJF burner. The calculated entrainment coefficients at different operating conditions for reacting and non-reacting CAFP IJF indicate that the entrainment rate for reacting jet is lower due to the diminution of density across the flame cross-section at each axial plane. The strong ambient air entrainment is observed within the interstitial space between consecutive fuel ports which promote air–fuel mixing. Additionally, unlike in Normal Jet Flame (NJF), a clear distinction between air and fuel entrainment is found to be essential for the current CAFP IJF burner configuration.

Detonation transition criteria from the interaction of supersonic shock-flame complexes with different shaped obstacles

The present study is an experimental investigation of the last stages of the deflagration-to-detonation transition. A fast flame following a lead shock was generated by passing a detonation wave through a perforated plate. The shock flame complex then interacts with an obstacle of different shape. We study the influence of the obstacle shape on the transition mechanism to a detonation. The obstacles studied are a single round or square obstacle, a flat plate, a C-shaped and an H-shaped obstacle. The experiments were performed in a thin transparent channel permitting high speed schlieren visualization. Stoichiometric propane-oxygen was investigated at sub-atmospheric conditions. For each obstacle configuration, the initial pressure was changed to modify the flame burning velocity and the Mach number of the leading shock. The burning velocity prior to the interaction was measured experimentally from the displacement velocity of the flame in the videos. This required estimating the speed of the gas ahead of the flame. A linear correction to the speed immediately behind the lead shock was applied using the shock change equations and the measured pressure gradient behind the lead shock in order to account for the non-steadiness of the lead shock and viscous losses to the walls. Three main findings were that the obstacle shape had a minimal influence on the critical flame strength required for transition, although obstacles with a forward facing cavity were able to suppress the transition by isolating the re-initiation event inside the cavity. The main transition mechanism for all geometries was the enhancement of the flame burning velocity through the flame interaction with the shock reflected on the obstacle leading to Richtmyer-Meshkov instability. Finally, it was found that the flame burning velocity of the initial flame required for transition was closely approximated by the Chapman-Jouguet burning velocity. Consistent with the visual observations, this supports the view that transition is favored when the flame is in phase with the acoustic waves, and strong internal pressure waves can be amplified.

Suppression of transonic buffet with plasma vortex generators

In the present paper, we report on the results of an experimental study of the possibility to control the transonic buffet on a rectangular wing using plasma vortex generators. The influence of the developed device on the flow consists in creating a longitudinal vortex in the boundary layer as a result of asymmetric energy supply at the surface of a small vertical wedge. The experiments were performed using a wing model with a supercritical airfoil in the range of free-stream Mach numbers 0.73 to 0.78 and Reynolds numbers Re = (2.64-2.8)·106. The experimental data obtained using the method of high-speed schlieren visualization and pressure distribution measurements in the wake of the model show that the technique allows one to control both the average flow characteristics and the characteristics of shock-wave oscillations.

Electrohydrodynamic gas flow in a positive corona discharge

When a sufficient high voltage is applied between a point and a plate in atmospheric air, a corona discharge is ignited and an electrohydrodynamic (EHD) force can be produced, resulting in an ionic wind of a few meters per second flowing from the point toward the plate. In this study, we aimed at characterizing the ionic wind EHD flow produced by DC positive point-to-plate corona discharges. This is realized with the help of a high-speed particle image velocimetry system and Schlieren visualizations. The obtained measurements allowed us to characterize precisely the ionic wind vs time, as well as its dynamics when the discharge is switched on. We highlighted the key role of the breakdown streamers in the ionic wind hydrodynamics. We discovered that, in the presence of breakdown streamers, the positive corona discharge produces a pulsed ionic wind whose frequency corresponds to the frequency of the current pulses. To explain this EHD result, we investigated and showed that each single current pulse is composed of several streamers or several branches of one streamer, this phenomenon being at the origin of a space charge mainly composed of positive ions. Finally, we highlighted that when the steady breakdown streamer regime takes place, the time-averaged current becomes greater than the theoretical values given by Townsend's law since it evolves nearly linearly with the high voltage.

Effects of subcavity in supersonic cavity flow

An experimental and numerical study is conducted on a rectangular open cavity with a length to depth ratio of 2 at Mach number 1.71 by placing a subcavity at different locations. The subcavity at the front wall has already been established as a passive control device experimentally. In addition, it has been observed that it can act as a passive resonator. However, in the current study, it is found that the location of the subcavity and its dimensions play a crucial role in determining the types of oscillations existing inside the cavity. Cavity models with a subcavity length to main cavity length of 0.2 (l/L = 0.20) were investigated by placing the subcavity at the front wall, aft wall, and simultaneously at both front and aft walls. High speed schlieren visualization revealed the presence of different shock features associated with the cavity flow field. Statistical techniques such as fast Fourier transform, spectrogram, coherence, and correlation are employed to analyze the unsteady pressure data. Numerical computations are carried out to validate the experimental results and also to explore the flow physics. The front wall subcavity acts as a passive control device with a maximum reduction of 34.1 dB in the sound pressure level for the most dominant tone, and there is also a notable reduction in the overall sound pressure level by 11.7 dB. In the case of front wall subcavity, the acoustic wave gets inclined as it interacts with the subcavity, thereby displacing the shear layer to form a dome-shaped structure. The aft wall subcavity acts as a passive resonator with distinct fluid-resonant oscillations and the respective modal frequencies differ widely from those predicted using Rossiter’s expression. The shear layer interacts with a recirculation region formed inside the subcavity at the aft wall, thereby mitigating the effect due to direct impingement of the shear layer on the aft wall. The subcavity at both walls acts as a passive suppression device with a reduction of 34.9 dB in the sound pressure level for the most dominant mode and also with a reduction of 14.5 dB in the overall sound pressure level.

Gas-heating phenomenon in a nanosecond pulse discharge in atmospheric-pressure air and its application for high-speed flow control

The interaction between the gas-heating phenomenon in a pulsed discharge in atmospheric-pressure air and the separated shear layer in the flow around the airfoil is discussed. The first half of the paper details the development of the modeling for gas heating in a pulsed discharge in atmospheric-pressure air and reviews recent research results. Particular attention is paid to the processes of fast and slow gas heating. In the latter half of the paper, the experimental results of the high-speed Schlieren visualization are presented and the interaction between the nanosecond-pulse-driven dielectric-barrier-discharge plasma actuator (ns-DBDPA) actuation and the density field is discussed, based on the periodic and time-averaged components of the Schlieren signal intensity. The time-averaged intensity of the contrast of the Schlieren signal that originates in the separated shear layer changes according to the normalized actuation frequency of ns-DBDPA, F+. As F+ increases from 0.1 to 2, the periodic component of the Schlieren signal intensity increases, resulting in a decrease in the time-averaged contrast of the Schlieren signal. When F+ > 2, the heated air caused by ns-DBDPA actuation is accumulated along the separated shear layer, resulting in an increase in the time-averaged contrast of the Schlieren signal.

Investigation of the second-mode instability at Mach 14 using calibrated schlieren

Second-mode wave growth within the hypersonic boundary layer of a slender cone is investigated experimentally using high-speed schlieren visualizations. Experiments were performed in AEDC Tunnel 9 over a range of unit Reynolds number conditions at a Mach number of approximately 14. A thin lens with a known density profile placed within the field of view enables calibration of the schlieren set-up, and the relatively high camera frame rates employed allow for the reconstruction of time-resolved pixel intensities at discrete streamwise locations. The calibration in conjunction with the reconstructed signals enables integrated spatial amplification rates ($N$ factors) to be calculated for each unit Reynolds number condition and compared to $N$ factors computed from both pressure transducer measurements and linear parabolized stability equation (PSE) solutions. Good agreement is observed between $N$ factors computed from the schlieren measurements and those computed from the PSE solutions for the most-amplified second-mode frequencies. The streamwise development of $N$ factors calculated from the schlieren measurements compares favourably to that calculated from the pressure measurements with slight variations in the $N$ factor magnitudes calculated for harmonic frequencies. Finally, a bispectral analysis is carried out to identify nonlinear phase-coupled quadratic interactions present within the boundary layer. Multiple interactions are identified and revealed to be associated with the growth of disturbances at higher harmonic frequencies.