Second-mode Waves Research Articles

Experimental investigation about the second-mode waves in hypersonic boundary layer over a cone at small angle of attack

An experiment investigating the second-mode instability on the sharp cone with a small angle of attack has been conducted. The fine structure in the boundary layer has been visualized by the Nano-tracer-based Planar Laser Scattering(NPLS) technique. The “rope-like” second-mode waves are found to still be the dominant structures before the transition of the boundary layer at 1° angle of attack and the leeside-forward and windside-aft of the transition have also been verified. The propagation velocity of the second-mode waves on the leeward side increases obviously as the disturbance evolving downstream. The development of the disturbance has been analyzed through the wall-fluctuation pressure. The amplification of amplitude is nonmonotonic along the circumferential direction and the M-factor patterns indicated that the disturbance development is delayed in three indentation regions: 55°⩽φ⩽65°,85°⩽φ⩽95° and 130°⩽φ⩽140°.

Three-dimensional wave packet in a Mach 6 boundary layer on a flared cone

High-resolution direct numerical simulations (DNS) were carried out to investigate the nonlinear breakdown process of a three-dimensional wave packet initiated by a short-duration pulse in a flared cone boundary layer at Mach 6 and zero angle of attack. For these simulations the cone geometry of the flared cone experiments conducted in the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University was considered. The computational domain covered a large extent of the cone in the azimuthal direction to allow for a wide range of azimuthal wavenumbers ( ) and to include shallow instability waves with small azimuthal wavenumbers. The simulation results indicated that the wave packet development was dominated by axisymmetric and shallow (small ) second-mode waves for a large downstream extent. Towards the downstream end of the computational domain a rapid broadening of the disturbance amplitude spectra was observed, which is an indication that the wave packet reached the strongly nonlinear stages. The disturbance spectra of the nonlinear regime, and the downstream amplitude development of the dominant disturbance wave components, provided conclusive evidence that the so-called fundamental breakdown was the dominant nonlinear mechanism. Furthermore, contours of the time-averaged Stanton number exhibited ‘hot’ streaks within the wave packet on the surface of the cone. Hot streaks have also been observed in the Purdue flared cone experiments using temperature sensitive paint (TSP) and in numerical investigations using DNS. The azimuthal streak spacing obtained from the wave packet simulation agrees well with that observed in the Purdue quiet tunnel experiments.

Influence of Nose-Tip Bluntness on Conical Boundary-Layer Instabilities at Mach 10

Hypersonic boundary-layer transition experiments are performed at the von Karman Institute for Fluid Dynamics in the low-enthalpy Longshot wind tunnel. Freestream Mach numbers are within the range , and freestream unit Reynolds numbers vary within the range . The model is a 7 deg half-angle cone, which is 800 mm long, with exchangeable nose tips for which the radii vary between 0.05 and 10 mm. The natural transition process is investigated using flush-mounted thermocouples, fast-response pressure sensors, and a laser-based schlieren flow visualization technique. The most amplified frequencies retrieved experimentally from wavelet analysis techniques compare excellently with linear stability theory results and confirm the inviscid nature of the instabilities observed along geometries with a small amount of nose-tip bluntness. The corresponding factors at the transition onset are inferred from the experimental location where transition is initiated. Schlieren images exhibit the typical rope shape of second-mode instabilities for the sharpest nose tips, but not along blunter geometries where instabilities peak outward of the boundary-layer edge. The different measurement techniques used show that the maximum amplitude of the second-mode waves is reached shortly after the location with the minimum wall heat flux. Schlieren images show that wave packets break down to turbulence near the middle of the transition region.

Experimental study of second-mode wave on a flared cone at Mach 6

Second-mode instability plays an important role in the transition of a hypersonic boundary layer. The second-mode wave on a flared cone at Mach 6 has been investigated experimentally through the Nanoparticle-tracer based Planar Laser Scattering (NPLS) technique in this paper. Different behaviors of the second-mode wave ranging from linear growth to deformation are visualized under different unit Reynolds numbers. The propagation velocity of the second-mode wave is quantitatively calculated, and the spectral properties of the second-mode wave have been analyzed by the power spectrum density. The characteristic frequency of the second-mode wave calculated from the NPLS images agrees well with the results measured by the transducers. Evolution of the wall-normal distribution of disturbance shows that high frequency harmonics are generated during the growth process of the second-mode wave and its normal distribution range shrinks with the increase in its frequency. The bispectral analysis indicates that the high degree of phase coupling may be the reason for the deformation of the second-mode wave. The nonlinear interaction between the disturbance waves is strong during the deformation stage of the second-mode waves.

Flat-plate hypersonic boundary-layer flow instability and transition prediction considering air dissociation

The effects of air dissociation on flat-plate hypersonic boundary-layer flow instability and transition prediction are studied. The air dissociation reactions are assumed to be in the chemical equilibrium. Based on the flat-plate boundary layer, the flow stability is analyzed for the Mach numbers from 8 to 15. The results reveal that the consideration of air dissociation leads to a decrease in the unstable region of the first-mode wave and an increase in the maximum growth rate of the second mode. High frequencies appear earlier in the third mode than in the perfect gas model, and the unstable region moves to a lower frequency region. When the Mach number increases, the second-mode wave dominates the transition process, and the third-mode wave has little effect on the transition. Moreover, when the Mach number increases from 8 to 12, the N-factor envelope becomes higher, and the transition is promoted. However, when the Mach number exceeds 12, the N-factor envelope becomes lower, and the transition is delayed. The N-factor envelope decreases gradually with the increase in the altitude or Mach number.

Transition control of Mach 6.5 hypersonic flat plate boundary layer

An artificial disturbance is introduced into the boundary layer over a flat plate to investigate the effect on the transition process in the Mach 6.5 wind tunnel at Peking University. A linear stability theory (LST) is utilized to predict the evolution of the eigenmodes, and the frequency of the artificial disturbance is chosen according to the LST results. The artificial disturbance is generated by glowing discharge on the surface of the plate close to the leading edge. The Rayleigh-scattering visualization and particle image velocimetry (PIV) measurements are performed. By comparing the experimental results with artificial disturbances with those under the natural condition (without artificial disturbances), the present paper shows that the second-mode instability waves are significantly stimulated by the artificial disturbances, and the boundary layer transition is effectively triggered.

Effect of glow discharge on hypersonic flat plate boundary layer

Glow discharge is introduced as an artificial disturbance to investigate the evolution of first- and second-mode instabilities in a hypersonic flat plate boundary layer. Experiments are conducted in a Mach 6.5 quiet wind tunnel using Rayleigh scattering visualization and particle image velocimetry (PIV). Detailed analysis of the experimental observations is provided. It is found that the artificially introduced 17 kHz disturbance, which belongs to the first-mode frequency band, can effectively enhance first-mode waves. Moreover, it can enhance second-mode waves even more intensely. Possible mechanisms to explain this phenomenon are discussed.

Newly identified principle for aerodynamic heating in hypersonic flows

Instability evolution in a transitional hypersonic boundary layer and its effects on aerodynamic heating are investigated over a 260 mm long flared cone. Experiments are conducted in a Mach 6 wind tunnel using Rayleigh-scattering flow visualization, fast-response pressure sensors, fluorescent temperature-sensitive paint (TSP) and particle image velocimetry (PIV). Calculations are also performed based on both the parabolized stability equations (PSE) and direct numerical simulations (DNS). Four unit Reynolds numbers are studied, 5.4, 7.6, 9.7 and$11.7\times 10^{6}~\text{m}^{-1}$. It is found that there exist two peaks of surface-temperature rise along the streamwise direction of the model. The first one (denoted as HS) is at the region where the second-mode instability reaches its maximum value. The second one (denoted as HT) is at the region where the transition is completed. Increasing the unit Reynolds number promotes the second-mode dissipation but increases the strength of local aerodynamic heating at HS. Furthermore, the heat generation rates induced by the dilatation and shear processes (respectively denoted as$w_{\unicode[STIX]{x1D703}}$and$w_{\unicode[STIX]{x1D714}}$) were investigated. The former item includes both the pressure work$w_{\unicode[STIX]{x1D703}1}$and dilatational viscous dissipation$w_{\unicode[STIX]{x1D703}2}$. The aerodynamic heating in HS mainly arose from the high-frequency compression and expansion of fluid accompanying the second mode. The dilatation heating, especially$w_{\unicode[STIX]{x1D703}1}$, was more than five times its shear counterpart. In a limited region, the underestimated$w_{\unicode[STIX]{x1D703}2}$was also larger than$w_{\unicode[STIX]{x1D714}}$. As the second-mode waves decay downstream, the low-frequency waves continue to grow, with the consequent shear-induced heating increasing. The latter brings about a second, weaker growth of surface-temperature HT. A theoretical analysis is provided to interpret the temperature distribution resulting from the aerodynamic heating.

Thermoacoustic Interpretation of Second-Mode Instability

A thermoacoustic interpretation of Mack’s second-mode instability is proposed. It is demonstrated that the fundamental mechanism of second-mode wave growth in hypersonic boundary layers is consistent with standing-wave thermoacoustically driven instability. The resonant nature of such modes is sustained by an acoustic impedance well between the wall (infinite impedance) and near the sonic line (secondary peak in impedance). A Lagrangian approach is adopted to show that such resonant standing waves derive energy from the base flow through thermoacoustic Reynolds stress, which results from the divergence of acoustic power inside the impedance well, and thermodynamic work. This treatment does not represent a complete energy closure (due to the neglect of viscosity), but it does provide insight toward a fundamental energy source and the physical mechanisms governing Mack’s acoustic second mode.

Experimental observation of the second-mode waves using PIV technique

Based on the Rayleigh-scattering visualization of the development of second-mode waves (Zhang and Lee in J Vis 20:7–12, 2017), in this article, we present the particle image velocimetry measurement results of the second-mode waves in hypersonic boundary layer on a flared cone with zero angle of attack. To solve the problem that it is difficult for the particles to enter the laminar boundary layer, we made a slot on the model wall to introduce the particles directly into the boundary layer. In hypersonic quiet wind tunnel, we obtain the velocity and dilatation distributions of the second mode and experimentally confirm that the second mode is an acoustic, longitudinal wave.

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.

Synchronization of second-mode instability waves for high-enthalpy hypersonic boundary layers

The stability of a hypersonic boundary layer for a $5^{\circ }$ half-angle cone at the Caltech T5 high-enthalpy flow conditions was investigated using direct numerical simulations. For the ‘linear’ stability investigations, the boundary layer was perturbed by small axisymmetric disturbances with very small amplitudes, and for the nonlinear regime, three-dimensional pulse disturbances with larger amplitudes were introduced. The surprising result from these investigations was that the 3D wave packet undergoes strong spatial modulations, which we have not observed for other experimental conditions (e.g. the Purdue BAM6QT). This modulation was found to be directly due to the synchronization between second-mode wave components and vorticity/entropy modes. Furthermore, it was found that a synchronization with slow acoustic waves leads to a sudden and strong emission of acoustic waves deep into the free stream, which was observed for both a linear wave train and a 3D nonlinear wave packet. Therefore, it can be concluded that this is a linear mechanism that is not suppressed by nonlinear effects.

Aerodynamic heating in transitional hypersonic boundary layers: Role of second-mode instability

The evolution of second-mode instabilities in hypersonic boundary layers and its effects on aerodynamic heating are investigated. Experiments are conducted in a Mach 6 wind tunnel using fast-response pressure sensors, fluorescent temperature-sensitive paint, and particle image velocimetry. Calculations based on parabolic stability equations and direct numerical simulations are also performed. It is found that second-mode waves, accompanied by high-frequency alternating fluid compression and expansion, produce intense aerodynamic heating in a small region that rapidly heats the fluid passing through it. As the second-mode waves decay downstream, the dilatation-induced aerodynamic heating decreases while its shear-induced counterpart keeps growing. The latter brings about a second growth of the surface temperature when transition is completed.

Optimization of a Mach-6 Quiet Wind-Tunnel Nozzle

Numerical simulations were conducted to optimize the shape and wall-temperature distribution of the Notre Dame Mach 6 quiet tunnel nozzle. The design was optimized by minimizing the overall nozzle length while maintaining sufficiently low disturbance amplification factors and uniform flow at the exit plane. The Boeing Computational Fluid Dynamics flow solver was used to compute laminar-mean-flow solutions for the various geometries and temperature distributions defined by a design of experiments. The Langley Stability and Transition Analysis Code was then used to compute amplification factors for Tollmien–Schlichting waves, second-mode waves, and Görtler vortices. Based on the square root of the sum of the squares of these -factors, response surfaces were generated that were used to optimize the nozzle design and wall-temperature distribution. Four nozzles with different lengths were developed, and an optimal wall-temperature distribution was determined for each. The total -factor was found to range from 5.1 to 7.9, with longer nozzles being more stable. All designs reflect an improvement on a baseline design developed in the late 1990s at Purdue University.

Optical Measurements of Transitional Events in a Mach-6 Boundary Layer

Results of aero-optical measurements of naturally occurring transitional structures—turbulent spots and second-mode wave packets—in a hypersonic laminar boundary layer are presented. Optical spectra of turbulent spots were similar to spectra for fully turbulent boundary layers, and the average thickness of the boundary layer during the turbulent spot was approximately 50% of the fully turbulent boundary layer. The convective speed of the leading edge of the spot was measured to be 0.95 of the freestream speed, whereas the trailing edge moves at 0.7 of the freestream speed. The dominant frequency of the wave packet structures was about 70 kHz, consistent with the theoretically predicted second-mode frequency; the average convective speed of the packets was measured to be 0.88 of the freestream speed. Using the frozen field hypothesis, the wave fronts were stitched together to reveal streamwise/spanwise topology of the packets. The packets were found to be fairly narrow, about in the spanwise direction, extending for in the streamwise direction.

Interactions between second mode and low-frequency waves in a hypersonic boundary layer

The stability of a hypersonic boundary layer on a flared cone was analysed for the same flow conditions as in earlier experiments (Zhang et al., Acta Mech. Sinica, vol. 29, 2013, pp. 48–53; Zhu et al., AIAA J., vol. 54, 2016, pp. 3039–3049). Three instabilities in the flared region, i.e. the first mode, the second mode and the Görtler mode, were identified using linear stability theory (LST). The nonlinear-parabolized stability equations (NPSE) were used in an extensive parametric study of the interactions between the second mode and the single low-frequency mode (the Görtler mode or the first mode). The analysis shows that waves with frequencies below 30 kHz are heavily amplified. These low-frequency disturbances evolve linearly at first and then abruptly transition to parametric resonance. The parametric resonance, which is well described by Floquet theory, can be either a combination resonance (for non-zero frequencies) or a fundamental resonance (for steady waves) of the secondary instability. Moreover, the resonance depends only on the saturated state of the second mode and is insensitive to the initial low-frequency mode profiles and the streamwise curvature, so this resonance is probably observable in boundary layers over straight cones. Analysis of the kinetic energy transfer further shows that the rapid growth of the low-frequency mode is due to the action of the Reynolds stresses. The same mechanism also describes the interactions between a second-mode wave and a pair of low-frequency waves. The only difference is that the fundamental and combination resonances can coexist. Qualitative agreement with the experimental results is achieved.

Rayleigh-scattering visualization of the development of second-mode waves

Rayleigh-scattering visualization of the development of second-mode waves

Hypersonic Wind-Tunnel Measurements of Boundary-Layer Transition on a Slender Cone

Boundary-layer transition was studied on a sharp 7 deg cone in two hypersonic wind tunnels at Mach numbers of 5, 6, 8, and 14 over a range of freestream Reynolds numbers between 3.3 and . High-speed schlieren measurements visualized the intermittent formation of instabilities and turbulent spots within the transitional boundary layer. Surface pressure and heat-transfer measurements revealed how the intermittent behavior of the boundary layer produces the mean character of these quantities. Transition at Mach 5 appeared to be initiated by a combination of first- and second-mode instabilities. These disturbances were isolated and surrounded by an otherwise smooth boundary layer. At higher Mach numbers, the boundary layer was dominated by second-mode instabilities, which covered most of the model before breakdown into turbulent spots. The spots remain surrounded by second-mode waves throughout the transitional region. These differences alter the pressure fluctuations and heat transfer profiles during transition. Higher frequency pressure measurements peaked upstream of the onset of transition because of the growth of second-mode instabilities. Lower frequency pressure fluctuations and the surface heat transfer did not rise significantly until further downstream where turbulent regions developed.

Quiet Tunnel Measurements of HIFiRE-5 Boundary-Layer Transition

The Hypersonic International Flight Research Experimentation (HIFiRE) program is a hypersonic flight test program executed by the Air Force Research Laboratory and Australian Defence Science and Technology Organisation. The principal goal of HIFiRE flight five is to measure hypersonic boundary-layer transition on a three-dimensional body. The HIFiRE flight tests are supported by a ground test campaign; this paper presents measurements of heat flux and boundary-layer transition in the Boeing/AFOSR Mach-6 Quiet Tunnel. This facility has been developed to provide quiet flow at high Reynolds number, with low noise levels comparable to flight. This tunnel’s good optical access enabled global measurement of the heat flux by means of temperature-sensitive paint. Two modes of transition were observed: transition along the centerline, suspected to arise from the amplification of second-mode waves in the boundary layer, and transition roughly halfway between the centerline and leading edges, probably due to the breakdown of crossflow vortices. Reducing the noise level from conventional to quiet substantially delayed both transition modes. Increasing the angle of attack from 0 to 4 deg delayed the crossflow transition mode on the windward side. Transition moved forward as freestream unit Reynolds number increased from to .

Pressure fluctuations beneath instability wavepackets and turbulent spots in a hypersonic boundary layer

AbstractTo investigate the pressure-fluctuation field beneath turbulent spots in a hypersonic boundary layer, a study was conducted on the nozzle wall of the Boeing/AFOSR Mach-6 Quiet Tunnel. Controlled disturbances were created by pulsed-glow perturbations based on the electrical breakdown of air. Under quiet-flow conditions, the nozzle-wall boundary layer remains laminar and grows very thick over the long nozzle length. This allows the development of large disturbances that can be well-resolved with high-frequency pressure transducers. A disturbance first grows into a second-mode instability wavepacket that is concentrated near its own centreline. Weaker disturbances are seen spreading from the centre. The waves grow and become nonlinear before breaking down to turbulence. The breakdown begins in the core of the packets where the wave amplitudes are largest. Second-mode waves are still evident in front of and behind the breakdown point and can be seen propagating in the spanwise direction. The turbulent core grows downstream, resulting in a spot with a classical arrowhead shape. Behind the spot, a low-pressure calmed region develops. However, the spot is not merely a localized patch of turbulence; instability waves remain an integral part. Limited measurements of naturally occurring disturbances show many similar characteristics. From the controlled disturbance measurements, the convection velocity, spanwise spreading angle, and typical pressure-fluctuation field were obtained.