Second-mode Instability Research Articles

Ionization and dissociation effects on boundary-layer stability

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Linear, nonlinear and transitional regimes of second-mode instability

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Influence of glow discharge on evolution of disturbance in a hypersonic boundary layer: The effect of second mode

This is the companion volume on the effects of artificial disturbance on the transition process of a boundary layer over a flat plate. The artificial disturbance with the frequency in the range of second-mode instability is introduced into the boundary layer by glowing discharge on the surface of the plate. Experiments are performed using Rayleigh-scattering visualization, wall pressure pulsations measurement, and high-frequency schlieren visualization in the Φ300 mm hypersonic quiet wind tunnel at Peking University. It is found that the second-mode instability waves are stimulated remarkably by the artificial disturbance, and the boundary layer transition is triggered effectively. The second-mode instability interacts with the first mode via a phase-lock mechanism, which leads to the rapid amplification of the first mode and the moving forward of transition location.

Preflight Boundary-Layer Stability Analysis of BOLT Geometry

Boundary-layer stability and laminar-to-turbulent transition are examined on the Boundary Layer Transition flight-test vehicle using predicted flow conditions at ascent and descent flight times. The parabolized stability equations technique is used predominantly for this analysis because it has proven to be efficient and accurate in modeling the transition process on other three-dimensional geometries. The various potential transition mechanisms are identified in the region outboard of the centerline to the leading edge, and their linear amplification is discussed. These mechanisms include second-mode and crossflow instabilities. Stationary crossflow is predicted to be the dominant mechanism for breakdown away from the centerline and leading edge, and nonlinear analysis is performed. The nonlinear parabolized stability equations are used for this analysis, and comparisons with a direct numerical simulation are performed. Partially through this verification, a physics-based technique to model the heating rates of nonlinearly developing stationary crossflow is assessed.

The influence of wavy wall on hypersonic boundary layer instability over a flared cone

The influence of wavy wall on the hypersonic boundary layer instability and the related aerodynamic heating are investigated over a flared cone. Experiments are conducted in a Mach 6 wind tunnel using Rayleigh-scattering flow visualization, fast-response pressure sensors and infrared thermography. Three sizes of wavy wall have been placed on the model in comparison with the smooth wall cone. The results show that compared to the smooth-wall cone, all the wavy-wall cones can suppress the second-mode instability to a certain degree and eliminate the local heating spot before transition is completed. Also, it is found that with the decrease of wavy wall wavelength, the transition location is shifted downstream.

Influence of glow discharge on evolution of disturbance in a hypersonic boundary layer: The effect of first mode

The evolution of the first- and second-mode instabilities in a hypersonic flat plate boundary layer is investigated. Experiments are conducted in a Mach 6.5 quiet wind tunnel using particle image velocimetry, Rayleigh-scattering flow visualization, and schlieren methods. Glow discharge is introduced as an artificial disturbance. The results show that an artificially introduced disturbance in the first-mode frequency range can excite a specific second-mode wave that is one of the high-order harmonics of the added disturbance. For the first time, we find a clear harmonic relationship between the first- and second-mode waves, as well as the phase lock phenomenon between them.

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°.

On the mechanism by which nose bluntness suppresses second-mode instability

ABSTRACT A physical mechanism by which nose bluntness suppresses second-mode instability is proposed. Considered are 7 degree half-angle straight cones with nose bluntness radii of 0.15 mm, 3.556 mm, 5 mm, 9.525 mm, 12.7 mm and 25.4 mm at tunnel conditions relevant to the AFOSR-Notre Dame Large Mach 6 Quiet Tunnel. It is shown that second-mode suppression is achieved via entropy layer modulation of the basic state density gradient. A weakening of the density gradient disrupts the acoustic resonance necessary to sustain second-mode growth. These results are consistent with the thermoacoustic interpretation which posits that second-mode instability can be modeled as thermoacoustic resonance of acoustic energy trapped within an acoustic impedance well. Furthermore, the generalized inflection point criterion of Lees and Lin is applied to develop a criterion for the existence of second-mode instability based on the strength of the basic state density gradient.

Local Wall Temperature Effects on the Second-Mode Instability

It has been shown that, in general, heating the wall beneath second-mode instabilities dampens them, whereas cooling the wall amplifies them. The purpose of this research was to determine the viability of localized wall temperature variations for controlling second-mode growth. In this paper, the results of a computational study were conducted where the wall temperature was varied locally and entirely along the Purdue flared cone at Mach 6. Such wall temperature variations could potentially be achieved actively by embedded heating/cooling systems or passively through vehicle material selection. It was found that heating the wall just downstream of the N1 neutral point amplifies second-mode growth, whereas heating the wall further downstream, toward the N2 neutral point, dampens second-mode growth. The opposite effect is found for wall cooling. It is shown by linear and nonlinear analyses that particular combinations of localized upstream cooling and downstream heating optimally dampen second-mode growth. Physically, this effect can be understood via modulation of the thermal boundary layer, which modifies the acoustic impedance well in which second modes resonate, and ultimately can be interpreted as a clockwise rotation of the stability diagram.

Injection-gas-composition effects on hypersonic boundary-layer transition

The thermal protection system in atmospheric-entry and hypersonic-cruise vehicles are oftentimes designed to ablate during their operation, thus injecting a mixture of various gases with distinct properties into the boundary layer. Such outgassing affects the propagation of instabilities within the boundary layer that ultimately originates the transition to turbulence. This work uses linear stability theory, in combination with the e method, to establish the underlying reason for the experimentally observed advancement/delay of transition in sharp slender hypersonic cones, when injecting lighter/heavier gases. Contrary to the current understanding and experimental correlations, this numerical analysis suggests that such a behaviour is not linked to the isolated effect of the injected gas’ molar weight, but to its combination with the blowing discontinuity, porosity and the appearance of a shocklet, consequence of the injected gas composition. The shocklet constitutes a density gradient that acts on second-mode instabilities like a thermoacoustic impedance.

Two-point, parallel-beam focused laser differential interferometry with a Nomarski prism.

A Nomarski polarizing prism has been used in conjunction with a focused laser differential interferometer to measure the phase velocity of a density disturbance at sampling frequencies ≥10MHz. Use of this prism enables the simultaneous measurement of density disturbances at two closely spaced points that can be arbitrarily oriented about the instrument's optical axis. The orientation is prescribed by rotating the prism about this axis. Since all four beams (one beam pair at each measurement point) propagate parallel to one another within the test volume, any bias imparted by density fluctuations away from the measurement plane on the disturbance phase velocity is minimized. A laboratory measurement of a spark-generated shock wave and a wind tunnel measurement of a second-mode instability wave on a cone model in a Mach 6 flow are presented to demonstrate the performance of the instrument. High-speed schlieren imaging is used in both cases to verify the results obtained with the instrument.

Piezoelectric pressure sensors for hypersonic flow measurements at high-temperatures

We present a microelectromechanical-systems (MEMS) piezoelectric pressure sensor designed for hypersonic flow measurements at extreme temperatures (>1000 °C). The sensing diaphragms have 700-μm diameter and are surface- and bulk-micromachined. The sensor employs aluminum nitride as a sensing layer due to its capability for high-temperature operation. We present the latest measurement results from a Ludwieg Mach-6 quiet tunnel, where prototype sensor data are compared against data from a state-of-the-art commercial sensor present in the same test. The prototype captures salient features of hypersonic flows including shock waves and second-mode instabilities indicative of laminar-to-turbulent transition. The prototype sensor also demonstrates superior signal-to-noise ratio in many test conditions. Prototypes have also demonstrated high-temperature operation by capturing audio while immersed in a butane flame (∼1200 °C).

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.

The secondary instabilities of stationary cross-flow vortices in a Mach 6 swept wing flow

The secondary instabilities of stationary cross-flow vortices in a Mach 6 swept wing flow are studied using Floquet theory. High-frequency secondary instability modes of ‘y’ mode on top of stationary cross-flow vortices, and ‘z’ mode concentrating on the shoulder of the stationary cross-flow vortex are found. The most unstable secondary instability mode is always the ‘z’ mode as in incompressible swept wing flows. A new secondary instability mode concentrating on the trough of the stationary cross-flow vortex is found. The balance analysis of disturbance kinetic energy shows that the new mode belongs to the class of ‘y’ mode. The growth rate of the new ‘y’ mode located on the trough of the stationary cross-flow vortex is significantly larger than that of the ‘y’ mode on top of the stationary cross-flow vortex, and is comparable with the growth rate of the ‘z’ mode. It is also found that the new ‘y’ mode with higher frequency can evolve into the ‘z’ mode further downstream. The role of the pressure fluctuation term, including the pressure diffusion and pressure dilatation, in the energy production of secondary instability modes, is also investigated. It is shown that the pressure diffusion will only enhance the growth rate of the ‘z’ mode with higher frequency, but has little influence on other types of secondary instability mode. However, the pressure dilatation term arising from non-vanishing velocity divergence will reduce the growth rates of all secondary instability modes.

Influence of transpiration cooling on second-mode instabilities investigated on hypersonic, conical flows

In the present study, the influence of active cooling on hypersonic boundary-layer transition at different Mach numbers, from 7 up to 10, is investigated. The analyses are carried out on a $$7^\circ$$ half-angle, blunted cone with different nose radii and various gas injection mass flow rates. In all cases, low mass fluxes, which do not inducing visible shocks in the schlieren images, are applied. As injection gas nitrogen is used. At the considered free stream conditions, second modes are the dominant boundary-layer instabilities, which are consequently the focus of this study. The stability analyses are performed by means of the stability code NOLOT, NOnLOcal Transition analysis, of the German Aerospace Center (DLR). The influence of different mass injections on the frequencies and growth rates of the second modes is analyzed in detail. The effect on the transition onset locations is discussed. The numerical predictions are compared with experimental results. The experimental data referred to in the present study were obtained in the DLR High Enthalpy Shock Tunnel Gottingen.

High-enthalpy models for boundary-layer stability and transition

The prediction of the transition dynamics of high-enthalpy boundary-layer flows requires appropriate thermodynamic and transport models. This work quantifies the influence of transport, diffusion, collision, equilibrium, and chemical-kinetics modeling on the stability characteristics and the estimated transition-onset location of canonical boundary layers. The computed behavior of second-mode instabilities is consistently highly dependent on the base-flow’s boundary-layer height. The Blottner-Eucken-Wilke transport model is seen to underpredict the boundary-layer height, hence overpredicting the growth-rate distribution and forecasting the transition onset to occur ∼38% sooner. The other low-order transport models (Brokaw and Yos) returned very close results to the most-accurate Chapman-Enskog model. The use of Gupta et al.’s collisional data instead of Wright et al.’s more accurate data is also seen to predict the transition onset to occur ∼8% closer to the leading edge. The modeling of mass diffusion and the chemical-equilibrium constant is observed to have a negligible influence on the boundary-layer height and transition-onset-location estimations (less than 5% and 2%, respectively). For the analyzed conditions, all chemical models predict the same transition-onset location (±1%); since at the streamwise positions where perturbations have reached sufficiently large amplitudes, the flow is close to equilibrium and thus independent of the reaction rates. The use of different transport models for the perturbation terms, while maintaining the same model for the basic state, leads to negligible differences in the predictions. This further reinforces the thesis that the boundary-layer height calculation is paramount to the simulation of the development of second-mode instabilities.

Local-Variable-Based Model for Hypersonic Boundary Layer Transition

Based on the numerical study of the existing model, certain inconsistencies of the model were first allocated. It was found that the second-mode instability dominating the transition process in hypersonic boundary layers was not simulated properly by the model, and a single transport equation for total fluctuating kinetic energy would make the model fail to be self-consistent. To eliminate these discrepancies, a laminar kinetic energy transport equation was developed in terms of local variables. Then, a time scale correction function capable of reproducing the hypersonic transition process dominated by the second-mode instability was constructed. In addition, the transport equation for the intermittency factor, in which the self-consistent production and dissipation terms were constructed, was also revised. On this basis, the transport equations for the laminar kinetic energy and intermittency factor were coupled with the shear stress transport model through the concept of effective turbulent eddy viscosity to form a local-variable-based model for hypersonic boundary layer transition. Finally, hypersonic transition flows over a flat plate and a straight cone are employed to test and verify the model. Numerical results illustrate that both the transition onset and the length of the transition region predicted by the model agree well with the experimental data.

Effect of Wall Blowing on Hypersonic Boundary-Layer Transition

An investigation of outgassing effects on boundary-layer transition was carried out. This joint computational–experimental work mimicked heat-shield pyrolysis outgassing in atmospheric reentry conditions. A slender 7 deg half-angle cone with air wall blowing through a porous section near the apex was tested in the VKI-H3 Mach 6 hypersonic blowdown noisy wind tunnel. The steady transition onset location was measured using infrared thermography, whereas gaseous-naphthalene-based planar laser-induced fluorescence imaging enabled the visualization and quantification of the spatial characteristics of the instabilities. Linear stability theory, combined with the semiempirical method with , was used to predict the location of transition onset in the same configurations. Studies were performed at different freestream unit Reynolds numbers and blowing rates. Numerical and experimental results agreed within the experimental uncertainties, and they coincided with the previously reported advancement of the transition location due to wall blowing. The wave numbers of the most amplified second-mode instabilities obtained with the linear stability theory matched the observations done with planar laser-induced fluorescence, suggesting it was the growth of such perturbations that led to the transitioning of the boundary layer. The porous section was seen to destabilize the boundary layer for nonblowing configurations. Regarding the upstream advancement of transition associated with wall blowing, the numerical analysis suggested that it is a consequence of the increase in the range of unstable frequencies in the wall-blowing region. Blowing nonuniformities in the cone’s longitudinal direction were observed to have no influence on the local transition location under noisy conditions.

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.