Transitional Hypersonic Boundary Layers Research Articles

Coherent structure tracking of the second Mack mode in transitional hypersonic boundary layers

The natural transition of hypersonic boundary layers (HBLs) is often expressed in terms of discrete modes and their linear stability. A frequent interpretation revolves around fast and slow acoustic modes interacting in the vicinity of the vortical/entropic branches of the continuous spectrum found from stability analyses. Yet several transition scenarios are contingent upon factors such as the spectral content of the free-stream disturbances, or the interactions between the discrete modes within the boundary layer and the free-stream disturbances near the leading edge which can be decomposed into vortical, acoustic and entropic nature based on the fluid-thermodynamic (FT) components. Yet the interpretations of linear stability applied to discrete modes can lead to semantic conflicts with the terminology of FT components. To clarify the current description of the processes involved, this study chooses an approach aimed at characterizing the dynamics of the second Mack mode in transitional HBLs through coherent structure tracking. The method involves decomposing the flow perturbations into acoustic, vortical and entropic content, and following their associated coherent structures over time. For this purpose, direct numerical simulations are carried out to investigate the dynamics of the second Mack mode instability in two-dimensional HBLs, considering a flow at Mach 6 over a cooled and an insulated wall. It is found that vortical structures coexist at different heights along the wall surface, forming alternating sign doublets around the critical layer and above the relative sonic line. These structures are found to merge in the region of maximum second Mack mode instability.

An effective control strategy for transitional hypersonic boundary layers

An effective control strategy is studied in this work to reduce aerodynamic heating inside transitional hypersonic boundary layers, which is of both scientific significance and practical importance. The experiments show that the use of grooved wavy walls covered with an acoustic transparent film can successfully reduce the growth of Mack's second mode, which delays transition and results in significant reduction of aerodynamic heating.

Heat-Transfer Gauge Arrays for Identifying Spot Initiation in Hypersonic Transitional Boundary Layers

The initiation and growth of turbulent spots in transitional hypersonic boundary layers can influence the transition length and the distribution of heat transfer and skin friction through the transitional region. There is debate in the literature about whether spots initiate in a small band at the start of transition or throughout the transitional region. This paper presents a new design of arrays of thin-film heat transfer specifically designed to detect whether spots initiate in a small band. The gauges were arranged in two spanwise rows at different streamwise locations and were tested on a 7° blunt cone in the T4 Stalker Tube. It is shown that such instrumentation is capable of identifying that some spots initiate between the rows when other spots have already formed upstream of the first row. This demonstrates that the breakdown of laminar boundary layers is not concentrated in a region of small streamwise extent in the current hypersonic flows.

Effect of Reynolds number on second-mode waves in transitional hypersonic boundary layers

The second-mode instability plays an important role in the natural transition of hypersonic boundary layer. In this paper, the Reynolds number effect on the second-mode waves has been experimentally investigated using the Nanoparticle-tracer based Planar Laser Scattering (NPLS) technique and PCB® fast response pressure sensors in Mach 6 quiet wind tunnel. The flow visualization results clearly capture the rope-like second-mode waves and the “quiet zone” before breakdown. The wavelength of second-mode waves is approximately twice the local boundary layer thickness, increasing with the streamwise distance and decreasing with the Reynolds number. The time delays between sensors indicate no significant Reynolds number effect on the propagation velocity of second-mode waves. The average velocity is about 0.82Ue. The characteristic frequencies are collated at different streamwise locations under different Reynolds numbers and show a linear proportion to Re/x. Based on the growth law of compressible conical boundary layer thickness, the characteristic frequency relation and wavelength relation are derived as a function of Reynolds number and streamwise distance. The theoretical estimation values agree well with the experimental results, which provides the potential feasibility to predict the characteristic frequency and wavelength in other tunnels.

Dilatational-wave-induced aerodynamic cooling in transitional hypersonic boundary layers

Abstract

Wall pressure beneath a transitional hypersonic boundary layer over an inclined straight circular cone

Properties of wall pressure beneath a transitional hypersonic boundary layer over a 7∘ half-angle blunt cone at angle of attack 6∘ are studied by Direct Numerical Simulation. The wall pressure has two distinct frequency peaks. The low-frequency peak with f≈10−50 kHz is very likely the unsteady crossflow mode based on its convection direction, i.e. along the axial direction and towards the windward symmetry ray. High-frequency peaks are roughly proportional to the local boundary layer thickness. Along the trajectories of stationary crossflow vortices, the location of intense high-frequency wall pressure moves from the bottom of trough where the boundary layer is thin to the bottom of shoulder where the boundary layer is thick. By comparing the pressure field with that inside a high-speed transitional swept-wing boundary layer dominated by the z-type secondary crossflow mode, we found that the high-frequency signal originates from the Mack mode and evolves into the secondary crossflow instability.

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.

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.

Aerodynamic Heating in Wall-Modeled Large-Eddy Simulation of High-Speed Flows

Aerospace vehicles flying at supersonic and hypersonic speeds are subject to increased wall heating rates caused by viscous friction with the gas environment. This extra heat is commonly referred to as convective aerodynamic heating. In wall-modeled large-eddy simulations, the near-wall region of the flow is not resolved by the computational grid. As a result, the effects of aerodynamic heating need to be modeled using a large-eddy simulation wall model. In this investigation, wall-modeled large-eddy simulations of turbulent high-speed flows are performed to address this issue. In particular, an equilibrium wall model is employed in high-speed turbulent Couette flows subject to different combinations of thermal boundary conditions and grid sizes as well as in transitional hypersonic boundary layers interacting with incident shock waves. Specifically, the wall-modeled large-eddy simulations of the Couette flow configuration demonstrate that the shear-stress and heat-flux predictions made by the wall model show only a small sensitivity to the grid resolution even in the most adverse case where aerodynamic heating prevails near the wall and generates a sharp temperature peak there. Additionally, the simulations indicate that the wall model predicts shear stresses and heat fluxes that are mostly proportional to the near-wall velocity in a manner that resembles an approximate power law. In the wall-modeled large-eddy simulation of hypersonic boundary-layer/shock-wave interaction, the model is tested against direct numerical simulations and experiments. It is shown to correctly capture aerodynamic heating and the overall heat transfer rate around the shock-impingement zone, despite the fact that the adverse pressure gradients in that region may involve nonequilibrium effects.

VITA measurements of transition in transitional hypersonic boundary layer flows

The variable interval time-averaging (VITA) technique is applied to the hot-wire measurements made in three axisymmetric, transitional hypersonic boundary layers. The average duration of conditionally sampled events is used to detect the transition region. It is found that the stability Reynolds number at the peak in the average duration of conditionally sampled events correlates well with the stability Reynolds number that is intermediate to the onset of transition and peak heating. This VITA-identified location of transition moves upstream under the effects of both an adverse pressure gradient and wall cooling; this agrees with previous experimental and computational studies. The VITA technique, therefore, offers an alternative method to obtain details of the location of transition in hypersonic stability experiments, in which hot-wire measurements of the transitioning boundary layers are made.

Hypersonic Transitional Boundary Layers

Surface thin-film gages have been used to determine the extent of the transition region, intermittency distribution, and disturbance convection velocities in the boundary layer on a sharp 5-deg half angle cone at Mach 7.4 in the Ames 3.5-ft Hypersonic Wind Tunnel. In addition, extensive hot wire space-time correlation measurements have been obtained in the wind-tunnel freestream and in the transitional hypersonic boundary layer on a cone-ogive-cylinder in the same facility. Disturbance convection velocities have been obtained from the longitudinal cross correlation measurements as a function of fluctuation scale and distance from the wall. The results of normal cross correlation measurements are also discussed.