Direct numerical simulations (DNS) were carried out to investigate the laminar–turbulent transition for a flared cone at Mach 6 at zero angle of attack. The cone geometry of the flared cone experiments in the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University was used for the simulations. In the linear regime, the largest integrated spatial growth rates (. Low grid-resolution simulations were carried out in order to identify the azimuthal wavenumber that led to the strongest growth rates with respect to the secondary instability for a fundamental and subharmonic resonance scenario. It was found that for the BAM6QT conditions the fundamental resonance is much stronger compared to the subharmonic resonance. Subsequently, for the case which led to the strongest fundamental resonance onset, detailed investigations were carried out using high-resolution DNS. The simulation results exhibit streamwise streaks of very high skin friction and of high heat transfer at the cone surface. Streamwise ‘hot’ streaks on the flared cone surface were also observed in the experiments carried out at the BAM6QT facility using temperature sensitive paint. The presented findings provide strong evidence that the fundamental breakdown is a dominant and viable path to transition for the BAM6QT conditions.

Direct numerical simulations of hypersonic boundary-layer transition for a flared cone: fundamental breakdown

Flow structures in transitional and turbulent boundary layers

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 consiste...

https://arc.aiaa.org/doi/pdf/10.2514/1.J057015

Thermoacoustic Interpretation of Second-Mode Instability

The interaction between an incident shock wave and a Mach-6 undisturbed hypersonic laminar boundary layer over a cold wall is addressed using direct numerical simulations (DNS) and wall-modelled large-eddy simulations (WMLES) at different angles of incidence. At sufficiently high shock-incidence angles, the boundary layer transitions to turbulence via breakdown of near-wall streaks shortly downstream of the shock impingement, without the need of any inflow free-stream disturbances. The transition causes a localized significant increase in the Stanton number and skin-friction coefficient, with high incidence angles augmenting the peak thermomechanical loads in an approximately linear way. Statistical analyses of the boundary layer downstream of the interaction for each case are provided that quantify streamwise spatial variations of the Reynolds analogy factors and indicate a breakdown of the Morkovin's hypothesis near the wall, where velocity and temperature become correlated. A modified strong Reynolds analogy with a fixed turbulent Prandtl number is observed to perform best. Conventional transformations fail at collapsing the mean velocity profiles on the incompressible log law. The WMLES prompts transition and peak heating, delays separation and advances reattachment, thereby shortening the separation bubble. When the shock leads to transition, WMLES provides predictions of DNS peak thermomechanical loads within at a computational cost lower than DNS by two orders of magnitude. Downstream of the interaction, in the turbulent boundary layer, the WMLES agrees well with DNS results for the Reynolds analogy factor, the mean profiles of velocity and temperature, including the temperature peak, and the temperature/velocity correlation.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112020009350

Shock-induced heating and transition to turbulence in a hypersonic boundary layer

The interaction between an incident shock wave and a Mach-6 undisturbed hypersonic laminar boundary layer over a cold wall is addressed using direct numerical simulations (DNS) and wall-modeled large-eddy simulations (WMLES) at different angles of incidence. At sufficiently high shock-incidence angles, the boundary layer transitions to turbulence via breakdown of near-wall streaks shortly downstream of the shock impingement, without the need of any inflow free-stream disturbances. The transition causes a localized significant increase in the Stanton number and skin-friction coefficient, with high incidence angles augmenting the peak thermomechanical loads in an approximately linear way. Statistical analyses of the boundary layer downstream of the interaction for each case are provided that quantify streamwise spatial variations of the Reynolds analogy factors and indicate a breakdown of the Morkovin's hypothesis near the wall, where velocity and temperature become correlated. A modified strong Reynolds analogy with a fixed turbulent Prandtl number is observed to perform best. Conventional transformations fail at collapsing the mean velocity profiles on the incompressible log law. The WMLES prompts transition and peak heating, delays separation, and advances reattachment, thereby shortening the separation bubble. When the shock leads to transition, WMLES provides predictions of DNS peak thermomechanical loads within $\pm 10\%$ at a computational cost lower than DNS by two orders of magnitude. Downstream of the interaction, in the turbulent boundary layer, WMLES agrees well with DNS results for the Reynolds analogy factor, the mean profiles of velocity and temperature, including the temperature peak, and the temperature/velocity correlation.

T HE performance of hypersonic transportation vehicles and reentry vehicles is significantly affected by the laminarturbulent transition of boundary-layer flows over vehicle surfaces, as transition has a first-order impact on the lift, drag, stability, control, and surface heating. For a reentry vehicle, transition can lead to an increase in the surface heating rate by a factor of five or more. Hence, the understanding of transition mechanisms and the prediction of transition locations are critical to the development of future hypersonic vehicles [1]. One important area of transition study is the effect of roughness on hypersonic boundary-layer transition. Despite several decades of experimental, theoretical, and numerical studies, the effect of surface roughness on transition is still not fully understood [2].Most previous research has focused mainly on tripping the flow using roughness elements. However, there have been a few reported experimental and numerical studies that demonstrate a delay of transition by roughness elements under certain circumstances. James [3] experimentally studied the effects of Mach number and surface roughness on boundary-layer transition using fin-stabilized hollow tube models in free flights. James found that, for someMach numbers, there exists an optimum roughness height that results in a longer laminar run on a rough surface than a smooth surface. In other words, the roughness element delays the transition process rather than promoting it. Holloway and Sterrett [4] performed a transition experiment in the Langley 20 in. Mach 6 tunnel using a flat plate embedded with spherical roughness elements. They found that, for the cases with the smallest roughness diameters, transition was delayed under certain flow conditions. Although they did not investigate the reasons or conditions behind the delay, they hypothesized that the roughness creates a separated laminar mixing layer that is more stable at higher Mach numbers.More recently, Fujii [5] performed experiments using a 5 deg half-angle sharp cone at Mach 7. The tests were completed at stagnation pressures of 2, 4, and 6 MPa. It was found that, for the higher-pressure cases, the onset of transition was delayed when the wavelength of the wavy wall roughness was roughly equal to that of the unstable second-mode wavelength. Although the delay effect is weak, it is still discernible, and the repeatability of the results is remarkably good. It was speculated that there is a relationship between the wavy wall wavelength and second-mode disturbance that leads to transition. However, the mechanism of the transition delay was unknown and not explored. In addition to experimental testing, several numerical studies have reported the roughness effects on transition delay. Marxen et al. [6] studied the disturbance growth on a flat-plate boundary layer atMach 4.8 with localized two-dimensional (2-D) roughness elements. They found the disturbance was strongly damped downstream of the roughness element around the separation region, which agrees with Holloway and Sterrett’s [4] hypothesis. However, the mechanisms were not investigated. At the same time, Duan et al. [7] from University of California, Los Angeles (UCLA) reported that a 2-D roughness element can damp disturbances if the element is placed downstream of the location where the slow hypersonic boundarylayer mode (mode S) and fast hypersonic boundary-layer mode (mode F) have the same phase velocity (the synchronization location). The details of the work by the UCLA group will be discussed in the next paragraph. Riley et al. [8,9] also numerically studied the stability characteristics of a Mach 4 hypersonic boundary layer over a wedge. On the surface of the wedge, they imposed convex or concave panel buckling (compliant panel) at different locations. They found that, when the panel is placed near the trailing edge of the wedge, the panel can move the boundary-layer transition further downstream. On the other hand, Egorov et al. [10] performed numerical simulations of a Mach 6 supersonic boundary layer over a grooved wavy plate. Their study was motivated by the numerical studies of Balakumar [11] and Egorov et al. [12], which showed the second mode remains neutral in the separated region on a 5.5 deg compression corner. Based on the result of the separated region, the intention of the study by Egorov et al. was to generate short local boundary-layer separations by thewavy wall to decrease disturbance growth. The wavy wall was in the form of nine round arc cavities. It was found that thewavywall design damps a range of high-frequency unstable disturbances that are relevant to the second-mode instability. Bountin et al. [13] later confirmed the results byEgorovet al. [10] that thewavywall damps the unstable secondmode in the high-frequency bandwhile it enhances them at lower frequencies. Their experimental data [13] also showed that the wavy wall damps disturbances, not only at the wavy wall wavelength but also at a wide range of disturbances in different frequencies with different wavelengths. Based on these results, they argued that the stabilization effect of the secondmodeby thewavywall is due to altering themean flow instead of an interference process between the second mode and the wavy wall itself. Since 2009, for the purpose of simulating hypersonic flow with finite height roughness elements, Duan et al. has developed a highorder cut-cell method [14]. The new method was then applied to simulating finite roughness elements in a hypersonic boundary layer at Mach 5.92 [7,14]. Different from the wavy wall idea, as in [5] and [10], they found that the relative location of the 2-D roughness Received 4 December 2014; revision received 7 April 2015; accepted for publication 8 April 2015; published online 8 June 2015. Copyright © 2015 by Kahei Danny Fong. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 1533-385X/15 and $10.00 in correspondence with the CCC. *Graduate Research Assistant, Mechanical and Aerospace Engineering Department. Student Member AIAA. ResearchAssociate,Mechanical and Aerospace EngineeringDepartment. Senior Member AIAA. Professor,Mechanical andAerospace EngineeringDepartment. Associate Fellow AIAA. Graduate Research Assistant, School of Aeronautics and Astronautics. Student Member AIAA. Graduate Student, School of Aeronautics and Astronautics. **Professor, School of Aeronautics and Astronautics. Associate Fellow AIAA.

Second Mode Suppression in Hypersonic Boundary Layer by Roughness: Design and Experiments

Hypersonic Ground Tests In Support of the Boundary Layer Transition (BOLT) Flight Experiment

This paper presents results from four different research projects currently ongoing at Purdue University. (1) Different criteria for detecting the edge of the boundary layer were investigated on the flared cone geometry. It was determined that a method based on the total enthalpy profile would be used for future edge-detection computations on the flared cone geometry. A Rod Insertion Method (RIM) roughness insert was measured using a Zygo ZeGage optical profiler. Experimental results with a single RIM insert are presented. Maximum second-mode magnitudes of nearly 27% were measured 2.5 cm upstream from where spectral filling and intermittency algorithms compute that transition has begun. (2) Preliminary data from a new model shows that high-frequency secondary instabilities of stationary crossflow waves are localized under the troughs of the stationary vortices. Measurements of the growth of the secondary instabilities are reported for two different vortices. (3) In order to better understand the effects that probe geometry has on measured pressure fluctuations, pitot measurements were taken using various sleeves which alter the forward-facing diameter of the probe. The results indicate a clear effect of probe size on the measured power spectral densities. Furthermore, it was found that the geometry effects are Reynolds number dependent. (4) Experiments on a cone with a slice and ramp were completed to determine if transitional shock wave-boundary layers interactions can be measured within the Boeing/AFOSR Mach-6 Quiet Tunnel. Initial experiments showed that with a newly designed model it is possible to measure transitional interactions.

Measurements in the Boeing/AFOSR Mach-6 Quiet Tunnel on Hypersonic Boundary-Layer Transition

Hypersonic Ground Tests With High-Frequency Instrumentation In Support of the Boundary Layer Transition (BOLT) Flight Experiment

A new 7 half-angle cone at 6 angle of attack was used to investigate the growth of secondary instabilities on hypersonic stationary crossflow waves. The new cone allows rotation of the sensor array before each run, independently of the rest of the cone. Good repeatability of the cone flow with respect to rotation was established. Measurements of secondary instabilities show the existence of at least two modes, each maximum in different areas of the stationary vortex. Experiments were also performed on a 30 half-angle cone probe equipped with two different pressure transducers to measure the disturbance level of a Mach 6 Ludweig Tube and compare the disturbance levels measured to another facility. It was found that the low frequency disturbance levels differed greatly between the two facilities. Third, RIM insert with 45 roughness elements was tested on a flared cone geometry. Peak second-mode pressure fluctuations of nearly 35% were measured, similar to previous results with a smooth wall. Temperature sensitive paint measurements showed a modified hot-cold-hot heating pattern. Fourth, preliminary measurements on a 7 half angle cone with a slice and flap were made to study free-shear layer transition in a low noise environment. Boundary-layer transition within the free-shear layer has been observed and is altered by the freestream noise levels.

Gregory McKiernan

Papers

Second Mode Suppression in Hypersonic Boundary Layer by Roughness: Design and Experiments

Hypersonic Ground Tests In Support of the Boundary Layer Transition (BOLT) Flight Experiment

Measurements in the Boeing/AFOSR Mach-6 Quiet Tunnel on Hypersonic Boundary-Layer Transition

Hypersonic Ground Tests With High-Frequency Instrumentation In Support of the Boundary Layer Transition (BOLT) Flight Experiment

Instability Measurements in the Boeing/AFOSR Mach-6 Quiet Tunnel