Boeing/AFOSR Mach-6 Quiet Tunnel Research Articles

Wall-cooling effects on secondary instabilities of Mack mode disturbances at Mach 6

In hypersonic boundary layers, Mack modes play a crucial role in flow instability, whose secondary instability is a hot research topic. Since hypersonic flight vehicles will probably work under high-stagnation temperature conditions, which significantly affect the aerodynamic heating calculation and aero-thermal protection design of hypersonic vehicles, it is necessary to compare the primary and secondary instabilities in high-stagnation temperature boundary layers and that in the Boeing/AFOSR Mach 6 quiet tunnel (BAM6QT). Herein, wall-cooling is adopted in order not to consider chemical reactions. With the same freestream temperature of 100 K, two Mach 6 boundary layers with the wall temperature of 20 and 600 K, corresponding to the cooled wall condition and the quiet wind tunnel condition, respectively, are chosen to conduct the linear/non-linear stability and the secondary instability analysis. Our results show that the most dangerous Mack mode originates from a fast discrete mode in the present cooled-wall flow and the most dangerous Mack mode is born from the slow discrete modes in BAM6QT boundary layers. Furthermore, when the primary amplitude of Mack mode disturbances is large, the fundamental resonance always dominates the secondary instability, resulting in steady streaky structures that have the largest amplitude in the spectrum. In addition, the present results point out that the distribution of the eigenfunctions of the fundamental modes and subharmonic modes are significantly different under various wall-temperatures. What is more, different ratios of wall temperature to incoming flow temperature have changed the spanwise wave-angle of the secondary disturbances.

Numerical Investigation of Nonlinear Boundary-Layer Transition for Cones at Mach 6

Direct numerical simulations were carried out for a straight and a flared cone at Mach 6 and zero angle of attack to investigate the effects of geometry on the linear and nonlinear stages of the laminar–turbulent transition process. The cone geometries and the flow conditions of the simulations are chosen to closely match those of the experiments conducted at the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University. In the linear (primary) instability regime the flared cone resulted in larger integrated growth rates ( factors) and a higher dominant second mode frequency. Investigations of the secondary instability regime revealed that the flared cone also leads to a stronger fundamental resonance, characterized by larger integrated growth rates of the secondary instability waves after resonance onset. For both cases, the so-called controlled fundamental breakdown simulations were carried out, which showed the development of similar patterns of streamwise hot streaks on the surface of the cones. Streamwise streaks were also observed in the Purdue experiments (for the flared cone only) using temperature-sensitive paint. A detailed comparison of the results obtained for both geometries indicated that the streak development is caused by the same nonlinear mechanisms.

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.

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

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 ($N$-factors) for the primary instability were obtained for a frequency of approximately $f=300~\text{kHz}$. 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.

Towards simulating natural transition in hypersonic boundary layers via random inflow disturbances

A random forcing approach was implemented into a high-order accurate finite-difference code in order to investigate ‘natural’ laminar–turbulent transition in hypersonic boundary layers. In hypersonic transition wind-tunnel experiments, transition is caused ‘naturally’, by free-stream disturbances even when so-called quiet tunnels are employed such as the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University. The nature and composition of the free-stream disturbance environment in high-speed transition experiments is difficult to assess and therefore largely unknown. Consequently, in the direct numerical simulations (DNS) presented here, the free-stream disturbance environment is simply modelled by random pressure (acoustic) disturbances with a broad spectrum of frequencies and a wide range of azimuthal wavenumbers. Results of a high-resolution DNS for a flared cone at Mach 6, using the random forcing approach, are presented and compared to a fundamental breakdown simulation using a ‘controlled’ disturbance input (with a specified frequency and azimuthal wavenumber). The DNS results with random forcing clearly exhibit the ‘primary’ and ‘secondary’ streak pattern, which has previously been observed in our ‘controlled’ breakdown simulations and the experiments in the BAM6QT. In particular, the spanwise spacing of the ‘primary’ streaks for the random forcing case is identical to the spacing obtained from the ‘controlled’ fundamental breakdown simulation. A comparison of the wall pressure disturbance signals between the random forcing DNS and experimental data shows remarkable agreement. The random forcing approach seems to be a promising strategy to investigate nonlinear breakdown in hypersonic boundary layers without introducing any bias towards a distinct nonlinear breakdown mechanism and/or the selection of specific frequencies or wavenumbers that is required in the ‘controlled’ breakdown simulations.