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

Abstract

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.

Direct numerical simulation of a hypersonic transitional boundary layer at suborbital enthalpies

“…Qualitatively similar transitional processes as those described above have been observed by Franko & Lele (2013) and Hader & Fasel (2019), albeit at much lower enthalpies, at which the gas behaves as calorically perfect. It is worth mentioning that, similarly to the results in Franko & Lele (2013), no clear overshoot in is observed downstream of the main upwards ramp in figure 1( a ).…”

“…The growth of the latter continues in a second stage along the plate for approximately another 600 boundary-layer thicknesses, and then leads to breakdown to turbulence. The qualitative aspects of this pathway to transition, which has already been observed at much lower stagnation enthalpies by Franko & Lele (2013) and Hader & Fasel (2019), appear to be robust to large increments in stagnation enthalpy, as shown by the present study. The ensuing turbulent boundary layer has a momentum Reynolds number of 3826 near the outflow.…”

Linear, nonlinear and transitional regimes of second-mode instability

“…This observation indicates that in the presence of unbiased spanwise variations upstream, fundamental resonance is the preferable mode of breakdown for a given 2-D second-mode wave. Fundamental resonance has also been observed to arise naturally in HBLs over flared cones by Hader & Fasel (2019, 2020).…”

“…This observation indicates that in the presence of unbiased spanwise variations upstream, fundamental resonance is the preferable mode of breakdown for a given 2-D second-mode wave. Fundamental resonance has also been observed to arise naturally in HBLs over flared cones by Hader & Fasel (2019, 2020. At further downstream locations, x > 3, the frequency spectrum is broadband, with no trace of dominance of the forcing harmonic, or its multiples.…”

“…High-resolution numerical schemes with minimal artificial dissipation greatly facilitate the resolution of the broad spectrum of spatio-temporal scales as they evolve during the different stages of transition (see e.g. Hader & Fasel 2019). The method employed in this work is described in § 2.…”