Numerical Investigation of Transition in a Flared Cone Boundary Layer at Mach 6

Abstract

Laminar-turbulent transition is investigated for a flared cone at Mach 6 using spatial Direct Numerical Simulations (DNS). The flow parameters used in the simulations discussed here closely match the laboratory conditions of the hypersonic transition experiments conducted at Purdue University. The objective of the present research is to make a contribution towards understanding of the nonlinear stages of transition in hypersonic boundary layers on a flared cone. Towards this end, the role of second-mode fundamental (K-type) and oblique breakdown is investigated using controlled transition simulations. For fundamental resonance, the parameter space was first explored by performing several low-resolution simulations in order to identify the cases that result in the strongest nonlinear interactions. Subsequently, a set of highly resolved fundamental and oblique breakdown simulations have been performed and the results are presented in this paper. Both fundamental and oblique breakdown lead to strong nonlinear interactions and were thus found to be viable candidates of nonlinear mechanisms that can lead to a fully turbulent boundary layer. The nonlinear interactions observed during these breakdown processes are discussed in detail. A detailed description of the flow structures that arise due to these nonlinear interactions is provided and the development of the skin friction and heat transfer during the breakdown is presented.

Transition scenario in hypersonic axisymmetrical compression ramp flow

“…The dominant mechanism appearing in these conditions relies on the amplification of broadband first oblique modes in the boundary layer, beating the second mode growth because of their upstream domain of instability. These oblique modes interact nonlinearly to create streaks such as already documented in many cases of supersonic and hypersonic transition (Fasel et al 1993;Laible et al 2009;Mayer et al 2011;Franko & Lele 2013Fasel et al 2015). Then, the nonlinear forcing linked to those streaks trigger a linear amplification mechanism, either due to centrifugal, baroclinic or the lift-up effect, in the mixing layer and reattachment region which lead to breakdown.…”

“…2011; Franko & Lele 2013, 2014; Fasel et al. 2015). Then, the nonlinear forcing linked to those streaks trigger a linear amplification mechanism, either due to centrifugal, baroclinic or the lift-up effect, in the mixing layer and reattachment region which lead to breakdown.…”

“…Yet, Arnal (1989) showed that the transition process in a hypersonic flow is highly dependent on receptivity, making the amplification of free stream disturbances via the non-normality of the linearized Navier-Stokes operator (Schmid 2007) a better candidate than the linear growth of an unstable global mode. While some boundary layer instabilities such as Mack (1975) second mode are already known to locally dominate the hypersonic flat plate boundary layer, many studies (Fasel, Thumm & Bestek 1993;Chang & Malik 1994;Laible, Mayer & Fasel 2009;Mayer, Von Terzi & Fasel 2011;Franko & Lele 2013Fasel, Sivasubramanian & Laible 2015) show that it is not the only possible cause of transition: oblique breakdown, which is linked to the streaks created by the nonlinear interaction of first oblique modes is also a possible candidate. This mechanism was first discovered by Thumm (1991) (see also Fasel & Thumm 1991;Fasel et al 1993) for a supersonic (Mach 1.6) boundary layer using DNS.…”

Görtler Instability and Transition in Compressible Flows

“…Although the fundamental breakdown simulated by Laible and Fasel [236] and Laible [241] was controlled rather than being caused by a natural scenario, they observed streamwise vortices (referred to as 'streaks') on the cone surface that were similar to those observed in quiet-tunnel experiments [9,180]. Fasel and coworkers [238,243] also performed DNS to investigate the fundamental breakdown on another ŕared cone at Mach 6, with the cone geometry and ŕow conditions representative of the experiments in the BAM6QT at Purdue University. Similar to the DNS of the ŕow over the NASA ŕared cone [236,241], the breakdown to turbulence over the Purdue ŕared cone was simulated using a disturbance input with speciőed frequency and azimuthal wavenumber.…”

“…The DNS conőrmed the typical pattern of 'hot' and 'cold' streaks appearing, disappearing and then reappearing in the strongly nonlinear transition regime close to the őnal breakdown. Fasel et al [243] further showed that the oblique breakdown can be another viable path to turbulence. They reported that this type of breakdown was only initiated by one pair of oblique second-Mack-mode disturbance waves with the same frequency and azimuthal wavenumbers, but with opposite sign.…”