Nonlinear instability of a supersonic boundary layer with two-dimensional roughness

Abstract

© © 2014 Cambridge University Press.Nonlinear instability in a supersonic boundary layer at Mach 4.8 with two-dimensional roughness is investigated by means of spatial direct numerical simulations (DNS). It was previously found that an important effect of a two-dimensional roughness is to increase significantly the amplitude of two-dimensional waves downstream of the roughness in a certain frequency band through enhanced instability and transient growth, while waves outside this band are damped. Here, we investigate the nonlinear secondary instability induced by a large-amplitude two-dimensional wave, which has received a significant boost in amplitude from this additional roughness-induced amplification. Both subharmonic and fundamental secondary excitation of the oblique secondary waves are considered. We found that even though the growth rate of the secondary perturbations increases compared to their linear amplification, only in some of the cases was a fully resonant state attained by the streamwise end of the domain. A parametric investigation of the amplitude of the primary wave, the phase difference between the primary and the secondary waves, and the spanwise wavenumber has also been performed. The transient growth experienced by the primary wave was found to not influence the secondary instability for most parameter combinations. For unfavourable phase relations between the primary and the secondary waves, the phase speed of the secondary wave decreases significantly, and this hampers its growth. Finally, we also investigated the strongly nonlinear stage, for which both the primary and the subharmonic secondary waves had a comparable, finite amplitude. In this case, the growth of the primary waves was found to vanish downstream of the transient growth region, resulting in a lower amplitude than in the absence of the large-amplitude secondary wave. This feedback also decreases the amplification rate of the secondary wave

Data-driven framework for input/output lookup tables reduction: Application to hypersonic flows in chemical nonequilibrium

“…In this section, the general equations governing hypersonic flows in chemical nonequilibrium are first recalled, followed by a brief description of the numerical framework used to solve these equations. Then, the two benchmark cases, a Mach-10 adiabatic laminar boundary layer in chemical nonequilibrium, initially studied by Marxen et al [1,2], and a Mach-5.92 SBLI are presented.…”

“…mosphere, based on the work of Marxen et al [1,2]. The thermodynamic and free-stream conditions are presented in Table I.…”

“…Chemical nonequilibrium effects have been shown to play an important role in the accurate simulation of flows at hypersonic conditions and in the computation of design characteristics, such as transition location or thermal loading [1][2][3][4]. Recent studies have identified these effects as causes of order-one changes in growth rates, response behavior, or sensitivities, even though the corresponding variations in first-order flow statistics have been modest.…”

Instability evolution in the hypersonic boundary layer over a wavy wall

“…In the previous subsection, the wavy wall is seen to modify the base flow. In light of results from Marxen et al (2010) and Marxen, Iaccarino & Shaqfeh (2014), the two-dimensional roughness acts as an amplifier for two-dimensional convective disturbances within a certain frequency band, and the source of an additional perturbation. In this subsection, how disturbances are convected and amplified by the wavy wall is examined.…”

Influence of upstream disturbances on the primary and secondary instabilities in a supersonic separated flow over a backward-facing step

“…This subharmonic resonance triad can accelerate the laminar-to-turbulent transition. Marxen, Iaccarino, and Shaqfeh 25 proposed that the transition is a slow resonant process between the primary and secondary waves in the presence of roughness in which the amplitudes of the excited fundamental and subharmonic secondary waves are augmented significantly. The transient evolution of the primary wave does not usually affect the secondary instability.…”