Numerical investigation of the nonlinear transition regime in a Mach 2 boundary layer

Abstract

The transition process in a supersonic flat-plate boundary layer at Mach 2 is investigated numerically using linear stability theory (LST) and direct numerical simulations (DNS). The experimental investigations by Kosinov and his co-workers serve as a reference and provide the physical conditions for the numerical set-up. In these experiments, the weakly nonlinear regime of transition was studied. This led to the discovery of asymmetric subharmonic resonance triads, which appear to be relevant for transition in a Mach 2 boundary layer. These triads were composed of one primary oblique wave of frequency 20kHz and two oblique subharmonic waves of frequency 10kHz. While the experimentalists have focused on this new breakdown mechanism, we have found that the experimental data also indicate the presence of another mechanism related to oblique breakdown. This might be the first experimental evidence of the oblique breakdown mechanism in a supersonic boundary layer. With the simulations presented here, the possible presence of oblique breakdown mechanisms in the experiments is explored by deliberately suppressing subharmonic resonances in the DNS and by comparing the numerical results with the experimental data. The DNS results show excellent agreement with the experimental measurements for both linear and nonlinear transition stages. Most importantly, the results clearly show the characteristic features of oblique breakdown. In addition, we also investigated the subharmonic transition route using LST and DNS. When forcing both the subharmonic and the fundamental frequencies in the DNS, a subharmonic resonance mechanism similar to that in the experiments can be observed.

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

“…Following what is common practice in nonlinear simulations of hydrodynamic stability (see for instance Eissler &Bestek 1996 andMayer et al 2011b), our simulations are denoted as DNS below.…”

“…Most of the previous numerical simulations of unsteady secondary instability have used the temporal approach, for example Ng & Erlebacher (1992) and Adams & Kleiser (1996), and only few were concerned with the spatial one (Eissler & Bestek 1996;Mayer, Wernz & Fasel 2011b). Bountin, Shiplyuk & Maslov (2008) carried out an experimental investigation.…”

Statistical inverse analysis and stochastic modeling of transition

“…These studies consider the so-called controlled deterministic transition. Laboratory experiments with such forcing have been successfully reproduced by means of numerical simulation (Mayer et al 2011). However, an approach in which transition is caused by a limited number of forced deterministic perturbations may not be representative of the operating conditions of a vehicle.…”

Numerical Simulation of Transition in Hypersonic Boundary Layers

“…For example, a second derivative at grid point x i can be calculated by differentiating the polynomial P N (x) twice according to 14) where the coefficients b i,j have different values for different grid points with index i (non-uniform grid), and are given by Laible's approach for the grid centered upwind difference stencils used for the discretization of the convective terms. In streamwise direction the numerical scheme is mainly stabilized by employing standard central difference stencils with reduced order up to the last three points where the discretization is switched to one-sided 5 thorder finite differences.…”