Direct Numerical Simulation of Impinging Shock Wave/Transitional Boundary Layer Interaction with Separation Flow

Abstract

The interaction of a spatially transitional boundary layer flow at freestream Mach number M = 2.0 with an impinging oblique shock wave (β = 35.56) is studied by means of direct numerical simulation (DNS). High amplitude (5%) three-dimensional isotropic disturbances are superimposed on the laminar profile for a Reynolds number based on the boundary layer displacement thickness of Re δ*0 = 1000 at the inlet plane of the computational box. Under the selected flow conditions, the interaction of the boundary layers with the incident shock wave produces three-dimensional separation, thus inducing a shock system (reflected waves and expansion fan). Linear-stability theory and DNS indicate that Λ-shaped vortices are generated in the separated shear layer due to the most unstable oblique mode, which can trigger the breakdown mechanism around the reattachment line. Energy spectral density of the wall-pressure indicates broadband spectra that are observed in the experimental result on shock/turbulent boundary layer interaction.

Computational study of a complex three-dimensional shock boundary-layer interaction

“…The simulation domain was found to be of insufficiently large enough scale to capture any large-scale shock motion and, therefore, the agreement between experimental and computational data was limited. An oblique SBLI at Mach 2.0 and Re δ * θ = 1000 was predicted using DNS by Tokura and Maekwa (2011). Good agreement between previous studies was found, although comparisons were limited due to the low Reynolds number used in the study.…”

“…Nevertheless, a broad variety of SBLI problems have been tackled using a range of computational methods with varying degrees of success (Bhagwandin & DeSpirito, 2011;Dolling, 2001;Oliver et al, 2007). These methods have included various forms of Reynolds Averaged Navier Stokes (RANS) approaches (DeBonis et al, 2010;Thivet, 2002;Vallet, 2007), unsteady RANS (URANS) (Barakos, Doerffer, Hirsch, Dussauge, & Babinsky, 2010;Hirsch, 2010a;Sandham, 2010), Detached Eddy Simulations (DES) (Garnier, 2009;Shams & Comte, 2010), Large Eddy Simulations (LES) (DeBonis et al, 2010;Eagle, Driscoll, & Benek, 2012;Hadjadj, 2012) and Direct Numerical Simulations (DNS) (Adams, 2000;Tokura & Maekwa, 2011). Clearly these methods provide different levels of modeling fidelity and sophistication along with concomitant resource demands.…”

“…In spite of this, some of the more recent studies indicate that there are only modest benefits of going to the much more demanding methods such as LES or DES. There are noted benefits of adopting a DNS approach, as seen in Tokura and Maekwa (2011), but these methods are particularly resource intensive. Within this context, and from the point of view of pragmatic engineering design, there is still a significant interest in understanding the capabilities of robust CFD tools that provide a measured balance between computational cost and solution fidelity.…”

Sound radiated from low Mach number turbulent boundary layer flows（Turbulent boundary layer on a smooth plate and over a small forward facing step）

“…where t is the time, is a Cartesian coordinate system, is the density, is the velocity vector, is the thermodynamic pressure, related to the density and temperature T by the dimensionless form of the perfect gas law, and is the total energy which is defined as (Tokura et al, 2011…”