Resolution effects in compressible, turbulent boundary layer simulations

Abstract

This paper presents the first systematic study of resolution in compressible, turbulent boundary simulations, and the best-resolved simulation carried out to date. Direct numerical simulation (DNS) and wall-resolved, implicit large-eddy simulation (ILES-NWR) were carried out for a turbulent boundary layer at a Mach number of M=2.3 and maximum momentum thickness Reynolds number of Reθi=2×103. The wall temperature was fixed at a constant value corresponding to the nominal adiabatic wall temperature. The flow was developed spatially from a laminar boundary layer similarity solution specified at the inflow, and transition to turbulence was promoted with an artificial body force trip. The effects of spatial resolution in the range of ILES-NWR, conventional DNS, and very strict DNS were considered. The finest grid in the spatial resolution study consisted of 3.3 × 1010 points, and maintained max(Δx1+,Δx2+,Δx3+)≤1 everywhere. With the resolution at the wall held at (Δx2+)w<1, statistics characterizing large-scale flow features converged for max(Δxi+)≤10, and agreed well with experimental data. Velocity spectra in the outer part of the boundary layer agreed well at low wavenumber for all grids in this range of mesh spacing, and increasing resolution acted to fill out the high-wavenumber end of the spectrum. In all cases, the resolved region of the spectrum agreed well with a well-validated model of the spectrum of isotropic turbulence. Thus, ILES-NWR can be concluded to converge seamlessly to DNS as the spatial resolution is increased. The low-wavenumber aspect of spatial resolution was examined by varying the width of the computational domain, with a fixed level of small-scale resolution. The primary influence of increasing domain width was to capture additional spectral content in low spanwise wavenumbers; other statistics were found to be identical. Further, turbulence statistics were found to be essentially independent of the domain width for values between two and eight times the maximum boundary layer thickness. This work predicts computationally, for the first time, the full velocity spectrum in the outer part of the boundary layer. In doing so, it justifies use of the ILES-NWR approach as long as the maximum grid spacing is less than 10 in inner units, and the domain width is at least two times the maximum boundary layer thickness.