Resolution effects in compressible, turbulent boundary layer simulations. (English) Zbl 1390.76207
Summary: 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) are carried out for a turbulent boundary layer at a Mach number of \(M = 2.3\) and maximum momentum thickness Reynolds number of \(\operatorname{Re}_{\theta i} = 2 \times 10^3\). The wall temperature is fixed at a constant value corresponding to the nominal adiabatic wall temperature. The flow is developed spatially from a laminar boundary layer similarity solution specified at the inflow, and transition to turbulence is promoted with an artificial body force trip. The effects of spatial resolution in the range of ILES-NWR, conventional DNS, and very strict DNS are considered. The finest grid in the spatial resolution study consists of \(3.3 \times 10^{10}\) points, and maintains \(\max(\Delta x_1^+, \Delta x_2^+, \Delta x_3^+) \leq 1\) everywhere. With the resolution at the wall held at \((\Delta x_2^+)_w < 1,\) statistics characterizing large-scale flow features converge for \(\max(\Delta x_i^+) \leq 10\) and agree well with experimental data. Velocity spectra in the outer part of the boundary layer agree well at low wavenumber for all grids in this range of mesh spacing, and increasing resolution acts to fill out the high-wavenumber end of the spectrum. In all cases, the resolved region of the spectrum agrees 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 is examined by varying the width of the computational domain, with a fixed level of small-scale resolution. The primary influence of increasing domain width is to capture additional spectral content in low spanwise wavenumbers; other statistics are found to be identical. Further, turbulence statistics are 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 the 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.
MSC:
| 76F65 | Direct numerical and large eddy simulation of turbulence |
| 76F50 | Compressibility effects in turbulence |
| 76N20 | Boundary-layer theory for compressible fluids and gas dynamics |
Keywords:
turbulent boundary layer; compressible flow; direct numerical simulation; implicit large-eddy simulation; resolutionReferences:
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