DNS of compressible turbulent boundary layers and assessment of data/scaling-law quality

Abstract

A direct-numerical-simulation study of spatially evolving compressible zero-pressure-gradient turbulent boundary layers is presented for a fine-meshed range of Mach numbers from 0.3 to 2.5. The use of an identical set-up for all subsonic and supersonic cases warrants proper comparability and allows a highly reliable quantitative evaluation of compressible mean-flow scaling laws and the settlement on a commonly accepted compressible mean-flow velocity profile in the considered Mach and Reynolds number range. All data are compared to the literature data-base where significant data scattering can be observed. The skin-friction distribution was found in excellent agreement with the prediction by the van Driest-II transformation. Contrary to the prevailing appraisal, the wake region of the mean-velocity profile is observed to scale much better with the momentum-thickness Reynolds number calculated with the far-field-viscosity than with the wall-viscosity. The time-averaged velocity fluctuations, density-scaled according to Morkovin’s hypothesis, are found to be noticeably influenced by compressibility effects in the inner layer as well as in the wake region. Allowing wall-temperature fluctuations affects neither the density nor velocity fluctuations.

Self-similar compressible turbulent boundary layers with pressure gradients. Part 1. Direct numerical simulation and assessment of Morkovin’s hypothesis

“…Quantities with an overbar represent quantities averaged in both the spanwise direction and time. The subscripts 'w' and 'e' refer to wall and free-stream quantities, respectively, see Wenzel et al (2018b) for details.…”

“…Additionally, ZPG cases are computed for both inflow Mach numbers with the same set-up to provide DNS of self-similar compressible TBLs with pressure gradients 243 reference data for all PG cases. In order to benefit from the verified reliability of the ZPG set-ups, see Wenzel et al (2018b), the same inflow Reynolds number of about Re θ ≈ 300 is chosen for all cases.…”

“…Caused by the non-characteristic behaviour of this BC, the additional application of numerical grid stretching and filtering and/or additional sponge zones is necessary if sound-wave reflection should be suppressed. At the inflow, a digital-filtering synthetic-eddy-method (SEM) approach is used to generate an unsteady, turbulent inflow condition, see Wenzel et al (2018b) or Wenzel (2019). The spanwise direction is treated as periodic.…”

An improved parallel compact scheme for domain‐decoupled simulation of turbulence

“…Kim and Sandberg 28 then developed the idea to decouple the compact scheme for parallel computations. [44][45][46] Recently, a similar approach was adopted by Capuano et al 47 in developing a parallel compact finite-volume scheme, who used a fourth-order explicit scheme and cell overlapping to decouple the compact scheme. Furthermore, Kim and Sandberg 28 proposed a decoupled sixth-order compact filter with a prediction-correction procedure.…”

“…They also discussed the effect of the number of ghost nodes, and eventually adopted one level of ghost nodes in DNS of boundary layer flows. [44][45][46] Recently, a similar approach was adopted by Capuano et al 47 in developing a parallel compact finite-volume scheme, who used a fourth-order explicit scheme and cell overlapping to decouple the compact scheme. Conservation is enforced by another application of the compact formula around interdomain interfaces.…”