Three dimensional high-order gas-kinetic scheme for supersonic isotropic turbulence I: Criterion for direct numerical simulation. (15th October 2019)

• Record Type: Journal Article
• Authors: Cao, Guiyu; Pan, Liang; Xu, Kun
• Is Part Of: Computers & fluids. Volume 192(2019)
• Publication Date: 2019-10-15
• Subjects: High-order gas-kinetic scheme -- Direct numerical simulation -- Compressible isotropic turbulence -- Supersonic regime.; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2019.104273
• Languages: English
• ISSNs: 0045-7930

Abstract

Highlights: Isotropic compressible turbulence at supersonic regime has been studied by the high-order gas-kinetic scheme. Detailed statistical solutions are provided as the benchmark solutions. The DNS solutions provide useful data for the construction of compressible LES model in supersonic regime. All these results and the analysis of physical mechanism are useful for the future study of isotropic compressible turbulence. Abstract: In this paper, we intend to address the high-order gas-kinetic scheme (HGKS) in the direct numerical simulation (DNS) of compressible isotropic turbulence up to the supersonic regime. To validate the performance of HGKS, the compressible isotropic turbulence with initial turbulent Mach number M a t 0 = 0.5 and Taylor microscale Reynold number R e λ 0 = 72 is simulated as a benchmark. With the consideration of robustness and accuracy, the WENO-Z scheme is adopted for spatial reconstruction in the current higher-order scheme. Statistical quantities are compared with the high-order compact finite difference scheme to determine the spatial and temporal criterion for DNS. According to the grid and time convergence study, it can be concluded that the minimum spatial resolution parameter κ max η 0 ≥ 2.71 and the maximum temporal resolution parameter Δ tini / τ 0 ≤ 27.08/1000 are adequate for HGKS to resolve the compressible isotropic turbulence, where κ max is the maximum resolved wave number, Δ tini is the initial time step, η 0 and τ 0 are the initial Kolmogorov length scale and time scale, respectively. Guided by such criterion, the compressible isotropic turbulence from subsonic regime M a t 0 = 0.8 to supersonic one M a t 0 = 1.2, and the Taylor microscale Reynolds number Re λ 0 ranging from 10 to 72 are simulated. With the high initial turbulent Mach number, the strong random shocklets and high expansion regions are identified, as well as the wide range of probability density function over local turbulent Mach number. All those impose great challenge for high-order schemes. In order to construct compressible large eddy simulation models at high turbulent Mach number, the ensemble budget of turbulent kinetic energy is fully analyzed. The solenoidal dissipation rate decreases with the increasing of Ma t 0 and Re λ 0 . Meanwhile, the dilational dissipation rate increases with the increasing of Ma t 0, which cannot be neglected for constructing supersonic turbulence model. The current work shows that HGKS provides a valid tool for the numerical and physical studies of isotropic compressible turbulence in supersonic regime, which is much less reported in the current turbulent flow study.