Assessment of the shear-improved Smagorinsky model in laminar-turbulent transitional channel flow

Abstract

In this paper, the shear-improved Smagorinsky model (SISM) is assessed in a K-type transitional channel flow. Our numerical simulation results show that the original SISM model is still too dissipative to predict the transitional channel flow. Two former reported empirical correction approaches, including a low-Reynolds-number correction and a shape-factor-based intermittency correction, are applied to further promote the capability of the SISM model in simulating the transition process. Numerical tests show that the shape-factor-based intermittency correction approach can correctly improve the transition-prediction capability of the SISM model, while the low-Reynolds-number correction approach fails. Furthermore, the shape-factor-based intermittency-corrected SISM model can capture the vortical structures during the transitional process very well and possesses the grid-insensitive characteristics. IntroductionIn modern research of turbulence, numerical approaches are becoming prevalent tools due to the rapid development of the computer science and numerical methods. There are three classical numerical methods, including the direct numerical simulation (DNS), Reynolds averaged Navier-Stokes (RANS), and large-eddy simulation (LES). In current engineering applications, the DNS is powerless due to the limitations in the computational resources and discretisation accuracy, and the LES is becoming increasingly popular, especially for unsteady flows and flows with massive separations, although the RANS is the commonly used method. The key problem for the LES is the subgrid-scale (SGS) stress term, which comes out due to the nonlinearity of the Navier-Stokes equations.There are many different SGS models (see the books by Pope[1] and Sagaut [2] for a review), and among these, the Smagorinsky eddy-viscosity model [3] (SM) is the simplest and most commonly used one. In the SM model, the SGS stress tensor τ ij is replaced by the following model

Nonequilibrium and morphological characterizations of Kelvin–Helmholtz instability in compressible flows

“…The Kelvin-Helmholtz instability (KHI) occurs at a perturbed interface between two fluids or two parts of the same fluid with different tangential velocities [1]. As an efficient and important initiating mechanism of turbulence and mixing of fluids [2][3][4][5][6][7], it plays crucial roles in various fields, ranging from high-energy-density physics [8], geophysics and astrophysics [9][10][11][12][13][14], inertial confinement fusion (ICF) [15][16][17], combustion [18][19][20], to Bose-Einstein condensate [21,22] and graphene [23], etc. Concretely, in geophysical and astrophysical situations, on the one hand, the fully developed KH billows are responsible for the formation of large-scale vortical structures in systems such as hurricane [9], galaxy spiral arms [10], heliopause [11,12], and solar wind interaction with the Earth's magnetosphere [13,14], leading to violent intermixing across shear layers; on the other hand, the significantly suppressed KH roll-ups contribute to the sufficiently long, stable and highly collimated supersonic astrophysical jets [16,[24][25][26] with length-to-width ratios as high as 100 or more, emanated from young stellar objects or active galactic nuclei [27], and jet-like long spikes observed in the high-energy-density laboratory astrophysics experiments [28].…”