ECCOMAS 2024

Investigation of length scale definition influence in LES models

  • Di Lavore, Enrico (UPC-CTTC)
  • Ruano, Jesus (UPC-CTTC)
  • Oliva, Asensio (CTTC-UPC)
  • Trias, Xavier (CTTC-UPC)

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Large Eddy Simulations (LES) have been increasing popularity due to the decrease of computational power cost. Indeed, engineering applications which have previously involved mainly RANS, are now shifting to LES. Many eddy-viscosity models have been developed during the last decades. Each of those has been developed to address different issues, as WALE model \cite{1999_Nicoud_WALE} vanished the Sub-Grid Scale viscosity $\nu_{SGS}$ by the cubic wall distance $\mathcal{O}(y^3)$. They all share a general structure, which derive from a dimensional analysis: $\nu_{SGS}=(C_m \Delta)^2 D(\bar{U})$, where in order appears the model constant, the length scale and the differential operator underlying the model. We will use the S3PQR model family \cite{2015_Invariants} . The aim of this paper is to investigate influence of length scale $\Delta$ definition, because most of the research has focused mainly on the model constant and differential operator roles. The main length scale definitions \cite{2007_ChauvetDelta} that will be compared are: i) volume cubic root $\Delta_{vol}=(\prod_{i=1}^{3}dx_i)^{\frac{1}{3}}$ \quad ii) maximum directional grid size $\Delta=max(dx_i)$ \quad iii) vorticity based $\Delta_{\omega}=\sqrt{N_x^2 \, dy\,dz + N_y^2 \, dx\,dz + N_z^2 \, dx\,dy }$ \quad where $N$ is the versor of the vorticity $\omega$ . Among others, the Shear Layer Adapted $\Delta_{SLA}$ and least square $\Delta_{lsq}$ length scales will be investigated. %SLA: unlocking the Kelvin- Helmholtz instability in the initial part of shear layers In order to do so, we first tune the model constant, then run a set of simulations in OpenFOAM to assess the $\Delta$ definition influence. Results for standard test cases such as a decaying Homogeneous Isotropic Turbulence (HIT) in a periodic cube and a turbulent plane channel will be presented and compared to reference cases.