A new algebraic turbulence model for the prediction of three-dimensional aeronautic flows.*

We report a new algebraic turbulence model (SED-SL) based on a structural ensemble dynamics (SED) theory of wall turbulence (She et al., 2017), a symmetry-based approach to quantifying wall turbulence. The model specifies a multi-layer profile of a stress length (SL) function in both wall-normal and streamwise direction, validated by empirical data from both experiments and simulations. After a successful simulation of transitional flat plate flows (APS meeting, 2016) and further applications to the flows over airfoils (APS meeting, 2017), we here report the results of its application to three dimensional flows over M6 wing and DLR-F4 wing/body. For the flow over M6 wing, the prediction of the Cp by simplified version of the SED-SL model has comparable quality to SA and SST model, but with much less complexity in parameter setting and computing time. For the flow over DLR-F4 wing-body, a significant improvement of the prediction accuracy of CL and CD is obtained with SED-SL, compared to SA and SST. Future applications of the SED-SL model to aeronautic flows would not only provide accurate prediction model for assisting aeronautic design, but also yield more knowledge about the flow physics.