应用结构系综理论发展壁湍流工程湍流模型

Abstract

One of the greatest challenges in computational modeling of real engineering flows is to derive physically sound turbulence models and to determine their (numerous) coefficients from the understanding of turbulence physics, which has been a bottleneck in turbulence studies for several decades for the lack of a sound theoretical framework. Here, we present a new symmetry-based approach, called structural ensemble dynamics (SED), and apply it to develop new turbulence models. The SED theory focuses on revealing the symmetry properties of wall-bounded flows including channel, pipe, turbulent boundary layer, RB convection, etc. We propose a concept of order function which preserves the dilation invariance due to the presence of wall, yielding a new parameterization for mean profiles in terms of physical multi-layer structure parameters (thickness, scaling, etc.). The SED can be applied to study the Reynolds-averaged Navier-Stokes equation with turbulence models whose defect is easily revealed under the multi-layer picture. We report here the improvement of the k - w model for pipe flow modeling, as well as the definition of a new algebraic model for compressible turbulent boundary layer (CTBL) modeling. The modified k-ω model, the so-called SED- k - w model, has achieved, for the first time, accurate prediction of both mean velocity and (streamwise) kinetic energy for a wide range of Reynolds number, with a 99% accuracy when compared to the Princeton experimental data. In addition, this study has laid a solid support to the universal Karman constant 0.45. Moreover, it points out the existence of a meso-layer with anomaly in energy dissipation, which explains both the outer peak and the approximate logarithmic law in the kinetic energy profile. Secondly, we report a new algebraic model, SED-SL model, which performs clearly superior in both accuracy and simplicity to the Baldwin & Lomax model for the modeling of CTBL. The SED-based models have two distinct features: the first is its accurate determination of the multi-layer structure, being the origin of the high accuracy, and the second is its physical description of the parameters in terms of local scaling and thickness. The latter makes possible of raising the accuracy of CFD models by considering the spatial variation of the physical multi-layer structure parameters in complex flows.