Validation of a closing procedure for fourth-order RANS turbulence models with DNS data in an incompressible...

Among factors affecting the accuracy of flow simulations with Reynolds-Averaged Navier-Stokes turbulence models is modeling turbulent diffusion processes. With the use of the Gram-Charlier series expansions, the turbulent diffusion in fourth-order one-point statistical closures of the Reynolds-Averaged Navier-Stokes equations can be modeled without introducing unknown model coefficients and without assuming turbulence being Gaussian. Terms representing turbulent diffusion processes in transport equations for second- and third-order velocity correlations do not require any modeling in such closures. In this regard, fourth-order closures are a more accurate alternative to lower-order closures where turbulent diffusion is modeled on semi-empirical or Gaussian turbulence assumptions. In the current paper, the accuracy of the closing procedure based on the Gram-Charlier series expansions is evaluated using data of direct numerical simulations in an incompressible zero-pressure-gradient turbulent boundary layer over a flat plate. One-point third-, fourth-, and fifth-order velocity moments were extracted for this purpose from the dataset collected by the Fluid Dynamics Group at the Universidad Politécnica de Madrid at two streamwise locations Re_θ= 4101 and 5200 that correspond to channels and pipes at δ⁺= 1331 and 1626. Results demonstrate that the truncated Gram-Charlier series expansions are an accurate approximation of the fifth-order velocity moments in the considered flow.