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A reference DNS database is presented, which includes third-and fourth-order moment budgets for unstrained and strained planar channel flow. Existing RANS closure models for third-and fourth-order terms are surveyed, and new model ideas are introduced. The various models are then compared with the DNS data term by term using a priori testing of the higher-order budgets of turbulence transport, velocity-pressure-gradient, and dissipation for both the unstrained and strained databases. Generally, the models for the velocity-pressure-gradient terms are most in need of improvement.

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Fully resolved simulation data of flow separation over 2-D humps has been used to analyze the modeling terms in second-moment closures of the Reynolds-averaged NavierStokes equations. Existing models for the pressure-strain and dissipation terms have been analyzed using a priori calculations. All pressure-strain models are incorrect in the highstrain region near separation, although a better match is observed downstream, well into the separated-flow region. Near-wall inhomogeneity causes pressure-strain models to predict incorrect signs for the normal components close to the wall. In a posteriori computations, full Reynolds stress and explicit algebraic Reynolds stress models predict the separation point with varying degrees of success. However, as with one-and two-equation models, the separation bubble size is invariably over-predicted.

Statistical data obtained from direct numerical simulations (DNS) are often used as reference data for validating turbulence models. Thus, accuracy of the DNS data itself is of particular importance for understanding the potential error in Reynolds-averaged Navier- Stokes (RANS) simulations. Recent studies demonstrate that when the DNS data is used to represent budget terms in the RANS equations, simulations of wall-bounded turbulent flows conducted with such equations (herein referred to as RANS-DNS simulations) produce unphysical results. The current paper analyzes the contribution that convergence of DNS statistics makes to this discrepancy. The Reynolds stresses and budget terms in the RANSequations are collected in a fully developed channel flow ( = ) at increasing sample sizes and analyzed using the RANS-DNS simulation. The results demonstrate that statistical convergence is not the only contributing factor to the spurious RANS-DNS results, and further study is required. Nomenclature U = mean flow velocity in the streamwise direction U ∞ = free stream velocity + = / U u τ P = mean flow pressure u, v, w = turbulent velocity fluctuations in streamwise, normal-to-wall, and spanwise directions u i = turbulent velocity fluctuation in the i-direction u τ = friction velocity h = half-channel width t = time t n = averaging time of DNS data δ = boundary layer thickness = boundary layer momentum thickness ν = kinematic viscosity 1 Assistant Professor, Mechanical Engineering, MSC01 1104, 1 UNM Albuquerque, NM, 87131-00011, AIAA Associate Fellow. 2 AIAA Member.