The present article assesses the capability of the partially averaged Navier-Stokes (PANS) method to reproduce accurately the self-sustained shock oscillations, also known as transonic buffet, ...occurring on airfoils and wings at transonic regime under certain conditions of Mach number and angle of attack. The test case under analysis is an OAT15A unswept wing at Mach number M∞=0.73 and Reynolds number Rec=3×106. The three-dimensional flow is studied by accounting for the wind tunnel walls adopted in the experiments of Jacquin et al. 1 in the simulations. The computations on a large-span, confined configuration reveal a strong three-dimensionality of the flow both before and after the buffet onset. Attention is paid to the comparison with unsteady Reynolds-averaged Navier Stokes (URANS) results, to show the benefits of PANS in resolving flow unsteadiness at different flow resolutions, especially on affordable CFD grids, at limited additional cost. In this context, the role of the mesh metrics and the local turbulence level in the formulation of the model is described, as well as the relation of this latter with the spatiotemporal discretization used for the numerical simulations. The aim is to extend the use of PANS and obtain accurate predictions of flow cases involving shock-wave boundary layer interactions without expensive approaches.
The ten-moment equations are considered as a first-order alternative of Navier-Stokes equations when the effect of heat transfer is negligible. This model takes the form of first-order hyperbolic ...conservation laws, which carry many numerical advantages. However, the applicability of this model is still limited due to the lack of appropriate turbulence models. Applying the Reynolds-averaging concept to the ten-moment model, a set of governing equations for turbulent flow can be obtained, which is referred to as the Reynolds-averaged ten-moment equations. The traditional turbulence models designed for the Reynolds-averaged Navier-Stokes (RANS) equations are not ideal for the Reynolds-averaged ten-moment equations, as the extra partial differential equations (PDEs) introduce second-order derivatives. These terms destroy the pure hyperbolic nature of the original system of equations, which consequently removes all numerical advantages of first-order systems. To maintain the first-order hyperbolic form, the desired turbulence model should remain in the same form. Recently, a hyperbolic-relaxation turbulence model has been proposed by the authors, which is developed by hyperbolizing Prandtl's one-equation model using a relaxation method known as the Chen-Levermore-Liu p-system. Unfortunately, developing a hyperbolic version of two-equation models using the same method is very difficult. This is because the diffusion coefficients of the two-equation models are more complicated than in the one-equation model. In this paper, another relaxation method, the Cattaneo-Vernotte approach, is used to develop the hyperbolic-relaxation form of classical two-equation models. The solution of the resulting equations exhibits dispersive wave behaviour. To study this feature, a dispersion analysis of the Reynolds-averaged ten-moment equations with the new turbulence models is presented. Several numerical experiments are studied to investigate the effect of the relaxation parameters. The derived turbulence models are then coupled to the Reynolds-averaged ten-moment equation and further validated by solving a canonical two-dimensional turbulent plane mixing-layer problem, planar free-jet problem, and circular free-jet problem.
The output from a direct numerical simulation (DNS) of turbulent channel flow at Re
τ
≈ 1000 is used to construct a publicly and Web services accessible, spatio-temporal database for this flow. The ...simulated channel has a size of 8πh × 2h × 3πh, where h is the channel half-height. Data are stored at 2048 × 512 × 1536 spatial grid points for a total of 4000 time samples every 5 time steps of the DNS. These cover an entire channel flow-through time, i.e. the time it takes to traverse the entire channel length 8πh at the mean velocity of the bulk flow. Users can access the database through an interface that is based on the Web services model and perform numerical experiments on the slightly over 100 terabytes (TB) DNS data on their remote platforms, such as laptops or local desktops. Additional technical details about the pressure calculation, database interpolation, and differentiation tools are provided in several appendices. As a sample application of the channel flow database, we use it to conduct an a-priori test of a recently introduced integral wall model for large eddy simulation of wall-bounded turbulent flow. The results are compared with those of the equilibrium wall model, showing the strengths of the integral wall model as compared to the equilibrium model.
This paper presents a novel CFD-driven machine learning framework to develop Reynolds-averaged Navier-Stokes (RANS) models. The CFD-driven training is an extension of the gene expression programming ...method Weatheritt and Sandberg (2016) 8, but crucially the fitness of candidate models is now evaluated by running RANS calculations in an integrated way, rather than using an algebraic function. Unlike other data-driven methods that fit the Reynolds stresses of trained models to high-fidelity data, the cost function for the CFD-driven training can be defined based on any flow feature from the CFD results. This extends the applicability of the method especially when the training data is limited. Furthermore, the resulting model, which is the one providing the most accurate CFD results at the end of the training, inherently shows good performance in RANS calculations. To demonstrate the potential of this new method, the CFD-driven machine learning approach is applied to model development for wake mixing in turbomachines. A new model is trained based on a high-pressure turbine case and then tested for three additional cases, all representative of modern turbine nozzles. Despite the geometric configurations and operating conditions being different among the cases, the predicted wake mixing profiles are significantly improved in all of these a posteriori tests. Moreover, the model equation is explicitly given and available for analysis, thus it could be deduced that the enhanced wake prediction is predominantly due to the extra diffusion introduced by the CFD-driven model.
•Turbulence closure trained for wake mixing using CFD-driven machine learning.•Trained model tested for different cases and demonstrated robustness.•Explicitly given model equation shown to be realizable and physically interpretable.
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