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A shock induced boundary-layer separation (SBLI) occurring in a duct at M = 1.4 has been analyzed using hybrid RANS-LES methods. The shock wave interacts with the turbulent wall boundary layers and triggers flow separation in the duct corners. The main purpose of the present work is to highlight the difficulties in modeling SBLI, particularly, when hybrid RANS-LES models are used. Results computed using different turbulence models are presented and discussed in comparison with available experimental data. Based on a number of simulations, some issues are addressed and some critical remarks are provided for potential improvements using turbulence-resolving modeling approaches in future work.

Turbulence-resolving simulations have been performed using hybrid RANS-LES approaches for the turbulent flow around a three-element high-lift configuration. The main purpose is to explore the effect of some modeling-related numerical aspects on the simulation of resolved velocity and pressure fluctuations as potent noise-generating sources. Along with a presentation of resolved instantaneous and mean flow features, the impact of the time step and the spanwise extent of the computational domain is investigated. It is shown that the temporal resolution and the spanwise extension of the computational domain impose effects not only on the prediction of mean flow, but more significantly on the correlation of resolved turbulent structures, which may consequently affect the accuracy of flow-generated noise properties.

A computational analysis on the influence of the transition for the NASA Trap Wing Model has been carried out, which is an extension of the work presented for the 1 st AIAA High Lift Prediction Workshop. The transition prediction is based on stability analyses with a database method in spanwise sections. Comparisons with experimental data are made to find appropriate N-factors for the e N method leading to the estimated interval 5< N

An embedded LES modelling approach is explored and verified using the PANS (Partially Averaged Navier-Stokes) model as a platform. With the same base model, the turbulence-resolving LES region is embedded by setting the PANS model coefficient to fk < 1 as distinguished from its neighboring RANS region, where fk = 1 is specified. The embedded LES approach is verified in computations of a turbulent channel flow and a turbulent flow over a hump. Emphasis is placed on the impact of turbulent conditions at the RANS-LES interface using anisotropic velocity fluctuations generated from synthetic turbulence. The effects of model coefficientfk in the LES region, as well as of the spanwise size of the computational domain and the grid resolution in this direction, are also investigated. It is shown that the embedded LES method based on the PANS modelling approach is computationally feasible and able to provide reasonable turbulence-resolving predictions in the embedded LES region.

Results presented at the 1 st AIAA High Lift Prediction Workshop (HiLiftPW-1) using the flow solver Edge are summarized for the trap-wing model with two different flap settings. A comparative study of three different turbulence models is carried out, including the Explicit Algebraic Reynolds Stress Model (EARSM), the k-ω SST model and the Spalart-Allmaras (SA) model. The comparison shows that the overall best agreement with experimental data is obtained with the SA model, which has also predicted the maximum lift at about the correct experimental incidence. The two other models predict a larger flap trailing edge separation and, consequently, resulting in an under-prediction of lift. A grid refinement study has been undertaken, indicating that the unstructured grids are of a high quality. A good prediction of the wing tip flow is obtained with the full viscous operator. A thin-layer approximation changes the tip vortex structure with large deviations from experimental pressure distribution. The inclusion of the flap and slat support systems gives improved predictions of the integrated forces and moments, as well as of pressure distributions. There is a small under-prediction of lift at higher incidences due to an under-prediction of the rear main wing and flap suction peaks causing an earlier lift break down. Transition prediction has also been carried out based on stability analysis in several typical span-wise sections. The output is used to specify laminar regions in the 3D calculations, which has improved the results further in good agreement with experimental data for aerodynamic forces, moments and pressure distributions.

A numerical study of the influence of turbulence models is conducted, of which part of the work has been contributed to the 4 AIAA Drag Prediction Workshop (DPW-4). Simulations have been carried out for three wing-body-tail configurations with three horizontal tail incidences and for one tail-off configuration. The computations consist of a grid refinement study and a downwash study with polar calculations to explore the trimmed condition and delta effects. Three turbulence models are used, including the Explicit Algebraic Reynolds Stress Model (EARSM), the k-ω SST model and the Spalart-Allmaras (SA) model. The grid refinement study, for which the flow is attached, shows rather small differences due to different models. The difference is about 10 drag counts between the highest and smallest drag values predicted, respectively, by the EARSM and the SA model. The polar calculations in the downwash study show also rather small differences, in which the same tendency for the drag prediction is observed as in the grid refinement study. The largest differences between the solutions due to different models are observed at the highest angles of attack, where the flow starts to separate after the shock on the wing.

This book gathers the proceedings of the Fifth Symposium on Hybrid RANS-LES Methods, which was held on March 19-21 in College Station, Texas, USA. The different chapters, written by leading experts, reports on the most recent developments in flow physics modelling, and gives a special emphasis to industrially relevant applications of hybrid RANS-LES methods and other turbulence-resolving modelling approaches. The book addresses academic researchers, graduate students, industrial engineers, as well as industrial R&D managers and consultants dealing with turbulence modelling, simulation and measurement, and with multidisciplinary applications of computational fluid dynamics (CFD), such as flow control, aero-acoustics, aero-elasticity and CFD-based multidisciplinary optimization. It discusses in particular advanced hybrid RANS-LES methods. Further topics include wall-modelled Large Eddy Simulation (WMLES) methods, embedded LES, and a comparison of the LES methods with both hybrid RANS-LES and URANS methods. Overall, the book provides readers with a snapshot on the state-of-the-art in CFD and turbulence modelling, with a special focus to hybrid RANS-LES methods and their industrial applications.

Based on the reconstruction series for subgrid-scale (SGS) stress tensor, SGS modellingis revisited. It is shown that, along with the first Leonard term in the series, the second term is alsoexploitable in relation to the viscous dissipation rate tensor, "ij , being further subjected to a Leonardexpansion. The approximation of "ij is discussed in analogy to RANS modelling. With the assumptionof anisotropy dissipation, it is shown that the second term can be approximated in terms of an eddyviscosityformulation, which, together with the first Leonard term, forms a two-term mixed model. Theresulting mixed model has been analyzed in LES of turbulent channel flow. The emphasis in the presentwork has been placed on the effect of model coefficients. The Leonard term may induce negative diffusionassociated to energy backscatter, while the second Smagorinsky term reinforces energy dissipation.Moreover, the modelled Leonard stresses have also been highlighted in the computation.

Unsteady computations are conducted for turbulent flow around the A310 three-element configuration at the incidence of ? s = 25.2°, where the stall has been claimed by wind tunnel test for a freestream Mach number of M ? = 0.22 and a chord-based Reynolds number of Re = 4.1 × 10 6. The time-dependent flow properties are explored using unsteady RANS (URANS) modelling with the Spalart-Allmaras model and an EARSM ? - ? model. The effect of the time step and the grid resolution is highlighted on the URANS-modelled periodical flow features. The computed results are compared with available experimental data. It is shown that the URANS modelling may pronounce a stalled flow at an incidence larger than the measured ? s, at which the existence of transition is uncertain around the leading edges of the slat and the main element. Some DES results have thus been invoked, indicating significant effects due to the specification of transition.

Using the Detached Eddy Simulation (DES) and an algebraic hybrid RANS-LES model, computations are conducted for the flow over a rectangular cavity at a Mach number of M ∞ =0.85. The emphasis is placed on the prediction of unsteady pressure patterns inside the cavity in terms of pressure fluctuations and deduced acoustic tonal modes in comparison with available experimental data. Furthermore, some resolved cavity flow features are also compared, for which a set of wall-resolved LES data is taken as reference. It is shown that both modelling approaches have produced similar results that are in good agreement with experimental or LES data. The DES modelling has generated somewhat reduced pressure fluctuations on the cavity floor. The hybrid model pronounces a less diffusive mixing layer over the cavity opening, which makes a slightly better prediction for the mean flow field.

Using a low-Reynolds number k ! model and its high-Reynolds number variant as base models, the Shear Stress Transport (SST) concept is examined in computations of flows around the RAE2822 airfoil and the DLR-F6 wind-body configuration. Both flows are characterized by local boundary layer separation. Based on an analysis of the net production for the turbulent kinetic energy, k, and for its specific dissipation rate, !, the rationale is highlighted behind the SST formulation that enables improved predictions of flow separation. It is shown that the SST formulation may make the modeling contain the growth of the production of k and, consequently, suppress the turbulent diffusion. Incorporating the SST assumption, the model responds more appropriately to the effect of an adverse pressure gradient in the boundary layer and produces more extended flow separation bubble than the original base model. Improvement due to the SST formulation is also observed in predictions of the shock location for the transonic aerodynamic flows considered in this work.

Numerical investigations are reported on the DLR-F6 wing-body configuration with and without fairing. The configurations have been adopted as test cases for the Third AIAA Drag Prediction Workshop. The addition of the fairing is to eliminate the flow separation bubble in the junction between the wing trailing edge and the fuselage. The computations have been carried out using two groups of unstructured grids with different sizes. In addition to the effect of incidences, studies of grid convergence have also been performed. The computational fluid dynamics solver Edge is used for the investigation. The calculations confirm that the flow separation can be removed in the wing-fuselage junction with the fairing. For this configuration, the results obtained with the two groups of grid are very similar. Without fairing, however, one group of grids has pronounced a lower lift and produced a more extended trailing-edge separation. Because no experimental data are available for the flow condition as swerved in Drag Prediction Workshop-3, additional calculations have been carried out with the clean wing-body configuration at the Drag Prediction Workshop-2 Reynolds number to validate the numerical results against available experimental data. Very good agreement is obtained, in particular, for the global forces and moments. The calculation indicates that, as compared with experimental data, the grid which predicts a relatively large separation region provides improved predictions.

Numerical computations were carried out on the DLR-F6 aircraft configuration. The aerodynamic forces were first computed using an explicit algebraic Reynolds stress (EARSM) formulation coupled with the standard k ! model, which was applied to both the DLR-F6 wing-body (WB) and wing-body-nacelle-pylon (WBNP) configurations. The drag polar was calculated for 2 [ 3 ,1.5 ]. As compared with experimental data, reasonable predictions were obtained for the pressure distributions, yet the lift coecient was somewhat over-predicted and the drag was underestimated for negative incidences. To investigate the eect of turbulence modeling, the flow around the WBNP configuration was computed for = 1 using dierent turbulence models. These include the EARSM k ! model, the Spalart-Allmaras (S-A) model, the SST model, the standard k ! model and a lowReynolds-Number (LRN) k ! model. It is shown that the models have reproduced a similar shock position on the upper wing surface, but that the S-A model returns an earlier one. In modeling flow regions with separation, various models have shown dierent behaviors. The SST model is in general more detective and responsive to flow separation in adverse pressure gradient boundary layers than other models. The LRN k ! model, by contrast, tends to reproduce suppressed separation bubbles. The other models possess performance which is intermediate between the SST model and the LRN k ! model.

A new wall boundary condition for the standard Wilcox’s k–ω model (1988) is proposed. The model combines a wall function and a low-Reynolds number approach, and a function that smoothly blends the two formulations, enabling the model to be used independently of the location of the first interior computational node. The model is calibrated using DNS-data for a channel flow and applied to a heat transfer prediction for a flow in a rib-roughened channel (Reb = 100 000). The results obtained with the new model are improved for various mesh sizes and are asymptotically identical with those of the standard k–ω turbulence model.

Large-eddy simulation of turbulent Rayleigh–Benard (RB) convection has been performed for a 6:1:6 open-ended domain for Rayleigh numbers ranging from 6.3 × 105 to 109 at Prandtl number of Pr = 0.71. The scaling analysis based on the LES data shows that the heat transfer follows a single relation of Nu = 0.162 Ra 0.286, which is consistent with the scaling law for the hard turbulence regime reported in several earlier experimental and DNS studies. The present LES also supports some earlier experimental and DNS findings that most of characteristic parameters can be scaled reasonably well with Ra number in the considered Ra number range using a single relation. Nonetheless, it is found that the scaling of several quantities shows a sensible offset from a single relation, and could be fitted better with the separate scaling relations for the soft and hard convective turbulence transitioned at about Ra = 4 × 107. It has been argued that the transition, reflected in the scaling relation, may be attributed to th...

Two different edge-based spatial discretization schemes are investigated. In the first approach the discretization is applied to the edge control surface formed by the sum of the element sub-surfaces. In the second approach, the discretization is carried out on each sub- surface. It is shown theoretically that the discretization approach on the sub-surfaces may lead to enhanced accuracy at the expense of higher computational cost. The two approaches are applied in two dimensions over an airfoil and to the DLR F6 configuration. The accuracy is evaluated by conducting grid convergence studies. The discretization scheme on the sub- surfaces gives approximately first order accuracy in two dimensions, the other scheme is even less accurate. For the DLR F6 configuration in three dimensions, however, both approaches exhibit similar accuracy close to the expected second spatial order. 1 . Polar calculations and grid convergence studies were undertaken for the DLR-F6 wing-body (WB) and the WB configuration with a fairing (WB-FX2B) added to the junction between the wing trailing edge and fuselage. A summary of the results from the DPW3 contributions was given by Vassberg et al. 2,3 with a statistical analysis presented by Morrison and Hemsch 4 . The conclusion of that investigation was that, after removing outliers, both results with flow solvers using structured and unstructured grids give satisfactory grid convergence and hence accuracy. The most accurate results were obtained with finite volume solvers that rely on structured grids. The computed results on unstructured grids were slightly less accurate and, in particular, more sensitive to the selected family of grids. In this paper we investigate the grid convergence and solution accuracy of two different edge-based spatial discretization techniques in an unstructured, node-centered finite volume solver. The two approaches are compared primarily in terms of their grid convergence properties and hence solution accuracy but also steady state convergence and computational costs are discussed. They are applied to the WB configuration on three different groups of successively refined grids with different characteristics. The WB configuration was chosen since it has an area of flow separation at the wing-body trailing edge junction and the variation in the computed results of different participants was larger compared to the WB-FX2B where the flow is attached. In addition to the DLR F6 WB configuration, a similar grid convergence investigation is carried out over a two-dimensional airfoil. In the following section the flow solver with its solution algorithms is described together with the two discretization algorithms. The numerical accuracy of a convection and diffusion operator is investigated for a simple model grid in two dimensions. This is followed by the numerical results for the two test cases with concluding remarks at the end. II. Solution Algorithm The CFD solver employed in the calculations is the Edge code (http://www.edge.foi.se/), which is an edge- and node-based Navier-Stokes flow solver applicable for both structured and unstructured grids 5-7 . Edge is based on a finite-volume formulation where a median dual grid forms the control volumes with the unknowns allocated in the dual grid centres. The governing equations are integrated explicitly with a multi-stage Runge-Kutta scheme to