Detached-eddy simulation (DES) is well understood in thin boundary layers, with the turbulence model in its Reynolds-averaged Navier–Stokes (RANS) mode and flattened grid cells, and in regions of massive separation, with the turbulence model in its large-eddy simulation (LES) mode and grid cells close to isotropic. However its initial formulation, denoted DES97 from here on, can exhibit an incorrect behavior in thick boundary layers and shallow separation regions. This behavior begins when the grid spacing parallel to the wall Δ∥ becomes less than the boundary-layer thickness δ, either through grid refinement or boundary-layer thickening. The grid spacing is then fine enough for the DES length scale to follow the LES branch (and therefore lower the eddy viscosity below the RANS level), but resolved Reynolds stresses deriving from velocity fluctuations (“LES content”) have not replaced the modeled Reynolds stresses. LES content may be lacking because the resolution is not fine enough to fully support it, and/or because of delays in its generation by instabilities. The depleted stresses reduce the skin friction, which can lead to premature separation.

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A new version of detached-eddy simulation, resistant to ambiguous grid densities

Detached-eddy simulation (DES) was first proposed in 1997 and first used in 1999, so its full history can be surveyed. A DES community has formed, with adepts and critics, as well as new branches. The initial motivation of high–Reynolds number, massively separated flows remains, for which DES is convincingly more capable presently than either unsteady Reynolds-averaged Navier-Stokes (RANS) or large-eddy simulation (LES). This review discusses compelling examples, noting the visual and quantitative success of DES. Its principal weakness is its response to ambiguous grids, in which the wall-parallel grid spacing is of the order of the boundary-layer thickness. In some situations, DES on a given grid is then less accurate than RANS on the same grid or DES on a coarser grid. Partial remedies have been found, yet dealing with thickening boundary layers and shallow separation bubbles is a central challenge. The nonmonotonic response of DES to grid refinement is disturbing to most observers, as is the absence of...

Detached-Eddy Simulation

The article gives an overview of the Scale-Adaptive Simulation (SAS) method developed by the authors during the last years. The motivation for the formulation of the SAS method is given and a detailed explanation of the underlying ideas is presented. The derivation of the high-Reynolds number form of the equations as well as the calibration of the constants is provided. The concept of SAS is explained using several generic examples and test cases. In a companion article, the model is applied to more complex industrial-type applications.

The Scale-Adaptive Simulation Method for Unsteady Turbulent Flow Predictions. Part 1: Theory and Model Description

The present author was asked to provide an update on the status and the more recent developments around the shear-stress transport (SST) turbulence model for this special issue of the journal. The article is therefore not intended as a comprehensive overview of the status of engineering turbulence modelling in general, nor on the overall turbulence modelling strategy for ANSYS computational fluid dynamics (CFD) in particular. It is clear from many decades of turbulence modelling that no single model-nor even a single modelling approach-can solve all engineering flows. Any successful CFD code will therefore have to offer a wide range of models from simple Eddy-viscosity models through second moment closures all the way to the variety of unsteady modelling concepts currently under development. This article is solely intended to outline the role of the concepts behind the SST model in current and future CFD simulations of engineering flows.

Review of the shear-stress transport turbulence model experience from an industrial perspective

Hybrid LES/RANS methods for the simulation of turbulent flows

High-resolution large-eddy simulation is used to investigate the mean and turbulence properties of a separated flow in a channel constricted by periodically distributed hill-shaped protrusions on one wall that obstruct the channel by 33% of its height and are arranged 9 hill heights apart. The geometry is a modification of an experimental configuration, the adaptation providing an extended region of post-reattachment recovery and allowing high-quality simulations to be performed at acceptable computing costs. The Reynolds number, based on the hill height and the bulk velocity above the crest is 10595. The simulated domain is streamwise as well as spanwise periodic, extending from one hill crest to the next in the streamwise direction and over 4.5 hill heights in the spanwise direction. This arrangement minimizes uncertainties associated with boundary conditions and makes the flow an especially attractive generic test case for validating turbulence closures for statistically two-dimensional separation. The emphasis of the study is on elucidating the turbulence mechanisms associated with separation, recirculation reattachment, acceleration and wall proximity. Hence, careful attention has been paid to resolution, and a body-fitted, low-aspect-ratio, nearly orthogonal numerical grid of close to 5 million nodes has been used. Unusually, the results of two entirely independent simulations with different codes for identical flow and numerical conditions are compared and shown to agree closely. Results are included for mean velocity, Reynolds stresses, anisotropy measures, spectra and budgets for the Reynolds stresses. Moreover, an analysis of structural characteristics is undertaken on the basis of instantaneous realizations, and links to features observed in the statistical results are identified and interpreted. Among a number of interesting features, a distinct ‘splatting’ of eddies on the windward hill side following reattachment is observed, which generates strong spanwise fluctuations that are reflected, statistically, by the spanwise normal stress near the wall exceeding that of the streamwise stress by a substantial margin, despite the absence of spanwise strain.

Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions

Investigation of wall-function approximations and subgrid-scale models in large eddy simulation of separated flow in a channel with streamwise periodic constrictions

A synopsis of important results obtained by seven partners in the Brite ‐Euram project LESFOIL sponsored by the European Union is presented. This project was devoted to assessing the feasibility of large-eddy simulations (LES)forthecomputationofthee owaroundanairfoil.Asatestcase,theAerospatialeA-airfoilat Re=2£10 6 and 13.3-deg angle of attack was chosen. All partners performed simulations of this e ow with various methods, most of which employed e nite volume schemes and various subgrid-scale models of eddy-viscosity type. The key results of theindividual partners’ publicationsarepresented ina comparativeway.Itis demonstratedthatthiscone guration with realistic conditions for aeronautical e ows is extremely demanding for LES. One reason is the need to achieve a threshold resolution for the adequate discretization of the attached and mildly separating boundary layer. The second and even more demanding requirement is the need for an adequate treatment of transition, which in the present computations was achieved by increased resolution.

Lessons from LESFOIL Project on Large-Eddy Simulation of Flow Around an Airfoil

In the present work we investigate the multiscale nature of the correlations for high frequency data (1 min) in different futures markets over a period of two years, starting on the 1st of January 2003 and ending on the 31st of December 2004. In particular, by using the concept of local Hurst exponent, we point out how the behaviour of this parameter, usually considered as a benchmark for persistency/antipersistency recognition in time series, is largely time-scale dependent in the market context. These findings are a direct consequence of the intrinsic complexity of a system where trading strategies are scale-adaptive. Moreover, our analysis points out different regimes in the dynamical behaviour of the market indices under consideration.

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Multi-scale correlations in different futures markets

I. Introduction.- II. Preparatory Work.- 1 Task 1: Subgrid models.- 1.1 Summary of work progress.- 1.2 Task 1.1: Grid generation.- Unstructured grids.- Structured C-grids.- 1.3 Task 1.2: Generation of database with DNS.- 1.4 Task 1.3: Development and evaluation of subgrid models in simple configurations.- Evaluated subgrid-scale models.- 1.5 Conclusion.- 2 Task 2: Near-wall models.- 2.1 Introduction.- 2.2 Overview of Research.- 2.3 Chalmers.- The Hybrid LES-RANS model.- 2.4 CERFACS.- 2.5 University of Karlsruhe.- 2.6 UMIST/QMW.- 2.7 Conclusions and Overall assessment.- 3 Task 4: Numerical methods.- 3.1 Introduction.- 3.2 Contribution by Chalmers.- Performance Assessment.- Speed-up.- Deferred correction.- PISO and SIMPLEC.- Spatial Discretisation.- 3.3 Contribution by Fluent.- Performance Assessment.- Discretization Scheme.- Accuracy assessment.- Velocity Profiles.- 3.4 Contribution by University of Karlsruhe.- Fourier solver for the p' equation.- Implications of 2D/3D Zonal refinement method on Fourier solver.- 3.5 Contribution by ONERA.- 3.6 Contribution by University of Surrey.- 3.7 Contribution by UMIST.- Solution of momentum equations.- Time-step control.- The pressure equation.- Domain decomposition and parallelization.- Partial diagonalisation.- Multigrid algorithm.- Performance Assessment.- 3.8 Achievements and recommendations.- III. The Airfoil Investigations.- 4 Task 5: Airfoil Computations.- 4.1 Introduction.- The Principal Airfoil Geometry.- Common Mesh.- 4.2 Contribution by Chalmers.- Numerical Method.- Boundary Conditions.- Convergence Criteria.- Computations.- Conclusions.- 4.3 Contribution by Alenia.- Objectives.- Numerical method.- Turbulence models.- Steady flow computations.- Unsteady RANS computations.- Conclusions.- Recommendations for future work.- 4.4 Contribution by CERFACS.- Numerical schemes.- Wall functions.- Airfoil Calculations.- Conclusions.- 4.5 Contribution by Dassault-Aviation.- Description of the Navier-Stokes code.- Towards LES.- Application to the A-airfoil.- Comparison of LES results using different SGS models.- Comparison between RANS and LES.- Conclusions.- 4.6 Contribution by FLUENT.- Model Description.- The Mesh.- Numerical Details.- Results.- Conclusions.- 4.7 Contribution by University of Karlsruhe.- LES resolution requirements.- Computational Efficiency.- Transition modelling.- Airfoil calculations.- Conclusions.- 4.8 Contribution by ONERA.- Simulation method.- Subgrid Scale Modelling.- Euler Flux Discretization.- 2D/3D coupling method.- Computational Setup.- Results and Discussion.- Conclusions.- 4.9 Contribution by QMW.- Overview.- The Numerical Method.- Simulations and Results.- Conclusions.- IV. Lessons Learned.- 5 Synthesis of the Airfoil Flow Simulations.- 5.1 Common Mesh Comparisons.- 5.2 Trailing edge geometry.- 5.3 Final Results Comparisons.- 5.4 Subgrid-Scale Modelling.- 5.5 Near-Wall modelling.- 5.6 Transition Treatment.- 5.7 Synthesis conclusions.- V. Conclusions and Outlook.- VI. References.- VII. Addresses of Partners.

C. Mellen

Papers

Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions

Investigation of wall-function approximations and subgrid-scale models in large eddy simulation of separated flow in a channel with streamwise periodic constrictions

Lessons from LESFOIL Project on Large-Eddy Simulation of Flow Around an Airfoil

Multi-scale correlations in different futures markets

LESFOIL: Large Eddy Simulation of Flow Around a High Lift Airfoil