SUMMARYThe separated turbulent ow past an inclined at plate with sharp leading and trailing edges was computed based on three di erent simulation approaches for a Reynolds number Rec = 20 000 and a high angle of attack =18• . The simulation techniques applied were the Reynolds-averaged NavierStokes (RANS) equations combined with a one-equation Spalart-Allmaras turbulence model, the largeeddy simulation (LES) based on an algebraic eddy-viscosity model, and a hybrid approach known as detached-eddy simulation (DES) applying a slightly modiÿed Spalart-Allmaras model in the entire integration domain. DES is a non-zonal coupling technique of RANS and LES developed in the hope of reducing the large computational resources required for LES computations of turbulent ows with practical relevance. However, the objective of the present study was not to compare the resources (CPU time, memory) required for all three techniques but to investigate and evaluate the quality of the predicted results for RANS, DES and LES. For this purpose, a test case which is favourable to the basic concept of DES and which places special emphasis on the LES part of the DES concept was chosen. This last issue was important since the modiÿed Spalart-Allmaras model applied as a subgrid scale model in the LES part is not as well validated as other models usually applied in LES. For this purpose, an LES prediction on a very ÿne grid served as a reference case for the evaluation. For all three techniques, predictions with di erent grid resolutions were carried out and compared with each other based on important integral parameters (e.g. Strouhal number, mean drag and lift coe cients and their standard deviations), the instantaneous and time-averaged ow structures, and higher-order statistics. As expected, the pure RANS calculation, although applied as unsteady RANS, failed to predict the unsteady characteristics of the separated ow. In contrast, the DES approach yielded reasonably the shedding phenomenon and some integral parameters. However, analysing the results in more detail led to remarkable deviations between the DES and LES predictions also when the same grid resolution was applied. Especially the free shear layer originating from the leading edge of the plate was not well reproduced by DES, showing strong deÿciencies of the model applied as a subgrid scale model. The reasons for this behaviour of the model were analysed in detail. Two basic causes were identiÿed; the ÿrst is given by some near-wall corrections in the ÿnite Reynolds number version of the model which are not working properly in the LES mode of DES. The second is a modiÿed deÿnition of the ÿlter width typically applied for DES, leading to strongly increased values of the eddy viscosity. A revised * Correspondence to: M. Breuer, LSTM, Universit at Erlangen-N urnberg, Cauerstr. 4, D-91058 Erlangen, Germany.† E-mail: breuer@lstm.uni-erlangen.de version of the S-A model taking both issues seriously into account was used as a subgrid scale model in the LES mode. As a direct consequenc...
Turbulence investigations of the flow past an unswept wing at a high angle of attack are reported. Detailed predictions were carried out using large-eddy simulations (LES) with very fine grids in the vicinity of the wall in order to resolve the near-wall structures. Since only a well-resolved LES ensures reliable results and hence allows a detailed analysis of turbulence, the Reynolds number investigated was restricted to Rec=105 based on the chord length c. Admittedly, under real flight conditions Rec is considerably higher (about (35-40)∙106). However, in combination with the inclination angle of attack α=18 deg this Rec value guarantees a practically relevant flow behavior, i.e., the flow exhibits a trailing-edge separation including some interesting flow phenomena such as a thin separation bubble, transition, separation of the turbulent boundary layer, and large-scale vortical structures in the wake. Due to the fine grid resolution applied, the aforementioned flow features are predicted in detail. Thus, reliable results are obtained which form the basis for advanced turbulence analysis. In order to provide a deeper insight into the nature of turbulence, the flow was analyzed using the invariant theory of turbulence by Lumley and Newman (J. Fluid Mech., 82, 161–178, 1977). Therefore, the anisotropy of various portions of the flow was extracted and displayed in the invariant map. This allowed us to examine the state of turbulence in distinct regions and provided an improved illustration of what happens in the turbulent flow. Thus, turbulence itself and the way in which it develops were extensively investigated, leading to an improved understanding of the physical mechanisms involved, not restricted to a standard test case such as channel flow but for a realistic, practically relevant flow problem at a moderate Reynolds number.
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