Boundary-Layer Transition, Separation, and Reattachment on an Oscillating Airfoil

Abstract

integral value obtained with this method results very close to that obtained with the potential/boundary-layer simulation. However, it seems that the better prediction of the local behavior of the friction drag is obtained with the Reynolds-stress closure method. Note that for the RANS simulations the values of c f obtained on both the upper and lower airfoil surfaces are reported. Because symmetry is not perfect, because of discretization errors, two slightly different lines can be distinguished. InFig.1b,thelocalfrictiondragcoefe cientdistributionsobtained by the RANS and the boundary-layer methods are compared to the theoretical results for the e at plate. In both cases, the friction drag on the proe le is higher than that on the e at plate in the leading-edge zone, although it is lower near the trailing edge. This behavior is consistent with the effects of the chordwise pressure gradient. Because the pressure distributions are practically the same in all of the simulations, the Reynolds-stress closure method predicts a larger variation of the local coefe cient c f with the pressure gradient than the potential/boundary-layer simulation. However, it is expected that RANS simulations give a better representation of the effects of the pressure gradient than the boundary-layer method; thus, it is not clear which solution is the most accurate in the leading-edge region. The computations were carried out on a Pentium III 500-MHz XION processor, with 512 MB RAM. The computing time for the case with 34,000 total cells was about 70 min for the standard k‐e closure method, 110 min for the RNG k‐e closure method, and 150 min for the Reynolds-stress closure method (with a few seconds for the potential/boundary-layer simulations ). Therefore, the Reynolds-stress closure method appears signie cantly more time consuming. In general, the RANS calculations seem to require computational resources, both memory and computing time, which would become prohibitive in three-dimensional calculations. Conclusions The capabilities of a solver of the RANS equations in predicting the friction drag overanairfoil havebeen investigatedthrough comparisonwith the valuesgiven by a coupled potential/boundary-layer method, for different Reynolds numbers. Preliminarily, the near-wall grid resolution required to obtain the grid independence ofthe friction drag in the RANScalculations has been assessed. It appears that, for all of the considered Reynolds numbers, a large amount of computational points is required, which would lead to an unaffordable mesh size in three-dimensional simulations. Even on these highly ree ned grids, the value of the global CF is overestimated by all of the turbulence models because they are not able to predict the boundary-layer transition. If comparison is made with the value given by the potential code coupled with a fully turbulent boundary layer, satisfactory agreement is obtained with the RNG k‐e and the Reynolds-stress closure models. The best global agreement is given by the RNG k‐e model. However, from the analysis of the chord distribution of the local c f , it appears that this is due to compensation between an overestimate near the leading edge and an underestimation at the trailing edge. The best local agreement is obtained, as expected, with the Reynolds-stress model; the only signie cant discrepancy with the BLOWS results is a less steep decrease of the c f near the leading edge. Because the pressure distribution is almost identical, it appears that the RANS simulation with this closure models predicts larger variations of the friction coefe cient with the pressure gradient.Becausethe boundary-layersolversare notwellsuitedfor e ows with high-pressure gradients, it is not clear whether the value of c f obtained by potential/boundary-layer simulation is indeed more accurate in the region near the leading edge. Finally, the RANS simulations require in general large computational time, and this increases signie cantly with the accuracy of the turbulence closure model. Thus, this analysis indicates that an accurate prediction of the friction drag around complex aeronautical cone gurations by RANSmethods remainsanextremelydife cult task with the present computer capabilities.