Detached-eddy Simulation Of Fluctuation In Wing Tip Vortex

Detached-eddy simulation (DES) is a combined method of turbulence simulationproposed by Spalart in1997. The basic thought is that: Method of RANS is applied inthe region of boundary layer, and method of LES is applied in the detached region.The methods are transformed automatically, judged by a length scale which is relatedwith grid scale. So a large amount of calculation in the boundary layer is avoided, atthe same time, an instantaneous flow field and fluctuation can be obtained in theregion of LES.Tip vortex is a complex flow, which is generated at the tip of a limited wing. Tipvortex has big gradients of velocity and pressure in three directions, which can resultin strong fluctuations. Besides, there is meandering in downstream of tip vortex in thepast research of experiments, which can result in extra fluctuations. DES can not onlyobtain fluctuations but also save a large amount of calculation, so it is used for thesimulation of tip vortex in this paper.Many simulations of tip vortex have been conducted by methods of RANS andDES. Comparison of the result of RANS and DES has been done. The influence onthe time-averaged quantities and fluctuations of grid density has been analyzed. Atlast, the influence of Reynolds number and attack angle has been analyzed.A thin flat tip vortex with10oattack angle was simulated by RANS-SA and DES,and three grids were used. The difference of the results of different methods anddifferent grids were obtained by analyzing the velocity、pressure and vorticity fields.The comparison shows that grid density has certain influence on results. The strengthof vortex increases with density. DES can get the small vortex better than RANS, andthe retention of vortex by DES is better than RANS.On the basis of prior work, a simulation of NACA0012with rounded tip wasconducted by RANS-SA and DES. The attack angle is10degree, and Reynoldsnumber is1.24×105. Octree grid refinement was used in the region of tip vortex toanalyze the influence of grid density on fluctuation. The comparison betweensimulation and experiment shows that DES can obtain more accurate result thanRANS. The influence of grid density on time-averaged quantity is less than20%, butthe influence on fluctuation is very significant. The peak value of fluctuation obtained by fine grid is about50%of experiment result. Besides, there is no meandering insimulation which is found in experiment.Then a simulation of NACA0012with squared tip was conducted in the methodof DES (Realizable k-ε model in RANS). The attack angle is12degree, and Reynoldsnumber is5105. Twice grid refinements have been done to catch smaller vortex andstronger fluctuations. The comparison shows that grid density has very significantinfluence on fluctuations. Fluctuations are mainly generated in shear layer, which rollup into secondary vortex and then merge with first vortex in suction surface.Instantaneous velocity fluctuations have significant differences with rms of velocityfluctuations. The fluctuations in near field have strong anisotropy. In the fardownstream, the fluctuation change to be Isotropic. The comparison with experimentshow that the peak time-averaged streamwise velocity at x/c=1/4almost equal withexperiment, and the peak value of turbulence kinetic energy there has an error of12%with experiment.At last, simulations with analogous conditions were conducted to analyze theinfluence of Reynolds number and attack angle on time-averaged quantities andfluctuations. The comparisons show that error of fluctuations of bigger Reynoldsnumber is bigger than that of lower Reynolds number at the same scale of grid. Thesecondary vortex and first vortex merge more slowly when Reynolds number andattack angle are bigger. The strength of fluctuation increase with the attack angleincreases.