Delayed Detached Eddy Simulation of Airfoil Stall Flows Using High Order Schemes

Abstract

An advanced hybrid ReynoldsAveraged Navier–Stokes/large eddy simulation (RANS/LES) turbulence model delayed detached eddy simulation (DDES) is conducted in thispaper to investigate the dynamic stall flows over 3D NACA0012 airfoil at 17 deg, 26 deg, 45 deg, and 60 deg angle of attack (AOA). The spatially filtered unsteady 3D Navier–Stokes equations are solved using a fifthorder weighted essentially nonoscillatory (WENO) reconstruction with a low diffusion ECUSP (LDE) scheme for the inviscid fluxes and a conservative fourthorder central differencing for the viscous terms. An implicit secondorder time marching scheme with dual time stepping is employed to achieve high stability and convergency rate. A 3D flat plate is validated for the DDES model. For quantitative prediction of lift and drag of the stalled NACA0012 airfoil flows, the detached eddy simulation (DES) and DDES achieve much more accurate results than the Unsteady ReynoldsAveraged Navier–Stokes (URANS) simulation. In addition to the quantitative difference, the DES/DDES and URANS also obtain qualitatively very different unsteady stalled flows of NACA0012 airfoil with different vortical structures and frequencies. This may bring a significantly different prediction if those methods are used for fluid–structural interaction. For comparison purpose, a thirdorder WENO scheme with a secondorder central differencing is also employed for the DDES stalled NACA0012 airfoil flows. Both the thirdand fifthorder WENO schemes predict the stalled flow similarly for lift and drag at AOA less than 45 deg, while at AOA of 60 deg, the fifthorder WENO scheme shows better agreement with the experiment than the thirdorder WENO scheme. The highorder scheme of WENO 5 also resolves more small scales of flow structures than the secondorder scheme. The prediction of the stalled airfoil flow using DDES with both the highorder scheme and secondorder scheme is overall significantly more accurate than the URANS simulation.