Hybrid RANS-LES simulations for separated flows using dynamic grids

A hybrid RANS-LES approach is used in this thesis to simulate the unsteady aerodynamic flows. Different cases are investigated such as high Reynolds number flows around a circular cylinder, flows over an Aerospatiale A-aerofoil at stall conditions and flows around a flapping wing with mesh deformation. The Dynamic Grid Detached Eddy Simulation (DG-DES) is an in-house solver developed at the University of Sheffield. It is a message passing interface (MPI) code which uses the URANS, DES and DDES techniques with dynamic grid capability. The RANS formulation is used in the code with one equation Spalart-Allmaras (S-A) turbulence model. The S-A turbulence model is used in the frame work of a common hybrid RANS-LES formulation termed as the Detached-Eddy Simulation (DES) and Delayed Detached-Eddy Simulation (DDES). The results presented in this research contain the simulations of the transonic speed steady state flows over the . RAE2822 and the ONERA M6 wing. These simulations are carried out using single and double precision versions of the solver with different simulation techniques. A good comparison of results with the experimental data is achieved. It has also served as a validation of new additions in the code made by the author. These include addition of the inviscid flux calculation schemes (AUSM and HLLC schemes), the turbulence scheme (DDES) and double precision implementation in the solver. A detailed analysis of the A-airfoil at the Reynolds number of 2x106 and angle of attack a = 13.3o has been carried out using the URANS, DES and DDES schemes. Encouraging results were obtained for different flow parameters including lift coefficient, drag coefficient and modelled stresses in comparison with the experimental data. It was observed that for this particular case, the DES scheme does not function in accordance with its original concept. Due to the thick trailing edge boundary layer, the switching to LES mode is done by the DES within the boundary layer. As per the basic principle of the DES scheme, the whole of the boundary layer is to be treated in RANS mode. This premature switching is known to cause the modelled stress depletion (MSD) in the flow domain. The implementation of DDES solves this irregularity and the LES to RANS switching is delayed to work in accordance with the basic DES principle by treating the whole of the attached boundary layer in the RANS mode. A detailed comparison of the Reynolds stresses is also carried out on the suction side with the experimental data. It is concluded that due to the premature switching from RANS to LES mode, the Reynolds stresses computed by the DES scheme are reduced at the trailing edge of the suction side. However, the DES simulation also predicts the flow separation at the suction side of the trailing edge in accordance with the experimental observations. The Reynolds stresses computed by the DOES scheme are similar to the URANS results. Both the URANS and DOES simulations fail to predict the trailing edge separation. It is argued that despite the premature switching, the DES scheme presents a better flowfield picture as compared with the DOES which is found to be overly dissipated for this particular case. It can be observed that this case may not be a well posed 'natural DES problem' because the flow separation is not very rapid as required by natural DES flows. The results from the DES solution clearly show that a reduced dissipative level for the thick boundary layers near trailing edge presents better quality of the solution, in contrast with RANS and DOES. Modelled and resolved turbulent stresses were calculated using DES and DOES schemes. It is observed that for this particular case the major contribution is from modelled stresses and the resolved stresses are negligible. The circular cylinder flow with aspect ratio of 2 is simulated at different Reynolds numbers of 1.4x105 , 3.6x106 and 8x106 The comparison of the resolved stresses is carried out with the experimental data and satisfactory results are obtained. The comparison of the modelled and resolved stresses is also carried out to highlight the impact of the resolved and modelled stresses for highly separated flows. A probe point is located two diameters downstream of the circular cylinder at the symmetry plane and instantaneous data for primitive variables is stored to compare the instantaneous results of primitive variables from the DES and ODES schemes. The power spectral density plot at the same point for both the DES and DOES schemes is compared to show the energy content with the size of the eddies (high frequency corresponds to smaller eddies). This shows the energy decay as represented by the Kolmogorov's energy spectrum. Two and three dimensional Delaunay Graph based mesh deformation was incorporated in the respective two and three dimensional versions of the solver DG DES. Initial results from both 2D and 3D solvers are presented. NACA0033 with a flexible tail is simulated using the 2D Delaunay Graph based mesh deformation. The results capture the flow physics well including the vorticity contours during the flapping motion. The computed coefficient of thrust (CT) for the case with the tail thickness b/c=0.S6 x 10-3 at Strouhal number of 0.34 is compared with the experimental data and produces 30% lower values. The MPI version of the DGDES solver is used to simulate the numerical simulation of flow over a NACA0012 wing with the mesh deformation capability. The NACA0012 wing (with a span of 4 times chord length) is simulated for oscillating motion. The wing is fully rigid and this case is essentially 2D oscillating wing. The resultant instantaneous coefficient of thrust is in good agreement with the experimental data.