Abstract
The prediction of coherent vortices with standard RANS solvers suffers especially from discretisation and modelling errors which both introduce numerical diffusion. The adaptive Vorticity Confinement (VC) method targets to counteract one part of the discretisation error: the one due to the discretisation of the convection term. This method is applied in conjunction with a hybrid RANS-LES turbulence model to overcome the overprediction of turbulence intensity inside vortex cores which is a typical deficiency of common RANS solvers. The third main source for numerical diffusion originates from the spatial discretisation of the solution domain in the vicinity of the vortex core. The corresponding error is analysed within a grid convergence study. A modification of the adaptive VC method used in conjunction with a high-order discretisation of the convection term is presented and proves to be superior. The simulations of a wing tip vortex flow are validated in terms of vortex velocity profiles using the results of a wind tunnel experiment performed by Devenport and colleagues (1996). Besides, the results are compared with another numerical study by Wells (2009) who uses a Reynolds Stress turbulence model. It turns out that the application of the modified adaptive VC method on the one hand reinforces the tip vortex, and on the other hand accelerates the axial flow which leads to a slight degradation compared to the experimental results. The result of Wells is more accurate close to the wing, but the result obtained here is superior further downstream as no excessive diffusion of the tip vortex occurs.
Highlights
Coherent tip vortices occur e.g. in the wake of lifting wings like aircraft foils, propeller blades or helicopter rotor blades and extend far downstream showing a slow decay
The adaptive Vorticity Confinement (VC) method targets to counteract one part of the discretisation error: the one due to the discretisation of the convection term. This method is applied in conjunction with a hybrid Reynolds-Averaged Navier-Stokes (RANS)-Large Eddy Simulation (LES) turbulence model to overcome the overprediction of turbulence intensity inside vortex cores which is a typical deficiency of common RANS solvers
This study focuses with greater detail on the evaluation of the adaptive VC method in combination with DES turbulence modelling
Summary
Coherent tip vortices occur e.g. in the wake of lifting wings like aircraft foils, propeller blades or helicopter rotor blades and extend far downstream showing a slow decay. The turbulent viscosity contributes to a stronger (artificial) diffusion in the simulation compared to real flows Pierson and Povitsky [8] applied the adaptive VC method for the prediction of the flow of a convected Taylor vortex and a helicopter tip vortex They used an Euler solver and realised the convection discretisation with an upwind, a linear upwind and a TVD scheme. The adaptive VC method will be assessed in comparison with experimental data from Devenport et al [1] They carried out wind tunnel measurements of a tip vortex trailing from a NACA0012 wing at Re = 530000.
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