Vorticity Confinement technique for preservation of tip vortex of rotating blade

Abstract

In this study the Vorticity Confinement (VC) approach is combined with Total Variation Diminishing (TVD) technique to avoid over-confinement and divergence of upwind secondorder of approximation schemes. The TVD schemes were combined with the first (constant confinement parameter e) and second (constant unit-less confinement parameter c) VC formulations and to adoptive vorticity confinement formulation by Hahn and Iaccarino. These VC techniques were applied to convected Taylor vortex. For the former two VC methods combination of the second-order upwind discretization scheme with VC shows significant over-confinement of convected vortex whereas the first-order discretization scheme leads to strong dissipation of vortex. While the latter VC technique shows acceptable results for first-order upwind scheme, it either diverges or strongly over-confines when the second-order upwind discretization scheme is adopted. The combination of VC with TVD shows flowfield close to analytical convected vortex for above listed VC methods. The proposed combined TVD and VC technique is applied to tip vortex generated by rotating blade and compared to experiment. The optimum value of vorticity confinement parameter is adjusted to these conditions. The grid generation issues and needed local grid refinement are discussed. Convergence of CFD algorithm with added vorticity confinement is confirmed. Application of VC to CFD code FLUENT shows much more close comparison to experimental results in terms of vortex velocity profile and size of vortex core compared to the same CFD code without VC approach.