Abstract
Direct numerical simulations were used to study the dynamics of a vortex ring impacting a wall at normal incidence. The boundary layer formed as the ring approaches the wall undergoes separation and roll-up to form a secondary vortex ring. The secondary ring can develop azimuthal instabilities which grow rapidly owing to vortex stretching and tilting in the presence of the mean strain field generated by the primary vortex ring. The stability of the secondary ring was investigated through complementary numerical experiments and stability analysis. Both perturbed and unperturbed evolutions of the secondary ring were simulated at a Reynolds number of about 645, based on the initial primary-ring propagation velocity and ring diameter. The linear evolution of the secondary vortex-ring instability was modelled analytically by making use of a quasi-steady approximation. This allowed a localized stability analysis following Widnall & Sullivan's (1973) earlier treatment of an isolated vortex ring. Amplitude evolution and growth-rate predictions from this analysis are in good agreement with the simulation results. The analysis shows that the secondary vortex ring is unstable to long-wavelength perturbations, even though an isolated ring having similar characteristics would be stable.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.