English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The non-dimensional energy of starting vortex rings typically converges tovalues around 0.33 when they are created by a cylinder piston or a bluff bodytranslating at a constant speed. To explore the limits of the universality ofthis value and to analyse the variations that occur outside of those limits, wepresent an alternative approach to the slug-flow model to predict thenon-dimensional energy of a vortex ring. Our approach is based on theself-similar vortex sheet roll-up described by Pullin. We derive the vorticitydistribution for the vortex core resulting from a spiralling shear layerroll-up and compute the associated non-dimensional energy. To demonstrate thevalidity of our model, we consider different velocity profiles of the vortexgenerator that follow a power-law with a variable exponent m. For a constantvelocity (m=0), our model yields a non-dimensional energy of E*=0.33. For aconstant acceleration (m=1), we find E*=0.19. For a constant velocity, weobtain realistic vorticity distributions by radially diffusing the vorticitydistribution of the Pullin spiral and predict a decrease of the non-dimensionalenergy from 0.33 to 0.28, in accordance with experimental results. Our proposedmodel offers a practical alternative to the existing slug flow model to predictthe minimum non-dimensional energy of a vortex ring. The model is applicable topiston-generated and wake vortex rings and requires only the kinematics of thevortex generator as input.

Estimating the non-dimensional energy of vortex rings by modelling their roll-up