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A Reynolds Number‐Based Blade Tip Vortex Model

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Abstract:

A mathematical model has been developed to estimate the temporal growth properties of helicopter blade tip vortices at any vortex Reynolds number. The uniqueness of the model is that it takes into account rotational stratification (Richardson number) effects on the distribution of turbulent viscosity inside the tip vortices. This model is combined with the effects of filament stretching in predicting the temporal evolution of the vortex. A turbulent growth model solves exactly for the tangential (swirl) velocity starting from the Navier‐Stokes equations by using a variation in eddy viscosity across the vortex core. This variation is a function of the local Richardson number, and the final solution becomes dependent on vortex Reynolds number. A parsimonious functional approximation is given to represent the induced velocity distribution in the tip vortices for practical applications. It is shown that the temporal core growth rate predicted by the new model increases with an increase in vortex Reynolds number, which is consistent with experimental observations. The predictions from the model were validated, wherever possible, with tip vortex measurements from both model‐scale and full‐scale rotors.

Document Type: Research Article

DOI: http://dx.doi.org/10.4050/JAHS.52.214

Affiliations: Alfred Gessow Rotorcraft Center, Department of Aerospace Engineering, Glenn L. Martin Institute of Technology, University of Maryland, College Park, MD

Publication date: July 1, 2007

More about this publication?
  • The Journal of the American Helicopter Society is the world's only scientific journal dedicated to vertical flight technology. It is a peer-reviewed technical journal published quarterly by AHS International and presents innovative papers covering the state-of-the-art in all disciplines of rotorcraft design, research and development. (Please note that AHS members receive significant discounts on articles and subscriptions.)

    Journal subscribers who are AHS members log in here if you are not already logged in.

    Authors can find submission guidelines and related information on the AHS website.

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