BBun: an unsteady vortex-ring panel method for interacting lifting bodies, box wings and propellers

Abstract

This report documents BBun (Blunt Body unsteady), a low-order code for the unsteady potential flow around one or more interacting three-dimensional bodies. The bodies are represented by vortex rings (piecewise-constant doublets) with a Neumann boundary condition; free vortex sheets are shed from the trailing edges and, optionally, from the tips, and convected in time, with an implicit unsteady Kutta condition. The report describes the choices that make the discretization consistent and convergent (a single desingularized kernel per wake line, a bordered factorization of the singular Neumann problem, interior velocity conditions for the nearly singular mode of ring-shaped bodies, the detection of the separation lines from the grid connectivity) and the extensions to several bodies, box wings, symmetric configurations (image method), non-lifting bodies, rigidly rotating bodies (propellers), the unsteady Bernoulli equation, a wake-body collision treatment and a strip-wise integral boundary layer. The verification and validation are reported in full: potential flow around a sphere, sensitivity and grid convergence, the two-dimensional limit, an independent vortex-lattice method, the NACA 0015 wing of McAlister and Takahashi (loads and chordwise pressures), the NACA 0012 profile drag, the biplane of Knight and Noyes, Prandtl's best wing system, Wagner's function and blade-element momentum theory for a propeller. A complete aircraft with counter-rotating tractor propellers illustrates the use of the code.

arXiv comment27 pages, 14 figures