wing interation in Vortex Lattice Method

camino123 · June 11, 2016, 10:13

hi,
how is considered wing interation in VLM programs?
i mean, if i have 2 wings, the interaction exists due to the considation that in each wing the program produce a grid of vortex ring that influence the velocity field around it, so each grid influence simultaneously the other, but in reality a second wing behind the first don't influence the behavior of the first one.

thanks for answers!

adrin · June 11, 2016, 15:31

Each ring and/or filament has a circulation associated with it. This circulation is ultimately obtained by imposing a no-flux boundary condition at the wing (on all collocation points that originate these filaments). This boundary condition is imposed via the Biot-Savart law, which basically solves a Poisson equation. The Poisson equation is global, so every point in the field affects all other points in the field. Consequently, when you have multiple wings in the field the vortex rings/filaments all impact each other. That is, when you apply the no-flux at a collocation point you apply the Biot-Savart law using _all_ vortices in the field.

Note again that the velocity due to these vortices follows the Poisson equation (it's a potential flow), so this is a global field where all points affect each other instantly. That is, the vorticity of the downstream wing _does_ influence the vorticity of the upstream wing. This is conceptually no different from the pressure field in incompressible flow, wherein pressure "travels" instantaneously everywhere (with infinite speed).

adrin

June 11, 2016, 10:13	wing interation in Vortex Lattice Method	#1
camino123 New Member Join Date: Apr 2016 Posts: 7 Rep Power: 10	hi, how is considered wing interation in VLM programs? i mean, if i have 2 wings, the interaction exists due to the considation that in each wing the program produce a grid of vortex ring that influence the velocity field around it, so each grid influence simultaneously the other, but in reality a second wing behind the first don't influence the behavior of the first one. thanks for answers!

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June 11, 2016, 15:31		#2
adrin Senior Member adrin Join Date: Mar 2009 Posts: 115 Rep Power: 17	Each ring and/or filament has a circulation associated with it. This circulation is ultimately obtained by imposing a no-flux boundary condition at the wing (on all collocation points that originate these filaments). This boundary condition is imposed via the Biot-Savart law, which basically solves a Poisson equation. The Poisson equation is global, so every point in the field affects all other points in the field. Consequently, when you have multiple wings in the field the vortex rings/filaments all impact each other. That is, when you apply the no-flux at a collocation point you apply the Biot-Savart law using _all_ vortices in the field. Note again that the velocity due to these vortices follows the Poisson equation (it's a potential flow), so this is a global field where all points affect each other instantly. That is, the vorticity of the downstream wing _does_ influence the vorticity of the upstream wing. This is conceptually no different from the pressure field in incompressible flow, wherein pressure "travels" instantaneously everywhere (with infinite speed). adrin