Induced downwash velocity for drag computation in Vortex Lattice Method (VLM)

Sehwan · August 9, 2017, 04:51

According to Low-Speed Aerodynamics by Katz and Plotkin, the downwash induced by the wing's streamwise vortex lines and the wake is used for computing the induced drag in Vortex Lattice Method.

Here, I cannot understand the reason why only the trailing (streamwise) segments of the wing-bound vortices are considered in obtaining the downwash for induced drag calculation while the spanwise segments of the wing-bound vortices are neglected.

In the VLM source codes, to satisfy a boundary condition at collocation points, an influence coefficient matrix is established by computing the induced velocity by the wing-bound vortices (streamwise and spanwise segments of the wing vortex rings).

During the phase of the influence coefficient computation using the same subroutine, the another influence matrix can be established by computing the normal velocity component induced by the streamwise segments of the wing vortex rings with influence of the spanwise vortex segements turned off. This is used for induced drag computation.

I've been following this procedure, and the prediction was accurate. However, I would like to know the reason why the spanwise bound vortices' influence is not considered in downwash compuation for the induced drag.

sbaffini · August 9, 2017, 07:00

If you look the neglected part, which is span aligned, you can see that it is a 2D like component which doesn't produce drag. I quote: "while the drag force, which is created by turning the two-dimensional lift vector by the wake-induced flow, becomes:", Katz&Plotkin, pp.173.

Put differently, is the spanwise variation of the circulation which is responsible for the induced drag.

Put still differently (see equation 8.12), it is the wake induced angle which modify the free stream angle of attack to produce the effective angle of attack.

Sehwan · August 13, 2017, 23:21

Thank you for your reply, Mr. Lampitella.
Now I got it.

ZakBristol · September 13, 2018, 15:33

I have tried using the trailing vortex to calculate induced velocity in VLM. However, that gave an incorrect solution.

What is the correct way of calculation induced velocity and angle of attack using VLm for any given camber,

Thanks

August 9, 2017, 04:51	Induced downwash velocity for drag computation in Vortex Lattice Method (VLM)	#1
Sehwan New Member Se Hwan Park Join Date: Aug 2017 Posts: 2 Rep Power: 0	According to Low-Speed Aerodynamics by Katz and Plotkin, the downwash induced by the wing's streamwise vortex lines and the wake is used for computing the induced drag in Vortex Lattice Method. Here, I cannot understand the reason why only the trailing (streamwise) segments of the wing-bound vortices are considered in obtaining the downwash for induced drag calculation while the spanwise segments of the wing-bound vortices are neglected. In the VLM source codes, to satisfy a boundary condition at collocation points, an influence coefficient matrix is established by computing the induced velocity by the wing-bound vortices (streamwise and spanwise segments of the wing vortex rings). During the phase of the influence coefficient computation using the same subroutine, the another influence matrix can be established by computing the normal velocity component induced by the streamwise segments of the wing vortex rings with influence of the spanwise vortex segements turned off. This is used for induced drag computation. I've been following this procedure, and the prediction was accurate. However, I would like to know the reason why the spanwise bound vortices' influence is not considered in downwash compuation for the induced drag.

August 13, 2017, 23:21		#3
Sehwan New Member Se Hwan Park Join Date: Aug 2017 Posts: 2 Rep Power: 0	Thank you for your reply, Mr. Lampitella. Now I got it. sbaffini likes this.

September 13, 2018, 15:33	issues with Katz method	#4
ZakBristol Member Zack Join Date: Dec 2015 Location: uk Posts: 35 Rep Power: 11	I have tried using the trailing vortex to calculate induced velocity in VLM. However, that gave an incorrect solution. What is the correct way of calculation induced velocity and angle of attack using VLm for any given camber, Thanks

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August 9, 2017, 07:00		#2
sbaffini Senior Member Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,195 Blog Entries: 29 Rep Power: 39	If you look the neglected part, which is span aligned, you can see that it is a 2D like component which doesn't produce drag. I quote: "while the drag force, which is created by turning the two-dimensional lift vector by the wake-induced flow, becomes:", Katz&Plotkin, pp.173. Put differently, is the spanwise variation of the circulation which is responsible for the induced drag. Put still differently (see equation 8.12), it is the wake induced angle which modify the free stream angle of attack to produce the effective angle of attack.