Prandtl’s calssical lifting-line theory - Seoul National...
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Aerodynamics 2017 fall -1- Incomp. Flow over Finite Wings < 5.5. The Lifting - Surface Theory and VLM Method > Prandtl’s calssical lifting - line theory Lifting surface theory Inappropriate for low-aspect-ratio wings and swept wings A more sophisticated model must be used 3 3 sin ) ( 4 4 r r d d r x dl dV π │ │ │ π Γ │ │ │
Transcript of Prandtl’s calssical lifting-line theory - Seoul National...
Aerodynamics 2017 fall - 1 -
Incomp. Flow over Finite Wings
< 5.5. The Lifting-Surface Theory and VLM Method >
Prandtl’s calssical lifting-line theory
Lifting surface theory
Inappropriate for low-aspect-ratio wings and swept wings
A more sophisticated model must be used
33
sin)(
44 r
rdd
r
xdldV
π│││π
Γ│││
Aerodynamics 2017 fall - 2 -
Incomp. Flow over Finite Wings
< 5.5. The Lifting-Surface Theory and VLM Method >
Vortex lattice method Bound vortex filament
l/4 from the front of the panel
Control point
Centerline of the panel at a distance 3l/4 from the front
Boundary condition
Vn = V∞ sinα + w = 0
Aerodynamics 2017 fall - 3 -
Three-Dimensional Incomp. Flow
< 6.1 Three-Dimensional Incompressible Flow >
* Irrotational * Incompressible
: continuity
Velocity field
Velocity potential
Laplace’s Equation
Aerodynamics 2017 fall - 4 -
Three-Dimensional Incomp. Flow
< 6.2 Source >
2D 3D
Aerodynamics 2017 fall - 5 -
Three-Dimensional Incomp. Flow
< 6.3 Doublet >
2D 3D
Aerodynamics 2017 fall - 6 -
Three-Dimensional Incomp. Flow
< 6.4 Flow over a Cylinder / Sphere >
2D 3D
