{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

f18_fall

# f18_fall - Fluids Lecture 18 Notes 1 Prediction of Lift 2...

This preview shows pages 1–3. Sign up to view the full content.

Fluids – Lecture 18 Notes 1. Prediction of Lift 2. Vortex Sheets Reading: Anderson 3.17 Prediction of Lift Limitations of Source Sheets A point source has zero circulation about any circuit. Evaluating Γ using its definition we have Γ ≡ − vector V · dvectors = V r dr = r 2 r 1 Λ 2 πr dr = Λ 2 π (ln r 2 ln r 1 ) = 0 which gives zero simply because r 1 = r 2 for any closed circuit, whether the origin is enclosed or not. A source sheet, which effectively consists of infinitesimal sources, must have zero circulation as well. x y V ds dr r 1 r 2 Λ Γ=0 λ Γ=0 This zero-circulation property of source sheets has severe consequences for ﬂow represen- tation. Any aerodynamic model consisting only of a freestream and superimposed source sheets will have Γ = 0, and hence L = 0 as well. Hence, lifting ﬂows cannot be represented by source sheets alone. This limitation is illustrated if we use source panels to model a ﬂow expected to produce lift, such as that on an airfoil at an angle of attack. Examination of the streamlines reveals that the rear dividing streamline leaves the airfoil off one surface as shown in the figure. The model also predicts an infinite velocity going around the sharp trailing edge. V source sheet model reality smooth flow−off (Kutta condition) Γ=0 =0 L’ L’ Γ>0 >0 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
On real airfoils the ﬂow always ﬂows smoothly off the sharp trailing edge, with no large local velocities. This smooth ﬂow-off is known as the Kutta condition , and it must be faithfully duplicated in any ﬂow model which seeks to predict the lift correctly. Changing
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

f18_fall - Fluids Lecture 18 Notes 1 Prediction of Lift 2...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online