Examples
The following are some suggestions for some simple but interesting
flows you may like to try
- Outside corner flow.
Flow in z-plane: Default free stream (any strength, angle=0).
Mapping: s = az^b with a=1, b=1.5 (critical point at the origin).
Streamlines: Click the mouse toward the left hand side of the grid at points above
the x axis. Clicking below the axis reveals another branch that overlaps the initial corner flow.
Notes: Changing the value of b in the mapping changes the angle of the corner, see the inside corner
example below.
- Inside corner flow.
Same as above, but with b=.5 (or anything less than 1) in the mapping, no critical points.
Notes: Choosing a value for 'a' less than 1 (say 0.5) will enable you to see more of the
mapped flow domain.
- Flow around a Joukowski airfoil.
Flow in z-plane: Free stream (any strength, any angle). Circle with k.c. centered
at about x=-.2, y= .2, Kutta condition at x=1, y=0.
Mapping: s = a(z + b/z) with a=1 and b=1 (critical points at x=+-1, y=0).
Streamlines: Click the mous to the left hand side of the grid outside the circle. Streamlines inside the circle map
to another branch of the flow that overlaps the airfoil flow.
Notes:You may vary the angle of attack of the airfoil by varying the free stream angle. Choosing the center
of the circle more to the left increases the thickness of the airfoil. Moving the center up results in an airfoil with
more camber. Note that, if you want a sharp trailing edge and a realistic mapped flow, then the circle must always
pass through x=1, y=0 with the Kutta condition located there.
- Flow out of a duct (the 'Borda Mouthpiece').
Flow in z-plane: Default free stream (any strength, angle = 0).
Mapping: s = a(exp(bz) + bz) with a=.5 and b=2 (critical points at x=0 y=+-PI/2).
Streamlines: Click the mouse to the left hand side between y=-1.57 and 1.57. Outside
of this range you will reveal other branches of the flow that overlap the duct exit flow.
Notes:You may vary the angle of attack of the airfoil by varying the free stream angle. Choosing the center
of the circle more to the left increases the thickness of the airfoil. Moving the center up results in an airfoil with
more camber. Note that, if you want a sharp trailing edge and a realistic mapped flow, then the circle must always
pass through x=1, y=0 with the Kutta condition located there.
- Flow over a half-body between parallel walls.
Flow in z-plane: Source at the origin, source at y=0, x=-1 of same strength.
Mapping: s = a.ln(z)-ib with a=0.5, b=PI/2.
Streamlines: Click mouse at a selection of points surrounding the origin.
Notes: It is possible to get flow past a closed body (a near circle) by adding a source of equal and
opposite strength to the others at y=0, x=-1.5 (i.e. a sink). The left hand source can alternatively
be replaced by a doublet to produce a similar effect.
Current Applet Version 1.0. Last HTML/Applet
update 11/11/96. Questions or comments please contact
William Devenport
