Ideal Flow Machine

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Examples
The following are some suggestions for some simple but interesting flows you may like to try

Using the ideal flow machine without mapping window...

Flow around a porous flat plate with blowing. Default free stream. Vertical source sheet of strength 2. Sheet may be any length but the result will be most satisfying if it covers about half of the total grid height.
Flow past a circular cylinder. Freestream, strength 1, angle 0 (the default). Doublet, strength 10, angle -180, at the center of the grid).
Flow past a circular cylinder with circulation. Same as above plus a vortex of any strength (say -5), on top of the doublet. (This is analogous to the flow past a spinning baseball.)
Flow past a Rankine halfbody. Default freestream. Source strength 5 at the center of the grid.
Flow past a Rankine oval. Same as halfbody but add a source of equal negative strength at the same height, but to the right of the original source.

Using the mapping window...

Outside corner flow (z-plane,z1-plane).
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 (z-plane,z1-plane).
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 (z-plane,z1-plane).
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') (z-plane,z1-plane).
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 (z-plane,z1-plane).
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 4.0. Last HTML/Applet update 8/20/98. Questions or comments please contact William Devenport