Whirly Aerodynamics

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2003-12-14 Rev. -12-17, -12-21, -12-29, 2004-01-01, -01-15, 2005-06-24, -12-09,
2007-03-04, 2008-01-22, 2010-02-15, -12-11, -12-30
[Search on date pattern to find latest changes, more than one may be found.]

Aero Intro
Wind Tunnel

Whirly Jig Page
www.windpower.org
Illustrated History of Wind Power

 

Whirly representation with wind arrowWhen I went exploring the Internet to get some information and suggestions about shapes of the ends of my whirlies, I found I was having to dig bits and pieces up from the depths of odd web sites like wind energy and weather and human powered vehicles (80 mph).  In particular, nothing came up on the lift effects of side mount hemispheres as on anemometers.  A spinning cup anemometer is considered a drag instrument (unlike a propeller anemometer.)

In the image, the wind is blowing from the top.  There are four forces applied to the whirly as shown.  Each force has its own moment arm R (center of rotation to center of force of the cup.)  Of the two drag forces F1 is bigger than F2 (next paragraph) and is usually the only force discussed.  But F3 and F4 both act clockwise.  Whether they are the same force or different depends on the cup shape (like the lack of symmetry here) and what is in the way (many anemometers have a good sized hub.) 2003-12-31

I learned early that the anemometer cup has totally different drag when it is open side upwind as opposed to dome side upwind.  This is the Drag Coefficient (Coefficient of Drag, CD or Cd), [http://www.windpower.org/ Site still exists, page with data now gone] which is "defined as the drag force per square meter frontal area of the object."] A round cup open upwind "has a very high CD of 1.42, whereas its CD is only 0.38 if you turn it 180 around a vertical axis." For other shapes: "A flat plate has a Cd of 1.28 while a prism (pointed tail) is 1.14 and a bullet 0.295 which is calculated with the formula Cd = D / (.5 * r * V^2 * A) where drag (D) is measured in a wind tunnel with density (r), velocity (V) and area (A) being measured." http://wright.nasa.gov/airplane/shaped.html   eSearch of 'wind drag of a cone' yields this site http://www.aerospaceweb.org/question/aerodynamics/q0231.shtml  which has point on ratings down the page of many shapes and discussions of why drag changes with wind velocity. Also links to other sites.   Start of a history of wind power with some drag discussion http://www.telosnet.com/wind/early.html 2010-12-11 [Lately I found
"The three cup anemometer developed by the Canadian John Patterson in 1926 and subsequent cup improvements by Brevoort & Joiner of the USA in 1935 led to a cup-wheel design which was linear and had an error of less than 3% up to 60 mph (97 km/h). Patterson found that each cup produced maximum torque when it was at 45 degrees to the wind flow. The three cup anemometer also had a more constant torque and responded more quickly to gusts than the four cup anemometer."
"The three cup anemometer was further modified by the Australian Derek Weston in 1991 to measure both wind direction and wind speed. Weston added a tag to one cup, which causes the cup-wheel speed to increase and decrease as the tag moves alternately with and against the wind. Wind direction is calculated from these cyclical changes in cup-wheel speed, while wind speed is as usual determined from the average cup-wheel speed." [and obviously requires measuring speed finely around the circle, not just rpm MF]  From http://en.wikipedia.org/wiki/Anemometer  2010-12-30]

While this difference in drag should be enough to make revolving occur, it does not explain the better performance of my units with a flange which adds drag, but which should add to the aerodynamic lift with upstream and downstream (edge on).  In the drawing, which represents the 4 extreme positions of a cup (upwind, downwind, cup to wind, dome to wind) the two side positions are drag, where the flange adds to drag equally while the dome has extreme difference as mentioned above. Choice of shapes for whirlies The upwind and downwind positions should be developing thrust (clockwise in this drawing), but how much? And how does having the cup open or flat across the opening make a difference?

I have a good sized squirrel cage blower that I kept out of the house furnace when we changed it recently - 3 speeds.  I had planned on using it to replace the blower from the swamp cooler that is mounted in the garage, but a wind tunnel sounds useful.

I went out and wired up the blower to medium and fixed up a switch.  Turned it on - lots and lots of wind, maybe too much.

The wind tunnel design will be fairly simple - a lead in section with a grid to straighten the air, a test section and a bit of out flow area, perhaps with another grid.  The test section has to allow for testing two kinds of force - drag along the air stream and lift across the air stream.  If I make the wind tunnel moveable, I could do a blow up or blow down as well as blow sideways.  The up or down could make measuring drag easier as it could be straight lifting of a weight instead of around a pulley.  It should be square, I guess for repositioning ease.  I will continue to explore the Internet and sketch.

I have been thinking more about building a wind tunnel.  With my usual impulsiveness, I pulled some wood that might make a box, then, with my somewhat less usual reserve, backed off from doing anything without a design.  During the day I sketched on a design with a completely different shaped box that focused on solving the measurement and balance devices, which evolved to a square box just for this and the blower and grill attached separately.  Also e-mailed Texas A&M about their wind tunnel and usage! [$350/hr]

 

"To measure the "lift" and "drag" of the models in the testing section, we used two Force probes from Vernier Instruments " http://www.fi.edu/flights/first/makebigger/index.html
 [Actually Vernier Software & Technology 13979 SW Millikan Way Beaverton, OR 97005-2886 phone 888.837.6437 fax 503.277.2440 email info@vernier.com ]

The Dual-Range Force Sensor has two ranges: 10N or 50N. It can be easily mounted on a ring stand or dynamics cart (mounting bracket included), or used as a replacement for a hand-held spring scale. Use it to study friction, simple harmonic motion, impact in collisions, or centripetal force. This force sensor is used for experiments in our physics, physical science, and middle school science lab manuals.
 
Dual-Range Force Sensor
DFS-BTA (For LabPro, CBL $99.00

 

    DFS-DIN (For ULI and Serial Box) $98.00

 

 
Well, that shoots this idea down, since I would need two, plus the interface, plus the software.  Even the individual gauges from other sources cost $45 or so.  Back to the balance scale idea.
These are the drawings, based on hand sketches done away from the computer, that work out the problems of a wind tunnel, adding the balances needed after concluding I did not want to spend the money for sensors.

The first design consideration was to be able to store the thing after having built it.  That means it has to defend itself (no odd bits sticking out) and fit in a 2x2 foot stack as do my various storage boxes.  To the right is the test section.  The upper half is fronted with 1/4" Plexiglas for viewing and some strength.  The back is 1/2" plywood for strength while the bottom section and top are 3/4" board for the same reason.  [As actually built, the upper front and top are a bent 1/4" Plexiglas sheet.]  Below is the sequence of blower, transition, straightening grill and test section.  The blower is one taken from my old furnace and may be too strong.

In the test section, the following factors are built in:  Not being able to accurately remount the test shape, it will be mounted on a turnable mount - a shaft with a square top section and a moderately flexible coupling at the bottom to a handle on a pivot.  The force will be measured by pulling from upstream and from the back (lower drawing) so mounting will depend on anticipating the forces.  The pulleys are grooved ball bearing replacement rollers for glass patio doors, washed clean with solvent and lightly oiled for ease of movement. I have a choice of putting weights on the scale pans or adjusting the pull on a spring and working out the force per inch of the spring. 2003-12-21

Wind tunnel drawing
Full blower layout drawing
A lot of additional problems.  If the shapes are made of sheet metal, the square shaft mount I was thinking of will interfere with air flow, perhaps too much.  I did some calculations with force and e-mailed a guy at NASA who confirmed that we are talking some pretty small forces. I wanted to be sure I had the correct result.  A 3"x3" flat plate (75x75 in the calcs) in a 10 mph wind at normal air density has only 1/3 ounce of force! 2004-01-01
Flat plate Cd = 1.28 0.093 N 0.3345 oz
Anemometer cup: Open end 1.42 0.10317 N 0.37109 oz
Domed end 0.38 0.02761 N 0.09931 oz
 I see why the Wright brothers did such a delicate balance with a drag plate formula.

 

Drawing of wind tunnel turntable version2004-01-09  I am continuing by building a basic test bed.  Instead of the box above, I am building a flat plate. The plate has two layers, the upper with a circle cut free on which are mounted a bar and a pulley.  The bar, lower center, pivots near the edge and supports an upright 532" square tube.  On this tube are to be mounted curved shapes, Plexiglas first, perhaps metal or glass later.  The wind will come from the left.  Weight will be placed on the hook below tied to a string to the center to keep the shape at the center.  By picking up the shape and reversing it, drag in various positions for the same wind can be tested.  The looping C shape is a slot cut in the lower piece of plywood, which permits the upper disk to be rotated right or left so the weight can indicate lift, two sides permitting either orientation for unsymmetrical pieces, like my existing glass.   Note that the unit can not measure drag and lift together or in quick sequence by rotating the piece as the one above can. [2004-01-15]  Ran the wind tunnel for the first time today, having installed the side and roof panels. Did not try to push in and reduce wind.  The mount is clearly too wobbly and the disk is somewhat off the centerline.  Shows lift, but needs more control and rigidity to be accurate.
 

2004-01-20  When I ran some further experiments, I feel I could demonstrate that there was reasonable lift, but I also demonstrated that rigidly mounting the shape on a square tube on the arm resulted in odd angles and difficulty adjusting the angle to zero.  One solution would have been to reconstruct the arm only to parallel arms with the test form mounted on a connector arm, always perpendicular to the wind, on a pivoting mount.  But there were several other irritating factors, like the weight of the hook, limits on centering the arm, etc.,  that I decided to put the effort into building something closer to the design further above where the model is on top of a pivoting post and measuring is done below.  Drawing of wind tunnel balance
I am changing the design to omit the pulleys and have balance arms directly on the vertical post.  Two nights ago, I made up the base disk and epoxied to it tubing for the lower pin and a 1/4" socket drive universal joint with square tubing to make a spline like connection. [drawing and picture below]  Upper arm ends are round tubing soldered into holes drilled in square tubing arms to hold nuts.  All carefully balanced with extra lead solder.  Tonight I found a back wall - 2x2x0.5" plywood and cut the shelves and the end pieces, drilling the shelves to align the pivot hole and the riser tube clearance hole. Glue it up in the warmer part of the day Thursday. Photo of wind tunnel balance
2004-02-19 - Did my first rough run with the new wind tunnel balance, very rough.  The basic results came out correctly and it seems possible to make some reasonable measurements, but so far the calculations (guessing at wind speed) are only bulk answers.
  I weighed two full boxes of nuts at work on the postal scale (to 0.1 ounce) and found that standard coarse 1/2" hex nuts weight 16.7 gm and 1/4" weigh 3.3 gm, which is nice because 5 1/4" nuts (16.5 gm) just about equal one 1/2" nut.  The ratio of the horizontal arms to the upright, from the pivot is 0.316, the gram weight is given under Arm. Adj. and the force in Newtons under N.
  As shown, the flat has 0.300N force, the Cup upwind 0.383N, Cup downwind 0.238N and the lift of the cup sideways is 0.093N.  Thus the difference in forces of drag is 0.145N or about 1.56 the cup sideways, but there would be two sideways in a 4 cup arrangement, so lift contribution should be about 0.310N vs. 0.145N for drag.  Similar work can be done with the P-Curve but it is harder to get reliable figures without more care since misalignment with the tail produces considerable changes. 2005-06-24

Object

Weight
Arm

Vertical
Arm

 

Force

Area

length

length

ratio

1/2"
nuts

1/4"
nuts

Arm Adj.

N

A

mm

mm

each>

16.7

3.3

gm

gm

(Drag/Lift)

m^2

Sample

125

250

0.5

3

2

56.7

28.35

0.278

drag

0.0056

Flat

136.525

431.8

0.316

5

4

96.7

30.57

0.300

drag

0.0056

Semi-C up wind

136.525

431.8

0.316

7

2

123.5

39.05

0.383

drag

0.0056

Semi-C down wind

136.525

431.8

0.316

4

3

76.7

24.25

0.238

drag

0.0056

Semi-C cross wind

136.525

431.8

0.316

1

4

29.9

9.45

0.093

lift

0.0028

Flat

136.525

431.8

0.316

7.5

125.3

39.60

0.388

drag

0.0056

P-Curve curve up wind

136.525

431.8

0.316

11

183.7

58.08

0.569

drag

0.0092

P-Curve curve dn wind

136.525

431.8

0.316

11

183.7

58.08

0.569

drag

0.0092

P-Curve tail up wind

136.525

431.8

0.316

1

16.7

5.28

0.052

lift

0.0028

P-Curve tail dn wind

136.525

431.8

0.316

1

3

26.6

8.41

0.082

lift

0.0028

 

 I need to buy another bike speedometer to calibrate the anemometer, since doing it in a car alone did not work.  I should probably enclose the wind tunnel test section as I felt I could feel a difference on my hand from the open side to the back wall.  [Did in fact enclose it] [Did buy another speedometer - 2 actually at Wal-mart - but have not yet calibrated it. Quiet air with enough light to make run in park. 2005-06-24]

The composite image below shows various views and details of the wind tunnel  
Upper left shows the relationship of the two sections from the back.  From left to right are the square test section, the long adjustable inflow area and the blower.  The blower is mounted on a plywood panel and can be stood upright at the right end.  The side walls of the inflow area are fastened to a rigid 1x4 collar near the test section and can be flexed in to cut down on the portion of the blower air taken in and thus the velocity (lower left). 
 The inflow area leads into the test section which is framed with a plywood back and bottom and a bent Plexiglas cover on two sides. (center bottom) 
Test section has two parts: the upper holds the shape on a rod from the measurement section below (right) all in a 2x2' box.  The upper end of the rod is 1/4" square to take fittings on the shapes.  A largish hole restricts the movement of the rod.  Off the bottom section of the rod are 4 equal arms with posts at the end, all the same weight.  A swivel from a 1/4" socket driver allows the rod to pivot (restricted by the hole at the top) while telescoping brass tubes permit rotation.  Using carefully weighed 1/2" and 1/4" bolt nuts, the forces on the shape can be balanced so the rod stays vertical in the center of the hole.  Slight friction of the pivot helps in centering. 2005-02-21
 

Wind tunnel montage

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