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Current Developments: 4
papers on Wind Turbine Anaylsis
In late 2004 I started some analysis of Vawt's in trying to help two friends,
Peter Sharp and Ray Pasquan with their Vawt designs. This generated a new
method for solving momentum theory, which led to some new results for
Hawt's as well. That shows that fixing Hawt blades at 1/2 the design
apparent wind angle or 1/3 the design nominal apparent wind angle gives a
broadbanded and benign design. Click and save as target to download my trigonometric Hawt analysis, with its optimal
pitch Vawt appendix. The Hawt aspects are further developed with drag and
tip corrections and a numerical example in a followup paper to be published
by AIAA and a slide presentation.
A third helps explain the
physical basis of the BEM approximation by critically applying Glauert's
presentation of Joukowski's general momentum theory of propellors to
windmills. In my Vawt algebraic analysis ,
fixed blade Vawts are narrow-banded, caught betweeen unsteady stall at low
speed ratio; and high drag penalty and over-induction and overloading with
"turbulent" backflow at high speed ratio but robust cyclic pitch
Vawts seem more promising.
Taken together, the papers effectively justify,solve,and extend Glauert's
original Hawt aside to his propellor theory with a properly grounded, and
more conclusive and consistent BEM treatment of Hawts AND Vawts.
A general advance is the general BEM energy
flux equation to show that the induced velocity can only differ from half
the velocity change in the direction of the apparent wind.
The specific Hawt advances are: 1)Exact
solution of Glauert’s optimum rotor 2) Posing,solution and understanding of
a new robust optimum criterion 3)Drag and
tip corrections to 1)&2) 4)Proof
that normal wind regimes and windshear
favour robust blade pitch over standard min drag to lift pitch 5)Reduction of general momentum theory to
absurdium 6)More sensible simpler equations for swirl expansion and decay
7) Prediction of hub vortex bursting 8)
showing that the ordinary BEM Hawt equations mean the dissipation of all
the swirl kinetic energy added at the rotor
And Vawt advances are 1)a Hawt-and-Betz-
consistent 2 pass BEM Model 2)its analytic
solution for tangent and passive pitch Vawts at high speed ratio 3)Proof
that these Vawts are more narrowbanded than Hawts, even without stall 4)
Cam profile for a robust cyclic pitch Vawt with the same height but broader
power peak 5)Relation
of isolated blade induced drag correction to Prandtl tip correction
2) Updated Pullpump for the Flutterwell
The first Pullpump prototype on the Flutterwell was a successful testbed
for the self-snifting capability. However the original pull pump configuration
used custom seals handcrafted from plasticised PVC which were very exposed
to abrading if not jamming with dirt on a less clean well, and could not
retain the head over a calm night. The ultra-convenient foot pump PE rising
main could not be obtained at the 4" size and semi rigid 20’ lengths
with connections proved no easier than PVC, though a bit cheaper.
The current second prototype incorporates the latest pull pump
configuration developed on the foot pumps with off-the-shelf seals well
protected from dirt . The dedicated static seal has to be spring-loaded to
maintain its static conformability despite potential contact every time the
pendulum passes through center . Ordinary leather foot valves do not
statically seal completely after all the hammering of pumping, and this
leakback of head can represent a major inefficiency for windpumps with the
intermittency of the wind. In all pull pumps, the ultimate hardstop will be
the bottom of the plunger against the bottom cylinder bush.
Again to protect the static leather seal, the inner cylinder pipe has
been changed from copper to PVC and for straightness and flow efficiency
sdr 21 will be tried first. Raingun 4" PE tubes are very thick wall to
take the high spraying pressures and to avoid buckling in the powered tight
winding. The biggest size of continous thin wall PE available is 3"
which is smaller than desirable. To get a 3" cylinder one could insert
3" thin wall copper DWV which is expensive and easily dented, or glue
an exterior 3.5' metal bushing (eg. 3.5" copper DWV) to a 3" PVC
cylinder. The bushing must be long for the PE glues and to bridge an
internal gap where the shuttle seal/valve clears enough to drain the water
column. Another bushing and gap may be needed above the highest static
water level to drain any renewed water column as the shuttle is raised
This system should allow one person to put
the entire pump into a high yield 4" deep well even through the
Flutterwell’s yaw bearing though the base will be redesigned to avoid
this..
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