| Unsteady Aerodynamics
as a Basis for AWE
Overview:
Unsteady aerodynamics is the messy real-world reality of all kite flight.
As oscillation fundamentals are understood & mastered, the conceptual
basis for AWE greatly expands.
Review:
Mechanical power typically involves a drive-train of rolling stress-wave
wave-guides called wheels, with only a fraction of embodied structure
actively loaded. Just as a cyclist pedals a bicycle, oscillating power
converts to continuous rotation by cranking levers. A lever does the work
of a far larger wheel with just a fraction of full wheel structure, but
over a limited, reversing, rotation range. Ancient lever variants confer
design flexibility, for example, a bell-crank re-vectors force
orthogonally.
Levers make lower fundamental harmonic operating modes practical, without
giant wheels. In bio-locomotion, this means flapping wings driven by
tendons. In AWE, wind-driven bio-mimetic foils, string, & levers can drive
generators.
The standard wind turbine is an expensive & massive object. To fly far
fancier specialized turbines at larger & larger scales means weight & cost
soon become critical, then hopeless. Flygens hardly help. Desperate
chasing of high-performance by the forced trading-away of
inherent-stability grows dependence on active flight-automation.*
Like basic turbines, practical oscillating wings are passive-controlled,
self-regulated by tuned coupled aero, inertial, & elastic forces. The
challenge is to optimize every phase of oscillation. Special lift
mechanisms in unsteady aerodynamics are a plus, offsetting discontinuous
trade-offs.
All in all, tensile mechanical-advantage driven by short-period kite-wing
oscillation is a major AWE scaling & cost solution.
Case Study: The Wing-Mill
Long reeling-cycles are a popular oscillation mode in many pioneering AWE
concepts. The recovery phase gap in generation is awkward. Short-period
loops & figure-of-eights, with brief embedded recovery phases at the upper
turns, are an effective alternative.
Self-oscillation is simple for a flapping-wing membrane wing-mill. A
tip-hung kite-wing is naturally sensitive to disturbance & tends to
self-oscillate in wind like a flag by a mix of pendulum &
unsteady-aerodynamic forces. Dutch-Roll oscillation, a major short-period
dynamic mode for conventional kites, traces frontal figure-of-eights.
Suspended wing-mill fly oblique eights. Characteristic motion of various
wings can range from a tight waggle suitable for close formations to
wide-swept lazy-eights.
A wingmill's flapping cycle outputs strong sinusoidal or sawtooth power
pulses. A high-amplitude-spike occurs by an air-hammer effect, as a
low-stretch wingmill "pops" on each tack. Optimal pre-tension of hung
wingmill is low static tension, with no slack in the relaxation/recovery
phase.
Current membrane wingmills are not too high in aspect ratio or the
flapping breaks up into subharmonics; there is easy usable power in a
broad working wing of L/D of ~5-15.
The right sort of tail on a hung wing-mill acts is a tuned oscillation
promoter & regulator. Flag motion is mostly unsteady-aerodynamic, with
some inertial action. Whip-lashing is the inertial component. [see links
below] Of all the world's country flags, Nepal's is uniquely
shape-optimized to flap in thin air & survive storms.
The critical speed for reliable flapping onset is set by the design. Early
onset can be triggered by a control nudge. Flapping frequency is dependent
on the wing's characteristic-length harmonics (span & chord), windspeed,
and line tension. An added kite-tail hosts a parade of aero-inertial
transverse waves, with back-reflected longitudinal waves promoting regular
self-tacking of the forebody wingmill. Quality flapping is a resonance
between a fundamental oscillation mode of the leading-edge wing & coupled
oscillations of the tail-flag.
Useful power is fundamental mode vibration; higher modes are parasitic.
Local short-period harmonics are damped out of the forewing by battens or
membrane stiffness, but tolerated toward the tapered tailend as a minor
stability cost.
Unsteady-Aero Operational Constraints:
Long-period reeling-cycles wear on kiteline. Short period cycling can
avoid reeling wear altogether or rely on small sections of ruggedized line
at pulleys or capstans.
Flogging, as destructive sail flapping is called, is a manageable wingmill
design issue. The British Admiralty's vast experience flogging flags
offers lessons: Re-hem flags as they fray; premature fraying is mostly
high-wind damage; a flag brought down when gale threatens lasts many
years. Passive flogging mitigation is workable: Ease halyard tension or
add a "cut-out" mechanism like the simple self-furling of an elastic lower
corner attachment. KiteLab has flown membrane wingmills for thousands of
hours from trees, thru many storms, & long hours under kites, without wear
as a problem.
High-wind flags are made smaller & thicker. This characterizes scaling
limits to membrane wing-mills, which with current materials can grow to
nicely to 1000m scale, but not much more; after which populous arrays
offer ultimate scalability.
In sailing, non-prepreg carbon fiber sandwiched between Mylar membrane is
reputed flog-damage resistant.
Cuben fiber, based on
UHMWPE, is also considered robust. Its
practical to make fairly large "solid" wing-mills of foams like EPP, but
even low-tech materials like bamboo & cardboard can comprise an unsteady
wing to power home or village.
There is an art to designing and tuning unsteady short-period systems for
utmost performance across wide wind ranges.
Conclusion:
Unsteady aero-to-mechanical dynamics is a fundamental basis for AWE.
Optimized unsteady aerodynamic performance is a key to success.
==================
* Toy-kite drag-stability and aerospace-UAV actuation-overhead are roughly
comparable control performance versus cost trades. Its as if a bulk
communications-theoretic thermodynamic burden is placed on intensive
aircraft control of any kind. Still, the kite trumps by safety,
simplicity, and scalability.
Links:
Previous work on flag physics is lead by-
Zhang Lab
Whip physics as studied by another lab-
Shape
of a Cracking Whip by Alain Goriely and Tyler McMillen
2002
CoolIP
~Dave Santos ,22Oct2010
M2369
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