Fluid reaction surfaces (i.e. – impellers) – Specific blade structure – Radial flow devices
Reexamination Certificate
2000-05-01
2003-01-07
Look, Edward K. (Department: 3745)
Fluid reaction surfaces (i.e., impellers)
Specific blade structure
Radial flow devices
C416SDIG002, C416SDIG005
Reexamination Certificate
active
06503058
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The subject invention is generally related to wind power turbines and is specifically directed to a family of airfoil configurations for optimizing the performance of the wind turbine.
2. Discussion of the Prior Art
Wind power turbines are well known. The turbine blades or airfoils are one of the primary factors in determining the efficiency of the system and thus are a critical factor in optimizing performance. Typically, the turbine rotor blade design proceeds by first identifying a family of airfoils to be employed and then determining the optimum spanwise distribution of solidity and twist in order to optimize the power coefficient at each spanwise location. This procedure often does not result in the structurally optimal blade for the specific application. Various efforts to optimize the blade configuration have been used over the years, with varying results.
By way of example, Zond Energy Systems, Inc. (the Assignee of the subject invention) has generally used a thinner airfoil configuration than its European counterparts. For example, the 34 meter blades manufactured by LM Glasfibre for Tacke's 70 meter TW1.5s system employ a 39% thick section at the 25% spanwise location as compared t a 24% thick section on the comparable Zond Z46/48/50 blades. Even at 40% span, the airfoil section is 30% thick. This has a significant impact upon drag, reducing the energy capture from these blades by as much as 10%.
Turbines currently on the market have rotor loading of approximately 0.42-0.45 kW/m
2
for machines certified IEC Class 1, 0.38-0.41 kW/m
2
for Class 2 and 0.33-0.38 kW/m
2
for Class 3. Taking a given wind turbine and then scaling both the rotor and drive train, including the generator, in proportion to each other it is a fairly straightforward series of calculations to determine the dependence of blade loads upon rotor size. If it is assumed that the rotor aerodynamics and solidity remain constant as the rotor is scaled, then the rated wind speed will remain constant for the various sized machines. For a turbine such as Zond's 750 kW series, the tip speed of 85 m/s is approximately the higher limit. Using this as a fixed tip speed, in can be determined that the rated shaft speed will scale inversely to the rotor:
&OHgr;
rated
=V
tip
/R
(Equation 1),
where &OHgr;
rated
is the rated shaft speed, V
tip
is the fixed tip speed and R is the rotor radius.
Since the rated power, P
rated
, scales as the rotor diameter squared for a fixed rotor loading, and since the rated power is a product of the rated torque and the rated shaft speed, it follows that the rated torque scales as the cube of the rotor diameter:
&OHgr;
rated
=P
rated
/&OHgr;
rated
=½(&rgr;
V
3
rated
C
p
&pgr;R
2
)(
R/V
tip
)−
R
3
(Equation 2)
The rated torque results from the in-plane aerodynamic forces acting over the length of the blade. Mathematically, it results from the summation of the product of theses forces and the moment arm over the length of the blade:
Q
rated
=
∫
r
hub
R
F
x
(
r
)
r
ⅆ
r
=
R
2
∫
r
hub
/
R
1
F
x
(
r
/
R
)
(
r
/
R
)
ⅆ
(
r
/
R
)
(
Equation
3
)
Where F
x
represents the in-plane forces per unit length.
The mathematical model for all wind turbine airfoils follows these equations. What remains is to develop a better understanding of these models in order to maximize airfoil design. At present certain aspects of the design are not clearly understood and the resulting airfoil designs of the prior art are less than optimum.
SUMMARY OF THE INVENTION
The combination of aerodynamic optimization and structural optimization in accordance with the teachings of the invention results in a new and novel airfoil design having substantially improved performance characteristics of airfoil designs of the prior art. The aforementioned mathematic modeling yields maximum aerodynamic criteria. This is then coupled with a structural analysis to modify the optimum aerodynamic design into a balance, substantially optimized airfoil configuration. The resulting airfoils of the subject invention have substantial performance impact on GAEP when compared to the airfoils of the prior art. The subject invention is an airfoil design based on the theoretical optimum aerodynamic structure modified as required to maximize structural integrity.
The subject invention is the result of an effort to maximize and optimize airfoil configuration and design by determining the important characteristics of the mathematical definition of the airfoil consistent with the above prior-art recognized mathematical modeling.
This procedure provides the criteria for maximizing airfoil performance to achieve highest GAEP while taking into consideration the aerodynamic design parameters as balanced against structural requirements. The methodology of the subject invention permits the design of airfoils of predictable performance while achieving necessary structural integrity.
As a result of this approach, the subject invention has resulted in a family of airfoils having operational and structural characteristics with substantially enhanced performance capability over prior airfoils used in the same or similar applications. The family of airfoils includes thickness-to-chord ratios ranging from 14% to 45%.
In accordance with the invention, if the rotors are scaled up proportionately (i.e., the solidity remains constant), then substitution of Equation 2 into Equation 3 results in the conclusion that F, at any equivalent spanwise location (i.e., r/R) scales as the rotor diameter:
F
x
≈R
(Equation 4)
For high lift-to-drag ratios, the in-plane forces in the outboard regions that dominate the structural loads result largely from the product of the dynamic pressure, the chord length, the lift coefficient, and the in-flow angle:
F
x
=q
rated
cC
1
sin &PHgr; (Equation 5)
where &PHgr; is the inflow angle.
Since the rotor is being scaled up, the chord, c, also scales as the rotor diameter. Since the rotor loading remains constant, q
rated
and sin&phgr; remain constant, it follows from Equations 4 and 5 that C1 remains constant along the blade as they are scaled up. Since none of the flow angles or blade geometry changes other than being scaled up, it follows that the out-of-plane forces per unit length also scale as the rotor diameter:
F
x
=q
rated
cC
1
cos &PHgr;≈
R
(Equation 6)
Therefore, the flapwise blade root bending moment My
rated
also scales as the rotor diameter cubed:
M
yrated
=
∫
r
hub
R
F
y
(
r
)
r
ⅆ
r
=
R
2
∫
r
hub
/
R
1
F
y
(
r
/
R
)
(
r
/
R
)
ⅆ
(
r
/
R
)
≈
R
3
(
Equation
7
)
In the subject invention, it has been determined that when the rotor is scaled up in diameter (keeping the solidity constant), while the rated power and tip speed both remain constant, the rated wind speed drops as the rotor diameter increases, according to the well-known relationship:
P
rated
=(½)&rgr;
V
3
rated
C
p
&pgr;R
2
(Equation 8)
Assuming the rated power is constant, this yields:
V
rated
≈R
−½
(Equation 9)
This leads to the conclusion that the rated tip speed ration, X, increases with the rotor diameter:
X
=(
V
tip
/V
rated
)≈
R
−⅔
(Equation 10)
For a constant tip speed.
In this instance, Equation 2 becomes:
Q
rated
=P
rated
/&OHgr;
rated
=P
rated
(
R/V
tip
)≈
R
(Equation 11)
Substituting Equation 3 into Equation 11, this yields:
F
x
≈1
R
(Equation 12)
Which is dramatically different than previously assumed. Looking again at Equation 5, in the methodology of the subject invention the dynamic pressure at outboard station is dominated by the tangential velocity, so the drop in rated wind speed has little effect on the dynamic pr
Selig Michael S.
Wetzel Kyle K.
Look Edward K.
McAleenan James M
Zond Energy Systems, Inc.
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