WO2007035758A1

WO2007035758A1 - Wind turbine blade comprising a boundary layer control system

Info

Publication number: WO2007035758A1
Application number: PCT/US2006/036526
Authority: WO
Inventors: Pasquale Michael Sforza
Original assignee: University Of Florida Research Foundation, Inc.
Priority date: 2005-09-19
Filing date: 2006-09-19
Publication date: 2007-03-29

Abstract

A blade (such as a wind turbine blade) that is adapted to be operably attached adjacent a rotatable hub, the blade defining: (1) a fluid inlet disposed adjacent a proximal portion of the blade; (2) a fluid outlet disposed adjacent a distal portion of the blade; and (3) a centrifugal flow passage that extends within an interior portion of the blade between the fluid inlet and the fluid outlet. The fluid inlet is preferably in gaseous communication with the fluid outlet via the centrifugal flow passage, and the blade is configured so that, when the blade is rotated about the hub at a particular velocity, fluid is drawn into the fluid inlet, moved through the centrifugal flow passage, and expelled out of the fluid outlet. The fluid is preferably compressed as it moves through the centrifugal flow passage.

Description

WIND TURBINE BLADE COMPRISING A BOUNDARY LAYER CONTROL SYSTEM

BACKGROUND OF THE INVENTION

Helicopters, wind turbines and other mechanical devices include rotating blades that are attached to a rotating hub and that extend in a radial, outward direction from the hub. For example, Figure 1 illustrates a wind turbine with blades 10 attached to a hub 20, and Figure 2 illustrates the outer profile of one of the turbine's blades 10. As shown in Figure 2, each blade 10 includes a leading edge 12, a trailing edge 14, a pressure surface 16, and a suction surface 18.

As the blade 10 is rotated about the hub, air flows from the blade's leading edge 12 to the blades' trailing edge 14 and a boundary layer forms along the surfaces of the blade 10 due to the friction between the air molecules and the surface of the blade 10. As the air molecules within the boundary layer move along the surface of the blade 10, this friction causes a loss in momentum, and eventually, the molecules in the boundary layer lose energy, causing the boundary layer to separate from the blade 10. When the boundary layer separates from the blade 10, a separation bubble forms behind the point of separation, which creates additional drag on the blade 10. In addition, the location where the boundary layer separates from the blade 10 can fluctuate, causing unstable areas of pressure around the blade 10.

Furthermore, radial momentum causes the air pressure on the blade 10 to increase as the radius from the hub 20 increases, which gives rise to centrifugal effects on the blade 10. In particular, as shown in the below equation in which p is the density of the air adjacent the blade and ω is the angular velocity of the blade 10, the pressure, p, increases as the radial distance, r, from the hub 20 increases.

— Φ = pω 2 r dr

The above-referenced centrifugal effects often disturb the boundary layer on the rotating blade 10, particularly at: (1) the blade's proximal end 24, which is adjacent to the hub 20; and (2) the blade's distal end 22.

Thus, there is a need for improved blades that are configured to perform with reduced boundary layer separation adjacent the blade. BRIEF DESCRIPTION OF THE DRAWINGS

Reference will now be made to the accompanying drawings, which are not necessarily drawn to scale, and wherein:

Figure 1 is a schematic illustration of a wind turbine.

Figure 2 depicts the outer profile of the blade shown in Figure 1.

Figure 3 illustrates a blade according to one embodiment of the invention.

Figure 4 illustrates a blade according to a further embodiment of the invention.

Figure 5 illustrates a blade according to yet another embodiment of the invention.

Figure 6a depicts a turbine blade coordinate system according to a particular embodiment of the invention.

Figure 6b shows the location of an exemplary separation boundary on a rotating wind turbine blade.

Figure 7 is a schematic diagram of a rotating blade having a passive boundary layer control system. The thickness of the blade is not shown in this figure.

Figure 8 is a schematic diagram of an internal compressor passage through a rotating blade. This figure shows axial inlet flow through the blade's porous inboard surface and the velocity triangle at the blade's outlet.

DESCRIPTION OF VARIOUS EMBODIMENTS OF THE INVENTION

Various embodiments of the present invention will be described more fully hereinafter with reference to the accompanying drawings. However, it should be understood that this invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Like numbers refer to like elements throughout. Blades (e.g., turbine blades) according to various embodiments of the invention are configured to perform with reduced boundary layer separation by drawing air into the blade (e.g., adjacent, and preferably immediately adjacent, the blades' proximal end) and expelling air out of the blade (e.g., adjacent, and preferably immediately adjacent, the blades' distal end). As shown in Figure 3, in one embodiment, the blade 10 includes: (1) an air inlet 101; (2) an air outlet 103; and (3) a centrifugal flow passage 105 extending within the blade's interior between the air inlet 101 and the air outlet 103.

In various embodiments, the air inlet 101 is disposed between the proximal end 24 of the blade 10 and a portion of the blade that is halfway between the blade's proximal and distal ends, and the air outlet 103 is disposed between the distal end 22 of the blade 10 and a portion of the blade 10 that is halfway between the blades proximal and distal ends. As the blade 10 rotates, the centrifugal effect resulting from the radial momentum of the rotating blade 10 draws air into the air inlet 101, compresses the air as it moves through the centrifugal flow passage 105 toward the distal end 22, and expels air out of the air outlet 103.

In certain embodiments of the invention, such as the embodiment shown in Figure 3: (1) the air inlet 101 is disposed on the blade's suction surface 18 adjacent (e.g., immediately adjacent) to the blade's proximal end 24, and (2) the air outlet 103 is disposed on (or adjacent to) the blade's trailing edge 14 adjacent to the blades' distal end 22. In particular embodiments, the blade 10 is configured so that when the blade 10 rotates about a hub, air is drawn into the air inlet 101, passes through the flow passage 105, and is expelled out of the blade 10 adjacent the blade's distal end 22 through the air outlet 103. This may help to control the boundary layer on the outside of the blade 10 by providing surface suction adjacent the blade's proximal end 24 and by expelling a jet of air adjacent the blade's distal end 22. As may be understood from the discussion above, in various embodiments of the invention, air is driven through the air Met 101, flow passage 105, and air outlet 103 by centrifugal forces that result from the rotation of the blade 10 about the hub 20. Accordingly, various embodiments of the invention provide a substantially passive system for moving air adjacent the blade 10.

Exemplary embodiments of the blade's air inlet, air outlet, and flow passage are described in greater detail below. Air Inlet

The air inlet 101 can take any suitable shape for allowing air to be drawn air into the blade 10. For example, in the embodiment shown in Figure 3, the air inlet 101 comprises a porous surface that is positioned on or adjacent the blade's suction surface 18 (e.g., in various embodiments of the invention, the air inlet 101 is defined within the blade's suction surface 18.) The air inlet 101 may, for example, comprise a slit, a hole, or a series of slits or holes.

Furthermore, the surface area of the air inlet 101 may be any suitable size for drawing in air as the air passes over the surface of the blade 10. For example, in various embodiments, the surface area of the air inlet 101 is less than or equal to about one-half of the size of the surface area of the blade's suction surface 18 or pressure surface 16. In other embodiments, the surface area of the air inlet 101 is less than about one-third of the size of the surface area of the blade's suction or pressure surface. For example, in the embodiment shown in Figure 3, the surface area of the air inlet 101 is less than or equal to about one-eighth of the size of the surface area of the blade's suction surface 18.

The air inlet 101 may be placed in any suitable position on the blade 10. For example, in various embodiments, the air inlet 101 is disposed between the proximal end 24 of the blade 10 and a portion of the blade that is positioned half way between the blade's proximal and distal ends. In the embodiment shown in Figure 3, the air inlet 101 is spaced apart from the proximal end 24 of the blade 10 by a distance that is less than about one-third of the length of the blade 10. In alternative embodiments, such as those shown in Figures 4 and 5, the air inlet 101 may be spaced apart from the proximal end 24 of the blade 10 by a distance that is less than about one-quarter of the length of the blade 10.

Air Outlet

The air outlet 103 may be of any suitable size or shape. For example, in the embodiment shown in Figure 3, the air outlet 103 comprises an elongated, substantially rectangular, slot-shaped opening. Figures 4 and 5 illustrate alternative embodiments in which the air outlet 103 comprises a hole having a substantially circular shape. The surface area of the air outlet 103 can be of any suitable size. For example, in various embodiments of the invention, the air outlet 103 has a surface area that is less than about 1/5 of the surface area of the blade's suction surface 18. For example, Figures 4 and 5 illustrate an air outlet 103 that has a surface area that is less than or equal to about 1/32 of the size of the surface of the blade's suction surface 18.

Furthermore, the air outlet 103 can be disposed in any appropriate location on or adjacent the blade 10. For example, in various embodiments, the air outlet 103 is disposed between the distal end 22 of the blade 10 and a portion of the blade 10 that is halfway between the blade's proximal and distal ends. In particular embodiments, the air outlet 103 is disposed adjacent (and, preferably, immediately adjacent) the blade's trailing edge 14. In the embodiment in Figure 3, the air outlet 103 is spaced apart from the distal end 22 by a distance that is less than or equal to about one-sixteenth of the length of the blade 10 and is disposed on the blade's trailing edge 14. Similarly, Figure 4 illustrates an alternative embodiment in which the air outlet 103 is spaced apart from the blade's distal end 22 by a distance that is less than or equal to about one-third of the length of the blade 10. In the alternative embodiment shown in Figure 5, the distal end 22 of the blade 10 defines a winglet 28, and the air outlet 103 is positioned on the trailing edge 14 of the winglet 28.

Flow Passage

The blade's flow passage 105 (which is preferably defined within the blade's interior) may be of any suitable size and shape. In various embodiments, the flow passage 105 is substantially tubular. In a particular embodiment, the internal passage is a duct with a cross-sectional area equal to (or less than) that of a circular pipe having diameter that is equal to the blade's maximum thickness.

Detailed Technical Discussion of a Particular Embodiment of the Invention

A more detailed discussion of particular technical aspects associated with various embodiments of the invention is provided below. It should be understood that this discussion is not intended to be limiting, and that particular embodiments of the invention may, for example, include more, less, or different components or structural features than those described in the examples below.

Nomenclature

Λ_duct ⁼ cross-sectional area of compressor blade passage

A_mu - suction surface area a_w = coefficient, Eq. 3 c - airfoil chord

Δc = extent of A_waii along the chord

C = absolute velocity in inertial frame p = pressure

P_t — stagnation pressure q = local relative velocity over rotating blade

Q = volumetric flow rate r - radial coordinate

R - radius swept by rotor blade tip

Re — Reynolds number based on chord and free stream velocity

Ro = Rossby number, U/Ωc s = extent of A_Waii along the span t — airfoil maximum thiclαiess

U₁V₁M' - non-dimensional velocity components along, normal to, and spanwise to the chord

U = free stream velocity x,y,z = physical blade surface coordinates along, normal to, and spanwise to the chord λ — blade tip speed ratio, U/ΩR p = density ξ,η,ζ = non-dimensional blade surface coordinates along, normal to, and spanwise to the chord

Ω = blade rotational speed

More Detailed Discussion of Background Technical Principles Most design methods for wind turbines are based on relatively simple notions of rotor blade aerodynamics. More and better field investigations and laboratory experiments in recent years have shown discrepancies between predicted and measured performance. These shortcomings have generally been traced to sophisticated aspects of rotor blade aerodynamics which have been neglected in the past, e.g., dynamic stall, three-dimensional boundary layer flow, etc. A major conclusion reached at the 1983 Horizontal Axis Wind Turbine (HAWT) Aerodynamics Specialists Meeting¹ was that these aerodynamic problems emerging from continuing experience with operating wind turbines must be understood if there were to be substantial improvements in design and prediction capabilities. A case in point was the realization that centrifugal effects permitted inboard regions of the wind turbine blades to produce more power than predicted by the use of local, two-dimensional, airfoil section coefficients. In 1985, NATO's Advisory Group for Aeronautical Research and Development (AGARD) held general conferences on propeller and helicopter aerodynamics while the American Wind Energy Association (AWEA) conducted their wind energy conference.

In the propeller conference, Bocci and Morrison² pointed out that "Some further development is required, in particular to take better account of viscosity, including centrifugal effects". Meanwhile, in the helicopter aerodynamics conference, Phillipe et al³ opined that "the major obstacle concerns the drag coefficient which is given as a function of angle of attack and Mach number, since 3-D unsteady rotor airfoil operating conditions can result in pressure distributions very different from those encountered in 2-D steady flow". Finally, in the wind energy conference, Savino and Nyland⁴ presented results of a flow visualization experiment on NASA's Mod-0 wind turbine which showed evidence of strong radial flow downstream of the separation line on the suction side of the blade. In addition, the location of the separation line was found to be 10% to 20% chord upstream of that for a non-rotating blade under corresponding flow conditions. Sforza's contemporaneous studies of three-dimensional boundary layer flows over ship-like bodies⁵ recognized similarities between the transverse curvature effects of these flows and those due to rotating blades.

In 1990, results of SERTs "combined experiment" on full-scale HAWTs amply demonstrated the phenomenon of three-dimensional effects in rotating blade boundary layers^6"10. Sforza used this experimental information in developing a review of research up to 1991 on boundary layer flows on rotating blades and found a number of interesting implications for wind turbine applications , demonstrating that the three-dimensional effects of rotation are significant, particularly for the inner half of typical wind turbine blades. Rotation was shown to have a generally beneficial effect in delaying separation and a deleterious effect on transition to turbulence, although there is much more information on the former than on the latter. Several overall wind turbine design alterations aimed at exploiting the useful effects of rotation, such as increasing the distance between the blade leading edge and the axis of rotation or installing leading edge vortex generators were described.

In 1994 another conference on the aerodynamics of rotorcraft was convened by AGARD and a session was devoted to wind turbines in recognition of the growing scientific importance of this sort of "rotorcraft". Snel and van Holten¹² presented a review of recent research on wind turbine aerodynamics in which they pointed out that rotation of the blade can act to dramatically alter the pressure and friction distributions from those based on 2-D predictions for the inboard sections of a rotating blade, thus delaying separation, and that "classical blade element analyses are not always reliable, perhaps due to more basic conceptual problems". At the 21st European Rotorcraft Forum in 1995, Beaumier and Houdeville¹³ reiterated the litany that using 2-D airfoil section coefficients, which is apparently still quite common in practice, is no longer acceptable "due to important 3-D effects that may occur and modify the aeroelastic behavior of the rotor".

In a paper on propeller analysis, Schulten¹⁴ described advances in propeller analysis beyond the classical actuator disc and blade element theory. He pointed out that in "the past 20 years, lifting line, lifting surface, Euler, and Navier-Stokes methods have been applied to advanced propellers with varying degrees of success". In the order listed, each method is more realistic than the previous one and therefore should provide more accurate results. This, however, is not always the case, especially since the more sophisticated methods, like Euler and Navier- Stokes, involve numerical analyses which can be prone to various errors. These field analyses, which rely on differential equations for the flow, are also heavy consumers of programming expertise and computer time. The Navier-Stokes method is the only one which incorporates viscous effects directly; the others are all basically inviscid analyses and require separate treatment of frictional effects. Schulten's conclusion, after reviewing the various methods, is that lifting surface methods are an affordable and generally reliable tool for parametric, and therefore, design studies.

The historical development of research on boundary layers on rotating blades has been described in some detail in Ref. 11. A major result that echoes throughout the early work on this problem (see, for example, Ref. 15) is that the ratio of local chord- wise distance, x, of a point on the blade, measured from the leading edge, to the span-wise coordinate, z, of that point, measured from the axis of rotation, correlates the extent of departure of the boundary layer flow from two- dimensionality (see Fig. Ia). When x/z « 1, i.e., far from the axis of rotation, the departure from two-dimensionality is likewise small and local strip theory should be reasonably accurate. As x/z increases, i.e., as the axis of rotation (z=0) is approached, three-dimensional effects increase, although the effects are found to be much less dramatic for turbulent flow than for laminar flow.

The general reasoning for this effect is that low-momentum flow is more strongly affected by rotation than high momentum flow so that the "fuller" turbulent boundary layer profile offers less potential for induced outboard span- wise flow. It is this sweeping out of the low momentum flow by centrifugal pumping which acts to keep the streamwise boundary layer more highly energized and therefore more separation resistant. It should be pointed out, however, that in the event separation does occur in the inboard region the low momentum eddy produced will be readily subject to centrifugal effects. The resulting span- wise flow of that fluid is likely to result in promoting separation in farther outboard

IA IR regions ^" . This is why the design of the entire blade is important. Indeed, it is no longer acceptable to dismiss careful treatment of the inboard region because it contributes little to the overall power produced. On the contrary, the inboard region appears to act like a catalyst, important to the global result although contributing very little to it directly (see Fig. Ib).

An additional consideration in the flow field development is that of transition to turbulence, particularly since rotational effects are more strongly felt for laminar than for turbulent flows. The local Reynolds number Rei based on the chord c and the local relative velocity q of the rotating blade of radius R is given approximately by (z/R)λRe. Here λ is the tip speed ratio of the blade and Re is the Reynolds number of the blade based on the chord and the oncoming wind speed U, i.e., the Reynolds number corresponding to the non-rotating state. For nominal conditions, say λ=5, c=0.3m, and U=IOnVs, the free stream Reynolds number Re ~ 200,000 and the local Reynolds number Rei ~ l,000,000(z/R). Thus the entire blade is operating near or within the transitional range of the Reynolds number, according to results for stationary wings. There appears to be relatively little work on transition to turbulence in rotating blade boundary layers although Kim¹⁹ has noted that: "the Coriolis force introduced by the system rotation could stabilize/destabilize turbulence". In addition, no consideration has yet been given to the question of surface roughness in regard to transition behavior. Therefore, this is one portion of the research where some degree of reliance must be placed on existing information and on parametric treatment of transition location.

Now we are at the point of considering the boundary layer analysis to be applied to the problem at hand. Srinivasan et al²⁰ employed a full Navier-Stokes analysis to directly treat the effects of viscosity in helicopter rotor flow fields while Beaumier and Houdeville¹³ used a quite complicated 3-D integral method to deal with the boundary layers in such flows. Snel and van Holten ², on the other hand, discussed efforts to simplify the 3-D boundary layer equations for the rotating blade to an extent which will render them useful in practical calculations. Sforza, in Ref. 11 cited above, had already traced the development of analyses of boundary layers over rotating blades which culminated in the sophisticated approach given by Morris²¹. This effort applied the concept of the appropriate coordinate system which is so useful in the analysis of singular perturbation problems by matched asymptotic expansions. The result is an elegant analog of the classical flat plate problem for the case of a rotating blade boundary layer.

Among the many important conclusions reached by Morris is that both the streamwise and normal components (u and v, respectively) of the velocity in the boundary layer are two-dimensional up to second order in the (small) expansion parameter h, which is proportional to the previously mentioned ratio x/z. The span- wise velocity component w, on the other hand, is directly proportional to the expansion parameter h, and therefore w ~ x/z. This suggests a separation of rotation effects is possible which should be applicable up to terms of third order in the expansion parameter, when h remains small. As the hub is approached, h grows and a different tack must be taken. Here the boundary layer equations are examined in the limit z -» 0 and simplifications arise which promise to again facilitate an efficient method of solution. Analysis of the Near Hub Region

The review of the literature described previously will aid in determining the most appropriate simplifications for the particular case of wind turbine rotors. The approach used to account for the viscous effects, as outlined previously, makes use of the boundary layer equations developed by Morris²¹. The simplifications inherent in this form of the governing equations, guided by the asymptotic analysis generated for the zero pressure gradient case, are expected to aid in the development of an efficient solution scheme for the variables of greatest importance for the problem at hand. The boundary layer equations, specialized to the near hub region, may be written as follows: dw dv du 1

— + — + — = -ςw dς dη dξ Ro² dw dw dw dp I d²w 1 / ^2 ,.. w — + v — + u — = — — + Z- + — r-ς-(w -l) (1) dς dη dξ dς Re dη² Ro^{2 K J} du du du dp 1 d²u 1 _(r. s, w — + v — + u — = — — + r- + — _τςw(2 - u) dς dη dξ dξ Re dη² Ro^{2 y} '

Shown are the continuity equation, the span-wise momentum equation, and the stream-wise momentum equation, respectively. The normal momentum equation merely notes that the pressure is constant across the boundary layer, as is typical in thin boundary layer theory. The quantities ξ, η, and ζ are the non- dimensional surface coordinates in the stream-wise, normal, and span-wise directions of the blade, respectively, and u, v, and w are the corresponding non- dimensional velocity components, whiles is a non-dimensional pressure and Re is the Reynolds number. Lengths are referred to a reference chord length c, velocities to the free stream velocity U, and the pressure to pU². Of particular interest are the solutions in the limit asς^* — » 0 and this is the reason for specializing Morrison's equations to the near hub region where ΩzlU= (ΩR/U)ζis small. The boundary condition at the wall is the no-slip condition, W=V=W=O, while at the outer edge the conditions are u=U[ϊ+(ΩR/U)²(c/R)²ζ²]^m and v=w=0.

It is clear that in addition to the Reynolds number, there is another parameter that appears, the Rossby number Ro = U/Ωc, which gives a measure of the importance of inertia forces compared to Coriolis forces in the relative frame of reference. This term may be written as Ro=[(c/R)λ]^~ι , thereby combining two other common wind turbine parameters: the tip speed ratio²²' ²³ λ—ΩRI U and the effective aspect ratio²²' ^{23> 24} of the blade clR. Unfortunately, design requirements tend to make tip speed ratio and aspect ratio move in the same direction so that rotation effects in the near hub region cannot be readily designed out by trading one off against the other.

The explicit effects of rotation near the hub, that is, for small ζ, can be seen in Eq.1. The continuity equation differs from the typical Cartesian form in that a sink term due to rotation-induced span- wise flow appears and has an effect similar to that produced by wall suction. This is a self-induced kind of boundary layer control arising merely from the rotation of the blade. As the Rossby number becomes very large this term vanishes and the standard three-dimensional Cartesian continuity equation is recovered. The contribution of rotation to the span-wise (^-direction) momentum equation is positive and therefore acts like a favorable pressure gradient along the span, with the effect being greatest near the wall, where the momentum is low (u is small). Similarly, in the chord-wise (indirection) momentum equation the extra term due to rotation is also positive since w is positive (outward flow along the span), and also tends to act like a favorable pressure gradient for the chord-wise flow. The effect would be greatest not at the wall, but somewhere in the middle of the boundary layer where the product w(2-ύ) is greatest in magnitude (w=w=0 at the wall and w=0at the boundary layer edge). Note that the velocities are normalized by the free stream velocity U and that as one moves away from the hub, the relative velocity outside the boundary layer is actually the quantity

but we are confining our attention to small values of ζ so that the quantity (2-«) is expected to remain positive. It has been noted in the previous studies cited that the effects of rotation are diminished in turbulent boundary layers, as compared to laminar boundary layers. Since turbulent boundary layer profiles are "fuller", the terms (1-w) and (2-u) appearing in the momentum equations will be smaller in magnitude than those for the laminar profiles throughout the boundary layer and therefore the effect of rotation should indeed be reduced²⁵. An Exemplary Passive Boundary Layer Control Technique

As described previously, under controlled conditions the rotation of the blade has a tendency to maintain attached flow to higher angles of attack than those achieved when there is no rotation. However, if there is a disruption of flow causing momentary separation, the effect of rotation will be to exacerbate the situation and the span-wise motion given to separation eddies are likely to cause massive separations farther out on the blade. Mitigation of the likelihood of developing separated flow over a wing can be accomplished by a number of means, including the following:

• Applying suction through that portion of the surface subject to separation

• Applying blowing over the surface or at the trailing edge of the wing

Both methods may require a means for suction or blowing situated within the wing itself. This may be merely appropriate duct work within the wing connected to a suitable pump located elsewhere.

Wings rotating in free space experience centrifugal effects that often disturb the boundary layer, particularly near the hub and near the tip. At the same time, blade motion makes implementation of conventional boundary layer control methods impractical. On the other hand, blades rotating within a casing take advantage of these effects to add or extract work from a fluid. The centrifugal compressor, for example, exploits centrifugal effects to ingest fluid at one pressure, compress it to a higher pressure, and exhaust it into a receiver. Various embodiments of the present flow control technique combine both the suction and injection strategies mentioned above into an integrated passive boundary layer control system. In particular embodiments of the present inventive techniques, at least one rotating blade (and preferably a plurality of blades e.g., of a wind turbine) includes a centrifugal compressor residing inside (or at least substantially inside) the rotating blade. This compressor supplies combined suction and blowing for the control of the boundary layer over the outside of the rotating blade, as shown in Fig. 2. (In other embodiments, the centrifugal compressor may be positioned outside the rotating blade.) Assuming that the blade surface is porous such that the normal component of velocity need not be zero at the surface, the conditions there are given by Eq. 1 as follows:

{ dη)_walι dξ Re {dη² )_walι

Note that the rotation has no direct effect on the curvature of the streamwise velocity profile at the wall, while it does directly affect that for the spanwise velocity profile. Of course, as the Rossby number becomes very large, the conventional boundary conditions for a three-dimensional boundary layer with surface transpiration are recovered. Since the spanwise and streamwise velocity gradients normal to the surface are positive, the application of suction at the wall, that is, v_waιι < 0, acts like a favorable pressure gradient thereby helping to keep the flow attached. Note that the rotational contribution to the spanwise flow also acts to make the spanwise pressure gradient more favorable, as expected. The intent of the new passive boundary layer control system is to apply suction to the inboard surface region so as to aid in maintaining attached flow under a broader range of operating conditions and thereby permitting the flow enhancement due to rotation to remain undisturbed. Computations for various non-rotating symmetric airfoils (including the NACA 0006 and 0007 airfoils) consider sinusoidal suction velocity distributions as shown below:

^Vwall = (3)

The coefficient a_w is a constant; x is the streamwise distance over which the suction is applied, starting at X₁ and ending at X₂. Values of a_w around unity for full-chord suction, and around 10 for slots about 0.1c in length, dramatically reduced the size of the separation bubble in the vicinity of the trailing edge. As a first approximation, we assume that the suction velocity required is c U

^Vwall ^ ~ _A CT" v V

Ac VRe

The quantity AcIc denotes the length of the suction gap as a function of the actual chord length and this should recover the appropriate magnitude of α_w in the more general requirement of Eq. 3. Then the suction flow rate is

Q = ^VvallAaH = ^V _WaU (^ΔΦ = ^~ i= (⁵)

VRe

The area through which the suction acts is A_waιι and has a streamwise extent denoted by Ac and a spanwise extent denoted by s. Typical conditions for a wind turbine, as mentioned in a previous section, are £/=10 m/s, i?e=200,000, and cl R-XId yields an approximate value for the required suction flow rate: Q=0.0037sR. Further considering a spanwise extent of R/6 yields Q=0.00062R², so that for R=20m, Q=0.25m /s (approximately 480cfm). The internal passage may be considered a duct with a cross-sectional area equal to that of a circular pipe of diameter t, the airfoil maximum thickness. Then the passage flow area is A_duct=0.785(t/c)²(c/R)²R², and for a 15% thick airfoil this yields an area A_duct-0.0033R², thus the average speed in the duct is W=QZA_dUCt=SJ m/s. These are all reasonable flow conditions which can be readily achieved in practice.

The integral internal compressor shown in Fig. 2 is essentially a standard centrifugal compressor with approximately axial entry and backward curved blades. The ideal static pressure rise across this compressor²⁶ is given by

Δp = P_lψ -P_hub

The variable W denotes the velocity relative to the blade passage. The ideal total pressure rise is equal to the static pressure rise plus the external effect as given below:

P_1J1P -P_1Mt - (7)

The variable C denotes the absolute velocity referred to a fixed frame of reference, P is the ideal power required, and Q is the volumetric flow rate through the passage. If we neglect the contribution near the hub, which is commonly done for cases where the flow enters the compressor approximately axially, this equation may be also written as follows: P = prl_pςΪQ - pr_llpQ _j ^Q[ _o (8)

^' 4 l_wip t "a""n- rAtip

The quantity ^ denotes the cross-sectional area of the passage and β is the angle between the velocity vector due to rotation and the relative velocity W and is set primarily by the local shape of the internal blade passage (i.e.,, forward or backward swept blades). With the low volumetric flow rates required for the suction boundary layer control (about 0.25 m³/s), the ideal power required for the typical wind turbine conditions considered is likewise very modest, on the order of a kilowatt, though of course taking account realistic efficiencies this may run up to 4 or 5 kilowatts. In the case of radial tipped blades {β=πll) the second term on the right-hand side of Eq. 8 is zero and, using the expression for the magnitude of Q in Eq. 5, we may form the ratio of power required by the internal compressor portion of the blade to the power generated (P_aVaιi) by the external turbine portion as follows:

This equation shows that for a given geometric and operational configuration of the integral compressor-turbine system the ratio of power required to power available drops off with the size of the rotor. Furthermore the magnitude of the ratio is proportional to the square root of the kinematic viscosity, the value of which for air is on the order of 0.0038m²/s and thus the power drain due to boundary layer control will be small. For typical values of the parameters in Eq. 9 the ratio is

Thus for a wind speed of lOm/s and a tip radius of 10m, only 1.2% of the power generated is necessary to drive the integral internal compressor. Of course, it is expected that the boundary layer control system will enable the rotor to consistently produce considerably more power than would be the case without it. Thus fluid is sucked into the interior of the blade through a porous section of blade skin near the hub (small r) and is forced through an interior passage within the blade toward the tip by centrifugal pumping. As the fluid in the interior passage moves toward the tip (large r) it is compressed to a high pressure and then blown out through a slit on the trailing edge of the blade. This integral centrifugal compressor is thereby capable of controlling the boundary layer over the outside of the rotating blade by providing surface suction near the hub and jet blowing near the tip, as shown by the schematic diagram in Fig.2. Since the centrifugal effects increase for both the outer flow over the blade and the inner flow within the blade, in various embodiments, there need not be any external control. That is, the control is automatic and passive ensuring not only improved performance, but increased reliability as well.

References

The following is a listing of the references cited via numerical superscript text in the "An Exemplary Passive Boundary Layer Control Technique" section above:

1. "First Meeting of Specialists on the Aerodynamics of Horizontal Axis Wind Turbines - A Summary of Findings, Issues, and Recommendations", NASA Wind Energy Project Office and Rocky Flats Wind Energy Research Center, Wichita, Kansas, 20-21 April, 1983.

2. Bocci, AJ. and Morrison, J.I.: "A Review of ARA Research into Propeller Aerodynamic Prediction Methods", in "Aerodynamics and Acoustics of Propellers", AGARD CP-366, February, 1985.

3. Philippe, J.J. et al: "A Survey of Recent Developments in Helicopter Aerodynamics", in "Helicopter Aerodynamics", AGARD LS-139, April, 1985.

4. Savino, J.M. andNyland, T. W.: "Wind Turbine Flow Visualization Studies", AWEA Wind Energy Conference, San Francisco, California, 26-30 August, 1985.

5. Sforza, P.M. et al: "Transverse Curvature Effects in Turbulent Boundary Layers", AIAA 87-1252, 19th AIAA Fluid Dynamics Conference, Honolulu, Hawaii, 8-10 June, 1987.

6. Butterfield, CP. et al: "Aerodynamic Pressure Measurements on a Rotating Wind Turbine Blade", SERI/TP-257-3695, May, 1990.

7. Butterfield, CP. and Nelsen, E.N.: "Aerodynamic Testing of a Rotating Wind Turbine Blade", SERI/TP-257-3490, January, 1990.

8. Butterfield, C.P.: "Three-Dimensional Airfoil Performance Measurements on a Rotating Wing", SERI/TP-217-3505, June, 1989. 9. Butterfield, CP. et al: "Comparison of Wind Tunnel Airfoil Performance Data with Wind Turbine Blade Data", SERI/TP-254-3799, July, 1990.

10. Musial, W.D. et al: "A Comparison of Two- and Three-Dimensional S809 Airfoil Properties for Rough and Smooth HAWT Rotor Operation", SERI/TP-257-3603, February, 1990.

11. Sforza, P.M.: "Effects of Rotation on Wind Turbine Blade Boundary Layers", IECEC 91-0853, Proceedings of the 26th Intersociety Energy Conversion Engineering Conference, Boston, Massachusetts, 3-9 August, 1991.

12. Snel, H. and van Holten, Th.: "Review of Recent Aerodynamic Research on Wind Turbines with Relevance to Rotorcraft", in "Aerodynamics and Aeroacoustics of Rotorcraft", AGARD CP-552, October, 1994.

13. Beaumier, P. and Houdeville, R.: "3D Laminar-Turbulent Boundary Layer Calculations on Helicopter Rotors in Forward Flight - Application to Drag Prediction", ONERA Rept. No. 1995-103, in the 21st European Rotorcraft Forum, St. Petersburg, Russia, 1 September 1995.

14. Schulten, J.B.H.M.: "Advanced Propeller Performance Calculation by a Lifting Surface Method", Jl. of Propulsion and Power, 12, 3, pp.477-485, May- June 1996.

15. McCroskey, WJ. et al: "Turbulent Boundary Layer Flow over a Rotating Flat Plate Blade", AIAA JL, 9, 1, pp.188-189, January, 1971.

16. Carpenter, PJ. : "Lift and Profile-Drag Characteristics of an NACA 0012 Airfoil Section as Derived from Measured Helicopter-Rotor Hovering Performance," NACA Technical Note 4357, September, 1958

17. Huyer, S.A., Simms, D., and Robinson, M.C.: "Unsteady Aerodynamics Associated with a Horizontal- Axis Wind Turbine," AIAA Journal, Vol. 34, No. 7, July, 1966, pp. 1410-1419

18. Schreck, S. and Robinson, M.: "Boundary Layer State and Flow Field Structure Underlying Rotational Augmentation of Blade Aerodynamic Response," Transactions of the ASME, Vol. 125, November, 2003, pp. 448-456

19. Kim, J.: "The Effect of Rotation on Turbulence Structure", in "Proc. of the 4th Symposium on Turbulent Flows, The University of Karlsruhe, Germany, pp. 6.14-6.19, 12-14 September 1983.

20. Srinivasan, G.R. et al: "Flowfield of a Lifting Rotor in Hover: A Navier-Stokes Simulation", AIAA Journal, 30, 10, pp. 2371-2378, October, 1992.

21. Morris, PJ.: "The Three-Dimensional Boundary Layer on a Rotating Helical Blade", Journal of Fluid Mechanics, 112, pp. 283-296, 1981.

22. Du, Z. and Selig, M.S. (2000): "The Effect of Rotation on the Boundary Layer of a Wind Turbine Blade," Renewable Energy, Vol. 20, pp. 167-181 23. Dumitrescu, H. and Cardos, V.: "Rotational Effects on the Boundary- Layer Flow in Wind Turbines," AIAA Journal, Vol. 42, No. 2, February, 2004, pp. 408-411

24. Chaviaropoulos, P.K. and Hansen, M.O.L.: "Investigating Three- Dimensional and Rotational Effects on Wind Turbine Blades by Means of a Quasi-3D Navier-Stokes Solver," Transactions of the ASME, Journal of Fluids Engineering, Vol. 122, June, 2000, pp. 330-336

25. Jessup, S.T., Schott, C, Jeffers, M., and Kobayashi, S.: "Local Propeller Blade Flows in Uniform and Sheared Onset Flows Using LDV Techniques," Proceedings of the 15^th Symposium on Naval Hydrodynamics, 1985, pp. 221-237

26. Greitzer, E.M., Tan, C.S., and Graf, M.B. (2004): Internal Flow - Concepts and Applications, Cambridge University Press, New York

Conclusion

Many modifications and other embodiments of the inventions set forth herein will come to mind to one skilled in the art to which these inventions pertain having the benefit of the teachings presented in the foregoing descriptions and the associated drawings. Therefore, it is to be understood that the inventions are not to be limited to the specific embodiments disclosed and that modifications and other embodiments are intended to be included within the scope of the appended inventive concepts. For example, although many of the embodiments described above relate to the flow of air adjacent wind turbine blades, the above techniques may be applied within the context of other types of fluids (e.g., gases other than air, or liquids) flowing adjacent other types of blades (e.g., compressor or propeller blades). Also, while various embodiments of the above invention are described as using a passive compressor, alternative embodiments of the invention may include an active compressor of any suitable type (which may, for example, in the case of a wind turbine, be powered by the wind turbine). Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation.

Claims

CLAIMSWhat is claimed is:

1. A blade that is adapted to be operably attached adjacent a rotatable hub, said blade defining: a fluid inlet; a fluid outlet; and a centrifugal flow passage that extends between said fluid inlet and said fluid outlet, wherein: said fluid inlet is in gaseous communication with said fluid outlet via said centrifugal flow passage, and said blade is configured so that, when said blade is rotated about said hub at a particular velocity, fluid is drawn into said fluid inlet, moved through said centrifugal flow passage, and expelled out of said fluid outlet.

2. The blade of Claim 1 , wherein said centrifugal flow passage is defined substantially entirely within an interior portion of said blade.

3. The blade of Claim 1, wherein said blade is configured so that, when said blade is rotated at said particular velocity, said fluid is compressed as it is moved through said centrifugal flow passage.

4. The blade of Claim 3, wherein said fluid is a gas.

5. The blade of Claim 1, wherein said blade is configured so that, when said blade is operably attached adjacent said rotatable hub, said fluid inlet is disposed adjacent a proximal end of said blade.

6. The blade of Claim 5, wherein said blade is configured so that, when said blade is operably attached adjacent said rotatable hub, said fluid outlet is disposed adjacent a distal end of said blade.

7. The blade of Claim 1 , wherein said blade is configured so that, when said blade is rotated at a particular velocity, a volume of said fluid is: (A) drawn into said centrifugal flow passage through said fluid inlet; (B) moved through said centrifugal flow passage to thereby compress said volume of fluid; and (C) discharged through said fluid outlet adjacent a distal end of said blade.

8. The blade of Claim 7, wherein said centrifugal flow passage is an elongate passage having a substantially circular cross section.

9. The blade of Claim 7, wherein said fluid inlet is disposed on a suction surface of said blade.

10. The blade of Claim 7, wherein said fluid outlet is disposed adjacent a trailing edge of said blade.

11. The blade of Claim 7, wherein said fluid inlet comprises a porous surface.

12. The blade of Claim 1, wherein said blade is substantially in the form of an airfoil.

13. The blade of Claim 1, wherein said blade is configured so that, when said blade is rotated at a particular velocity, a centrifugal effect resulting from radial momentum of said blade: (A) draws said fluid into said centrifugal flow passage through said fluid inlet; (B) moves said fluid through said centrifugal flow passage to thereby compress said fluid; and (C) discharges said fluid through said fluid outlet adjacent a distal end of said blade.

14. A wind turbine comprising: a rotatable hub; and a plurality of elongate blades extending outwardly from said rotatable hub, wherein each particular one of said blades defines: an air inlet; an air outlet; and a centrifugal flow passage that extends between said air inlet and said air outlet, wherein: said air inlet is in gaseous communication with said air outlet via said centrifugal flow passage, and said blade is configured so that, when said blade is rotated about said hub at a particular velocity, air is drawn into said air inlet, moved through said centrifugal flow passage, and expelled out of said air outlet.

15. The wind turbine of Claim 14, wherein said centrifugal flow passage is defined substantially entirely within an interior portion of said particular blade.

16. The wind turbine of Claim 14, wherein said particular blade is configured so that, when said particular blade is rotated at said particular velocity, said air is compressed as it is moved through said centrifugal flow passage.

17. The wind turbine of Claim 14, wherein said air inlet is disposed adjacent a proximal end of said particular blade.

18. The wind turbine of Claim 14, wherein said air outlet is disposed adjacent a distal end of said particular blade.

19. The wind turbine of Claim 14, wherein said particular blade is configured so that, when said particular blade is rotated at said particular velocity, a volume of air is: (A) drawn into said centrifugal flow passage through said air inlet; (B) moved through said centrifugal flow passage to thereby compress said volume of air; and (C) discharged through said air outlet adjacent a distal end of said blade.

20. The wind turbine of Claim 19, wherein said centrifugal flow passage is an elongate passage having a substantially circular cross section.

21. The wind turbine of Claim 19, wherein said air inlet is disposed on a suction surface of said particular blade.

22. The wind turbine of Claim 19, wherein said air outlet is disposed adjacent a trailing edge of said particular blade.

23. The wind turbine of Claim 19, wherein said air inlet comprises a porous surface.

24. The wind turbine of Claim 19, wherein said particular blade is substantially in the form of an airfoil.

25. A wind turbine comprising: a rotatable hub; and a plurality of elongate turbine blades extending outwardly from said rotatable hub, wherein each particular one of said blades comprises: an air inlet; an air outlet that is in gaseous communication with said air inlet via an air flow passage; and a compressor that is adapted for:

(A) receiving a volume of gas that has entered said particular blade through said air inlet;

(B) after said step of receiving said volume of gas, compressing said volume of gas; and

(C) after said step of compressing said volume of gas, directing said compressed volume of gas for discharge out of said air outlet.

26. The wind turbine of Claim 25, wherein said compressor is disposed within said particular turbine blade.

27. The wind turbine of Claim 25, wherein: said compressor is an elongate flow passage that extends between said air inlet and said air outlet; and said air inlet is in gaseous communication with said air outlet via said flow passage.

28. The wind turbine of Claim 27, wherein said air inlet is disposed adjacent a proximal end of said particular turbine blade.

29. The wind turbine of Claim 28, wherein said air outlet is disposed adjacent a distal end of said particular turbine blade.

30. The wind turbine of Claim 25, wherein said air outlet is disposed adjacent a distal end of said particular turbine blade.

31. A method of reducing boundary layer separation adj acent a blade that is rotating about a central, rotating hub, said method comprising: drawing a volume of gas into an interior portion of said blade through an air inlet that is disposed adjacent a proximal surface of said blade; after said step of drawing said volume of gas into said internal portion of said blade, compressing said volume of gas; and after said step of compressing said volume of gas, expelling said compressed volume of gas out of said interior portion of said blade via an air outlet.

32. The method of Claim 31 , wherein said air outlet is disposed adjacent a distal end of said blade.

33. The method of Claim 32, wherein said blade is a wind turbine blade.