The present invention relates to generally the field of energy conversion. More particularly, the invention relates to apparatus and methods for generating power (such as electrical power) for use by a population of consumers or even a single consumer.
With global energy consumption increasing day by day there is a high demand for energy, and particularly energy produced by methods which do not contribute to global warming. Where fossil fuels are used for energy generation, it is generally desired to improve the efficiency of turbines used to convert the chemical energy of the fuel into other forms of energy such as kinetic or electrical energy. For turbines having a higher efficiency, lower amounts of fuel need be be combusted to provide a unit of output energy.
Since the earth's natural energy reserves are becoming depleted and prices of oil and natural gas are relatively high, new sources of clean, abundant and inexpensive energy are urgently required.
It is surprising that despite the huge energy reservoirs contained in the atmosphere and in rivers, streams, lakes, and submarine currents all over the world, only a very small proportion is harvested by present day energy conversion apparatus and at high cost. For example, prior art wind turbines used for generating power in excess of 1 MW are of significant size and weight, and furthermore are very expensive to build. Another disadvantage is the very low efficiency of generation, which is constrained (at least theoretically) by Betz's limit Even domestic scale wind turbines are not overly useful given the low efficiencies inherent in the designs.
It is an aspect of the present invention to overcome or ameliorate a problem of prior art energy conversion means. Alternatively, it is an aspect to provide an economically viable alternative to prior art energy conversion means.
The discussion of documents, acts, materials, devices, articles and the like is included in this specification solely for the purpose of providing a context for the present invention. It is not suggested or represented that any or all of these matters formed part of the prior art base or were common general knowledge in the field relevant to the present invention as it existed before the priority date of each claim of this application.
In a first aspect, but not necessarily the broadest aspect, the present invention provides an energy conversion turbine comprising: a central shaft having a rotational axis, a plurality of blades in mechanical connection with and disposed around the central shaft, wherein the turbine is configured such that fluid flowing about the blades causes the temperature about one blade face to become lower than the temperature about the opposing blade face.
In one embodiment of the turbine, the blades are airfoil-shaped.
In one embodiment of the turbine, the blades are mounted between two concentric cylinders, the concentric cylinders being substantially coaxial with the rotational axis of the central shaft. In one embodiment of the turbine, the inner concentric cylinder is in mechanical connection with the central shaft.
In a second aspect, there is provided a power conversion machine comprising: a fluid accelerator, a throat having a fluid inlet and a fluid outlet, and the turbine as described herein disposed within the throat and rotatable therein, wherein the machine is configured such that fluid accelerated by the fluid accelerator is caused to pass through the throat so as to cause rotation of the turbine.
In one embodiment of the power conversion machine, the fluid accelerator is a conduit having a fluid inlet and a fluid outlet, the conduit fluid outlet being in fluid communication with the throat fluid inlet.
In one embodiment of the power conversion machine, the conduit is a convergent nozzle.
In one embodiment of the power conversion machine, the fluid accelerator accelerates the fluid velocity by means requiring energy input.
In one embodiment of the power conversion machine, the means requiring energy input is a fan configured to accelerate and drive fluid toward the turbine.
In one embodiment of the power conversion machine, the fan is rotatable within the throat, and is coaxial with the turbine.
In one embodiment of the power conversion machine, the means requiring energy input is a moving object to which the machine is attached. For example, the power conversion machine may be attached to an aircraft with movement of the aircraft forcing air through the machine
In one embodiment, the power conversion machine comprises a fluid decelerator configured to decelerate fluid exiting the turbine.
In one embodiment of the power conversion machine, the fluid decelerator is a conduit having a fluid inlet and a fluid outlet, the conduit fluid inlet being in fluid communication with the throat fluid outlet.
In one embodiment of the power conversion machine, the conduit is a divergent nozzle. In one embodiment of the power conversion machine, the throat is a Venturi-like throat. In one embodiment, the power conversion machine comprises two or more turbines as described, all turbines being coaxial.
In one embodiment, the power conversion machine comprises a fluid flow straightener configured to straighten to flow of fluid entering the throat or exiting the throat.
In one embodiment, the power conversion machine comprises two fluid flow straighteners, the first straightener configured to straighten to flow of fluid entering the throat, and the second straightener configured to straighten flow of fluid exiting the throat.
In one embodiment, the power conversion machine comprises more than two fluid flow straighteners placed in between a fan and a turbine, or between two consecutive turbines.
In a third aspect the present invention provides a method of generating power comprising the steps of: providing the power conversion machine as described herein, providing fluid flow to the turbine, the fluid flow being incident on the leading edges of the blades, the fluid flow being sufficient to cause the central shaft to rotate, and harnessing the power generated from the rotational output of the central shaft.
In one embodiment, the method comprises the step of providing energy input to the means requiring energy input (where present) so as to accelerate and drive fluid toward the turbine.
The drawings are not shown at any specific scale.
Reference throughout this specification to “one embodiment” or “an embodiment” means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases “in one embodiment” or “in an embodiment” or “in some embodiments” in various places throughout this specification are not necessarily all referring to the same embodiment, but may. Furthermore, the particular features, structures or characteristics may be combined in any suitable manner, as would be apparent to one of ordinary skill in the art from this disclosure, in one or more embodiments.
Similarly it should be appreciated that the description of exemplary embodiments of the invention, various features of the invention are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of streamlining the disclosure and aiding in the understanding of one or more of the various inventive aspects. This method of disclosure, however, is not to be interpreted as reflecting an intention that the claimed invention requires more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects lie in less than all features of a single foregoing disclosed embodiment. Thus, the claims following the Detailed Description are hereby expressly incorporated into this Detailed Description, with each claim standing on its own as a separate embodiment of this invention.
Furthermore, while some embodiments described herein include some but not other features included in other embodiments, combinations of features of different embodiments are meant to be within the scope of the invention, and from different embodiments, as would be understood by those in the art.
In the claims below and the description herein, any one of the terms “comprising”, “comprised of” or “which comprises” is an open term that means including at least the elements/features that follow, but not excluding others. Thus, the term comprising, when used in the claims, should not be interpreted as being limitative to the means or elements or steps listed thereafter. For example, the scope of the expression a method comprising step A and step B should not be limited to methods consisting only of methods A and B. Any one of the terms “including” or “which includes” or “that includes” as used herein is also an open term that also means including at least the elements/features that follow the term, but not excluding others. Thus, “including” is synonymous with and means “comprising”.
The present invention is predicated at least in part of the finding that an energy conversion mean having one or more turbines with particular features may generate similar amounts of power to conventional wind turbines but at a lower cost and/or greater efficiency. The present energy conversion turbine may be made with a great reduction in size, height, and weight, and may in some embodiments be portable. In some embodiments, the present turbines may achieve an efficiency higher than that set by Betz's limit.
The advantage of portability provides the ability to generate electrical or mechanical energy at the place of consumption, thereby potentially negating the need for power grids, long transmission and distribution lines.
Furthermore, the portable and compact nature of some embodiments of the present turbine allow for attachment to a moving land, sea or air vehicle so as to harvest considerable energy from the surrounding atmosphere or water when they are placed in direct contact with the environment.
In functional terms the present energy conversion turbine is, in some embodiments, able to transform the thermal power received from an incoming fluid flow (such as air or water, as an exemplary gas and liquid respectively), into mechanical power when the fluid impinges upon the airfoils of the turbine. This power may be recovered as rotational mechanical energy from the shaft of the device. The rotational mechanical energy may be used to drive an electrical generator of the type well known to the skilled artisan, or with optional gearing means, used to propel a vehicle.
In some embodiments, the velocity of the fluid entering the turbine is increased by means requiring energy input and in such situations, the power generated by the present turbine is greater than that input. In some circumstances, the output may be at least about 2, 3, 4, 5, 6, 7, 8, 9, or 10 fold that input.
The present turbine may comprise two or more concentric cylinders (and preferably two) and a series of airfoils (such as at least about 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, or 20), which are suitably placed on and fixed between the cylinders, occupying part of the space separating both cylinders. The airfoils are positioned so as to provide a specific attack angle (and in some embodiments a fixed attack angle) with reference to the airflow direction.
The cylinders may be coaxial with a central shaft; such that at certain rotational velocities, the transformation of the thermal energy of the incident airflow into mechanical energy is effected. This energy may be used to drive either a mechanical system or an electrical system attached onto the shaft. The power that the incident airflow at a certain velocity applies to the airfoils spinning at a certain rotational velocity, is much less than the mechanical power generated by the rotating airfoils, and extracted from the thermal energy of the passing airflow, the relation between the generated power and the applied power can be greater than one, and indeed any multiple. In some embodiments the multiple may be ten or more.
This amplified output power may be delivered to either a mechanical or an electrical element, attached to a rotational shaft, as shown in
The airfoils placed between the two cylinders may form a predetermined angle (the attack angle) with reference to the airflow direction. The attack angle may be greater than zero, equal to zero or less than zero, or greater than about 10°, however embodiments with higher efficiencies have an exaggerated value of the attack angle of greater than about 15°, 20°, 25°, 30°, 35°, or 45°. In some embodiments the attack angle is in excess of 45°, and may be greater than about50°, 55°, 60°, 65°, 70°, 75°, 80°, or 85°, for instance. At such large attack angles (which are significantly higher than those typically used for airfoils in the aeronautical arts, whereby angles of up to about 10° are typical), the turbine produces more relative power gain, as demonstrated mathematically infra. By relative power gain it is meant the relationship of generated power/applied power is greater than unity.
In order to ensure that the turbine spins as smoothly as possible, the airfoils between the two cylinders should be placed symmetrically so as to provide for a balanced rotation. In some embodiments it is possible, however, to place the airfoils in another disposition with little or no negative effect.
The number of airfoils placed between the two cylinders of the turbine, may be as large as allowable with reference to the dimensions of the turbine overall, so as to obtain a maximum of generated power. Efficiencies are further improved where the airfoils are separated one to each other, a medium distance at least the width of the airfoils. The separation distance between the airfoils is to avoid aerodynamic interference between each other.
In theory, the size of the two cylinders of turbine is unrestricted, however practical manufacturing considerations may preclude the use of very large or very small elements.
Similarly, there are no theoretically restrictions as to the materials that may be employed to fabricate the airfoils and the cylinders. In practice, however, in order to achieve a light structure for the turbine and its easy handling, it is recommended to use plastic materials, resin, acrylic, among other materials for manufacturing the airfoils. For manufacturing the cylinders, a light alloy or light metal such as aluminum, or a light hard plastic may be used.
In order to support the weight of the whole turbine, its rotational shaft (103) may be strong enough, and therefore may be fabricated from a high tensile steel rod or similar material.
The rotational shaft is typically be placed in the center of the turbine, and fixed to the inner cylinder (101) with light and strong rods (104) of equal length. In one embodiment, 8 such rods are used. Alternatively another type of fixing means may be used to attach the center rotational shaft to the inner cylinder.
The airfoils between the two cylinders may be fixed with screws and nuts, a strong adhesive, welding or any other means deemed suitable by the skilled artisan.
It is preferred that all the inner and outer surfaces of the cylinders, and also the surfaces of the airfoils be fabricated to be smooth, so as to reduce the drag force exerted by the fluid flow against the surfaces, in order to reduce power losses due to the drag force.
The airfoils may have any geometrical configuration that function so as to have the effect of transforming the thermal energy of the passing airflow, into mechanical power in the shaft. In some embodiments, the airfoils are configured so as to provide a factor 1 or greater than 1 of the input power received for the airfoils from the airflow entering the turbine.
In one embodiment, the airfoils are the same or similar to those used in the aeronautical arts. In aeronautics, an airfoil-shaped body moved through a fluid produces an aerodynamic force. The component of this force perpendicular to the direction of motion is called lift. The component parallel to the direction of motion is called drag. Subsonic flight airfoils typically have a characteristic shape with a rounded leading edge, followed by a sharp trailing edge, often with a symmetric curvature of upper and lower surfaces. Foils of similar function designed with water as the working fluid are called hydrofoils.
Again in reference to aeronautics, the lift on an airfoil is primarily the result of its angle of attack and shape. When oriented at a suitable angle, the airfoil deflects the oncoming air (for fixed-wing aircraft, a downward force), resulting in a force on the airfoil in the direction opposite to the deflection. This force is known as aerodynamic force and may be resolved into two components: lift and drag. Most foil shapes require a positive angle of attack to generate lift. This “turning” of the air in the vicinity of the airfoil creates curved streamlines, resulting in lower pressure on one side and higher pressure on the other. This pressure difference is accompanied by a velocity difference, via Bernoulli's principle, so the resulting flow about the airfoil has a higher average velocity on the upper surface than on the lower surface. The lift force may be related directly to the average top/bottom velocity difference without computing the pressure by using the concept of circulation and the Kutta-Joukowski theorem
Returning back now to the use of airfoils in the context of the present invention, when the turbine rotates the airfoils' relative attack angle aA that the airflow “sees”, is different from the airfoils' real attack angle αR depending on the rotational velocity. For instance, suppose that the airfoils' real attack angle αR is 45°. In this condition when the angular velocity (RPM) of the turbine is zero, the airflow (with a horizontal linear velocity Vt), “sees” the airfoils with a relative attack angle αA which is equal to the real attack angle αR (that is to say, 45°). However, when the turbine reaches an RPM such that it makes the mean peripheral velocity equal to Vφ (RPMh), the airflow will “see” an airfoils' relative attack angle aA equal to zero. For another rotational velocity varying between zero and RPM h, the airfoils' relative attack angle aA will vary between 45° and zero.
Without wishing to be limited by theory in any way, it is proposed that when the airflow passes through the turbine's airfoils, the airflow above the airfoils travels at a greater velocity than that passing under the airfoils. Accordingly, the air pressure above the airfoil is less than the down pressure in the airfoils (Bernoulli equation), as a consequence the temperature above the airfoils becomes lower than the temperature below the airfoils. That is to say, the airflow loses thermal energy when passing through the turbine's airfoils. Part of this thermal energy lost is transmitted directly to the airfoils, and transformed into kinetic energy when the turbine rotates. Finally this energy is transmitted to the shaft of the turbine. Another part of the thermal energy lost in the upper side of the airfoils, is returned to the environment, when the airflow coming from the upper side of the airfoils, joins and hits the airflow passing downward the airfoils. With this mechanism the energetic equilibrium in the system is restored.
The particular RPM at which the turbine generates a maximum relative power gain (generated power/applied power) is a value lying somewhere between zero and RPM h. In this situation, supposing that the real attack angle is 45°, the airflow will “see” an apparent attack angle, which is very little, of the order of 15° (this occurs only for the RPM that generates maximum relative power gain). In this situation the drag force, and so the airflow's drag power applied to the airfoils will be very little. However, since the lift force of the airfoils in this situation, is far greater than the drag force, then the generated power will be far greater than the drag power, that is to say that there takes place a transformation of power due to the interaction between the turbine airfoils and the incoming airflow. This power transformation causes a relative power gain which is very large (and in some instances 10 or more).
The power generated by the turbine versus its rotational velocity RPM follows a curve that begins with zero RPM and zero generated power. Then, it goes to a maximum value of generated power at an intermediate value of RPM, and finally, it ends with zero generated power at a maximum value of RPM. The curve of the applied power begins with a maximum value at RPM equal to zero, and then the applied power diminishes as RPM increases. Finally this curve ends up with a minimum value of the applied power which is greater than zero.
A brief and approximate calculation and only for explaining the working basis of the present turbine, is given below. Suppose that a static airfoil is placed initially at an exaggerated attack angle of 45°, within an airflow of velocity Vφ, as shown in
In this situation the Drag Force FD is very large. Then:
Applied power=FD*Vφ;
Generated power=FL*VL=FL*0=0
Now consider that the airfoil moves vertically with a velocity VL=0.577735 Vφ. That is to say,
V
L
/V
φ=0.577735=Tg30°.
In this condition the flow with velocity Vφ, “sees” the airfoil with an attack angle equal to 45°−30°=15° and the new condition that the airflow will “see” is shown in
So in this new condition:
Power applied by the airflow to the airfoil=FD*Vφ=PA
Power generated by the airfoil=PG=VL*FL=0. 577735 Vφ*FL
So that
Power Gain=0.577735Vφ,×FL/(FD×Vφ)=0.577735FL/FD
It is known in the aeronautical arts that many airfoils in this condition (attack angle of 15°) have a force relation
FL/FD
which is 30, 50 or even more, so that if one used for example
F
L
/F
D=50
then the Power Gain=0.577735*50=28.88, this being an unexpectedly large gain.
It is to be noted that there is an exact geometrical calculation for the former analysis, but the numerical differences compared to the approximate calculation given above are minor
With these calculation bases and correcting for a circular movement, it is possible to obtain numerical values and curves. For instance for Turbine #1, with the following measures:
And with the following experimental measurements for the airfoils used in Turbine #1:
With all of the previous quantities, and applying corrections for the circular movement, and geometrical formulas outside of the scope of this abstract, the following table and
Turbine #1 was built and measurements made with the previous mentioned parameters and with a real attack angle of 42.5°, and a maximum relative power gain (generated power/ applied power) of 10 was obtained. It is worthwhile to notice, that in all the previous calculation, the efficiency of the airfoils (FL/FD) was very low, reaching a maximum value of 16.72. In the aeronautical arts this is considered to be a very low value for an airfoil efficiency.
While useful, the turbine may be augmented with means for accelerating fluid on the upstream side, and optionally also means for decelerating fluid on the downstream side of the turbine. Two fundamental physical principles may exploited in the design and operation of the present energy conversion machine, namely, the fluid velocity multiplication that takes place within a fluid convergent nozzle, and the enormous mechanical power that may be developed by the lift force on a suitably designed fan blade or streamlined turbine airfoil as described supra.
A fluid flowing past the surface of an airfoil-shaped body or fan blade, placed at a suitable attack angle a, exerts a surface force on it (
For a fluid flowing in a pipe or a duct and impacting a set of (one or more) rotary blades that has been suitable placed within the fluid passage, and facing the flow, the Reynolds Number is defined as Re=pcVφ/μ where ρ and μ are the fluid density and the fluid viscosity, respectively; Vφ is the velocity of the free-stream fluid flow, and c is the chord of the blade. If the Reynolds Number is greater than about 500,000, and turbulence is somehow kept to a minimum, then the ratio L/D becomes large, usually much greater than 1. In this case, if forces acting on the blades are allowed to perform a mechanical work, it is well known that the mechanical power developed on the rotary shaft attached to the blades is proportional to Vφ3. Therefore, the useful power generated may be increased simply by augmenting the fluid velocity Vφ before the fluid flow strikes the blades. This is done by making the fluid flow pass first by an accelerating chamber or convergent nozzle.
Henceforth some fundamental assumptions are made: First, In order to properly apply the Bernoulli Equation, the fluid is assumed to be laminar, incompressible and inviscid (Page 99 of Ref.1, as cited as the end of this detailed description). Liquid fluids will be considered as incompressible. In the case of a gas fluid, like air, it will be considered as incompressible if the fluid flow speed striking the turbine or fan blades is kept below 0.3 Mach, i.e., below 102 m/s, for air. Fluid viscosity is assumed to be very small to ensure an inviscid fluid (Page 94 of Ref.1). Second, Reynolds Number for the turbine blades is not less than 500,000. Third, Internal surfaces in contact with the fluid inside the machine are very well polished, so, apart from the fluid entrance and the fluid exhaust, the machine has no fluid leakage.
Convergent and divergent nozzles may be used in a power conversion machine incorporating fluid acceleration and deceleration.
The cross-sectional area as seen by the fluid flow at the entrance of the convergent nozzle is given by
A
p1=(π/4)D12 (1)
The cross-sectional area as seen by the fluid flow at the exit of the convergent nozzle is given by
A
φ2=(π/4)(D+d)(D−d) (2)
It may be shown by applying the continuity equation that if the fluid velocities at the entrance of the FAC and at the exit of the FAC are Vφ1 and Vφ2, respectively, and the cross-sectional areas at the entrance of the FAC and at the exit of the FAC are Aφ1 and Aφ2, respectively, then
V
φ2=(Aφ1/Aφ2)Vφ1 (3)
The parameter Fluid Velocity Multiplier kf is defined as
k
f=(Aφ1/Aφ2)=Vφ2/Vφ1 (4)
Fluid velocity Vφ2may be made greater than Vφ1 by making the multiplying factor kf greater than 1 , i.e., by making Aφ1>Aφ2.
If geometric parameters D and d are fixed so it will be the FAC exit cross-sectional area Aφ2, according to Eq. (2). Hence the fluid velocity multiplier kf may be increased by making the input cross-sectional area Aφ1 bigger than the FAC exit area Aφ2. Since
A
φ1=(π/4)D12 (5)
Aφ1 may be increased by making input diameter D bigger. For this purpose the latter is defined as
D
1
=D+kd (6)
Where k is an integer, (k=0, 1, 2, 3 . . . ). The value k=0 corresponds to the case when the energy conversion machine uses no convergent nozzle.
Then, by substituting Eq. (6) in Eq. (5)
A
φ1=(π/4)(D+kd)2 (7)
substituting Eq. (7) and Eq. (2) in Eq. (4),
k
f(D+kd)2/(D+d)(D−d) (8)
The fluid-acceleration chamber may have many possible shapes, but to simplify its manufacturing and to minimize turbulence the shape shown in
The length of the convergent nozzle may be may be calculated from the formula
I
n
=kd/(2 tan β) (9)
As is shown at pages 3-7 of Ref. 2, the increase in wind velocity caused by a convergent nozzle brings about a reduction of a few degrees in the airflow temperature and this fact may be exploited to extract water out of the atmosphere as a useful byproduct of the convergent nozzle. As to the internal concentric truncated cones, shown in nozzles in
In some embodiments, the guide vanes are thin rigid elements that may be made of materials like metal, plastic, carbon fiber, glass fiber, etc. The larger the number of these sub nozzles the less the turbulence, but the greater becomes the drag force and the weight of the FA chamber.
Hence a compromise becomes apparent.
l>ln7>ln6>ln5>ln4>ln3>ln2>ln1>0
In
V
φ4
=V
φ3
/k
f (10)
On the other hand, the divergent nozzle input and output cross-sectional areas, Aφ3 and Aφ4, respectively, are also related by
A
φ3=(Aφ4/kf) (11)
Where kf is given by Eq. (8)
k
f=(D+kd)2/(D+d)(D−d) (8)
And k is an integer, (k=0, 1, 2, 3 . . . ). The value k=0 corresponds to the case when the energy conversion machine uses no divergent nozzle.
The purpose of the divergent nozzle is to reduce the fluid speed Vφ3 at its entrance, and preferably as much as possible to minimize fluid power loss at its exit. As in the case of the convergent nozzle, the slope angle β of the divergent nozzle is taken to be not greater than 10° so as to minimize turbulence. In the case of a symmetrical energy conversion machine, defined as one having convergent and divergent nozzles of identical shape and size, the divergent length In may be calculated also from Eq. (9).
In some embodiments, the turbine is the same or similar to the Thermal Airfoil Turbine, as described in Reference 3. As an example of this turbine,
As shown in
An alternative FAC shape is shown in
An aerodynamic fluid turbine may be formed by a set of rotary streamlined airfoils or blades placed and attached around the periphery of an internal central circular cylinder of diameter d, and surrounded by another external circular cylinder of diameter D (D>d>0), as is shown in
The primary function of the flow straighteners is to increase the laminarity of the flow before the fluid strikes the airfoils. There may be several cylindrical vanes in a flow straightener but again a compromise may be apparent between the number of vanes and its weight and the increase in drag force they bring about.
The Exhaust Chamber (which may be arranged by result of rotating a convergent nozzle like as shown in
The purpose of the exhaust chamber is to gradually reduce the fluid velocity from its value vφ in the throat down to the value vφo just outside the exhaust chamber and thus to decrease the power of the exhaust fluid as much as possible. (See
The total length of the energy conversion machines shown in
L=2ln+lth (12)
Where lth is the throat length equal to 4lt for both machines. In general,
lth=Nlt (13)
Where N is the total number of spaces of length lt that may be accommodated in the throat length. The total width of the energy conversion machine is
W=D+kd (14)
A feature of the energy conversion machine is the fact that the fluid turbines are placed in a position perpendicular to the direction of the fluid flow, with their blades all facing the oncoming flow. As a result, all the turbine blades are impacted simultaneously by the fluid flow.
In general, energy conversion machines may be classified as open chamber or closed chamber energy conversion machines. In the open chamber variety the operating fluid may enter and leave the machine, as shown in
There are at least two ways of having the fluid flow within the energy conversion machine: it may be artificially generated at the entrance of the FA chamber by one fan or within the throat by one or more fans. In this case the energy conversion machine may be open or closed.
Alternatively, if the fluid is external to the machine, it may be captured by the FA chamber by allowing it to enter the chamber. Hence, for an open chamber energy conversion machine, the FA chamber or converging nozzle has the following functions: 1. To capture or generate the fluid flow. 2. To increase the fluid velocity, and 3. To conduct the flow toward the Venturi-like throat. In the throat the flow will impinge on one or more sets of turbine foils or fan blades which in accordance to aero dynamical laws will extract part of the flow thermal energy. Thus the energy conversion machine may generate more mechanical energy than the input flow kinetical energy, as shown in the calculation results of Table I.
The open chamber energy conversion machine may be stationary and the external fluid flow may be a wind flow, a tidal flow, a submarine current, a stream, or a river current. Alternatively the machine may be mobile, and in contact with the external fluid, i.e., it may be carried by a vehicle moving at a velocity Vφ1 through the surrounding fluid. In this case the FA chamber of the energy conversion machine may be used to capture the fluid and to increase its velocity up to a certain value Vφ2. In the event the energy conversion machine used is hermetically closed or placed within a fixed location like a house room, the fluid flow is created artificially by one fan placed within the FA chamber or one or more fans placed within the throat. In the latter case, the energy conversion machine may be open or closed.
As shown in
The Venturi-like throat houses the turbines or fans which are placed coaxially inside it. The fan shafts may be interconnected, or not. The purpose of the fans is to generate mechanical and/or electrical energy out of an incoming fluid that has been previously accelerated in a convergent nozzle. Usually the turbine airfoils or the fan blades are placed forming a setting angle γ with the flow direction of about 45 °, as may be seen in
A particular variety of the acceleration fluid machine, the symmetrical energy conversion machine, is shown in
Mechanical Power Calculations Consider a fluid turbine (which may also be an electric fan, with driving motor M, like the one shown in
V
φ2
=V
φ3
k
f
V
φ1 (15)
Where the fluid velocity multiplier kf is given by Eq. (8). It is worth noting than in a conventional wind turbine where no throat is present normally Vφ3<Vφ2 because the turbine blades decelerate the incoming wind speed Vφ2. (Reference 4, page 6). But in an energy conversion machine due to the presence of the throat velocities Vφ3 and Vφ2 are the same if an inviscid fluid is assumed.
V
φ2
=V
φ
V
B (16)
The angle formed by the apparent velocity vφ and the blade chord c is the attack angle a, and the angle formed by the chord c and the plane of rotation is the setting angle y. From
φ=α+γ (17)
Henceforth it will be assumed that the turbine blades have a constant setting angle y, a constant thickness t, a constant chord c, and a constant span s. The latter is given by
s=(D−d)/2 (18)
From
V
φ
=V
φ2/sin φ (19)
If flow angle φ is less than 90°, it may be seen from Equations (19) and (15) that the following inequality is fulfilled for an energy conversion machine
Vφ>Vφ2>Vφ1 (20)
Forces dD and dL are given by (Reference 4, page 10)
dD=C
D
ρV
φ
2
cdr/2 (21)
dL=C
L
ρV
φ
2
cdr2 (22)
Where CD=Drag coefficient of blade; CL=Lift coefficient of blade; p=Density of the accelerated fluid.
The torque on the blade element, dT, may be shown to be given by (Reference 4, p.11)
dT=ρV
φ
2(CL sin φ−CD cos φ)crdr/2 (23)
This torque around the central axis of rotation causes the rotary movement of the blade element. Accordingly if the turbine has Nb blades, it may be readily shown that the average mechanical power developed by the turbine on its shaft is
P
g
=N
b
ωρV
φ
2(CL sin φ−CD cos φ)c(D2−d2)/16 (24)
Where ω is the turbine rotational speed in radians per second which may be converted into n, revolutions per minute (RPM) by
ω=πn/30 (25)
By combining Eq. (24) and Eq. (25)
P
g=(π/480)ρ(CL sin φ−CD cos φ)Nbc(D2−d2)nVφ2 (26)
On the other hand, it may be readily shown that
n=15 [NpρNb(D2−d2)c(CL sin φ−CD cos φ)/(πlt)]1/2Vφ (27)
Where lt is the turbine's moment of inertia about its rotational axis, and Np is the total (integer or fractional) number of periods the turbine rotates to reach constant speed n, when starting from n=0. Np is a quantity that may be measured experimentally for each turbine.
By substituting Eq. (27) into Eq. (26) the following relationship is obtained
P
g
=[πN
p/(16lt)]1/2 [ρNbc(D2−d2)(CL sin φ−CD cos φ)]3/2Vφ3 (28)
Equation (28) clearly indicates that in order to maximize the mechanical power generated by a single turbine it is more effective to increase velocity Vφ (By increasing fluid velocity Vφ2 in the Venturi-like throat) than increasing factors (CL sin φ−CD cos φ), Nb, c and or (D2−d2). This approach may be used to design an energy conversion machine, and for this purpose the FA chamber is used to to increase the incoming fluid velocity Vφ so that the fluid reaches the Venturi-like throat with maximum speed Vφ2.
The total mechanical power generated may also be increased by augmenting the number of fluid turbines (or fans, for that matter). If Nt identical fluid turbines each with Nb blades are contained within the Venturi-like throat of an accelerated fluid machine, the total mechanical power generated by the Nt fluid turbines is:
P
g=(π/480)ρ(CL sin φ−CD cos φ)NbNtc(D2−d2)nVφ2 (29)
Calculation of the Mechanical Power Gain for an AF Machine The input power of the fluid at the inlet of an energy conversion machine is given by
P
φi
=ρA
1
V
φ1
3/2 (30)
Where Ai is the inlet cross-sectional area at the entrance of the FA chamber of diameter D+kd, as shown in
A
1=(π/4)(D+kd)2 (31)
And the input fluid power may be expressed as
P
φi=(πΣp/8)(D+kd)2Vφ13 (32)
But, by using Eq. (8),
(D+kd)2=(D+d)(D−d) kf (33)
Then Pφi may be written as
P
φi=(πρ/8)(D+d)(D−d)kfVφ13 (34)
By combining Eq. (19) with Eq. (15), Vφ may be expressed as
V
φ
=k
f
V
φ1/sin φ (35)
By substituting Eq. (35) in Eq. (26),
P
g=(π/480)ρ(CL sin φ−CD cos φ)Nbc(D2−d2)nkf2Vφ12/sin2φ (36)
Which for Nt identical AF turbines may be written as
P
g=(π/480)ρ(CL sin φ−CD cos φ)NbNtc(D2−d2)nkf2Vφ12/sin2φ (37)
Let us now define the Mechanical Power Gain, or Efficiency, Gpm, of the energy conversion machine as
G
pm=Pg/Pφi (38)
And by substituting Equations (34) and (37) into Eq. (38), for Nt turbines
G
pm
=[k
f/(60 sin2φ)][ρ(CL sin φ−CD cos φ)NbNtc](n/Vφ1) (39)
It may be seen from Equation (39) that the mechanical power gain Gpm may be increased effectively by making the fluid velocity multiplier kf as large as possible and this may be done simply by increasing the value of the integer k for the accelerating nozzle as may be seen from Eq. (8). Another less effective way consists of increasing the ratio (n/Vφ1), and/or increasing the value of ratio CL/CD and/or parameters c, Nb, and Nt.
The Accelerated Fluid Turbine System may operate in a self-sustained regime if
Gpm>1 (40)
According to Eq. (39) for an energy conversion machine this inequality is equivalent to
[kf(60 sin2φ][ρ(CL sin φ−CD cos φ)NbNtc](n/Vφ1)>1 (41)
Equation (41) is the condition for an energy conversion machine to achieve a self sustained movement, and this is quite feasible to obtain as shown in the example below.
Numerical results are shown below for an Accelerated Wind Turbine For an Accelerated Wind Turbine (AWT), which is a particular type of an energy conversion machine in which the operating fluid is the wind, with parameters: D=50 cm; d=30 cm; CD=0.040163; CL=0.46852; c=15 cm; s=10 cm; φ=45°; Vφ1=5 m/s; Nb=8 blades; Nt=4 turbines; n=900 rpm, and by applying Equations (8), (9), (15), (1 9), (32), (37) and (38), respectively, the results shown in Table I were obtained for kf, ln, Vφ2, φ, Pφi, Pg, and Gpm, both for k=1, and k=2.
Thus for this particular AWT and wind speed it is possible to achieve a self-sustained motion and generate a mechanical power of 4.820 kW for k=2.
Instead of aerodynamic fluid turbines, like the one shown in
Henceforth, in order to differentiate the schematic diagram of an aerodynamic fluid turbine, like the one shown in
Similarly, to facilitate modular construction of the energy conversion machines, both the divergent and convergent nozzles, like the ones shown in
The front and back faces of both types of building boxes will normally be left open to allow the interconnection of modules, but the side faces will normally be closed to avoid fluid leakage. When interconnecting these building blocks together the fluid is allowed to flow from an open inlet nozzle of diameter D+kd to one or more electric fans placed coaxially in the throat only through the annular fluid passage bounded by external diameter D and internal diameter d, to finally exit the machine through an open outlet nozzle of diameter D+kd, if the latter is used, otherwise the outlet will be just one of the throat annular ends.
With the above mentioned building blocks it is possible to build a large variety ofenergy conversion machines. As an example,
lth=Nlt (42)
Assuming the fluid is incompressible, the maximum number of fans and fluid straighteners that may be placed coaxially within the throat is only limited by the shear stress appearing in internal walls and rotary blades due to the fluid viscosity μ that tend to close the flow passage as the number of fans is increased. Such an upper limit is established experimentally. If the fluid is a liquid (such as water) it may be considered incompressible for all practical engineering purposes (Page 29 of Reference 1). If the fluid is a gas like air it may be considered as incompressible if the flow velocity in the throat is kept below about 0.3 Mach (Page 128. of Reference 1). This is an important property of the present energy conversion machines which normally cannot be achieved in conventional wind turbines, because they are generally designed to extract kinetic energy from the incoming wind, thus reducing its speed. On the contrary, in an accelerated fluid machine the incoming fluid is first accelerated in the FA chamber before striking turbine airfoils or fan blades placed in the Venturi-like throat.
There are at least two possible modes of operation for the electrical motor of an electrical fan. It may operate either as an electrical motor proper, or as an electric generator. In the first case a power supply is connected to the motor leads in order to create or reinforce the fluid flow. In the second case the motor leads are connected to an electric load and the rotary fan blades may spin as the result of a previously accelerated fluid impacting onto them. The accelerated fluid may be produced by one or more electric fans acting as starting motors or, it may stem from a natural source like the wind, airflow or a water flow made to enter into the fluid acceleration chamber. When the latter situation takes place it may be considered that the fluid acceleration chamber has captured the external fluid flow. The fan blades mounted on the periphery of the fan rotor spin either when driven by the fan motor, or when impacted by the accelerated fluid flow. According to Faraday's Law, a voltage may be induced between the open leads of the fan motor that then performs as an electric generator capable of converting the rotational movement of the blades into an electrical current. Thus an electrical fan may operate either as a motor or as a generator. In the first case the fan will be referred to as a motor fan and in the second case either as a generator fan or a fluid (air, wind or water) turbine. The axes or shafts of the motor fan(s) and the generator fan(s) may be mechanically attached, or may be unattached but keeping always their co linearity.
Enclosed within the Venturi-like throat there may be at least one fan working as a generator fan, but it is possible for one or more of the electric fans to perform as motor fans. For example, in
Both motor fans and generator fans may be physically identical or very similar, except perhaps for their internal electrical resistance. In fact, as is shown in Section Self Sustainable Fluid Electric Generator it is usually desirable for the total internal resistance of the generator fans to be much lower than the total internal resistance of the motor fans. In addition, the motor and the generator may be either dc or ac machines. Likewise, the blades of both motor fans and generator fans may be identical or very similar.
Accelerated Fluid Machines may be classified either as mechanical motors or as electric generators. In the first case there is no generation of electric energy, but just mechanical energy by mechanical fans or fluid turbines as their blades are rotated by a previously accelerated fluid. In the second case the mechanical energy generated is converted into electrical energy by one or more electric generator fans or by an ad hoc electric generator attached to the turbines shaft. Hence, depending on whether the intervening fluid is air or water, there are 5 main types of energy conversion machines, namely, the Air Motor (AM), the Water Motor (WM), the Air Electric Generator (AEG), the Water Electric Generator (WEG), and the Accelerated Wind Turbine (AWT).
The AW turbine in the example shown in
Note that basically the same energy conversion machine shown in
Any suitable material, like plastic, metal, etc., may be used to manufacture the fluid acceleration chamber and the exhaust chamber, provided it is light and resistant to degradation by the environment. The internal walls of the chambers have to be as smooth as possible to minimize power losses caused by the wall shear stress. In the remainder of this specification it will be assumed that the internal walls of the chamber are perfectly polished and have no leaks.
Regarding the thickness of the chamber walls, it is desirable for it to be as little as possible in order to keep machine weight as low as possible, but without compromising its sheltering properties.
Regarding the fan blades of the energy conversion machine, they may be made out of plastic materials, resin, acrylic, or others. The two cylinders may be made with a light metal such as aluminum, or a light and hard plastic as well, etc., but weight may be minimized without compromising the material endurance and strength.
Important as to the possible values for the geometrical parameters D and d, the only requirement they may satisfy is: 0<d<D. As may be seen from Eq. (28), the useful power Pg generated by the fan or turbine blades is proportional both to (D2−d2) 3/2 and to Vφ3. Hence the greater the values of these quantities the greater the generated power will be.
It should be noted that although it is possible to use inlet and outlet terminations with k=0, (i.e., no nozzles)such embodiments are less preferred on the account of the larger turbulence of the exhaust terminations and the lack of the convergent nozzle to amplify the incoming fluid velocity.
According to Equations (4) and (10) it is readily apparent that the fluid acceleration chamber multiplies the incoming fluid velocity Vφ by a factor kf, whereas the exhaust chamber divides the fluid velocity vφ3 in the throat by the same factor if the accelerated fluid machine is symmetrical. Of course the greater the value of k the greater will be the size of the machine, according to Eq. (9), the parameter kf, according to Eq. (8), and the generated power Pg, according to Eq. (37). On the other hand, the greater the value of k the smaller the output velocity vφ4, according to Eq. (10), and the turbulence and power losses at the output.
The power Pφ2 that is applied to the fan blades is
P
φ2=ρAφ2Vφ23/2 (43)
And the input power of the fluid at the inlet of the open chamber energy conversion machine is given by
P
φi
=ρA
φ1
V
φ1
3/2 (30)
By combining Equations (3) (4), and (30)
P
φ2=kf2Pφi (44)
Thus, according to Equations (8), and (44), the higher the value used for the parameter k the higher will be the fluid velocity multiplier kf and the fluid power Pφ2 applied to the turbine blades. In conventional design of horizontal axis wind turbines the oncoming wind power Pφi is applied directly to the turbine blades. In contrast, in these Accelerated Wind Turbines there is applied first the oncoming wind power Pφi to the FA chamber to increase it kf2 times up to the power Pφ2 which is then applied to the turbine blades. As a result the power Pφ2 of the fluid impacting the wind turbines may be made many times bigger than the power Pφi of the external wind. This in turn results in accelerated wind turbines with much higher efficiency than conventional HAWT machines.
In what follows it may be stressed that if an energy conversion machine is shown as implemented solely with fans, it is clear that it may also be implemented with thermal airfoil turbines, and vice versa.
A vehicle moving in a fluid with a certain velocity Vφ1 gives rise to a flow of such a fluid at the same velocity. The flow is present in a certain finite neighborhood in contact with the moving vehicle. On account that this fluid flow contains thermal and kinetic energy, the space surrounding this vehicle may be considered as an energy space. The extent, boundaries and properties of the energy space at each point have as yet to be evaluated. However it is apparent that a suitable energy conversion machine placed in the vehicle in motion and in contact with this energy space will be able to extract part of the energy contained in the latter.
A fluid panel may include any structure composed of more than one energy conversion machine forming a wall or flat panel that may be attached to a vehicle or placed on a platform or on a stationary building for the purpose of capturing part of the energy contained within the surrounding energy space. Typically a fluid panel may be a Wind Panel or a Water Panel if the fluid in the energy space is a wind, or water, respectively. In the first case, the wind panel is attached to a vehicle, fixed building, or platform immersed in the energy field. Typically it may be mounted at the roof or on the sides of the vehicle and facing the wind, or it may be submerged in water if the vehicle moves in this medium.
Fluid panels may alternatively be placed on a stationary structure, such as the roof of a house or building to extract energy from the wind or may be submerged and attached to the bottom of a body of water such as a stream, river, sea, etc., to extract energy from the underwater flows. A basic building block that may be used to implement a fluid panel is shown in
A Fluid Electric Generator (FEG or FE generator) may be defined to include an energy conversion machine that produces electric energy out of a previously accelerated fluid flow.
To implement the FEG two fundamental elements are required: First, an accelerated fluid flow within the Venturi-like throat; Second, one or more electric fans placed coaxially within the latter in such a way that their hub diameters coincide with the diameter d of the inner cylinder, and the fan blades occupy partly or totally the empty space of width (D−d)/2 in the throat as is shown in
At least one of the electric fans placed coaxially within the throat may be operated as a generator fan or turbine, i.e., its electric leads are not connected to a power supply but instead they are left open or connected to an electric load, and its blades are allowed to rotate as the result of being impacted by the accelerated fluid.
There are at least two ways for accelerating a fluid flow, namely: 1. by allowing the surrounding fluid external to the machine to enter the fluid acceleration chamber where it is accelerated on account of the continuity equation. In this case the FA chamber has the function of capturing part of the fluid surrounding the machine; 2. By artificially generating the fluid flow inside the Venturi-like throat by operating one or more fans as motors proper. This is done by connecting the motor fan electric leads to a power supply. In the first case, the fluid flow is accelerated within the fluid acceleration chamber reaching its final velocity Vφ2 at the throat. When the fluid flow is artificially created, the fluid acceleration chamber may be open or closed. This may be done with the arrangement shown in
In another arrangement, it is possible to place an electric fan with a diameter not greater than D1=D+kd at the entrance of the FE generator, as is shown in
It should be noted that for accelerated wind turbines and for water electric generators fan F at left entrance in
Both in the vertical water electric generator (WE generator), shown in
A particular form of a fluid electric generator is the Accelerated Wind Turbine (AWT or AW turbine), an example of which is shown in
By applying the continuity equation it may be readily show that the relationship between wind speeds vφ and vφ2 is given by either one of the following equations
Vφ2=kfVφ1 (15)
Where kf is given by Eq. (8) as
k
f=(D+kd)2/(D+d)(D−d) (8)
Example Assuming k=1 , vφ1=20 Km/h; D=0.5 m, and d=0.31 m, the result is D+d=0.81 m; Vφ2=85.26 km/h. In other words, the fluid acceleration chamber in this case multiplies the entering wind speed by a factor greater than 4, which leads to a considerable increase in the generated power and efficiency of the AW turbine, as may be seen from Eq. (29) and Eq. (39) in Sections Mechanical Power Calculations and Calculation of the Mechanical Power Gain for an AF Machine.
Notice that in order to achieve a higher output power in a conventional horizontal axis wind turbine (HAWT), usually the size (length) of the blades is augmented to increase the area swept by the blades. However, usually no attempt is made to obtain higher output power by increasing the velocity of the incoming wind before it impacts the blades. In contrast, in the present Accelerated Wind Turbine, the velocity of the wind outside is increased in the fluid accelerating chamber by a speed multiplying factor kf, given by Eq. (8). This approach of raising the wind speed to increase the wind turbine efficiency is much more effective and economical than making the blade size bigger, taking into account that output power is proportional to the cubic power of the wind speed striking the blades, as shown in Eq. (28), Section Mechanical Power Calculations, and that a bigger blade means a heavier one, a greater moment of inertia lt, and hence, a lower turbine rotational velocity n, and a smaller generated power Pg, as shown by Equations (27) and (28).
The Fluid Electric Generator may be viewed as a system with one input and one output. The input is the electrical power applied to the electric motor or motors (by a battery, mains or a power supply). The output is the useful electrical power developed at the electric load. Also, the FEG may be initially viewed as composed of two main active components, namely, one equivalent electric motor, and one equivalent electric generator. The purpose of the electric motor is to produce the accelerated fluid. The purpose of the electric generator is to extract energy from the accelerated fluid and to convert it into electrical energy. Thus the FEG may be represented by the model shown in
The electrical power gain of the FEG is defined as
G
pe
=P
o
/ P
i (45)
Where P0 is the electrical power developed by the machine at the load resistance RL, and Pi is the electrical power applied by the power supply to the electric motor.
The FEG machine may operate as a self sustainable generator if the electrical power gain Gpe is greater than unity. The following will show that the FEG may be self sustainable if a certain relationship among the motor input resistance Ri, the generator output resistance R0, the applied input voltage vi, and the electromotive force vg is fulfilled. For the worst case of maximum input power, the counter electromotive force vgc=0, and
Pi=vi2/Ri (46)
But, for maximum power transfer it may be shown that
P
o
=v
g
2/(4Ro) (47)
For self-sustained operation, it is required that
Gpe>1 (48)
This in turn requires that
Po>Pi (49)
Or
v
g
2/(4Ro)>vi2/Ri (50)
From Eq. (50), the condition required for the FE generator to be self sustainable may be obtained:
v
g>2(Ro/Ri)1/2vi (51)
For example, if the motor and the generator are chosen such that Ro=10−2Ri then for self-sustained operation, it is required that
Vg>0.2Vj
Output voltage in open circuit: 15.54 V
The Vertical Accelerated Water Machine is in one embodiment an open chamber accelerated fluid machine positioned in a vertical or upright position between a superior reservoir or water tank 1 , and an inferior reservoir or water tank 2, as shown in
It will be assumed that water tank 1 is large (compared to nozzle diameter D1), and in contact with the atmosphere both at level 0 and at level 1, where some tiny perforations may be made to allow the entrance of air but not water leak. Therefore pressure at level 0 of water tank 1 is p0=0, and at level 1 is pi=0. Water velocity at level 0 is V0=0, and at level 1 is:
V1=√[2gh0] (52)
But according to the continuity equation, water flow velocity al level 2, is given by
V
2
=A
1
V
1
/A
2 (53)
Where the cross sectional areas A1 and A2 seen by the falling water stream at levels 1 and 2 are
A
1=π(D+kd)2/4 (54)
A
2=π(D+d)(D−d)/4 (55)
V
2=(D+kd)2V1/[(D+d)(D−d)] (56)
Note that water velocity at level 2 is obtained by multiplying velocity at level 1, V1 by the Water Velocity Multiplier factor kf, given by
k
f=[(D+kd)2/(D+d)(D−d)] (8)
Which is always greater than 1 if 0<d<D, which is always the case for an energy conversion machine.
Length h1 of the AWM may be chosen to prevent cavitation from taking place by ensuring that water pressure al level 2, p2, satisfies the following relationship
p2>Water vapor pressure pv=−97.09 kPa, at 30° C. (57)
On the other hand, by applying Bernoulli Equation to a water flow line between levels 1, and 2, it is obtained, assuming a steady, inviscid, and incompressible flow,
p
2=(½)ρ(V12−V22)+ρgh1 (58)
p
2=(ρ/2)(V12)(1−kf2)+ρgh1>pv (59)
h
1=(1/ρg)p2+(kf2−1)h0 (60)
For the accelerated water machine to be realizable it is required then that
p2>pv (61)
And
h1>0 (62)
Now defining p2min as the minimum value of pressure p2 that makes height h1 as given by Eq. (60) equal to zero.
Thus, from Eq. (60):
p
2min=(1−kf2)(ρgh0) (63)
Now defining kfmax as the maximum value of kf for which p2min=pv. This is an upper bound for factor kf to fulfill realizability conditions:
p2>p2min>pv (64)
h1>0 (65)
And
kf<kfmax (66)
Thus
k
fmax=√[1−(pv/ρgh0)] (67)
If Inequalities (64) and (66) are satisfied, cavitations will not take place.
For example, supposing h0=0.3 m, D=0.5 m, and d=0.3 m, p=995.7 Kg/m3, g=9.8 m/s2, then
k=1:
kfmax=5.85
kf=4<kfmax
k=2:
kfmax=5.85
kf=7.56>kfmax
So, discarding k=2, and taking k=1. Then
V
1=√[2(9.8)(0.3)]=2.42 m/s
V
2
=k
f
V
1329.70 m/s
And
p
2min=(1−kf2)(pgho)=−43,910.37 Pa
Taking
p2=Δ40,000.00 Pa>Δ43, 910.37 Pa>pv=−97,090 Pa
Then,
H
1=(1/pg)P2+(kf2−1)h0=0.40 m
Note that in order to get V2=9.70 m/s with a free water jet using just gravity, the required tank depth h0 plus the termination length hi would have been:
h
0
+h
1
=V
2
2/(2 g)=4.8 m
Whereas with the water motor for achieving the same speed it is only required that
h
0
+h
1=0.3+0.4=0.7 m, and p2=−40 KPa,
An 85.42% height reduction results. This is a definite advantage of the present accelerated water energy conversion machine over conventional hydraulic machines, and may be achieved by by making h1>0, and p2>P2min—By applying Bernoulli Equation at levels 2 and 3 and noting that V2=V3 the following equation is obtained
p
3
=p
2
+ρgh
2 (68)
If P2>pv, then p3, p4, etc., will all be greater than pv, and no cavitations will take place.
For example, assuming h2=0.25 m, and the same geometrical parameter values as before,
P3=P2+Pgh2=−40,000.00+(995.7)(9.8)(0.25)
p
3=−37,560.54 Pa>pv=−97,090 Pa
Suppose that Nr identical axial fans (water turbines), each with Nb blades, are placed within the water velocity enhancer of cross-sectional area A2 given by Eq. (55). Then for the following parameters, with just one turbine (Nt=1), having Nb=8 blades, blade coefficient values: CD=0.040163; CL=0.46852, blade span s=0.09 m; blade chord c=0.175 m, D=0.5 m, d=0.3 m, φ=45 °, h0=0.15 m, n=900 rpm, and by applying Equations (8), (52), (53), (19), (30), (29), (38), (63), (67), (60), and (9), respectively, the results shown in Table IV are obtained for the parameter kf, fluid velocities V and V2, relative fluid velocity Vφ, input flow power Pφi, generated mechanical power Pg, mechanical power gain Gpm; P2min; kfmax; h1, and nozzle length ln. The calculations were done for two values of parameter k, namely:
k=1, and k=2, and assuming p2=−18,000 Pa>p2min; P=995.7 kg/m3; g=9.8 m/s2.
For k=1 , generated power Pg (37.438 kW) is much greater than input power Pφi (1.262 kW), and may be used to drive an electrical generator, which in turn may be used to power a pump and the remaining electric appliances of the house. Alternatively the pump may be driven directly by the rotary water turbines. Thus for this particular AW machine it is possible to achieve self sustained motion (Gpm=29.68>1), and generate a mechanical power of 37.438 KW. Of course, the power generated may be increased by a factor Nt simply by using Nt>1 water turbines. Even substantially better results are obtained for k=2, as may be seen from the results of Table II. Since for k=1, ln turned out to be greater than h-i , the length of the top nozzle is taken as h−i=0.41 m rather than In=0.95 m, with very little increase in turbulence as the water flow accelerates in the upper nozzle.
In order to make realizable the accelerated water energy machine the following conditions may be satisfied
ho>0 (69)
h1>0 (70)
p2>p2min (71)
And p2min is given by Eq. (63) for the symmetric AW Machine. Equation (69) implies that water tank 1 may never be allowed to empty. If a water pump is used for replenishing the water tank 1 it is required then that the refill time of the latter may be less than the time required to empty it. Accordingly the water flux Qp from the water pump is greater than the water flow Q−i, that is to say
Qp>Q1 (72)
Where
Q1=A1V1 (73)
An open chamber horizontal water machine may be implemented using an open chamber AW machine like the one shown in
The design of a horizontal water electric generator is very similar to that of the vertical water electric generator as explained supra with reference to the Vertical Accelerated Water Machine, except that gravity has no effect in this circumstance. Additionally the water pressure po at depth ho and at the entrance of the machine is
po=pgh0 (74)
This is greater than atmospheric pressure, as may be seen from
Consider the horizontal water electric generator shown schematically in
For the water flow line between positions 0 and 1 inside the WE generator, and assuming steady, inviscid, and incompressible flow Bernoulli Equation may be written as
p
o+p(V02)/2=p1+ρ(V12)/2
Hence
p
i
=p
o−ρ(V12−V02)/2
But
V12=kf2V02
And
V0=Vφi
And kf is given by Eq. (8). Then
p
1
=p
o
−p(kf2−1)V02/2 (75)
If V0 and ho are known, then kfmay be chosen to make sure that pi will be greater than −97,090 Pa to prevent the occurrence of cavitations.
Thus
k
fmax=√{1+[2(p0−pv)/ρV02]} (76)
And
V
0max=√{2(p0−pv)/[ρ(kf2−1)]} (77)
Of course, the higher the value of po, the higher may be the values of kfmax and V0max.
In
Open Fluid Acceleration Machine with Radial Fans
The open fluid acceleration machine using radial fans may be implemented by connecting by their straight section two radial fans like the ones shown in
Two or more energy conversion machines of different cross-sectional areas, like the ones shown in
D
2
+k
2
d
2
D
1 (78)
Where this the throat diameter of the machine 1, as shown in
D1+k1d1 (79)
Where k1 is an integer (k1=0, 1, 2, 3 . . . ).
On the other hand, if the fluid speed at the entrance of AFM1 nozzle is vφ fluid speeds in AFM1 throat and AFM2 throat are, respectively,
Vφ1=kf1Vφi (80)
Vφ2=kf2Vφ1=kf1kf2Vφ1 (81)
Where kf1 and kf2 are given from Eq. (8) by
k
f1=(D1+k1+d1)2/[(D1−d1)(D1−d1)] (82)
k
f2=(D2+k2d2)2/[(D2+d2)(D2−d2)] (83)
Eq. (81) may be generalized for j turbines in tandem (j=2, 3 . . . etc.), and the fluid velocity in throat of nth turbine may be written as
Vφj=kf1kf2 . . . kfjVφ1 (84)
Where
k
fj=(Dj+kjdj)2/[(Dj+dj)(Dj−dj)] (85)
Of course if power generated separately by each energy conversion machine are Pg1, Pg2, Pg3, etc., the total power Pg generated by j machines in tandem will be
P
g
=P
g1
+P
g2
+ . . . P
gj (86)
Accelerated Fluid Machines may also be implemented in a closed chamber arrangement, where the operating fluid (typically air or water) is confined and not allowed to escape to the environment. Two possible shapes for the closed chamber that may be used for axial fans and thermal airfoil turbines are the constant cross-sectional area toroids, shown in
In addition, two large similar electric fans, each of diameter D1+kd1; are placed in the middle of the curved section of the toroid for the purpose of creating the fluid that will make the turbines spin, after being accelerated in the accelerating nozzles N1 and N3. The fluid created by the fans is made to circulate in a single direction, for example clockwise and is decelerated in diverging nozzles N2 and N4.
A third shape for the closed chamber that may be used with radial (centrifugal) fans consists of two identical open chamber energy conversion machines for radial fans, like the one shown in
The closed fluid acceleration chamber may be used in all energy conversion machine applications, except for wind generator applications that require an open chamber. On the other hand, the open fluid acceleration chamber in any of its varieties may be used in all AFM applications including accelerated wind turbine applications.
In the next sections various possible applications of the accelerated fluid machines are proposed.
Any moving land, air or water vehicle may generate all or part of the electricity it requires by using an Accelerated Fluid Electric Generator, either in open chamber or in closed chamber fashion, attached to the structure of the vehicle. In
For high power requirements, a battery of several water electric generators fed from the same water tank or reservoir may be used, as is shown in
For capturing wind coming from several directions, several Accelerated Wind Turbines each pointing at a different direction may be placed in horizontal platforms separated vertically from each other, as shown in
The main embodiment presented herein is the accelerated fluid machine and its variations, namely, the water electric generator, the air electric generator, and the accelerated wind turbine. Combinations of energy conversion machines like the fluid panel and the tandem energy conversion machines have also been proposed to achieve higher power generation. It is proposed to employ symmetrical energy conversion machines and electric brushless dc axial fans with high flowrate Q to implement each of them.
A preferred manner to implement the air electric generator, the design process may be divided into two parts, namely, the mechanical power calculations, and the electrical power calculations. The mechanical power calculations are carried out as explained in sections Mechanical Power Calculations, Calculation of the Mechanical Power Gain for an AF Machine, and Condition for Self-Sustained Movement of the Fluid Turbines. The purpose of these calculations is to determine the required number of fans, Nt, the number of revolutions per minute, n, for a given fluid speed Vφ1, the input power P, the generated power Pg, and the mechanical power gain Gpm to ensure a self sustainable movement, i.e. Gpm>1. Once this is achieved the electric power calculations are carried out as explained in sections Electrical Power Calculations, and Self Sustainable Fluid Electric Generator, keeping in mind that the electrical power gain Gpe may be greater than 1 for self sustainability; hence the total input resistance R, of the motor fan(s), the total output resistance R0 of the generator fan(s), applied input voltage vi; and the generated voltage vgmay fulfill Inequality (51).
For example, assuming an air electric generator having D=0.5 m, d=0.3 m, Nt=4 identical fans, each with Nb=8 blades; n=900 rpm, and the following blade parameters: CD=0.040163; CL=0.46852, span s=0.09 m; chord c=0.175 m, φ=45°, k=1, and Vφ1=8.25 m/s. Then, by applying Equations (8), (9), (15), (19), (32), (37) and (38), respectively, the results shown in Table V were obtained for kf, nozzle length ln, vΦ2, vφ, input fluid power Pφi, generated mechanical power Pg, and mechanical power gain Gpm.
A preferred manner to implement an Accelerated Wind Turbine is shown schematically in
The power Pφi of the incoming wind flow at the entrance of both machines is given by:
P(pi=TTp(D+kd)2vφ13/8 (87)
According to Betz's Law for conventional wind turbines, the maximum power P, a HAWT may capture from the incoming wind is 59.3%, i.e., HAWT power efficiency≦59.3%.
From Eq. (26), it may be readily shown that for a HAWT with Nb blades, chord c, the useful mechanical power generated, Pg, is given by
P
g=(π/480)p(CL sin<p−CD cos φ)Nbc[(D+kd)2−d2)]nvφ12 (88)
For this AWT, on the other hand, Eq. (26) is used to calculate Pg
P
g=(π/480)p(CL sin φ−CD cos<p)Nbc(D2−d2)nvφ2 (26)
Where Vφ is given by Eq. (35) as
V
φ
=k
f
V
φ1/sin φ (35)
And the mechanical power gain (Efficiency) for both machines is defined as
G
pm
=P
g
/Pi (38)
Equations (87), (88), (26), (35), and (38) may be used to design a HAWT and an AWT.
Example Assuming the following data to be the same for both HAWT and the AWT machines: vφ1=10 m/s Nb=3 blades, k=2, coefficient values: CD=0.040163; CL=0.46852, D=0.5 m, d=0.3 m, blade chord c=0.15 m and n=900 rpm. Then, by applying previous data and Equations (8), (9), (35), (87), (88) or (26), and (38), obtained respectively are the results shown in Table VI for the fluid velocity multiplier kf; nozzle length ln, relative fluid velocity in AWT throat, vφ; input power Pφi; generated mechanical power Pg, and mechanical power gain Gpm. Observe that the power generated by the HAWT is 110.61 W, whereas the power generated by this AW turbine is 1,807.34 W, i.e., 16 times greater. On the other hand, for this AWT the power gain Gpm exceeds 100%, which is not possible for the HAWT.
The Airflow Motor is an apparatus capable of converting part of the thermal energy carried by an internally accelerated airflow into a significant amount of mechanical energy which can be much greater than the applied mechanical energy used to move a fan that produces the airflow. The Airflow Motor in this preferred embodiment is composed of a housing or empty chamber consisting of a converging inlet nozzle, a Venturi-like throat, a diverging outlet nozzle; a fan, and one or more thermal airfoil turbines (Reference B1) that are placed within the Venturi-like throat, as shown in
The converging inlet nozzle and the diverging outlet nozzle are funnel-cone terminations which purpose is, respectively, to accelerate the incoming airflow or to decelerate the outgoing airflow.
The Venturi-like throat is the straight and narrowest component of the airflow motor and is placed between the inlet nozzle and the outlet nozzle. It is formed by concentric cylinders, the exterior cylinder having an internal diameter D, and the interior one having an external diameter d (0<d<D). In the air passage formed in the Venturi-like throat, the airflow velocity Vφ reaches its maximum value. The Venturi-like throat can be built by joining together basic construction modules, each of length lt and formed by two concentric cylinders, as the one shown in
The purpose of the basic construction module is either to house one thermal airfoil turbine, as shown in
The purpose of the fan is to produce the airflow destined to impact the airfoils of the thermal airfoil turbines. The fan can be placed at the entrance of the inlet nozzle or at the entrance of the Venturi-like throat. In the latter case the transversal dimensions (large interior diameter D and small external d) may coincide with the transversal dimensions of the thermal airfoil turbines. The fan can be driven either by an electric motor, or in small scale applications by a drill attached to its shaft.
The thermal airfoil turbine is the most fundamental part of the airflow motor.
When the turbine is placed in the Venturi-like space, the airflow produced by fan F flows in a passage of cross-sectional dimension (D−d)/2, the Venturi Channel. The cross sectional area Ai of the Venturi channel is given by
Ai=(π/4)(D+d)(D−d), m2 (B1)
If the Venturi-like throat is empty, i.e., if it does not contain any turbine, the power consumed by the empty chamber when an airflow of velocity Vφ flows in the Venturi-like throat is given by
Pec=(½)ρAiVφ3, W (B2)
The airfoils are a fundamental part of the Thermal Airfoil Turbine. For better performance of the turbine it is recommended to use well recognized commercial aerodynamic airfoils such as models SD-7037 and HN-227 PRO, or 4-digit, 5-digit and 6-digit NACA airfoils.
When an airflow with a velocity Vφ hits on the airfoils, there appear on them two perpendicular forces (Reference B2), namely, a drag force FD which opposes the airflow velocity, and a lift force FL, which generates a torque T on the turbine shaft causing the turbine to spin with a rotational speed n (in rpm). The value of the rotational speed depends on the value of the load driven by the turbine. At maximum load, the turbine does not rotate (n=0), and the torque T is a maximum. When the turbine has no load attached to its axis, n is a maximum (free-running condition), and the Torque is zero.
The generated power PG is given by
P
G=(π/30)(T)(n), W (B3)
As shown in
Ap=(c)(D−d)/2, m2 (B4)
The drag power and the generated power are given respectively by
P
D=(½)ρNaNsCDAp cos αVφ3, W (B5)
And
P
G=(½)ρNaNsCLAp sin αVφ3, W (B6)
Where Na is the number of airfoils, Ns is the number of identical stages in the turbine placed in the Venturi-like section. CD and CL are respectively the drag coefficient and the lift coefficient of the airfoil at airflow velocity Vφ, and for a Reynolds number given by
R
N=(Vφc/v)cos α (B7)
Where v is the fluid kinematic viscosity (equal to 1.46×10 −5 for air), and a is the static attack angle of the airfoils. Although in the prototypes to be presented further down use is made of rectangular airfoils like the ones shown in
From
A thermal airfoil turbine may be designed to operate at the range of rotational speeds at which the difference PG−PD is positive, and within this range it is sought to operate at or near the rotational speed (and load) that produces the maximum value for difference PG−PD. In the case of this particular turbine, the optimum load is the one corresponding to n=65 rpm.
The input mechanical power Pi to the thermal airfoil turbine is defined as
P
i
=P
ec
+P
D (B8)
Where Pec is the power consumed by the empty chamber as given by Eq. (B2).
The efficiency of the thermal airfoil turbine is defined as
ηt=(PG/PD) (B9)
And the airflow motor efficiency is defined as
ηAM=(PG/P1)(100) (B10)
In the case of the thermal airfoil turbine given above as an example, the following values for power and efficiencies were obtained with Vφ=4.4 m/s and n=65 rpm,
P
D=1.012 W; Pec=7.715 W; PI=8.727 W; PG=1.634 W
ηt=(1.634)(100)/(1.012)=1.6146
ηAM =(1.634)(100)/(8.727)=18.72%
The turbine efficiency and the airflow motor efficiency for this particular turbine are very low. However, the airflow motor is generally designed for the purpose of obtaining as large values as possible for both efficiencies ηt and ηAM. Airflow motor efficiencies greater than 50% are possible if the thermal airfoil turbine and the empty chamber are properly designed.
It is worth noting that the above values of PD, Pec, and PG for this example turbine were obtained for an airflow velocity Vφ1=4.4 m/s. However if the airflow velocity is increased to a velocity Vφ2>Vφ1 all of these power values are increased by a factor (Vφ2 /Vφ1)3. Hence if airflow velocity were duplicated to Vφ=8.8 m/s, all previous power values would be increased by a factor of 8.
In order to establish mathematically the performance of the thermal airfoil turbine, power calculations are made for an aerodynamic airfoil whose cross-sectional area is inclined forming a real attack angle ar, and which is free of moving vertically with a velocity Vv in the presence of a horizontal airflow of velocity Vφ, as appears in
Making a composition of the velocities obtains the vector diagram of
Vv=Vφ tan αi (B11)
By carrying out a point by point graphical analysis (not shown) it may be shown that the velocity vector Vφ “sees” the airfoil as having an apparent angle, αapp, instead of the actual (or real) angle, as shown in
From the graph in
αapp=αr−αI (B12)
i.e., the airflow “sees” the airfoil as having an apparent angle which is equal to the difference between the real angle and the induced angle.
For the particular case in which the induced angle and the real angle are equal (αr=αI), the apparent angle would be zero, i.e., the airfoil appears before the airflow as having an attack angle equal to zero. In this case the following takes place:
Under these conditions the following expressions can be written
Vertical velocity: Vv=VT tan αi
Lift force: FL
F
L
=C
L
ρA
app
Vφ
2/2=(CLρArVφ2/2)cos αi (B13)
Drag force: FD
F
D
=C
D
ρA
app
Vφ
2/2=(CDρAri Vφ2/2)cos αi (B14)
Where
Aapp=Apparent area of airfoil as seen by airflow velocity Vφ
Ar=Real area of airfoil
Using the above expressions, the respective powers are given by
Vertical power generated:
P
G
=F
L
V
v=(CLρArVφ2/2)cos αiVφ tan αi=
P
G
=F
L
V
v=(CLρArVφ3/2)sin αi (B15)
Drag power consumed:
P
D
=F
D
Vφ=(CDρArVφ2/2)cos αiVφ=
P
D=(CDρArVφ3/2)cos αi (B16)
Reynolds Number
R
N
=VφL
app
/v=(VφLr/v)cos αi (B17)
Where v is the airflow kinematic viscosity; Lapp is the apparent length (apparent chord) of the airfoil, and Lr is the real airfoil length (real chord)
Airfoil Efficiency=ηt=Power generated/Power consumed=
ηt=(CL/CD)tan αi (B9)
From the above expressions it can be concluded
(a) The power generated is greatly established by the flow velocity Vφ, and if the inclination angle and induction angle increase this power increases as sin ai, whose maximum value is 1
(b) The drag power, in contrast, decreases as cos αi. However for an effective decrease of cos αi and the drag power, the vertical velocity is very large
(c) The power efficiency improves as ai increases, but there may be an inclination of the airfoil and the vertical velocity may be large in order to obtain such an improvement
(d) Since the Reynolds Number diminishes as ai increases, then airfoil coefficients CL and CD require a large value of the flow velocity Vφ, so that they can reach values where the bubble effects decrease and allow a better performance of the airfoils
(e) According to Eq. (B11), in order to increase Vv, it is convenient to increase the induced angle αI, in such a way that αapp=αr−αI tends to zero, and ai tends to the static attack angle a,. This is a desirable situation because then the airfoil efficiency CL/CD increases and so also do both the airflow motor efficiency and the useful power generated. For such reasons the static attack angle αr is chosen to be large enough, for example in the range 35≦αr<55. Larger values of the static attack angle αr may be less preferred because according to Eq. (B 17) the Reynolds number can decrease too much, which will lead in turn to a reduction of the airfoil efficiency CL/CD. This feature of the thermal airfoil turbine contrasts with that of conventional turbines in which the static attack angle αr is usually very low (tending to zero). Hence conventional turbines have relatively smaller efficiency (less than 59.3, according to Betz's law). However thermal airfoil turbines can have a much higher efficiency because they operate at a much higher value of the static attack angle αr (Typically at least about 45° and up to about 50°, or up to about 55°).
(f) Since in a thermal airfoil turbine the airflow “sees” the airfoil at an apparent angle approaching 0°, the airfoil is almost transparent to the airflow. As a result the airfoils do not decelerate significantly the airflow, i.e., the airflow velocity Vφ entering the turbine remains practically the same as the airflow velocity at the output of the turbine. (See also
(g) It can be noted that as the inclination of the airfoil increases so does the vertical velocity, but in contrast the lift force decreases because it depends on the factor cos αi. Hence for an infinite vertical velocity, the power generated is not infinite on account of the fact the lift force diminishes to zero, and, as indicated by Equation (B15), the power generated has a limit determined by the airflow velocity Vφ.
Thermal airfoil turbines can be viewed as an aerodynamic subsystem, as the one shown in
In contrast, at the output of the subsystem there appear three energies, namely, the output internal energy Uo which is proportional to the temperature difference (To−Ta) of the outgoing airflow; the output airflow kinetic energy, which is practically the same as the input kinetic energy on account of the fact that the outgoing flow velocity and the incoming airflow velocity remain practically the same if power losses in the throat (Bearing losses and drag losses in the cylinders) are neglected; and the output rotational energy Kg which manifests itself in the torque that arises on the turbine shaft. Since To is always less than Ti, this implies that Uo<Ui. The difference Uo−Ui there appears as the output rotational energy Kg. Hence, energy balance is maintained (Ui+Kφ=Uo+Kφ+Kg).
Several proof of concept (POC) prototypes for the airflow motor now follow. An aim is to design a low-power airflow motor prototype with an efficiency exceeding 50%. For evaluating the performance of the airflow motor, as a benchmark or reference the theoretical maximum efficiency of a horizontal axis wind turbine (HAWT) will be used, which according to Betz's law is 59.3%.
In order to maximize the air motor power efficiency, powers PD and P ec are minimized, and at the same time power PG is maximized.
If Vφ is constant it can be seen from Eq. (B2) that the power consumed by the empty chamber, Pec, can be minimized by reducing the cross sectional area Ai of the airflow passage within the Venturi-like throat. According to Equation (B1), this can be done by making the product (D+d)(D−d) as small as possible while keeping the airfoil height (D−d)/2 greater than zero. In the prototypes to be presented the following values were chosen: airfoil height=9 cm; D=50 cm and d=32 cm. At Vφ=20 m/s, the theoretical power consumed by the empty chamber, according to Eq. (B2), is Pec=570.35 W.
Maximization of turbine efficiency.
According to Eq. (B9), in order to maximize the thermal airfoil turbine efficiency ηt, the ratio (PG/PD) is maximized An effective way of achieving this is by increasing the Reynolds Number RN. As is shown in Ref. B4, as the Reynolds number increases so does the maximum lift/drag ratio. This means it is possible to both increase the power generated by the turbine and the turbine efficiency simply by increasing the Reynolds number. This can be done, according to Eq. (B7) by increasing either the airflow speed Vφ in the Venturi throat, or the airfoil chord length, c, or by increasing both. If maintain the current framework is maintained (empty chamber) of the airflow motor by keeping unchanged parameters D=50 cm and d=32 cm, both PG, ηt and ηAM simply can be augmented by increasing the length c as much as possible. However there is an upper limit to the maximum value of c. It can be shown that the chord length, the number of airfoils Na, the attack angle and the diameter d of inner cylinder are related by
c=πd/(Na sin α) (B18)
And the horizontal width we of the internal and external cylinders is given by
wc=c cos α (B19)
By combining Equations (B18) and (B 19), the following relationship is obtained for the chord length c as a function of parameters d, Na and wc
c=[(πd/Na)2+wc2]1/2 (B20)
Rearranging Eq. (B20)
N
a
c=[(πd)2+(Nawc)2]1/2 (B21)
On the other hand, by combining Equations (B4) and (B6)
P
G=(¼)ρNacCL(D−d)sin αVφ3 (B22)
Hence, in order to obtain a generated power PG as large as possible one way of doing it is by increasing the product Na c as much as possible. But according to Equation (B21), this can be done by increasing either d, or w c, or both. For this prototype the value of d was fixed at d=32 cm. Table A below shows the values calculated for the product Na c, for d and N a fixed at d=32 cm and Na=4 blades, for values of the cylinder width w c varying between 16 and 20 cm.
For comparison purposes the value of the product (Na c) is shown to correspond to the values d=32 cm, Na=4 airfoils, wc=16 cm, and c=26.50 cm, which were used in Prototype #2. For this airflow motor PG=210.47W, and PD=32.57 W were obtained, for an airflow velocity equal to 22.38 m/s (See Table D below). However, it can be seen from Table A, that there is room for improvement if greater values for c, for w c, or both are chosen. For example, with d=32 cm, Na=4 airfoils, wc=20 cm, c=32.12 cm, and Nac=128.48 cm, which represents an improvement of (128.48−106)/106*100=21.21%. It is to be expected that PG for these values will increase at least in the same proportion up to PG=255.10 W, and by using a turbine with two identical stages (Ns=2) it is possible to reach PG=510.2 W.
One way of increasing the power generated by the thermal airfoil turbine, P G, consists in decreasing the airfoil height (D−d)/2, and/or increasing the airfoil chord c. In fact, from Eq. (B22) if parameters of a turbine 1 are changed to convert it into a turbine 2, keeping the same static attack angle a, it can be shown that
(PG2/PG1)=[ρ2Na2c2CL2(D2−d2)/ρ1Na1c1CL1(D1−d1)](Vφ2/Vφ1)3 (B23)
Now, assuming there is no change in the air density (ρ2=ρ1), and that lift coefficients do not change appreciably (CL2=CL1), Eq. (B23) can be written as
(PG2/PG1)=[Na2c2(D2−d2)/Na1c1(D1−d1)](Vφ2/Vφ1)3 (B24)
Eq. (B24) can be used to calculate the relation (PG2/ PG1) when the number of airfoils (Na) changes, and the airfoil height (D−d)/2, and/or the airfoil chord c change.
For the specific case where the number of airfoils is kept the same (Na2=Na1), Eq. (B24) can be rewritten as
(PG2/PG1)=[c2(D2−d2)/c1(D1−d1)](Vφ2/Vφ1)3 (B25)
But, from the continuity equation:
(Vφ2/Vφ1)3=[(D1+d1)(D1−d1)/(D2+d2)(D2−d2)]3 (B26)
Now plugging numerical values of geometric parameters in Equations (B25) and (B26) to obtain the relationship (PG2/PG1). For example, assuming D1=D2=0.5 m; d1=0.32 m; d2=0.36 m; c1=0.265 m; c2=0.29 m
(Vφ2/Vφ1)=1.226 (B27)
(Vφ2/Vφ1)3=1.8424 (B28)
And
PG2=1.568 PG1 (B29)
These results indicate that by reducing airfoil height from 0.09 m to 0.07 m, and by increasing the chord length c from 0.265 m to 0.29 m, the airflow velocity Vφ increases by a factor of 1.226, and the generated power increases by a factor of 1.568.
It can be shown that the separation s between the airfoils placed over the internal preferably satisfy the following relationship
s≦πd/Na (B30)
On the other hand, it can be shown that
s=c sin α (B31)
To avoid inter-airfoil interference, s=c. From Eq. (B23)
N
a
≦πd/s (B32)
N
a≦(πd)/(c sin α) (B33)
And
c≧(πd)/(Na sin α) (B34)
For Na=4 airfoils, d=0.32 m y α=50°
c=(π0.32)/(4 sin 50°)=0.328 m (B35)
For c=0.32 m, and N a=4 airfoils, the minimum separation between consecutive airfoils is from Eq. (B24)
s=(0.32)sin 50°=0.245 m (B36)
For c=0.32 m, d=0.32 m y α=50°, it is not possible to increase Na beyond Na=4.
In order to attain maximum efficiency and maximum useful power with the airflow motor, a suitable load is attached to the turbine shaft so that this operates at the rotational speed at which the difference PG−PD is a maximum. In the case of the example turbine given before this occurs at n=65 rpm, as shown in
The procedure consists then in routinely testing several gear sets until finding one that produces maximum value for PG−PD. First, the turbine is placed in the Venturi throat of the airflow motor. An electric drill attached to the fan shaft is used to move the fan blades and thus create the airflow that is going to impact the turbine airfoils. First the turbine is tested in its free-running condition, i.e., when its shaft is not attached to the fan shaft. Both the torque Td0, N.m, applied by the drill to the fan and the fan speed nFo are measured. With these two values the power applied by the drill to the fan is calculated by the formula
P
d0=(π/30)Td0nF0, W (B37)
Next the turbine is geared-up to the fan, using the gear set that produces maximum PG. In this condition, both the drill torque Td and the fan rotational speed nF are measured. The power Pd supplied by the fan under this condition is calculated from the formula
P
d=(π/30)TdnF, W (B38)
If Pd turns out to be less than Pd0 this means that the turbine is actually generating power and produces an extra torque Te above Td0 on the fan shaft that helps to reduce the power Pd applied by the drill to the fan. In this condition, the total torque Tf applied to the fan shaft is
T
r
=T
d0
+T
e (B39)
This torque Tf can then be used to calculate the total power Pf applied to the fan both by the drill Td0 and the turbine Te. This power can then calculated by the formula
P
f=(π/30)TfnF, W (B40)
In order to calculate Pf, the extra torque Te is evaluated first, as is shown below.
This torque is necessary to overcome the drag power PD introduced by turbine airfoils plus the gear losses Pg. Gear losses Pg can be estimated as 7.5 W per turbine, and drag power PD can be calculated from the well known formula
P
D=(½)ρCDApNsNaVφ3 cos α, W (B41)
Where ρ is the air density, ρ=1.23 kg/m3, CD is the airfoil drag coefficient, and Ap is the planform area of airfoils given by
A
p
=c(D−d)/2 (B42)
Na is the number of airfoils, Vφ is the velocity of the airflow in the Venturi section, α is the attack angle, and Ns is the number of identical stages in the turbine placed in the Venturi section.
The total power loss PLoss is then given by
P
Loss
=P
D
+N
s
P
g (B43)
On the other hand PLoss and the extra torque Te are related by the formula
P
Loss=(π/30)TenF, W (B44)
Hence
T
e=(30/π)(PLoss/nF), N.m (B45)
The power generated PG by the turbine can be calculated from
P
G
=P
f
−P
d
, W (B46)
Drag power PD is calculated from
P
D
=P
f
−P
d0
, W (B47)
Turbine efficiency ηt is defined as
ηt=(PG/PD) (B48)
Finally, the airflow motor efficiency ηAM is defined as
ηAM=(PG/Pd)100 (B49)
Several POC prototypes of the airflow motor have been designed, built and tested and values on performance have been obtained. The main features Prototype #3, are shown in Table B below. The main parameters of this airflow motor prototype having a two stage turbine, and operating at a fan rotational velocity of 1412 rpm, are given.
In Table C measured values for several quantities are shown
Using measured values of Table C, and parameters of Table B, the following quantities were calculated.
From Eq. (B37),
P
d0=(π/30)Td0nF0=(π/30)(5.328)(1,412)=787.82 W
From Eq. (38),
P
d=(π/30)TdnF=(π/30)(3.2)(1,412)=473.17 W
It can be observed that Pa turned out to be less than NO. This result means that the 2-stage turbine is in fact generating power.
From Eq. (B42) and Table 2,
A
p
=c(D−d)/2=(0.265)(0.5−0.32)/2=0.02385 m2
From Eq. (B41) and Table 2,
P
D=(½)ρCDApNsNaVφ3 cos α=
PD=(½)(1.23)(0.09)(0.02385)(2)(4)(23.9)3 cos 50=92.67 W
From Eq. (B43) and Table B, with Pg=7.5 W, and Ns=2 stages,
P
Loss
=P
D
+N
s
P
g=92.67+(2)(7.5)=107.67 W
Now, by substituting above result in Eq. (B45)
T
e=(30/π)(PLoss/nF)=Te=(30/π)(107.67/1,412)=0.73 N.m.
And, by substituting previous value in Eq. (39), with Td0=5.328 N.m.,
T
f
=T
d0
+T
e=5.328+0.73=6.056 N.m.
Now, from Eq. (40),
P
f=(π/30)TfnF=(π/30)(6.056)(1412)=895.47 W
And, from Eq. (B46) and previous result, the generated power PG, is
P
G
=P
f
−P
d=895.47Δ473.17=422.3 W
From Eq. (B47), drag power, PD, is calculated as
P
D
=P
f
−P
d0=895.47−787.82=107.65 W
Finally, from previous results and Equations (B48) and (B49), the turbine efficiency ηt, and the airflow motor efficiency ηAM can be calculated, respectively, as
ηt=(PG/PD)=(422.3/107.65)=3.92
ηAM=(PG/Pd)(100)=(422.3/473.17)(100)=89.25%
In Table D below, values of PD, PG, Pd, ηt, and ηAM are shown for 3 POC prototypes of the airflow motor built and tested.
1. From Table D it can be seen that as the product (N s N a c) from the value 90 cm of Prototype #1, to the value 106 cm of Prototype #2, up to the value 212 cm of Prototype #3, the power generated PG increases from 140 W, to 210.47 W, up to 422.3 W, respectively, and the airflow motor efficiency ηM increases from 25.93%, to 43.18%, up to 89.25%. Greater values of the generated power PG, and airflow motor efficiency i Am can undoubtedly be achieved simply by increasing even more the product (N s N a c). The latter can be done by increasing the number of stages, Ns, the number of airfoils per stage, Na, or the chord length c, or all of them. However, Na only can be increased to before reaching the value where the phenomenon of airfoil interference appears.
2. For practical reasons it is not recommended to increase the number of stages beyond N s=2. Instead it is a better option to increase the value of the chord length c, which implies increasing the value of the turbine horizontal width w c, according to Equations (B33) and (B34).
3. The airflow motor efficiency of Prototype #3 reaches 89.25% which far beyond the Betz limit (59.3%). To the best of Applicant's knowledge no prior art turbine can achieve such a high efficiency.
4. A self sustained movement airflow motor (i.e., a motor efficiency above 100%) may be obtained. One possible way of achieving this is, for example duplicating the chord length c of by Prototype #3 (i.e., by making c=53 cm), but this calls for increasing the cylinder lengths w c from 16 cm up to w c=53 cos 50°=34.07 cm, according to Eq. (B 19). In addition to that, the diameter d of the internal cylinder has also to be increased. All of this requires a structural change of the whole system.
The following values were obtained for the airflow motor with 2 identical turbines of 4 airfoil each, airfoil chord c=0.265 m; airfoil height=0.09 m; D=0.5 m; d=0.32 m, and using a gear ratio 1:2.56 for the turbine geared up to the fan.
When operating the fan at 1,555 rpm, Prototype #3 was capable of generating 625.8 W and the efficiency for the airflow motor reached 105.87%. By duplicating the fan rotational speed the airflow motor can be expected to produce 5 kW and even a much higher efficiency. Hence the goal to design a POC prototype with efficiency greater than 50% has been achieved in excess.
As explained farther above and shown in
Reference 1: Fundamentals of Fluid Mechanics, Sixth Edition SI Version, By: B. R. Munson, D. F. Young, T. H. Okiishi, and W. W. Huebsch. Publisher: John Wiley & Sons, 2010
Reference 2: United States Patent Application Publication, Use of Air Internal Energy and Devices, by Hirshberg, I, Pub. No. : US 2008/0061 559 A1, Pub. Date: Mar. 13, 2008
Reference 3: United States Patent Application Publication, Thermal Airfoil Turbine, by Luis Indefonso Solorzano, Pub. No.: 2011 0097209 A1, Pub. Date: Apr. 28, 2011
Reference 4: Wind Turbine Blade Analysis using the Blade Element Momentum Method, Version 1.1 , by Grant Ingram, Creative Commons Attribution-ShareAlike 3.0 Unported License, Oct. 18, 2011.
Reference B1. Published United States Patent Application NO.20110097209 (Solorzano), Luis Reference B2. Vennard, John k., “Elementary Fluid Mechanics”. 4th Edition. Published 1940/00/ . . . Publisher John Wiley & Sons Inc.
Reference B4. Miley, S. J., “A catalog of low Reynolds number airfoil data for wind turbine applications/S. J. Miley “(http://wind.nrel.gov/public/library/3387.pdf)
In the description provided herein, numerous specific details are set forth. However, it is understood that embodiments of the invention may be practiced without these specific details. In other instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description.
In the following claims, any of the claimed embodiments can be used in any combination.
Number | Date | Country | |
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Parent | 12589578 | Oct 2009 | US |
Child | 14953653 | US |