Patent Application
20160079829
This patent application is submitted for the Accelerated Fluid Machine (AFM or AF machine), an apparatus capable of operating as an economical and efficient energy machine driven by a fluid that has been previously accelerated. The AF machine extracts part of the internal or thermal energy carried by the fluid, and converts it into either mechanical or electrical energy. Typically the fluid that drives the machine can be air, wind or water in whose case the machine can be called an Accelerated Airflow Machine (AAM), an Accelerated Wind Turbine (AWT), or an Accelerated Water Machine (AWM), respectively. The Accelerated Fluid Machine in any of its varieties requires no fuel and produces no contamination at all.
Given present day high energy costs and alarming global warming stemming mainly from the burning of fossil fuels such as carbon and oil, methods and techniques for generating clean, and renewable energy have become urgent for the preservation of the planet and for improving effectively the quality of life of human beings. The AF machine will play a significant role to achieve the above mentioned goals.
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 tiny proportion of it is extracted by present day energy devices and at very high costs. The AF machines have the capabilities of exploiting these reservoirs in a very efficient and economical way that surely will cause a definitive change of the world energy paradigm.
Nowadays wind turbine for generating powers in excess of 1 MW have very large dimensions, heights and weights as well as being very expensive to build and very damaging to flying fauna and the landscape. Other disadvantages of these machines are the difficulty to carry them from one place to another and their very low efficiency which is constrained by Betz's limit.
Accelerated Fluid Machines on the other hand can generate similar powers than conventional wind turbines but at a small fraction of the cost of the latter and with a great reduction in size, height, and weight, and they can be portable devices. Additionally, AF machines can be portable devices, and achieve efficiencies much higher than Betz's limit and as a bonus cause no harm to flying fauna.
Another interesting feature of the AF machine is that due to its portability feature the electrical or mechanical energy can be generated locally in the place where is needed. This surely will bring about a significant change in the world energy paradigm as power grids, long transmission and distribution lines will no longer be required as electricity can be generated by AF machines locally in every building, factory or home where is needed.
Taking into account that any moving land, sea or air vehicle is surrounded by an energy space, AF machines when installed in such vehicles can harvest considerable energy from the surrounding atmosphere or water when they are placed in direct contact with the environment.
Two fundamental physical principles are exploited in the design and operation of the AF machine, namely, the fluid velocity multiplication that takes place within a fluid convergent nozzle, and the enormous mechanical power that can be developed by the lift force on a properly designed fan blade or streamlined turbine airfoil.
A fluid flowing past the surface of an airfoil-shaped body or fan blade, placed at a suitable attack angle α, 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=ρcVφ/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 can 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
The following references are used in this patent application:
Henceforth some fundamental assumptions are made: First, In order to apply safely Bernoulli Equation, the fluid is assumed to be laminar, incompressible and inviscid (Page 99 of Ref.1). Liquid fluids will be considered as incompressible. In the case of a gas fluid, like air or wind, 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 or wind. 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 These are important components of an accelerated fluid machine.
The cross-sectional area as seen by the fluid flow at the entrance of the convergent nozzle is given by
A
φ1=(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 can be readily 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)
Let us now define the parameter Fluid Velocity Multiplier K as
k
f=(Aφ1/Aφ2)=Vφ2/Vφ1 (4)
Fluid velocity Vφ2 can be made greater than Vφ1 simply 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 can 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 can be increased by making input diameter D1 bigger. For this purpose we define the latter 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 AF machine uses no convergent nozzle.
Then, by substituting Eq. (6) in Eq. (5) we obtain
A
φ1=(π/4)(D+kd)2 (7)
By substituting Eq. (7) and Eq. (2) in Eq. (4), we obtain
k
f=(D+kd)2/(D+d)(D−d) (8)
The fluid-acceleration chamber can have many possible shapes, but to simplify its manufacturing and to minimize turbulence the shape shown in
The length of the convergent nozzle can be can be calculated from the formula
l
n
=kd/(2 tan β) (9)
As is shown in 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 can be exploited to extract water out of the atmosphere as a useful by-product of the convergent nozzle.
As to the internal concentric truncated cones, shown in nozzles in
l
n
>l
n7
>l
n6
>l
n5
>l
n4
>l
n3
>l
n2
>l
n1>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 AF machine uses no divergent nozzle.
The purpose of the divergent nozzle is to reduce the fluid speed Vφ3 at its entrance 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° to minimize turbulence. In the case of a symmetrical AF machine, defined as one having convergent and divergent nozzles of identical shape and size, the divergent length ln can be calculated also from Eq. (9).
From now on, by fluid turbine we mean one similar to the Thermal Airfoil Turbine, as described in Reference 3. As an example of this turbine,
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 AF machines shown in
L=2ln+lth (12)
Where lth is the throat length equal to 4lt for both machines. In general,
l
th
=Nl
t (13)
Where N is the total number of spaces of length lt that can be accommodated in the throat length.
The total width of the AF machine is
W=D+kd (14)
An important feature of the AF 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, AF machines can be classified as open chamber and closed chamber AF machines. In open chamber variety the operating fluid can enter and leave the machine, as shown in FIGS. (6) and (10). On the other hand, closed chamber AF machines to be explained later are hermetically closed to the external fluids.
There are two ways of having the fluid flow within the AF machine: It can 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 AF machine can be open or closed.
Alternatively, if the fluid is external to the machine, it can be captured by the FA chamber by allowing it to enter the chamber. Hence, for an open chamber AF 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 AF machine can generate more mechanical energy than the input flow kinetical energy, as shown in the calculation results of Table I.
The open chamber AF machine can be stationary and the external fluid flow can be a wind flow, a tidal flow, a submarine current, a stream, or a river current. Alternatively it can be mobile, and in contact with the external fluid, i.e., it can be carried by a vehicle moving at a velocity Vφ1 through the surrounding fluid. In this case the FA chamber of the AF machine can be used to capture the fluid and to increase its velocity up to a certain value Vφ2. In the event the AF machine used is hermetically closed or placed within a fixed location like a house room, the fluid flow has to be created artificially by one fan placed within the FA chamber or one or more fans placed within the throat. In the latter case, the AF machine can 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 can 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 can be seen in
A particular variety of the acceleration fluid machine, the symmetrical AF machine, is shown in
Consider a fluid turbine (which can 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 noticing 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 AF 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 α, and the angle formed by the chord c and the plane of rotation is the setting angle γ. From
φ=α+γ (17)
Henceforth we will assume the turbine blades have a constant setting angle γ, 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 can be seen from Equations (19) and (15) that the following inequality is fulfilled for an AF machine
V
φ
>V
φ2
>V
φ1 (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
cdr/2 (22)
Where CD=Drag coefficient of blade; CL=Lift coefficient of blade; ρ=Density of the accelerated fluid.
The torque on the blade element, dT, can 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 can 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 can be converted into n, revolutions per minute (RPM) by
ω=πn/30 (25)
By combining Eq. (24) and Eq. (25) we obtain
P
g=(π/480)ρ(CL sin φ−CD cos φ)Nbc(D2−d2)nVφ2 (26)
On the other hand, it can 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 can be measured experimentally for each turbine.
By substituting Eq. (27) into Eq. (26) we obtain the important relationship
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 is the approach we will use to design our AF machines and for this purpose we use the FA chamber to increase the incoming fluid velocity Vφ1 so that the fluid reaches the Venturi-like throat with maximum speed Vφ2.
The total mechanical power generated can 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 AF machine is given by
P
φi
=ρA
1
V
φ1
3/2 (30)
Where A1 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 can be expressed as
P=(πρ/8)(D+kd)2Vφ13 (32)
But, by using Eq. (8),
(D+kd)2=(D+d)(D−d)kf (33)
Then Pφi can be written as
P
φi=(πρ/8)(D+d)(D−d)kfVφ13 (34)
By combining Eq. (19) with Eq. (15), we can express Vφ as
V
φ
=k
f
V
φ1/sin φ (35)
By substituting Eq. (35) in Eq. (26), we obtain
P
g=(π/480)ρ(CL sin φ−CD cos φ)Nbc(D2−d2)nkf2Vφ12 sin2 φ (36)
Which for Nt identical AF turbines can be written as
P
g=(π/480)ρ(CL sin φ−CD cos φ)NbNtc(D2−d2)nkf2Vφ12 sin2 φ (37)
Let us now define the Mechanical Power Gain, or Efficiency, Gpm, of the AF machine as
G
pm
=P
g
/P
φi (38)
And by substituting Equations (34) and (37) into Eq. (38), we obtain for Nt turbines
G
pm
=[k
f/(60 sin2 φ][ρ(CL sin φ−CD cos φ)NbNtc](n/Vφ1) (39)
It can be seen from Equation (39) that the mechanical power gain Gpm can be increased effectively by making the fluid velocity multiplier kf as large as possible and this can be done simply by increasing the value of the integer k for the accelerating nozzle as can 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.
Condition for Self Sustained Movement of the Fluid Turbines We state that the Accelerated Fluid Turbine System is operating in a self sustained movement regime if
G
pm>1 (40)
According to Eq. (39) for an AF machine this inequality is equivalent to
[kf/(60 sin2 φ)][ρ(CL sin φ−CD cos φ)NbNtc](n/Vφ1)>1 (41)
Equation (41) is the condition for an AF machine to achieve a self sustained movement, and this is quite feasible to obtain as we show in the example below.
Numerical Results—Accelerated Wind Turbine For an Accelerated Wind Turbine (AWT), a particular type of an AF 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), (19), (32), (37) and (38), respectively, the results shown in Table I were obtained for kf, ln, Vφ2, Vφ, 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 AF 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 we can build a large variety of fan AF machines. As an example,
l
th
=Nl
t (42)
Assuming the fluid is incompressible, the maximum number of fans and fluid straighteners that can 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 has to be established experimentally. If the fluid is a liquid, like water, it can be considered incompressible for all practical engineering purposes (Page 29 of Reference 1). If the fluid is a gas like air or wind it can 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 AF 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 two possible modes of operation for the electrical motor of an electrical fan. It can 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 can spin as the result of a previously accelerated fluid impacting onto them. The accelerated fluid can be produced by one or more electric fans acting as starting motors or, it can 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 we say 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 can 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 can operate either as a motor or as a generator. In the first case we will refer to the fan 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) can be mechanically attached, or can be unattached but keeping always their co linearity.
Enclosed within the Venturi-like throat there must 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 can 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 can be either dc or ac machines. Likewise, the blades of both motor fans and generator fans can be identical or very similar.
Accelerated Fluid Machines can 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, water or wind, there are 5 main types of AF 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).
Notice that basically the same AF machine shown in
Any suitable material, like plastic, metal, etc., can 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 document we will assume 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 AF machine, they can be made out of plastic materials, resin, acrylic, or others. The two cylinders can be made with a light metal such as aluminum, or a light and hard plastic as well, etc., but weight must 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 must satisfy is: 0<d<D. As can 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.
Note. Although it is possible to use inlet and outlet terminations with k=0, i.e., no nozzles, it is not recommended 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 Vφ1 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
=ρA
φ2
V
φ2
3/2 (43)
And the input power of the fluid at the inlet of the open chamber AF machine is given by
P
φi
=ρA
φ1
V
φ1
3/2 (30)
By combining Equations (3) (4), and (30) we obtain
P
φ2
=k
f
2
P
φi (44)
Important 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 Pv 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 our Accelerated Wind Turbines we apply 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 can 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 must be stressed that if an AF machine is shown as implemented solely with fans, it is clear that it can also be implemented with thermal airfoil turbines, and vice versa.
Energy Space 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 can 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 AF 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.
Fluid Panel We define a fluid panel as any structure composed of more than one AF machine forming a wall or flat panel that can 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 can 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 can be mounted at the roof or on the sides of the vehicle and facing the wind, or it can be submerged in water if the vehicle moves in this medium
Fluid panels can alternatively be placed on a stationary structure, such as the roof of a house or building to extract energy from the wind or can 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 can be used to implement a fluid panel is shown in
Fluid Electric Generator A Fluid Electric Generator (FEG or FE generator) is an AF 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 has to 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 basically 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 simply 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 can be open or closed. This can 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
Take notice that for accelerated wind turbines and for water electric generators fan F at left entrance in
In all fluid electric generators the power supply used by the motor fans can be either ac or dc, depending on whether the fan motor is an ac machine or a dc one. Also, in an FE generator the generator fan outputs can be connected in series to obtain the total generated voltage as the sum of the individual voltages generated by the fluid turbines. In addition, if two or more fan motors are used to generate the accelerated fluid, they can be connected in parallel in order to increase the speed of the accelerated fluid within the throat. As to the number of fans that can be used there can be as few as one or as many as there can be physically placed within the throat. The fans can all be placed onto the same shaft in whose case they all rotate at the same angular velocity. Or, they can be physically separated although maintaining its co linearity.
Both in the vertical water electric generator (WE generator), shown in
Accelerated Wind Turbine 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 we can readily show that the relationship between wind speeds Vφ1 and Vφ2 is given by either one of the following equations
V
φ2
=k
f
V
φ1 (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, we get 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 can 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 our 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 It, and hence, a lower turbine rotational velocity n, and a smaller generated power Pg, as shown by Equations (27) and (28).
Electrical Power Calculations The Fluid Electric Generator can 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, we can view the FEG initially 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 we can represent the FEG by the model shown in
We define the electrical power gain of the FEG as
G
pe
=P
o
/P
i (45)
Where Po 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.
Self Sustainable Fluid Electric Generator The FEG machine can operate as a self sustainable generator if the electrical power gain Gpe is greater than unity. In the following we will show that the FEG will be self sustainable if a certain relationship among the motor input resistance Rh the generator output resistance Ro, 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
P
i
=v
i
2
/R
i (46)
But, for maximum power transfer it can be shown that
P
o
=v
g
2/(4Ro) (47)
For self sustained operation, it is required that
G
pe>1 (48)
This in turn requires that
P
o
>P
i (49)
Or
v
g
2/(4Ro)>vi2/ (50)
From Eq. (50), we finally obtain the condition required for the FE generator to be self sustainable as
v
g>2(Ro/Ri)1/2vi (51)
Example If the motor and the generator are chosen such that Ro=10−2R1, then for self sustained operation, it is required that
V
g>0.2vi
An Experimental Result
Since Inequality (49) was fulfilled we conclude that this rather rudimentary AE generator just behaves as a self sustainable machine.
A Vertical Accelerated Water Machine The Vertical Accelerated Water Machine is just 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
We will assume 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 can 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 p1=0. Water velocity at level 0 is V0=0, and at level 1 is:
V
1=√[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)
Let us 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 AF machine.
Length h1 of the AWM has to be chosen to prevent cavitation from taking place, i.e., we have to make sure that water pressure al level 2, p2, satisfies the following relationship
p
2>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, we obtain, assuming a steady, inviscid, and incompressible flow,
p
2=(1/2)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
p
2
>p
v (61)
And
h
1>0 (62)
Let us now define p2min as the minimum value of pressure p2 that makes height h1 as given by Eq. (60) equal to cero.
Thus, from Eq. (60) we have
p
2min=(1−kf2)(ρgh0) (63)
Let us now define kfmax as the maximum value of kf for which p2min=pv. This is an upper bound for factor kf to fulfill realizability conditions:
p
2
>p
2min
>p
v (64)
h
1>0 (65)
And
k
f
<k
fmax (66)
Thus
k
fmax=[√−(pv/μgh0)] (67)
If Inequalities (64) and (66) are satisfied, cavitations will not take place.
Example: Let us suppose h0=0.3 m, D=0.5 m, and d=0.3 m, ρ=995.7 Kg/m3, g=9.8 m/s2, then
k=1:
k
fmax=5.85
k
f=4<kfmax
k=2:
k
fmax=5.85
k
f=7.56>kfmax
So, we discard k=2, and take k=1. Then
V
1=√[2(9.8)(0.3)]=2.42 m/s
V
2
=k
f
V
1=9.70 m/s
And
p
2min=(1−kf2)(ρgho)=−43,910.37 Pa
Let us take
p
2=−40,000.00 Pa>−43, 910.37 Pa>pv=−97,090 Pa
Then,
h
1=(1/ρg)p2+(kf2−1)h0=0.40 m
Take notice 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 h1 would have been:
h
0
+h
1
=V
2
2/(2g)=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! This is a definite advantage of our accelerated water machine over conventional hydraulic machines, and can be achieved by simply by making h1>0, and p2>p2min.
By applying Bernoulli Equation at levels 2 and 3 and noticing that V2=V3, we get
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.
Example Assuming h2=0.25 m, and the same geometrical parameter values as before, we get
p
3
=p
2
+ρgh
2=−40,000.00+(995.7)(9.8)(0.25)
p
3=−37,560.54 Pa>pv=−97,090 Pa
Power Calculations for a Vertical AW Machine Let us suppose that Nt 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), we obtain, respectively, the results shown in Table II for the parameter kf, fluid velocities V1 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; ρ=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 can be used to drive an electrical generator, which in turn can be used to power a pump and the remaining electric appliances of the house. Alternatively the pump can 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 can be increased by a factor Nt simply by using Nt>1 water turbines. Even substantially better results are obtained for k=2, as can be seen from the results of Table II. Since for k=1, ln turned out to be greater than h1, the length of the top nozzle is taken as h1=0.41 m rather than ln=0.95 m, with very little increase in turbulence as the water flow accelerates in the upper nozzle.
Realizability Conditions for the Vertical Accelerated Water Machine It is important to take into account that in order to make realizable the accelerated water energy machine the following conditions have to be satisfied
h
o>0 (69)
h
1>0 (70)
p
2
>p
2min (71)
And p2min is given by Eq. (63) for the symmetric AW Machine. Equation (69) implies that water tank 1 can never be allowed to empty. If a water pump is used for replenishing water tank 1 it is required then that the refill time of the latter must be less than the time required to empty it. Accordingly the water flux Qp from the water pump has to be greater than the water flow Q1, that is to say
Q
p
>Q
1 (72)
Where
Q
1
=A
1
V
1 (73)
A Horizontal Water Machine An open chamber horizontal water machine can 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 in Section A Vertical Accelerated Water Machine, except that gravity has no effect now. Additionally the water pressure P0 at depth ho and at the entrance of the machine is
p
o
=μgh
0 (74)
This is greater than atmospheric pressure, as can 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 can be written as
p
o+ρ(V02)/2=p1+ρ(V12)/2
Hence
P
1
=P
o−ρ(V12−V02)/2
But
V
1
2
=k
f
2
V
0
2
And
V
0
=V
φi
And kf is given by Eq. (8). Then
p
1
=p
o−ρ(kf2−1)V02/2 (75)
If V0 and ho are known, then kf must be chosen to make sure that p1 will be greater than pv=−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 can be the values of kfmax and V0max.
Radial Fans In
Open Fluid Acceleration Machine with Radial Fans The open fluid acceleration machine using radial fans can be implemented by connecting by their straight section two radial fans like the ones shown in
Tandem Accelerated Fluid Machines Two or more AF machines of different cross-sectional areas, like the ones shown in
D
2
+k
2
d
2
=D
1 (78)
Where D1 is the throat diameter of the machine 1, as shown in
D
1
+k
1
d
1 (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 Vφ1, then the fluid speeds in AFM1 throat and AFM2 throat are, respectively,
V
φ1
=k
f1
V
φi (80)
V
φ2
=k
f2
V
φ1
=k
f1
k
f2
V
φ1 (81)
Where kf1 and kf2 are given from Eq. (8) by
k
f1=(D1+k1d1)2/[(D1+d1)(D1−d1)] (82)
k
f2=(D2+k2d2)2/[(D2+d2)(D2−d2)] (83)
Eq. (81) can be generalized for j turbines in tandem (j=2, 3 . . . etc.), and the fluid velocity in throat of nth turbine can be written as
V
φj
=k
f1
k
f2
. . . k
fj
V
φ1 (84)
Where
k
fj=(Dj+kjdj)2/[(Dj+dj)(Dj−dj)] (85)
Of course if powers generated separately by each AF 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
gi (86)
Closed Chamber for AF Machines Accelerated Fluid Machines can also be implemented in closed chamber, 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 can be used for axial fans and thermal airfoil turbines are the constant cross-sectional area toroids, shown in
A third shape for the closed chamber that can be used with radial (centrifugal) fans consists of two identical open chamber AF machines for radial fans, like the one shown in
The closed fluid acceleration chamber can be used in all AF 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 can be used in all AFM applications including accelerated wind turbine applications.
Industrial Applicability In the next six sections various possible applications of the accelerated fluid machines are proposed.
Mobile AF Machines in Land, Air, and Sea Vehicles Any moving land, air or water vehicle can 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
A Battery of Water Electric Generators For high power requirements, a battery of several water electric generators fed from the same water tank or reservoir can be used, as is shown in
An Accelerated Wind Turbine Array For capturing wind coming from several directions, several Accelerated Wind Turbines each pointing at a different direction can be placed in horizontal platforms separated vertically from each other, as shown in
The drawings are not referenced to any scale and do not have a referenced scale among them.
The main innovation presented in this document is the accelerated fluid machine and its main varieties, namely, the water electric generator, the air electric generator, and the accelerated wind turbine. Combinations of AF machines like the fluid panel and the tandem AF machines have also been proposed to achieve higher power generation. We suggest employing symmetrical AF machines and electric brushless dc axial fans with high flowrate Q to implement each of them. As to the best way to carry out the water electric generator, this has been explained already in sections A Vertical Accelerated Water Machine, Power Calculations for a Vertical AW Machine, and Realizability Conditions for the Vertical Accelerated Water Machine.
Regarding the best way to implement the air electric generator, the design process can 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 Pi, 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 must be greater than 1 for self sustainability; hence the total input resistance Ri of the motor fan(s), the total output resistance Ro of the generator fan(s), applied input voltage vi, and the generated voltage vg must fulfill Inequality (51).
Example Let us assume 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 III were obtained for kf, nozzle length ln, Vφ2, Vφ, input fluid power Pφi, generated mechanical power Pg, and mechanical power gain Gpm.
The best way 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
φi=πρ(D+kd)2Vφ13/8 (87)
According to Betz's Law for conventional wind turbines, the maximum power Pi a HAWT can capture from the incoming wind is 59.3%, i.e., HAWT power efficiency ≦59.3%.
From Eq. (26), it can 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)ρ(CL sin φ−CD cos φ)Nbc[(D+kd)2−d2)]nVφ12 (88)
For our AWT, on the other hand, we use Eq. (26) to calculate Pg
P
g=(π/480)ρ(CL sin φ−CD cos φ)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
/P
i (38)
Equations (87), (88), (26), (35), and (38) can 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), we obtain, respectively, the results shown in Table IV 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 our AW turbine is 1,807.34 W, i.e., 16 times bigger! On the other hand, for this AWT the power gain Gpm exceeds 100%, which is not possible for the HAWT.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/GB2013/050901 | 4/8/2013 | WO | 00 |
