WO2017023155A1 - Spiral turbine - Google Patents

Spiral turbine Download PDF

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Publication number
WO2017023155A1
WO2017023155A1 PCT/MX2015/000112 MX2015000112W WO2017023155A1 WO 2017023155 A1 WO2017023155 A1 WO 2017023155A1 MX 2015000112 W MX2015000112 W MX 2015000112W WO 2017023155 A1 WO2017023155 A1 WO 2017023155A1
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Prior art keywords
spiral
turbine
working fluid
fluid
efficiency
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PCT/MX2015/000112
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Spanish (es)
French (fr)
Inventor
Víctor Manuel GONZÁLEZ ROBLES
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González Robles Víctor Manuel
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Priority to PCT/MX2015/000112 priority Critical patent/WO2017023155A1/en
Publication of WO2017023155A1 publication Critical patent/WO2017023155A1/en

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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01D—NON-POSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
    • F01D1/00—Non-positive-displacement machines or engines, e.g. steam turbines
    • F01D1/34—Non-positive-displacement machines or engines, e.g. steam turbines characterised by non-bladed rotor, e.g. with drilled holes
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
    • F01D—NON-POSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
    • F01D1/00—Non-positive-displacement machines or engines, e.g. steam turbines
    • F01D1/34—Non-positive-displacement machines or engines, e.g. steam turbines characterised by non-bladed rotor, e.g. with drilled holes
    • F01D1/36—Non-positive-displacement machines or engines, e.g. steam turbines characterised by non-bladed rotor, e.g. with drilled holes using fluid friction

Definitions

  • a steam turbine reaches efficiencies in the range of! 10 ai 37% [Ref. 1], while a modern combined cycle plant can reach efficiencies of the order of 55% [Refs. 2];
  • gas turbines and steam turbines are used, which are built in several nozzle-wing stages; they are very delicate mechanical devices and whose construction is very specialized [Ref. 3].
  • Huge efforts are currently being made to increase its efficiencies [Refs. 4-6].
  • the Tesla turbine uses the micro-forces that originate the shear forces; nevertheless, and despite the simplicity of its operation, it has not been developed at an industrial level because in its design it seems to deprive empiricism despite the renewed interest that has aroused in recent years; In addition to the previous year, their efficiency has not been determined with precision, Tesla himself assured that his turbine would work with efficiency of 90%, although in the tests carried out they reached 40% [Ref. 7). Some modern builders report efficiencies ranging from 30 to 59 percent [Ref. 8].
  • the turbine described here also uses the micro-forces or frictional forces as is the case of the Tesla turbine, but the fluid is forced to describe a spiral path along which the fluid is giving its energy to the system so Gradual and efficient
  • This turbine consists essentially of a spiral analogous to the rope of an old clock with a very narrow pitch, suitable for the use of micro-forces.
  • the spiral is imprisoned between two circular plates and the broken assembly inside a cylindrical housing.
  • Figure 1 shows, from left to right, a circular plate (1) that has a solid axis [2), the spiral (3) and the plate on the right (4) that has a hollow axis (5), whereby the working fluid comes out.
  • Figure 2 shows the fixed cylindrical housing [1 ⁇ together with the injection valve that regulates the Rujo (in black) and the spiral (2) together with the axes rotating with angular velocity W [in gray).
  • the intermediate circumference (3) represents the hollow shaft through which the fluid flows perpendicular to the plane of the figure, while the small solid circle (4) represents the solid axis of the counterface.
  • the spiral of total length L, of width O and with step b that can be fixed or not, depending on the type of working fluid and its temperature.
  • the conduit through which the fluid passes then has the dimensions; L (length), O (width) and height b e
  • step b has two parts a know bf: The thickness of the material used to build the spiral
  • the spiral is held between two flat circular plates, one of them perforated by a tube that serves two functions: it acts as an axis and is at the same time the fluid's outlet duct.
  • the second plate on the one hand imprisons the turn and on the other has a solid axis of rotation smaller than the tube.
  • Figure 4 shows the device working.
  • the inner spiral simulates the trajectory of a particle of the working fluid that starts at the injection valve and ends at the outlet shaft-tube in the left central part.
  • the associated Archimedes spiral is a spiral whose radius decreases when the angle grows (counterclockwise ⁇ , is described by the function:
  • step b is composed of two parts o, and b ⁇ .
  • r is given by the thickness of the boundary layer at one or two edge diameters, that is:
  • ⁇ ⁇ is the thickness of the boundary layer at the distance x from the edge as shown in Figure 7.
  • equation (5) the first term on the right is associated with the torque due to the impulse of the fluid while the second one represents the torque produced by the generator and the residual friction, that is, it is assumed that the coefficient of friction type, and r , has two parts: one associated with residual friction and 0 , while the other, I, is associated with the generator that is supposed to have a linear behavior
  • Equation (5) has no analytical solution, however it can be solved numerically. However, in order to obtain some important algebraic relationships in order to achieve a good turbine design, some conceptual simplifications can be made that allow an analytical solution to be obtained. Indeed, assuming that:
  • Equation (6) can be easily solved, its solution is:
  • the length L of the spiral is selected which p then of (p1) we can find the minimum radius R m of the turbine, this is
  • the constant C of the system can be calculated by (9) obtaining C-13.81.
  • L can be cleared, obtaining: is given by the expression (3) and the step was taken
  • a spiral turbine with a non-constant pitch is illustrated in Figure 8, in this case it has a step that increases linearly with the angle ⁇ , which makes it suitable for an adiabatic expansion of the gas as occurs in a steam turbine.

Abstract

The invention relates to a spiral turbine designed to use the micro-forces from the drag caused by a fluid on the walls of the conduits thereof, i.e. the shear stress through the boundary layer. Unlike traditional turbines with various nozzle-blade stages or the Tesla turbine with a disk rotor, the rotor of the turbine according to the invention is formed from a rotary spiral inserted between two circular disks or plates. One of said plates has a simple solid shaft while the other one has a hollow shaft via through which the working fluid comes out. The stator is a simple cylindrical casing on which the injection valve that regulates the fluid is arranged. The working fluid transmits its energy to the system in a smooth and very efficient manner. The equation of motion of the system can be digitally solved without too much difficulty, but it is also possible to develop a mathematic linear model of the turbine-generator system with an analytical solution. This solution allows important relationships to be obtained for this category of turbines and also allows the estimation of the dimensions of the turbine being designed. A spiral steam turbine has a similar design, but with a linearly increasing pitch. The dimensions thereof depend on the initial and end conditions of the working fluid. To summarise, the construction and design thereof are very simple, and its efficiency is close to 100% with appropriate selection of the length of the spiral and the dimensions of other important parameters that can be easily calculated.

Description

TURBINA EN ESPIRAL DESCRIPCIÓN  SPIRAL TURBINE DESCRIPTION
1, Antecedentes y campo técnico  1, Background and technical field
Una turbina de vapor alcanza eficiencias en el rango de! 10 ai 37% [Ref. 1], mientras que una central moderna de ciclo combinado puede alcanzar eficiencias del orden del 55% [Refs. 2]; en estas centrales se usan turbinas de gas y turbinas de vapor que son construida en varias etapas tobera-alabe; son ingenios mecánicos muy delicados y cuya construcción es muy especializada [Ref. 3]. Actualmente se realizan ingentes esfuerzos para aumentar sus eficiencias [Refs.4-6 ]. A steam turbine reaches efficiencies in the range of! 10 ai 37% [Ref. 1], while a modern combined cycle plant can reach efficiencies of the order of 55% [Refs. 2]; In these plants, gas turbines and steam turbines are used, which are built in several nozzle-wing stages; they are very delicate mechanical devices and whose construction is very specialized [Ref. 3]. Huge efforts are currently being made to increase its efficiencies [Refs. 4-6].
Por otra lado la turbina Tesla usa las micro-fuerzas que originan los esfuerzos cortantes; sin embargo, y a pesar de ia sencillez de su funcionamiento, no ha sido desarrollada a nivel industrial debido a que en su diseño parece privar el empirismo no obstante ei renovado interés que ha suscitado en los últimos aliss; además de ío anterior, la eficiencia de las mismas no ha sido determinada con precisión, Tesla mismo aseguraba que su turbina trabajaría con eficiencia del 90%, aunque en las pruebas realizadas alcanzaron el 40% [Ref. 7). Algunos constructores modernos reportan eficiencias que van dei 30 al 59 por ciento [Ref.8]. On the other hand, the Tesla turbine uses the micro-forces that originate the shear forces; nevertheless, and despite the simplicity of its operation, it has not been developed at an industrial level because in its design it seems to deprive empiricism despite the renewed interest that has aroused in recent years; In addition to the previous year, their efficiency has not been determined with precision, Tesla himself assured that his turbine would work with efficiency of 90%, although in the tests carried out they reached 40% [Ref. 7). Some modern builders report efficiencies ranging from 30 to 59 percent [Ref. 8].
La turbina aquí descrita también usa las micro-fuerzas o fuerzas de fricción como es el caso de la turbina Tesla, pero el fluido es forzado a describir una trayectoria en espiral a lo largo de la cual el fluido va cediendo su energía al sistema de manera gradual y eficiente. The turbine described here also uses the micro-forces or frictional forces as is the case of the Tesla turbine, but the fluid is forced to describe a spiral path along which the fluid is giving its energy to the system so Gradual and efficient
2. Descripción detallada 2. Detailed Description
Esta turbina consiste esencialmente de una espiral análoga a ia cuerda de un reloj antiguo con un paso muy estrecho, adecuado para ei uso de las micro-fuerzas. La espiral está aprisionada entre dos placas circulares y el conjunto rota dentro de una carcasa cilindrica. En la Figura 1 se muestran, de izquierda a derecha, una placa circular (1) que tiene un eje sólido [2), la espiral (3) y la placa de la derecha (4) que tiene un eje hueco (5), por ef cual sale el fluido de trabajo. This turbine consists essentially of a spiral analogous to the rope of an old clock with a very narrow pitch, suitable for the use of micro-forces. The spiral is imprisoned between two circular plates and the broken assembly inside a cylindrical housing. Figure 1 shows, from left to right, a circular plate (1) that has a solid axis [2), the spiral (3) and the plate on the right (4) that has a hollow axis (5), whereby the working fluid comes out.
En el estado estacionario de la turbina la espiral rota con una velocidad angular constante, W. Ei fluido de trabajo entra ai conducto estrecho y va cediendo gran parte de su energía de una manera continua a lo largo de toda ia espiral. Ei proceso resultante es extraordinariamente eficiente. In the steady state of the turbine the spiral rotates with a constant angular velocity, W. The working fluid enters the narrow duct and yields a large part of its energy in a continuous manner along the entire spiral. The resulting process is extraordinarily efficient.
En ia figura 2 se muestra la carcasa cilindrica fija [1} junto con la válvula de inyección que regula el Rujo (en negro) y la espiral (2) junto con los ejes rotando con velocidad angular W [en gris). La circunferencia intermedia (3) representa el eje hueco por ei cual sale el fluido perpendicularmente ai plano de la figura, mientras el círculo solido pequeño (4) representa al eje sólido de la contracara. Figure 2 shows the fixed cylindrical housing [1} together with the injection valve that regulates the Rujo (in black) and the spiral (2) together with the axes rotating with angular velocity W [in gray). The intermediate circumference (3) represents the hollow shaft through which the fluid flows perpendicular to the plane of the figure, while the small solid circle (4) represents the solid axis of the counterface.
La espiral de longitud total L, de ancho O y con paso b que puede ser fijo o no, dependiendo dei tipo de fluido de trabajo y de su temperatura. El conducto por donde pasa el fluido tiene entonces las dimensiones; L (longitud), O (ancho) y altura be The spiral of total length L, of width O and with step b that can be fixed or not, depending on the type of working fluid and its temperature. The conduit through which the fluid passes then has the dimensions; L (length), O (width) and height b e
Nótese que el paso b tiene dos partes a saben bf : El grosor del material empleado para construir la espiral Note that step b has two parts a know bf: The thickness of the material used to build the spiral
be: Altura del conducto por donde pasa el fluido.  be: Height of the duct where the fluid passes.
Estos dos parámetros no son constantes, en general, como se discutirá en una sección posterior. Es claro queThese two parameters are not constant, in general, as will be discussed in a later section. It's clear that
Figure imgf000004_0001
Figure imgf000004_0001
Como ya se mencionó, la espiral está sostenida entre dos placas circulares planas, una de ellas perforada por un tubo que cumple dos funciones: actúa como eje y es a la vez conducto de salida dei fluido. La segunda placa por un lado aprisiona a la espira y por el otro tiene un eje de giro sólido de radio menor al del tubo.  As already mentioned, the spiral is held between two flat circular plates, one of them perforated by a tube that serves two functions: it acts as an axis and is at the same time the fluid's outlet duct. The second plate on the one hand imprisons the turn and on the other has a solid axis of rotation smaller than the tube.
Una vez ensambladas las partes, la turbina se ve como se muestra en la Figura 3, en la que pueden verse: Once the parts are assembled, the turbine looks as shown in Figure 3, in which you can see:
(1) La base  (1) The base
(2) La espiral  (2) The spiral
(3) Eje que conecta al generador eléctrico  (3) Shaft connecting to the electric generator
(4) Discos o placas circulares que sostienen o aprisionan a ta espiral  (4) Circular discs or plates that hold or imprison the spiral
(5) Sellos que evitan fugas del fluido (tipo anillos, de resorte o de laberinto)  (5) Seals that prevent fluid leakage (rings, spring or labyrinth type)
(6) Válvula de Inyección del fluido  (6) Fluid Injection Valve
(7) El escape o salida de) fluido  (7) The escape or exit of) fluid
(8) La carcasa cilindrica  (8) The cylindrical housing
En la figura 4 se muestra el dispositivo funcionando. La espiral interior simula la trayectoria de una partícula del fluido de trabajo que empieza en la válvula de inyección y termina en el tubo-eje de salida en la parte central izquierda.  Figure 4 shows the device working. The inner spiral simulates the trajectory of a particle of the working fluid that starts at the injection valve and ends at the outlet shaft-tube in the left central part.
3. Cólculo de los parámetros principales 3. Calculation of the main parameters
Se describen dos casos principales, el de una espiral de paso constante y el de una espiral con el paso que crece linealmente, adecuada para una turbina de vapor. A) ESPIRAL DE PASO CONSTANTE Two main cases are described, the one of a spiral of constant step and the one of a spiral with the step that grows linearly, suitable for a steam turbine. A) CONSTANT STEP SPIRAL
Al DESCRIPCIÓN DE LA ESPIRAL TO THE SPIRAL DESCRIPTION
La espiral de Arquimedes asociada es una espiral cuyo radio decrece cuando el ángulo crece
Figure imgf000005_0010
(en ei sentido contrario al de tas manecillas del reloj}, es descrita por la función:
Figure imgf000005_0001
The associated Archimedes spiral is a spiral whose radius decreases when the angle grows
Figure imgf000005_0010
(counterclockwise}, is described by the function:
Figure imgf000005_0001
donde es el radio mayor inicial, b el paso y el rango de β va de cero a un ángulo máximo
Figure imgf000005_0009
determinado por ia condición el radio menor de la espiral.where is the initial major radius, b the step and the range of β goes from zero to a maximum angle
Figure imgf000005_0009
determined by the condition the smaller radius of the spiral.
Figure imgf000005_0008
Figure imgf000005_0008
La longitud de esta espiral es:
Figure imgf000005_0002
The length of this spiral is:
Figure imgf000005_0002
En la Figura 5 se observa ia misma espiral de la Figura 1, pero en ella se indican los radios mayor y menor respectivamente, además el paso b de la espiral y el radio r del
Figure imgf000005_0007
In Figure 5 the same spiral of Figure 1 is observed, but in it the major and minor radii are indicated respectively, in addition the step b of the spiral and the radius r of the
Figure imgf000005_0007
conducto por el cual sale el fluido. La cota mínima para r esconduit through which the fluid flows out. The minimum dimension for r is
Figure imgf000005_0004
Es claro que
Figure imgf000005_0004
It's clear that
Figure imgf000005_0003
Figure imgf000005_0003
A.2 ESTIMACIÓN DEL PASO A.2 STEP ESTIMATION
Como ya se dijo en la descripción de la turbina, el paso b se compone de dos partes o, y b¡. As already stated in the description of the turbine, step b is composed of two parts o, and b¡.
Estimación de ia altura del conducto (Obsérvese la Figura 6).Estimation of duct height (See Figure 6).
Figure imgf000005_0011
Figure imgf000005_0011
Este es un parámetro crucial, sin embargo nada fácil de calcular. En ei estado del arte se propone que r está dado por el grosor de la capa límite a uno o dos diámetros del borde, esto es:
Figure imgf000005_0005
This is a crucial parameter, however nothing easy to calculate. In the state of the art it is proposed that r is given by the thickness of the boundary layer at one or two edge diameters, that is:
Figure imgf000005_0005
donde δ{χ) es ei grosor de la capa limite a ia distancia x del borde como se muestra en la Figura 7. where δ {χ) is the thickness of the boundary layer at the distance x from the edge as shown in Figure 7.
Una estimación de ia altura de la capa límite ó, está dada por Blasius [Ref.9]. An estimate of the height of the boundary layer or, is given by Blasius [Ref. 9].
donde:
Figure imgf000005_0006
4 where:
Figure imgf000005_0006
4
Figure imgf000006_0006
Figure imgf000006_0006
Respecto del parámetro
Figure imgf000006_0004
dependerá det tamaño de la turbina y de ios esfuerzos que tenga que soportar el material con el que se construye la misma. Para fines del ejemplo que sigue se asumirá que b/es el doble de bt. Regarding the parameter
Figure imgf000006_0004
It will depend on the size of the turbine and the efforts that the material with which it is built has to support. For the purposes of the following example, it will be assumed that b / is twice that of b t .
A.3 UN MODELO MATEMÁTICO SIMPLIFICADO A.3 A SIMPLIFIED MATHEMATICAL MODEL
Con el fin de poder hacer una estimación de la longitud L de la espiral o equivalentemente de
Figure imgf000006_0003
mediante el uso de la expresión (2), se presenta a continuación un modelo matemático sencillo que describe al sistema. Esta es una ecuación diferencial para el sistema turbina-generador:
Figure imgf000006_0001
In order to be able to estimate the length L of the spiral or equivalent of
Figure imgf000006_0003
Through the use of the expression (2), a simple mathematical model describing the system is presented below. This is a differential equation for the turbine-generator system:
Figure imgf000006_0001
Donde  Where
Figure imgf000006_0005
Figure imgf000006_0005
En la ecuación (5) el primer término de la derecha está asociado al torque debido al impulso dei fluido mientras que el segundo representa el torque producido por ei generador y por ia fricción residual, es decir, se asume que el coeficiente tipo fricción, yr, tiene dos partes: una asociada a la fricción residual y0, mientras que ia otra, Yo , esté asociada al generador que se supone tiene un comportamiento linealIn equation (5) the first term on the right is associated with the torque due to the impulse of the fluid while the second one represents the torque produced by the generator and the residual friction, that is, it is assumed that the coefficient of friction type, and r , has two parts: one associated with residual friction and 0 , while the other, I, is associated with the generator that is supposed to have a linear behavior
Figure imgf000006_0002
La ecuación (5) no tiene solución analítica, sin embargo puede resolverse numéricamente. Ahora bien, con el propósito de obtener algunas relaciones algebraicas importantes a fin de lograr un buen diseño de le turbina se pueden hacer algunas simplificaciones conceptuales que permiten obtener una solución analítica. Efectivamente, asumiendo que:
Figure imgf000006_0002
Equation (5) has no analytical solution, however it can be solved numerically. However, in order to obtain some important algebraic relationships in order to achieve a good turbine design, some conceptual simplifications can be made that allow an analytical solution to be obtained. Indeed, assuming that:
Figure imgf000007_0008
Figure imgf000007_0008
(a ecuación (5) puede escribirse como:
Figure imgf000007_0001
(to equation (5) can be written as:
Figure imgf000007_0001
donde v es la velocidad tangencial dd fluido y la constante C está dada por:
Figure imgf000007_0002
where v is the tangential velocity dd fluid and the constant C is given by:
Figure imgf000007_0002
La ecuación (6) puede resolverse fácilmente, su solución es:
Figure imgf000007_0003
Equation (6) can be easily solved, its solution is:
Figure imgf000007_0003
La velocidad para di estado estacionario { t → ∞) está dada por:
Figure imgf000007_0004
The speed for di steady state {t → ∞) is given by:
Figure imgf000007_0004
Con las ecuaciones (7), (9) y ia de la eficiencia
Figure imgf000007_0005
With equations (7), (9) and efficiency ia
Figure imgf000007_0005
es posible calcular la longitud L de la espira como se hace en el ejemplo de la siguiente sección.It is possible to calculate the length L of the loop as in the example in the following section.
De la expresión (9) es claro que la velocidad del fluido a ia salida de la turbina, Vm, después de haber recorrido la longitud L de la espiral determina la eficiencia dada por (10), se obtiene la expresión
Figure imgf000007_0006
From the expression (9) it is clear that the velocity of the fluid at the outlet of the turbine, V m , after having traveled the length L of the spiral determines the efficiency given by (10), the expression is obtained
Figure imgf000007_0006
donde D es una constante dada por eficiencia ef dada por (11) es una función
Figure imgf000007_0007
where D is a constant given by efficiency and f given by (11) is a function
Figure imgf000007_0007
monótonamente creciente con la longitud L monotonously increasing with the length L
A.4 CALCULANDO LA LONGITUD DE LA ESPIRAL Y OTROS PARÁMETROS IMPORTANTES A.4 CALCULATING THE SPIRAL LENGTH AND OTHER IMPORTANT PARAMETERS
Para estimar ios parámetros principales de una turbina en espiral, es necesario partir de ciertos datos determinados por las circunstancias. Esto se muestra en el problema tipo y su solución que se presentan a continuación: PROBLEMA. Supóngase que se tiene una fuente de agua con rapidez
Figure imgf000008_0014
y se desea poner a trabajar un generador de energia eléctrica con una potencia
Figure imgf000008_0013
que trabaja de manera óptima a una frecuencia f = 180 rpm, con un torque Encuéntrense los parámetros más importantes de la turbina en espira!.
Figure imgf000008_0012
To estimate the main parameters of a spiral turbine, it is necessary to start from certain data determined by the circumstances. This is shown in the type problem and its solution presented below: TROUBLE. Suppose you have a water source quickly
Figure imgf000008_0014
and you want to put to work an electric power generator with a power
Figure imgf000008_0013
which works optimally at a frequency f = 180 rpm, with a torque Find the most important parameters of the turbine!
Figure imgf000008_0012
SOLUCIÓN. SOLUTION.
Se asume por sencillez que la frecuencia de ia turbina en e) estado estacionario es ta misma que ia del generador, esto es,
Figure imgf000008_0016
pm y por lo tanto tienen la misma velocidad angular w. It is assumed for simplicity that the frequency of the turbine in e) steady state is the same as that of the generator, that is,
Figure imgf000008_0016
pm and therefore have the same angular velocity w.
Ei fluido debe salir dei sistema cuando ya no puede 'empujarlo', por ello ia rapidez o velocidad de salida dei fluido
Figure imgf000008_0015
Figure imgf000008_0001
The fluid must leave the system when it can no longer 'push it', therefore the speed or speed of the fluid exit
Figure imgf000008_0015
Figure imgf000008_0001
donde Rm es ei radio mínimo y w la velocidad angularwhere R m is the minimum radius and w the angular velocity
Figure imgf000008_0002
Figure imgf000008_0002
Se selecciona ia longitud L de ia espiral tai que
Figure imgf000008_0003
p entonces de (p1) podemos encontrar ei radio mínimo Rm de la turbina, este esThe length L of the spiral is selected which
Figure imgf000008_0003
p then of (p1) we can find the minimum radius R m of the turbine, this is
Figure imgf000008_0004
Figure imgf000008_0004
Además la eficiencia de la turbina es es decir una eficiencia del 94%. In addition the efficiency of the turbine is an efficiency of 94%.
Figure imgf000008_0005
Figure imgf000008_0005
Ahora se estima ia constante μτ, característica de) sistema. Asumiendo que ei generador tiene un comportamiento ideal en el cual el torque y la energia generada son directamente
Figure imgf000008_0017
The constant μ τ , characteristic of the system, is now estimated. Assuming that the generator has an ideal behavior in which the torque and energy generated are directly
Figure imgf000008_0017
proporcionales al numero de revoluciones por minuto y como el torque es igual a una fuerza F aplicada perpendic¾larmente en el radio dei generador Ra (que suponemos igual entonces la tuerza también es proporcional las rpm o a ia velocidad tangencial proportional to the number of revolutions per minute and as the torque is equal to a force F applied perpendicularly in the radius of the generator Ra (which we assume the same then the nut is also proportional to the rpm or tangential speed
Figure imgf000008_0010
Figure imgf000008_0010
De aquiFrom here
Figure imgf000008_0006
Figure imgf000008_0006
Supóngase que la fricción residual es igual ai 5% de la originada por ei generador, entonces,
Figure imgf000008_0009
Suppose the residual friction is equal to 5% of that generated by the generator, then,
Figure imgf000008_0009
La constante C del sistema puede calcularse mediante (9) obteniéndose C - 13.81. Usando la expresión (7) se puede despejar L, obteniéndose:
Figure imgf000008_0007
Figure imgf000008_0008
está dada por la expresión (3) y se tomó el paso
Figure imgf000008_0011
The constant C of the system can be calculated by (9) obtaining C-13.81. Using the expression (7) L can be cleared, obtaining:
Figure imgf000008_0007
Figure imgf000008_0008
is given by the expression (3) and the step was taken
Figure imgf000008_0011
mientras que a se obtiene de la expresión que da ia energía de) fluido a la salida de ia espiral, se obtiene:
Figure imgf000009_0001
while a is obtained from the expression that gives the energy of the fluid at the exit of the spiral, it is obtained:
Figure imgf000009_0001
Finalmente se obtiene el número de vueltas de la
Figure imgf000009_0008
Finally you get the number of laps of the
Figure imgf000009_0008
espiral 0f/2n que resulta igual a 9.6.  spiral 0f / 2n that is equal to 9.6.
A. S UN COMENTARIO SOBRE LA CONTINUIDAD A. S A CONTINUITY COMMENT
Debe ser evidente que para satisfacer el principio de conservación de masa, el agua debe entrar a la turbina pulverizada por la válvula de inyección de forma tal que ocupe un ¿rea efectiva 4 veces menor que el área real del conducto.  It should be clear that to satisfy the principle of mass conservation, water must enter the turbine sprayed by the injection valve in such a way that it occupies an effective area 4 times smaller than the actual area of the duct.
B) TURBINA DE VAPOR EN ESPIRAL (O ESPIRAL DE PASO VARIABLE). B) SPIRAL STEAM TURBINE (OR VARIABLE STEP SPIRAL).
B.1 DESCRIPOCtÓN DE LA ESPIRAL B.1 SPIRAL DESCRIPTION
En la figura 8 se ilustra una turbina en espiral con paso no constante, en este caso tiene un paso que aumenta lineaimente con el ángulo Θ, lo que la hace adecuada para una expansión adiabática del gas como ocurre en una turbina de vapor.  A spiral turbine with a non-constant pitch is illustrated in Figure 8, in this case it has a step that increases linearly with the angle Θ, which makes it suitable for an adiabatic expansion of the gas as occurs in a steam turbine.
La espiral asociada en este caso está descrita por la función:
Figure imgf000009_0002
The associated spiral in this case is described by the function:
Figure imgf000009_0002
donde es el radio {mayor) inicial de la espiral, mientras los coeficientes están dados en términos de
Figure imgf000009_0007
, eí paso inicial, el final y la longitud de ta espiral respectivamente; estos parámetros dependen de las presiones y temperaturas iniciales y finales seleccionadas para el gas (vapor) de trabajo. Los coeficientes estén dados porwhere is the initial {major) radius of the spiral, while the coefficients are given in terms of
Figure imgf000009_0007
, the initial step, the end and the length of the spiral ta respectively; These parameters depend on the initial and final pressures and temperatures selected for the working gas (steam). The coefficients are given by
Figure imgf000009_0005
Figure imgf000009_0003
Figure imgf000009_0005
Figure imgf000009_0003
La longitud de esta espiral es:
Figure imgf000009_0004
The length of this spiral is:
Figure imgf000009_0004
es el radio medio de la turbina. It is the average radius of the turbine.
Figure imgf000009_0006
Figure imgf000009_0006
Figure imgf000009_0009
Figure imgf000010_0001
Figure imgf000009_0009
Figure imgf000010_0001

Claims

REIVINDICACIONES
1. Esta es la primera turbina en forma de espira! que usa tas micro-fuerzas debidas ai arrastre que un fluido provoca sobre las paredes de sus conductos, es decir los esfuerzos cortantes, a través de la capa límite. 1. This is the first spiral-shaped turbine! which uses the micro-forces due to the drag that a fluid causes on the walls of its conduits, that is to say the shear forces, through the boundary layer.
2. El rotor es una espiral aprisionada entre dos placas circulares (discos) y el estator está formado por una carcasa cilindrica. Una de las placas tiene un eje sólido, mientras que la otra tiene un eje hueco por ei cual sale el fluido de trabajo. 2. The rotor is a spiral trapped between two circular plates (discs) and the stator is formed by a cylindrical housing. One of the plates has a solid shaft, while the other has a hollow shaft from which the working fluid comes out.
3. Ei fluido de trabajo entra ai sistema por una válvula situada en la carcasa cilindrica, que regula el flujo de inyección. 3. The working fluid enters the system through a valve located in the cylindrical housing, which regulates the injection flow.
4. Ei fluido de trabajo cede su energía de una manera suave y muy eficiente, de hecho, la eficiencia de la misma puede acercarse ai 100% seleccionando adecuadamente la longitud ¿ de ia espiral {o equivalentemente ei número de vueltas), ei ancho a y el paso ¿>de la misma, 4. The working fluid yields its energy in a smooth and very efficient way, in fact, its efficiency can be close to 100% by properly selecting the length ¿of the spiral {or equivalently the number of turns), the width a and the step ¿> of it,
5. Se ha desarrollado un modelo matemático lineal del sistema turbina-generador cuya solución es analítica. Esta solución permite calcular las dimensiones de la turbina que se esté diseñando. 5. A linear mathematical model of the turbine-generator system has been developed whose solution is analytical. This solution allows to calculate the dimensions of the turbine that is being designed.
6. Una conclusión o consecuencia del modelo matemático indica que ia eficiencia de la turbina es una función monótonamente creciente de la longitud L de ia espiral, mientras que ia potencia de ia turbina aumenta con ei ancho a de ia misma. 6. A conclusion or consequence of the mathematical model indicates that the efficiency of the turbine is a monotonously increasing function of the length L of the spiral, while the power of the turbine increases with the width of the same.
7. Una turbina de vapor en espiral (o turbina en espiral de paso variable) tiene un diseño análogo, pero con paso que crece tineaimente. Los parámetros de ia misma, están determinados por las condiciones iniciales y finales del fluido de trabajo. 7. A spiral steam turbine (or variable pitch spiral turbine) has an analogous design, but with a pitch that grows tineaimente. The parameters thereof are determined by the initial and final working fluid conditions.
8. En resumen, su construcción y diseño, en ambos casos (espiral de paso constante y espiral de paso variable), son muy sencillos y su eficiencia se acerca ai 100% seleccionando adecuadamente ios parámetros tal y como se indica en el punto 4 de este resumen. 8. In summary, its construction and design, in both cases (spiral of constant pitch and spiral of variable pitch), are very simple and its efficiency is close to 100% by properly selecting the parameters as indicated in point 4 of this summary.
PCT/MX2015/000112 2015-08-05 2015-08-05 Spiral turbine WO2017023155A1 (en)

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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB191015640A (en) * 1910-06-29 1911-05-11 Francesco Lamberti Improvements in Turbines.
GB191024001A (en) * 1909-10-21 1911-07-06 Nikola Tesla Improved Method of Imparting Energy to or Deriving Energy from a Fluid and Apparatus for use therein.
US4003672A (en) * 1973-09-27 1977-01-18 Joseph Gamell Industries, Incorporated Internal combustion engine having coaxially mounted compressor, combustion chamber, and turbine
US20030068226A1 (en) * 2001-10-09 2003-04-10 Anneken James G. Direct condensing turbine
GB2477101A (en) * 2010-01-21 2011-07-27 Simon Higgins Friction disc turbine having a stack of circular discs with raised spiral ridges
EP2775095A1 (en) * 2013-03-04 2014-09-10 Piotr Jeute Radial turbine

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB191024001A (en) * 1909-10-21 1911-07-06 Nikola Tesla Improved Method of Imparting Energy to or Deriving Energy from a Fluid and Apparatus for use therein.
GB191015640A (en) * 1910-06-29 1911-05-11 Francesco Lamberti Improvements in Turbines.
US4003672A (en) * 1973-09-27 1977-01-18 Joseph Gamell Industries, Incorporated Internal combustion engine having coaxially mounted compressor, combustion chamber, and turbine
US20030068226A1 (en) * 2001-10-09 2003-04-10 Anneken James G. Direct condensing turbine
GB2477101A (en) * 2010-01-21 2011-07-27 Simon Higgins Friction disc turbine having a stack of circular discs with raised spiral ridges
EP2775095A1 (en) * 2013-03-04 2014-09-10 Piotr Jeute Radial turbine

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