TERMOTECNIA II FACULTAD DE INGENIERIA UNLP
Turbinas de vapor Apuntes de cátedra
MECÁNICA Y ELECTROMECÁNICA 2018
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Contenido Introducción ..................................................... ............................................................ ....................................................... 4 Aplicaciones ....................................................................................................................................................................... 4 Componentes ...................................................................................................................................................................... 5
Principales...................................................................................................................................................... ...................................................................................................................................................... 5 Secundarios.................................................................................................................................................... .................................................................................................................................................... 6 Principio de funcionamiento .......................................................... ........................................................... .......................... 7 Clasificación ....................................................................................................................................................................... 7 Contrapresión y condensación ..................................................................................... ....................................................... 9 Diseños de álabes de turbina .......................................................... ........................................................... ........................ 10 Características operativas y constructivas de etapas de acción y reacción .................. ..................................................... 11 Configuraciones de etapas ................................................................................................................................................ 13 Rangos de operación de las diferentes etapas ........................................................................ ........................................... 14
Turbina de acción pura (Curtis y Roteau) ....................................................................... .................................................................................................... ............................. 16 Turbinas de reacción con etapa Curtis ......................................................................................................... ......................................................................................................... 17 Toberas ............................................................................................................................................................................. 17
Velocidad del sonido y número de Mach........................................................................ ..................................................................................................... ............................. 18 Formas de toberas y difusores................................................................ ...................................................................................................................... ...................................................... 19 Relaciones adicionales entre propiedades....................................................................... .................................................................................................... ............................. 20 Efectos al variar la contrapresión....................................................................... ................................................................................................................. .......................................... 21 Toberas de vapor........................................................ ............................................................ ........................................... 22
Tobera considerando pérdidas ........................................................................... ..................................................................................................................... .......................................... 23 Características constructivas de las toberas ................................................................................................. ................................................................................................. 23 Admisión total o parcial ......................................................................... ............................................................................................................................... ...................................................... 25 Derrame con vapor húmedo .................................................................. ......................................................................................................................... ....................................................... 26 Sobre enfriamiento ................................................................................ ....................................................................................................................................... ....................................................... 26 Análisis de etapa Móvil Mó vil de acción con Euler .................................................................................. .................................. 27
Geometría y dimensiones principales de etapa de acción ........................................................................ ............................................................................ .... 27 Euler y Primera ley de la l a termodinámica ........................................................................ ..................................................................................................... ............................. 27 Diseño de etapa de acción ...................................................................... ............................................................................................................................ ...................................................... 28 Potencia desarrollada en etapa de acción .................................................................................... ..................................................................................................... ................. 29 Rendimiento de etapa de acción .................................................................................................................. .................................................................................................................. 30 Limitaciones de la potencia y el rendimiento .............................................................................................. .............................................................................................. 32 Análisis de etapa Móvil Mó vil de reacción con Euler ................................................................................................... .............. 32
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Empuje axial ................................................................................................................................................ ................................................................................................................................................ 38 Análisis de rueda Curtis ..................................................................................... ........................................................... .... 38
Análisis de la potencia de la etapa Curtis ideal ........................................................................... ............................................................................................ ................. 39 Limitaciones a la potencia desarrollada en etapa Curtis ........................ .............................................................................. ...................................................... 39
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Introducción La turbina de vapor (TV) es una turbomáquina térmica motora, que transforma la energía contenida en un fluido en estado de vapor con elevada presión y temperatura (entalpía), en trabajo mecánico de rotación sobre su eje para el accionamiento de máquinas, o para la generación de energía eléctrica en centrales térmicas de generación. Al igual que en todas las turbomáquinas, la transferencia de energía entre vapor y máquina ocurre en álabes móviles. El pasaje de vapor sobre los álabes móviles genera una fuerza neta en dirección tangencial aplicada a una cierta distancia del eje de rotación dando lugar a un torque generado. La sumatoria de todos los torques generados, multiplicado por la velocidad angular de rotación del eje, dan la potencia generada por la TV. Las TV a condensación son aplicadas para la impulsión de generadores eléctricos, operando en un ciclo Rankine o combinado, en centrales térmicas de generación. Las TV del tipo contrapresión son utilizadas en la industria para impulsión de máquinas de procesos, bombas, compresores, etc., donde el vapor que sale de la turbina generalmente es utilizado dentro del proceso productivo y/o también puede poseer extracciones de vapor en diferentes puntos de la TV para alimentar procesos productivos a diferentes presiones. Su comprobada confiabilidad, y versatilidad en la industria de procesos hacen que sigan siendo muy utilizadas hasta la actualidad. El rango de potencias disponibles va desde 1 kW hasta 1.500.000kW (1,5 GW), con eficiencias isoentrópicas que varían según el tamaño desde 20 a 90 % dependiendo d ependiendo principalmente del tamaño y aplicación. Centrales eléctricas con turbinas de vapor poseen menor costo inicial, comparadas con hidroeléctricas, solares, eólicas etc. En la mismas el vapor puede alcanzar presiones de hasta 310 bar (Presión critica del agua 220 bar) y temperaturas de hasta 550 ºC (temperatura critica del agua 375 ºC), expandiéndose hasta presiones inferiores a la de la atmosfera. Tales expansiones del vapor significan un salto entálpico isoentrópico cercano a los 1300 Kj/kg. Si se compara con la energía necesaria para un salto de agua en centrales hidroeléctricas, sería necesario un salto de agua de 13 km de altura para igualar la energía específica del vapor. La turbina de vapor posee para grandes potencias, la mejor relación potencia-tamaño, comparada con otras máquinas térmicas generadoras. La turbina actual fue desarrollada de forma paralela e independiente por Gustav Laval en Suecia y Charles Parson en Inglaterra a finales del siglo XIX.
Aplicaciones Según el Mercado Eléctrico Mayorista de Argentina, el 64% de la matriz total de generación de energía eléctrica se realiza a partir de energía de origen Térmica y nuclear tal como se observa en la tabla 1. Del 61% correspondiente a energía térmica, el 72% se realiza por medio de Turbinas de vapor y ciclos combinados, tabla 2. Mientras que del 3% correspondiente a energía nuclear el 100% se realiza a través de TV. En EEUU la generación por medio de TV y CC alcanza el 77% y en el mundo mundo al 66 %. Para aplicaciones industriales son ampliamente utilizadas en refinerías petroquímicas, industrias farmacéuticas, procesamiento de alimentos, papeleras, industria del azúcar y para cogeneración. La búsqueda de fuentes de energía renovable es una necesidad que se plantea en la actualidad. La utilización de energía a partir de biomasa crece año a año en todo el mundo, siendo utilizadas TV cada vez de mayores capacidades y rendimientos superiores.
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Tabla 1: Resumen de Capacidad Instalada MEM en MW. Fuente: MEM de Abril de 2015, CNEA-Argentina
Tabla 2: Resumen de Capacidad Instalada MEM en MW. Fuente: MEM de Abril de 2015, CNEA-Argentina
Componentes Los componentes que constituyen una turbina de vapor clásica se pueden clasificar en principales y auxiliares:
Principales
Rotor: es la parte móvil de la turbina, compuesta por un eje o tambor axial con diferentes hileras de álabes dispuestos de forma radial. Estator o carcasa: parte fija que contiene y soporta al rotor apoyado sobre los cojinetes radiales, además de disponer álabes fijos dispuestos en sentido radial, sellos, válvulas, y otros elementos necesarios para el funcionamiento de la TV. Toberas: órganos fijos montados sobre los diafragmas cuya finalidad es guiar al vapor y convertir energía de presión a energía cinética, generando un flujo de vapor correctamente guiado a elevada velocidad para luego incidir en los álabes móviles del rotor. En la tobera tiene lugar una expansión del vapor. Álabes: órganos que van solidarios al rotor de forma radial que tienen por finalidad recibir cantidad de movimiento del vapor generando un par y potencia sobre el eje de rotación. Diafragmas: tabiques ubicados en el interior de la carcasa donde se sostienen los álabes fijos. Soporta la diferencia de presión a ambos lados del álabe fijo dando estanqueidad a los fines de que el vapor fluya únicamente por las toberas.
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Secundarios
Sellos: evitan fugas de vapor de la turbina hacia el exterior por el huelgo comprendido entre carcasa y eje. También evitan los cortocircuitos en álabes móviles y fijos a los fines de que el vapor fluya por la parte activa del álabe. Sistemas de Válvulas
De parada: corta el flujo de vapor de entrada.
De seguridad : alivio de la presión interior al
De control y regulación.
exceder la presión admisible.
Permite la regulación de cantidad y calidad del vapor de admisión a la turbina a los fines de mantener algún parámetro de funcionamiento controlado (velocidad de giro, potencia, etc.)
Sistema de aceite: proporciona lubricación hidrodinámica en cojinetes. Puede actuar como sistema servoasistido para el accionamiento de mandos de regulación, de cierre rápido y/o de seguridad. Sistemas de vacío y condensado: Condensador, bombas, trampas de condensado, etc. Sistemas de protección: corte por sobre-velocidad, por baja presión aceite, o por vibraciones excesivas indicando un desbalance ocasionado por rotura de algún componente o por ensuciamiento (adhesión de depósitos sólidos sobre el rotor).
Figura 1: Rotor y carcasa (partida horizontalmente)
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Figura 2. Componentes básicos de una TV multiválvulas y admisión mixta
Principio de funcionamiento El vapor proveniente de la caldera, es dirigido hacia la turbina, previamente pasando por la válvula que regula el vapor de ingreso. El vapor dentro de la turbina, se expande al atravesar diferentes etapas de álabes fijos y móviles. La aparición de fuerzas tangenciales sobre los álabes móviles de rotor, debido a la interacción con el flujo de vapor, es la causa del torque y la potencia generada sobre el eje de la máquina. El principio de funcionamiento de la TV es descripto por la teoría de Turbomáquinas de Euler.
Clasificación Existen en la bibliografía de TV numerosas clasificaciones, clasi ficaciones, entre las cuales se destacan: Según el número de etapas:
1. Turbinas mono-etapa, se utilizan para potencias entre 1 kW y 60 MW aprox. (Acc. máquinas). 2. Turbinas multi-etapa, potencias superiores a 60 MW, M W, logran mayores rendimientos (Generación eléctrica). Según la cantidad de válvulas:
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1. Turb Turbin inas as de acci acción ón:: el el sa salto entálpico se realiza enteramente en los álabes fijos . 2. Turbinas de reacción: el salto entálpico entálpico se realiza realiza tanto en los álabes álabes fijos com o en los móviles. Cuando Cuando se real realiz izaa ent enter eram amen ente te en l s álabes móviles, es de reacción pura. Según la dirección del flujo de vapor en el rodete:
1. Axiales, Axiales, el paso de vapor se realiza siguiendo la dirección del eje de la turbina . 2. Radiales, Radiales, el vapor circul circul a principalme principalmente nte en dirección dirección radial. No son utili utilizada zada s actualmente. 3. Diagonales: el paso del apor se realiza en diagonal (radial +axial). Según el tipo de extracción:
1. Extracción controlada: ediante una válvula se controla la presión de extrac ión, mientras varia la carga de la turbina o de la dem anda. 2. Extrac Extracció ciónn sin control control:: se usan para para alim aliment entar ar regene regenerad radore ores, s, donde donde la presi presi n de extracción varía con la carga de la turbina. Según el tipo de admisión:
1. Admisión simple: la ad isión de vapor en la turbina se realiza a través de una única entrada. 2. Admisión mixta: posee o más admisiones de vapor en diferentes etapas. Es tilizada para grandes demand demandas as de pote potenci nciaa e lapsos cortos de tiempo. Según la cantidad de cuerpos:
1. Único cuerpo: La expan pan ión completa del vapor se realiza en un único rotor y carcasa. 2. Compuestas (Compound ): La La expa expans nsió iónn del del vap vapor or se se real realiz izaa en en dife difere rent ntes es cue cue pos en función de la pres presió ión, n, alta alta,, media edia y b aja presión, con el fin de reducir costos de fabricación adecuando materiales y diseño a la presión que anejan. La figura figura 3 esquematiz esquematizaa los diferente diferentes ti tippos de TV, TV, mi mientras que la figura 4 mu muestra las diferentes configuraciones de TV compuestas.
Figura 3: Esquemas de tipos de turbinas de 1 sólo cuerpo
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Figura 4: Configuraciones más comunes de cuerpos de TV
Figura 5: Corte de TV compuesta de 3 cuerpos en tándem de doble flujo en baja presión.
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El condensador usualmente trabaja con vacio y debe soportar enormes esfuerzos tendientes al colapso de la estructura debido a la diferencia de presiones entre interior y exterior sobre las paredes del mismo. Además, debe generar estanqueidad evitando el ingreso de aire al circuito de vapor, lo cual genera corrosión en los componentes. La turbina que funciona con condensador usualmente descargará en la zona de vapor húmedo, procurando que el titulo de vapor no descienda de 0,9 lo cual evita una masiva masiva formación de gotas de agua que al desplazarse a elevada velocidad erosionan los álabes al impactar sobre ellos. Si la descarga de vapor no tiene lugar en un condensador, la turbina descarga en la zona de vapor sobrecalentado y se denomina de contra presión, lo cual ocurre en industrias de procesos donde el vapor proveniente de la turbina es utilizado por ejemplo para algún proceso productivo. La figura 6 describe el salto entálpico llevado a cabo en ambos tipos de turbinas.
Figura 6: Salto entálpico en turbinas de contrapresión y condensación.
Diseños de álabes de turbina
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De reacción (0<σ <=1) Tur ina Parsons:
el salt saltoo entá entálp lpic icoo se se real realiz izaa part partee en á labes fijos y parte en álabes
móviles del rotor. La expan expansió siónn del del vapor vapor se realiza realiza tanto en álabes fijos (tobera) como móviles, por ello el alto entálpico en cada álabe (fij (fijoo y mó móvi vil) l),, es es una una frac fracci ción ón del del salto total total de la etapa, pudiendo pudiendo trabajar con menore menore s velocidades de rotación y meno menore ress pér pérdi dida das. s. La expa expans nsió iónn que que t iene iene luga lugarr con conll llev evaa a que que la la pre presi sión ón y tem tempera peratu tura ra de cienda consecutivamente en álabes fijos y móviles. Los álabes solidarios lidarios al rotor poseen poseen efecto efecto de tobera tobera móvil móvil dand dand lugar a una aceleración del vapor a su paso. La transferencia e energía entre vapor y álabe ocurre de la com inación de ambos efectos, tran transf sfer eren enci ciaa de de can canti tida dadd de de mov movim imii nto del vapor al rotor por cambio en la dirección de l fluido (tal como ocurre en acción acción)) y acele acelerac ración ión del del vapor vapor sob sob e el álabe móvil que genera, por la tercera ley de Newton, una fuerza igual y contra contraria ria sobre sobre los álab álabes, es, dando dando lug lugar al principio principio de reacción reacción.. La figura 7 esquemat esquematiz iz ambos tipos de diseños de álabes álabes dand dandoo una ilustra ilustració ciónn clara clara a las diferencias en en el principio de funcionamiento, y a l progreso de la presión y la velocidad del vapor a lo largo de la et apa.
Figura 7: Principio de funcionamiento de álabes de acción y reacci ón.
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embargo se hace necesario que los huelgos entre etapa fija y móvil sean reducidos para evitar fugas (zona 2 en figura 8 de acción) Las mayores velocidades del vapor en etapas de acción requieren de mayores velocidades tangenciales del vapor, requiriendo de mayor diámetro y/o velocidad de rotación, respecto de las etapas de reacción. Las mayores velocidades tangenciales del rotor necesarias en álabes de acción, justifican que sean montados sobre discos, mientras que álabes de reacción se montan sobre un eje o tambor. Las mayores presiones que manejan las etapas de acción, requieren de sellos más estrechos entre los diafragmas y el eje con el fin de evitar cortocircuitos cor tocircuitos y fugas (zona 1 en figura 8) Etapas de reacción bien diseñadas pueden alcanzar mayores rendimientos que las de acción. Para ello, es necesario controlar los cortocircuitos de vapor entre álabes móviles y carcasa, causados por la presión decreciente a lo largo del álabe. El control de los cortocircuitos se logra con diseños de huelgos internos más estrechos además de la utilización de sellos en la punta de los álabes móviles (zona 2 en figura 8 de reacción) En álabes de reacción la aceleración del vapor en los álabes móviles genera grandes esfuerzos de reacción no sólo en la dirección tangencial para generar torque y potencia, sino que también en dirección axial, que deben ser compensados por cojinetes axiales, pistón compensador, o mediante una configuración de flujo dividido opuesto.
Se concluye que las etapas de acción son de construcción más sencilla y por ende económica, volviéndose más robustas y confiables pudiendo ser utilizadas para altas presiones, pero alcanzando menores rendimientos comparadas con etapas de reacción.
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Configuraciones de etapas Existen dos configuraciones de etapas con álabes de impulso, i mpulso, mientras que con álabes de reacción sólo una:
Etapa de presión ( Rateau): tobera fija + álabes móviles de impulso Etapa de velocidad ( Curtis): Tobera fija +etapa de álabes móviles de impulso+ álabes fijos para redireccionar el vapor+ álabes móviles de impulso. Etapa de reacción: etapas de álabes fijos y móviles consecutivos de reacción
La siguiente imagen esquematiza las diferentes etapas mencionadas.
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Figura 12: Rangos de operación típicos de los diferentes tipos de TV.
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Turbina de acción pura (Curtis y Roteau)
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Turbinas de reacción con etapa Curtis
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Velocidad del sonido y número de Mach En un conducto que contiene un fluido compresible en reposo, se crea una pequeña perturbación con un pistón tal como se ilustra en la figura 15. Como consecuencia se establece una onda de presión infinitesimal prologándose a la velocidad del sonido c.
Figura 15: formación de onda de presión infinitesimal desplazándose a velocidad del sonido. Definiendo un volumen de control que contenga la onda de presión Por continuidad debe cumplirse que
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Para procesos isoentrópicos vale:
"!# $ % &' %% ( % ) * % * % +
Reescribiendo las ecuaciones anteriores
)
Reemplazando en se obtiene:
Puede verse que “c” depende únicamente de las propiedades del fluido y de la temperatura estática del fluido. Se define el número de mach como:
Formas de toberas y difusores
,- /.
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Siendo
9 $ ( ( 1 3 4 5 678 , :
Se obtiene finalmente:
;(,-<
La ecuación precedente relaciona el área del conducto con el gradiente de presiones, existiendo los diferentes casos descriptos en la tabla 3: Tabla 3: casos posibles de relación de áreas y gradientes de presión para flujos
Casos
=0 ,- ( ,- > ( 0 >0
Tobera ( Subsónico
,- = ( =0
Sónico
Supersónico
>0 ,- ( ,- > ( 0 =0
Difusor Subsónico
,- = ( >0
Sónico
Supersónico
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? (I,- % 2 (J&' "" EFFDGH&' D ? (I,- % 2 (J&''
A partir de la definición de densidad total o de estancamiento:
También se obtiene la densidad total o de d e estancamiento como:
FFD !!D ""D
Valores , y se encuentran tabulados para aire con k=1,4 para diferentes valores de d e Mach (Cengel página 930). Cuando la velocidad del fluido alcanza la velocidad del sonido, se cumple que M a=1 definiéndose propiedades críticas, críticas, las cuales son únicamente función del tipo de fluido
?K % 2 ( L ?K % 2 (&' L ?K 0MNON L ?K 0PQPR L
Para el caso particular del vapor sobrecalentado sobr ecalentado se obtiene:
Para otros gases se obtiene:
?K % 2 (&'' ?K 0N2RN
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Figura 16: derecha: gráfico de presiones a lo largo de la tobera. Izquierda: esquema de una tobera convergente y
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Aplicando balance de energía entre la entrada y salida para el sistema abierto en régimen permanente a una tobera convergente:
dcd Ae 0f g ? ' (2 /? '
Considerando proceso adiabático y sin transferencia de trabajo, la velocidad de salida es:
/' W 2h 2h?&' ? En la mayoría de los casos, la velocidad de entrada puede ser despreciada frente al santo entálpico (corroborar tal aseveración)
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Figura 22: esquema de admisión parcial
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Grados de reacción hasta 0,2-0,25 se acostumbran llamar etapa de acción.
En la tobera ocurre la conversión de energía térmica [h =h(presión; =h(pr esión; temperatura)] en energía cinética del vapor.
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~~
Como el ángulo en este caso es mayor a 90º se cambia el signo del segundo término y se toma cada término en módulo o se toma como el ángulo suplementario.
w/
/ • •
(A)
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Lo que demuestra la importancia de tener un valor elevado de U para generar la máxima potencia. El rendimiento máximo se obtiene reemplazando el ó en la ecuación de rendimiento:
Œ @m % ~
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