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Simulación del comportamiento aerodinámico de 3 perfiles NACA mediante el uso de dinámica = de fluidos computacional (CFD)

Simulation of the aerodynamic behavior of 3 NACA profiles using computational fluid (CFD)

 

Marcelo Esteban Calispa Aguilar.[1]<= ![endif]>, Ariel Alexander Andrade Jaramillo.[2]<= ![endif]> & Juan Luis Díaz Castillo.[3]<= ![endif]>

 

Recibido: 09-04-2020 / Revisado= : 13-05-2020 / Aceptado: 16-06-2020 / Publicado: 03-07-2020

<= o:p> 

 Abstract.                                          =          = DOI: https://doi.org/= 10.33262/cienciadigital.v4i3.1282<= /span>

The simulation of aerodynamic elements using computational fluid dynamics (CFD), in the aeronautical industry represents a fundamental pilla= r in the development of new technologies and optimization of existing models. The aim of this study is to evaluate the behaviour of 3 profiles commonly used = and defined by the National Aeronautics Committee (NACA) through ANSYS and comp= are the results obtained with previously published simulations. To obtain this information, models with control volumes for each profile, using CAD models based on the NACA specifications were created. In addition, it was necessar= y to define the boundary conditions within the simulation of finite volumes. The study allows a better understanding of parameters such as the pressure cont= our, speed contour, flow lines and Mach number that are characteristic of each profile, with their advantages and disadvantages. The resulting simulations determined a better overall performance of profile 63002 (5 digits) compare= d to profiles 4415 and 0012 (4 digits), confirming the established in the bibliography. Furthermore, the study allowed a better learning of aerodynam= ics (fluid mechanics) which, as far as the authors have investigated, has been little used in the Ecuadorian academic environment.

Keywords: NACA profiles, computational fluid dynamics, aerodynamics, ANSYS simulation.

Resumen.

La simulación de elementos aerodinámicos mediante la dinámica de fluidos computacional (CFD por sus siglas en inglés), en la industria aeronáutica representa un pilar fundamental en el desarrollo de nuevas tecnologías y optimización de modelos ya existentes. El presente estudio tiene por objeti= vo evaluar el comportamiento de 3 perfiles usualmente usados y definidos por el comité nacional de aeronáutica (NACA) a través de ANSYS y comparar los resultados obtenidos con simulaciones previamente publicadas. Para obtener = esta información, se creó modelos con volúmenes de control para cada perfil, usa= ndo modelos CAD en base a las especificaciones NACA, además, fue necesario defi= nir las condiciones de frontera dentro de la simulación de volúmenes finitos. El estudio permite definir y observar cual es el contorno de presión, además, contorno de velocidad, líneas de flujo y numero Mach que son parámetros característicos de cada perfil, con sus ventajas y desventajas. Las simulaciones resultantes sugieren un mejor desempeño general del perfil 630= 02 (5 dígitos) comparado con los perfiles 4415 y 0012 (4 dígitos), confirmando= lo establecido en la bibliografía. Adicionalmente, el estudio permitirá un mej= or aprendizaje de aerodinámica (mecánica de fluidos) que, hasta donde los auto= res han investigado, ha sido poco utilizado en el medio académico ecuatoriano. =

Palabras clave: Perfiles NACA, dinámica de fluidos computacional, aerodinámica, simulación ANSYS.

Introducción.

El desarrollo y uso de software que permiten sim= ular el comportamiento de elementos aerodinámicos han presentado facilidades considerables no solamente en la industria aérea, sino también en áreas com= o la energía eólica y la aerodinámica de vehículos. Las ventajas de desarrollar simulaciones principalmente se relacionan al ahorro y optimización de tiempo que tomaría realizar un trabajo experimental, siempre y cuando los resultad= os de la simulación y experimentación no difieran considerablemente. Por este motivo siempre es requerida una validación de resultados que podría llevars= e a cabo al compararlos con estudios previos.

El estudio del comportamiento de estos elementos nace en el año 1915, como un comité aeronáutico antecesor de la NASA en Est= ados Unidos y que se enfocaría en desarrollar y mejorar el existente armamento militar aéreo. Sin embargo, en la actualidad, el uso de las regulaciones de este Comité Consultivo Nacional de Aeronáutica (NACA) se ha diversificado de tal forma que puede ser utilizado no solo en perfiles aerodinámicos aéreos = para aeronaves, sino también para elementos que constituyen turbinas eólicas y q= ue usan perfiles de este tipo debido a sus mejores prestaciones aerodinámicas.=

El estudio del comportamiento de este tipo de configuración de perfiles de alas de avión (principal aplicación) han sido usualmente tratadas como un régimen lineal, sin embargo, en algunas otras aplicaciones este análisis no ha sido suficiente. Para entender un poco de = la terminología, se describe a continuación brevemente ciertos conceptos que s= erán usados en este estudio.

Las ecuaciones que rigen el fenómeno a simular e= stán definidas en la mecánica de fluidos, las cuales principalmente deberán ajustarse a la ecuación de energía, continuidad, momento, Bernoulli, etc., = sin embargo, se la resolución de las ecuaciones que se presenten será muy complicada sin el uso de un software de dinámica computacional. Por este motivo, se asume que las ecuaciones están definidas e incluidas en el softw= are (ANSYS) que es utilizado en el presente estudio. En la figura 1 se muestra = los principales elementos considerados para describir un perfil de un ala de av= ión.

Figura 1. Representación esquemática de elementos en perf= iles de aviones

            Fuente: Elaboración propia.<= /p>

De los principales elementos se puede definir el= perfil alar como la forma de la sección del ala que se observa transversalmente. E= l borde de Ataque es la parte delantera del ala que primero toma contacto con el fl= ujo de aire al cual estará sometido el perfil.

Adicionalmente se define el borde de salida como= la parte posterior del perfil, la línea que une la parte posterior de todos los perfiles del ala. Por otro lado, los extradós e intradós son la parte super= ior e inferior del perfil entre los bordes de ataque y salida respectivamente. = Se puede observar también que se define un espesor máximo como la distancia má= xima entre el valor de extradós e intradós.

Una de las principales variantes en la configura= ción de los elementos del perfil es la línea de cuerda la cual es una línea imaginaria que va entre los bordes de ataque y de salida en cada perfil ala= r. La Curvatura por otro lado es la curva del ala desde el borde de ataque al borde de salida. La curvatura máxima se refiere a la de la superficie super= ior (extradós) y la media a la de la superficie inferior (intradós) y curvatura media a la equidistante a ambas superficies. Finalmente, se puede definir a= el ángulo α como el ángulo que hay entre la dirección del viento y el per= fil alar (más concretamente con la cuerda)

Es importante mencionar por otro lado como la NA= CA clasifica los distintos perfiles de acuerdo con numeración de cuatro o cinco dígitos, serie 16, serie 6, serie 7 y serie 8, como se muestra en la tabla = 1 a continuación con sus ventajas y desventajas.

Tabla 1. Clasificación de perfiles NACA

Familia

Ventajas

Desventajas

Aplicaciones<= b>

4-Dígitos

1. Buenas características de pérdida.                                              =    2. Pequeño movimiento del centro de presión en un amplio rango de = velocidad.                                              =     3. La asperidad tiene poco efecto

1. Bajo coeficiente de elevación máximo.                   2. Resistencia relativa alta.

3. Alto momento de lanzamiento.

1. Aviación general.               2= . Colas horizontales.                 SIMÉTRICO:                       =      3. Jets supersónicos.             4. Palas de helicópteros.                 5. Mortajas.               6.Cohetes/aletas de misi= l

5-Dígitos

1. Mayor coeficiente de elevación máximo.                  2. Momento de lanzami= ento bajo.                   3. La asp= eridad tiene poco efecto.

1. Mala conducta de pérdida.                                 2. Resistencia relativamente alta.

1. Aviación general.               2. Bombarderos a pistón, transportes.                           3. Viajeros.=                              4. jets de negocios.

Series-16

1. Evita picos de baja presión.       

2. Baja resistencia a alta velocidad.

1. Elevación relativamente baja.

1. Hélices de aviones.            2. Hélices de barco.

Series-6

1. Alto coeficiente de elevación máximo.                  2. Muy bajo arrastre = sobre un pequeño rango de condiciones de operación.               3. Optimizado para alta velocidad.

1. Alto arrastre fuera del rango óptimo de condiciones de operación.                    2. Momento de lanza= miento alto.                3. Mala cond= ucta de pérdida.                             =     4. Muy susceptible a la asperidad.

1. Hélices de aviones.            2.= jets de negocios.               3. Entren= adores de jet.         4. Chorros supersónicos.

Series-7

1.  Muy bajo arrastre sobre un pequeño ra= ngo de condiciones de operación.                                              =    2. Momento de lanzamiento bajo.

1. Coeficiente de elevación máximo reducido.                       2. Alto arrastre= fuera del rango óptimo de condiciones de operación.                    3. Mala conducta de pérdida.                                 4. Muy susceptible a la asperidad.

Rara vez se usa.

Series-8

Desconocido

Desconocido

Usado muy raramente

F= uente: Elaboración propia.

A pesar de que la mayoría de las simulaciones publicadas en la actualidad están más relacionadas con un régimen lineal, existe pocos datos relacionados a las pérdidas en perfiles de alas finitas.= De las pocas publicaciones que incluyen el tema de pérdidas, no ofrecen detall= es de fuerza y momento después de la posición inicial. Se han presentado tambi= én estudios puramente teóricos que han demostrado una relación consistente ent= re el coeficiente de elevamiento versus el ángulo de ataque, utilizando difere= ntes perfiles NACA.

De acuerdo con los anteriormente mencionado, se requiere el cálculo de ciertas características que nos ayuden a comparar los resultados de cada uno de los resultados simulados, ya sea con valores tabulados o presentados con publicaciones previas. Algunos de estos valores= son definidos en la teoría de aerodinámica tal como número Mach, líneas de fluj= o, número de Reynolds, coeficiente de presión (Cp), perfi= les de velocidades y presiones. El presente estudio se enfocará en la obtención y comparación de estos valores con datos de entrada obtenidos de bibliografía reciente.

El enfoque de las simulaciones en la actualidad = son muchas, cada una con sus variaciones, ventajas y desventajas. Tales simulaciones pueden tener más énfasis en muchos ángulos de ataque sobre el perfil aerodinámico en la fuerza de levantamiento y la turbulencia = que se genera al momento que uno de estos perfiles experimenta un despegue, en = los números de Reynolds que se presentan usualmente en estos perfiles, e incluso algunas de las simulaciones sirven para validación de perfiles NACA utiliza= ndo no solo ANSYS como software de simulado, sino también otros programas de simulado tales como AutoDesk.

Por este motivo, y en función de lo descrito en = esta sección de introducción, el principal objetivo del trabajo es simular el comportamiento de tres perfiles NACA (4415, 0012, 63206), hallando sus respectivas líneas de flujo, coeficientes de presión, perfil de velocidades, tomando en cuenta condiciones iniciales que han sido sugeridas en la bibliografía. Dichos resultados serán comparados con trabajos similares que= han usado distintos softwares CFD. Por otro lado, el estudio plantea el uso de = este tipo de simulaciones para un mejor aprendizaje de la aerodinámica y mecánic= a de fluidos en la educación de pregrado en Ecuador.

Metodología.

Para lograr resultados c= on precisión es deseable generar una variedad de geometrías en 2 y 3 dimension= es. Esto permite que se pueda modificar los ángulos de ataque y por ende los resultados que pueden ser optimizados con cada modificación. Por este motiv= o se define como se procedió al desarrollo de las geometrías y a su simulación en ANSYS. La simulación de los tres perfiles se lo realiza en las mismas condiciones iniciales y de frontera para comparar cual presenta un mejor de= sempeño.

Generación de geometrías.<= o:p>

Los perfiles NACA selecc= ionados a ser analizados serán de las siguientes series: 4415, 0012 y 63006; los cu= ales estarán bajo las siguientes condiciones de frontera:

·      =    Las ecuaciones que gobiernan el comportamiento d= e un fluido son las de Navier – Stokes.

·      =    Flujo Turbulento: Shear Stress Transport (modelo de esfuerzo cortante).=

·      =    Estado Estable (no interviene la variable tiempo= ).

·      =    Monofásico: Aire como gas ideal.

·      =    Flujo subsónico, número MACH:0.7.

·      =    Ángulo de ataque α =3D 17°.

·      =    Temperatura 288 K.

·      =    Número de Reynolds: 9x106=

·      =    Densidad del aire: 0.688 kg/m3

Estos perfiles están disponibles en la página oficial para la generación de perfiles, Airfoil Tools (http://airfoiltools.com/airfoil), sitio-web con los parámetros precisos y confiables para las dimensiones de perfiles NACA. El = uso de los perfiles ya implementados en dicha página web son los recomendados b= asados en la literatura.

Con las coordenadas obtenidas y una vez introducidas todos los valores, se genera un archivo el cual puede ser importado desde el software SOLIDWORKS. El objetivo es, una = vez importado, extruir y generar un sólido en 3D que pueda ser evaluado y simul= ado en ANSYS.

Simulación en ANSYS.<= /o:p>

Las simulaciones se realizarán con el objetivo de recolectar datos sobre el número MACH, las lí= neas de flujo, fuerza aerodinámica, el coeficiente de presión y el contorno de velocidades que se generan cuando los perfiles se encuentran en los parámet= ros antes expuestos. Con el uso de ICEM CFD, software que proporciona herramien= tas de geometría sofisticadas para generación de mallas, post-procesamiento y herramientas de optimización de mallas. Este software ha sido desarrollado = para simulaciones que utilizan dinámica de fluidos computacional. Las herramient= as de generación de cuadrícula ofrecen la capacidad de crear paramétricamente cuadrículas a partir de la geometría en cuadrículas hexaédricas, tetraédric= as e híbridas, estructuradas, no estructuradas y de bloques múltiples que consis= ten en celdas hexaédricas, tetraédricas, piramidales y prismáticas; y formatos = de cuadrícula cartesiana combinados con condiciones de frontera.

 Una vez generada el mallado del perfil se utiliza el Workbench Mecha= nical de ANSYS Versión Estudiantil 2019R3. Se generaron los modelos en 2D de Volúmenes Finitos, se usa este tipo de método porque en torno a cada punto de esta malla se construye un volumen de control que no se translapa con los de los puntos vecinos, de esta forma el volumen total de fluido resulta ser igual a la suma de volumenes de control considerados.

Figura 1. Modelo de volúmenes finitos del Perfil alar NACA 4415 <= o:p>

Fuente: Elaboración propia.

El modelo fue mallado con elementos tridimensionales hexaédricos con la especificación del SOLVER en este caso para análisis por CFD y se obtuvo:

Tabla 2. Elementos de mallado, Elementos Hexaédricos

Domain

Nodes

Elements

Fluid

85918

42833

Tetrahedra

Wedges

Pyramids

0

128

0

Hexahedra

Polyhedral

 

42705

0

 

Fuente:<= /b> Elaboración propia.

La densidad del aire por= lo general tiene un valor que oscila entre 1.2 kg/m3 y 1.3 kg/m3, pero para tener resultados más apegados a la realidad de vuelo en las probe= tas se opta por una altitud promedio de 12 800 pies de altura que deben operar = en aeropuertos o aeródromos, por consecuente la densidad del aire bajará considerablemente hasta un valor de 0.688 kg/m3

Con las condiciones de frontera antes especificadas se procedió a determinar por medio de cálculos= los siguientes parámetros:




Donde:

c =3DVelocidad del sonido

R=3DConstante de los gases

γ =3DRatio de calor específico

T=3DTemperatura

u=3D Velocidad libre del aire

M=3D Número Mach

Re=3DNúmero de Reynolds

μ=3D Viscosidad Dinámica

ρ=3D Densidad

Análisis y discusión de resultados.

 

Número de MACH.

Figura 3. Número NACH perfil NACA = 4415

Fuente:<= /b> Elaboración propia.

 

Figura 4.  Número MACH perfil NACA 0012

Fuente:<= /b> Elaboración propia.

Figura 5.<= span style=3D'font-size:12.0pt;line-height:115%;font-family:"Times New Roman",se= rif'> Número MACH perfil NACA 63006

            Fuente:<= /b> Elaboración propia.

Como se puede observar l= os 3 perfiles NACA, el que más resalta por el equilibrio del número MACH es el d= e la serie 63006 por lo que es recomendable para aviones que rompen la barrera d= el sonido (supersónicos) dando mejor características en vuelos a altas velocid= ades en cambio las demás probetas presentan un contrate de valores MACH por lo t= anto tendrán limitantes estructurales de velocidad (subsónicos). Este valor MACH= es variable en función a la temperatura y altitud, es decir, a menor temperatu= ra y mayor altitud el número MACH aumenta o viceversa.

Líneas de flujo (streamlines).

Figura 6. Líneas de flujo perfil N= ACA 4415

Fuente:<= /b> Elaboración propia.

 

Figura 7. Líneas de flujo perfil NACA 0012

Fuente:<= /b> Elaboración propia.

Figura 8. Líneas de flujo perfil NACA = 63006

Fuente:<= /b> Elaboración propia.

Se puede observar en pri= mera instancia que los perfiles de velocidades o líneas de flujo representan un comportamiento que se esperaba en base a la bibliografía. Identificamos el comportamiento del vector velocidad a lo largo del perfil en un ángulo de ataque de 17 grados, como se definió en la figura 2. Adicionalmente, en base al código de colores se pue= de sugerir una mayor concentración de turbulencias en los perfiles 4415 y 0012 compara= do con el perfil 63006.

Los valores de velocidad= que hemos obtenido se asemejan bastante con los valores obtenidos por Petrilli et al. 2014, trabajo que se enfoca en el comportamiento y optimización del perfil en su punto de salida y ángulo de ataque.

Se identifica que tanto = a ángulos de ataque de 17 y 18 grados, existe una pérdida de sustentación, esto se de= be a que existe una separación del flujo laminar ósea del aire suave sobre el pe= rfil alar, dando lugar a un flujo turbulento. Estas líneas de flujo podrían ser observadas de mejor manera y comprobadas si se realiza experimentación con modelos a escala dentro de un túnel de viento. Lamentablemente es una de las restricciones actuales del estudio.  

Fuerza aerodinámica.<= o:p>

Figura 9. = Fuerza aerodinámica perfil NACA 4415<= /span>

Fuente:<= /b> Elaboración propia.

Figura 10. Fuerza aerodinámica perfil NACA 0012

Fuente:<= /b> Elaboración propia.

Figura 11. Fuerza aerodinámica perfil NACA 63006

 

 

 

 

 

 

Fuente:<= /b> Elaboración propia.

La fuerza de sustentació= n es importante debido a que es la fuerza que mantiene al ala (avión) estable. D= icha fuerza es generada por la masa de aire a través del perfil alar, siempre es perpendicular a la trayectoria de vuelo independientemente de la altitud del avión. Se observa que, en base a los resultados mostrados, el perfil 63006 muestra el mayor valor de vector fuerza, por lo que podemos sugerir que este perfil es el que presentara una mejor fuerza sustentadora. Esto se ajusta a= los resultados que se ha presentado en otros estudios en los que, en base a exp= erimentación y estudios empíricos, se utiliza este perfil para aumentar el coeficiente de sustentación. Por otro lado, los perfiles (0012, 4415) las fuerzas son de m= enor valor. Con esto se comprueba que los perfiles de 5 dígitos tienen un mayor desarrollo comparados con los perfiles de 4 digititos, y son considerados c= omo una evolución de los perfiles NACA

Los perfiles 4415 generan fuerzas de sustentación incluso cuando el Angulo de ataque es igual a cero. Este tipo de perfiles ofrecen menor resistencia al avance, sin embargo, no producen tanta sustentación. Por otro lado, en el perfil 0012 a medida que aumenta el ángulo de ataque tiende a tener un mejor comportamiento con resp= ecto al centro de presiones.

Coeficiente de presión.

Figura 12. Coeficiente de presión perfil NACA 4415

Fuente:<= /b> Elaboración propia.

            Figura 13. Coeficiente de presión perfil NACA 0012

Fuente:<= /b> Elaboración propia.

                Figura 14. Coeficiente de presión perfil NACA 63006<= /p>

Fuente:<= /b> Elaboración propia.

Los cálculos de los coeficientes de presión sirven en el estudio para identificar lugares críti= cos de cada perfil NACA pronosticando la presión del aire como se logra observar que en todos los bordes de ataque de estos perfiles estarán soportando la máxima presión que se genera. Las consecuencias de este análisis están relacionadas a una mejor selección de materiales de fabricación, por ejempl= o, en base a las condiciones de frontera.

Los coeficientes obtenid= os de la simulación tienen un valor máximo de 7 o cercano a este valor, lo cua= l se puede observar claramente en las figuras 12, 13 y 14. Estos valores son los= que se usualmente se recomiendan en aerodinámica para tener una mayor presión e= n el intradós que en el extradós, lo cual genera una buena sustentación de los perfiles.

 =

<= b>Contorno de velocidades.

            Figura 15. Contorno de velocidades perfil NACA 4415

<= v:shape id=3D"Imagen_x0020_10" o:spid=3D"_x0000_i1027" type=3D"#_x0000_t75" style= =3D'width:307.5pt; height:208.5pt;visibility:visible;mso-wrap-style:square'>

Fuente:<= /b> Elaboración propia.

Figura 16. Contorno de velocidades perfil NACA 0012

Fuente:<= /b> Elaboración propia.

 

Figura 17. Contorno de velocidades perfil NACA 63002

Fuente:<= /b> Elaboración propia.

Se puede observar claramente que el perfil 4415, se producen una mayor concentración de velocidades en el borde de salida, lo cual podría relacionarse a una mayor concentración de turbulencias. A pesar de que el perfil 0012 también es de = la familia de 4 dígitos, es considerable la reducción del perfil de velocidade= s en el borde de salida. Por último, en el perfil 63002 en base al código de col= ores se observa que es mucho mejor la distribución del perfil de velocidades.

Nuevamente se puede atribuir mejores resultados al ser de una serie mejorada que la de 5 dígito= s. Sin embargo, no se podría generalizar y decir que el perfil de 6 dígitos siempre será el mejor. Existirán aplicaciones específicas en las que cada u= no de los perfiles son recomendados. Como ejemplo podemos anotar el uso de perfiles 4415 para vuelos en los que se tenga poca carga (pasajeros) como en paracaidismo o aeronaves dedicadas a fumigación. Otro ejemplo común de apli= caciones de perfil 0012 es en aeronaves para acrobacias aéreas o perfiles para hélic= es de helicópteros.

Como se muestra en literatura actual publicada, y en la cual se baso el presente estudio, ha sido posible obtener resultados similares para los tres perfiles utilizando un software diferente para el desarrollo de las simulac= iones de dinámica computacional. <= /span>

Trabajo futuro.

Se plantea el uso del presente trabajo como punto de partida para la simulación de otros perfiles NACA definidos, no solamente en perfiles de alas de avión sino, además, en perfiles de álabes de turbinas eólicas que permitirán la optimización y aprovechamiento de velocidades de viento presentes en el entorno local. Dic= ha optimización se puede enfocar en el uso de nuevos y mejores mallados al mom= ento de utilizar la simulación dinámica. Por otro lado, es importante tener siem= pre presente que esto puede conllevar a un costo computacional mayor, a veces innecesario.

Conclusiones:

El objetivo principal pl= anteado del estudio se ha logrado cumplir. Los resultados han permitido la evaluaci= ón de parámetros que caracterizan a cada uno de los perfiles recomendados para ciertos usos por NACA. El uso de dinámica computacional ha sido verificado mediante el análisis y comparación de resultados con bibliografía publicada actual.

Los resultados de forma general sugieren un mejor comportamiento y desempeño del perfil NACA 63002 (número MACH, perfil de velocidades, presiones y líneas de flujo), con las mismas condiciones de frontera e iniciales que el resto de los perfiles. A pesar de que es un tema aun en desarrollo, las simulaciones muestran claram= ente las ventajas del uso de software y su versatilidad para cambio de condicion= es de entrada, dimensiones con resultados en tiempo real.

Los resultados obteni= dos permiten confirmar que existe un mejoramiento de los perfiles (de 4 dígitos= a perfiles de 5 dígitos) como lo demuestra el perfil 63002, enfocándose la literatura en mejoramiento de sustentación. Sin embargo, existirán aun así aplicaciones que sugerirán un uso perfiles 4415 y 0012 debido a su entorno = de aplicación.

Adicionalmente, el presente estudio será de mucha utilidad en el proceso de aprendizaje de asignaturas de relacionadas con la mecánica de fluidos y aerodinámica, con = una visión futura de comprobación en experimentos a escala en túneles de viento= .

= Referencias bibliográficas.<= /o:p>

= NASA. The National Advisory Commi= ttee for Aeronautics. Shooting for the Sky Helped Us Reach for the Stars 2019; 1.

= Parakkal JU, Kadi K El, El-Sinawi A, et al. Numerical analysis of VAWT wind turbines: Joukowski vs classical NACA rotor’s blades. Energy Procedia 2019; 158: 1194–1201= .

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PARA CITAR EL ARTÍCULO INDEXADO.

 

 

<= span style=3D'font-size:10.5pt;line-height:106%;font-family:"Helvetica",sans-ser= if; color:#333333;background:white'>Calispa Aguilar, M. E., Andrade Jaramillo, A. A., & Díaz Castillo, J. L. (2020). Simulación del comportamiento aerodinámico de 3 perfiles NACA mediante el uso de dinámica de fluidos computacional (CFD). Ciencia Digital, 4(3), 42-59.

https://doi.org/10.33262/cienciadigital.v4i3.1282<= /a>

 

 


 

 

 

El artículo que se publica es de exclusiva responsabilidad de los autores y no necesariamente reflejan el pensamiento de la Revista Ciencia Digital.

 

El artículo queda en propiedad de la revista y, por tanto, su publicación parcial y/o total en otro medio tiene que ser autoriz= ado por el director de la Revista Cien= cia Digital.

 

 

 

<= o:p> 

 

 



[1] Escuela Super= ior Politécnica de Chimborazo, Chimborazo - Ecuador, Facultad de Ingeniería Mecánica, marcelo.calispa@espoch.edu.= ec, ORCID: 0000-0002-4085-8488,

[2] Escuela Super= ior Politécnica de Chimborazo, Chimborazo - Ecuador, Facultad de Ingeniería Mecánica, ariel.andrade@espoch.edu.ec, ORCID: 0000-0002-2003-0333

[3] Escuela Super= ior Politécnica de Chimborazo, Chimborazo - Ecuador, Facultad de Ingeniería Mecánica, juanluis.diaz@espoch.edu.ec, ORCID: 0000-0001-9284-278X<= /span>

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