{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"provenance":[],"toc_visible":true},"kernelspec":{"name":"python3","display_name":"Python 3"},"language_info":{"name":"python"}},"cells":[{"cell_type":"markdown","source":["Descripción del campo fluidos\n","Asignatura: Mecánica de Fluidos\n","\n","Departamento: Ciencia y Tecnología de Materiales y Fluidos\n","\n","Centro: Escuela Universitaria Politécnica de Teruel\n","\n","Profesor: Adrián Navas Montilla"],"metadata":{"id":"-WRfZ6q8LiL8"}},{"cell_type":"markdown","source":["# Movimiento armónico simple de un sistema cilindro-pistón isotermo\n","\n","Este cuaderno ha sido desarrollado por una estudiante 2º curso del Grado en Ingieniería Electrónica y Automática (EUPT-UNIZAR) como ejercicio voluntario en el marco del PIIDUZ 5494 \"Python en ciencias e ingeniería: creación colaborativa\"\n","\n","Autora: Nerea Pilar Yagüe Lorente\n","\n","Profesor: Adrián Navas Montilla\n","\n","Asignatura: Temodinámica Técnica y Fundamentos de Transmisión de Calor\n","\n","---\n","**Enunciado propuesto:**\n","\n","Considere un dispositivo cilindro pistón en equilibrio con volumen inicial $V_0$, área transversal $A$ y masa del pistón $m_p$, que encierra una masa $m_a$ de aire a temperatura constante, $T$. En el otro lado del pistón, actúa la presión atmosférica. Para pequeños desplazamientos del pistón (respecto a $V_0$/$A$) alrededor de su posición de equilibrio, se puede demostrar que su movimiento sigue un movimiento armónico simple. Utilice la segunda ley de Newton para obtener la ecuación de movimiento del pistón, asumiendo que la longitud total del sistema es mucho mayor que la amplitud de los desplazamientos y considerando que el sistema está en posición horizontal. Prepare un Notebook de Python en el que describa el problema y lo resuelva siguiendo la plantilla proporcionada. Debe incluir una breve derivación explicada de la ecuación de movimiento utilizando sintaxis Latex y Markdown, así como un diagrama de sólido libre del sistema indicando las fuerzas.\n","\n","---\n","**Ayuda:**\n","Un sistema dinámico de segundo orden no amortiguado viene dado por la ecuación:\n","\n","$$ \\ddot{x} + \\omega^2 x =0$$\n","\n","donde $\\omega$ es la frecuencia angular del sistema. Nótese que $x$ es la posición respecto al punto de equilibrio, $dx/dt=\\dot{x}$ es la velocidad y $d^2x/dt^2=\\ddot{x}$ es la aceleración del sistema.\n","\n","La ecuación diferencial anterior es de segundo orden y se puede escribir como un sistema de 2 ecuaciones de primer orden:\n","\n","$$ \\frac{d}{dt}X = \\left(   \\begin{array}{c} -\\omega^2 x \\\\ \\dot{x} \\\\ \\end{array} \\right) $$\n","\n","con\n","\n","$$ X = \\left(   \\begin{array}{c} \\dot{x} \\\\ x  \\end{array} \\right)$$\n","\n"],"metadata":{"id":"WHNhex6deYN1"}},{"cell_type":"markdown","source":["##Derivación de la ecuación del movimiento cilindro-pistón\n","\n","A continuación se va a explicar la derivación de la ecuación del movimiento para un sistema cilindro-pistón cuyos datos son:\n","- Masa del pistón: $ m_p $\n","- Masa del aire encerrada: $ m_a $\n","- Área del pistón: $ A $\n","- Volumen inicial: $ V_{0} $\n","- Presión atmosférica: $ P_0 $\n","- Temperatura constante: $ T $\n","- Longitud $ L=\\frac{V_{0}}{A} $\n","\n","La fuerza neta que se ejerce sobre el pistón es igual a la suma de la fuerza que ejerce el gas encerrado más la fuerza que ejerce la presión atmostérica. Dado que $P=\\frac{F}{A}$, entonces $F=P\\cdot A$. Además, al ejercerse en la misma dirección pero en sentidos contrarios, la fuerza que ejerce la presión atmosférica se pone con signo negativo, dando lugar a:\n","\n","$$F_{neta} = P(x) \\cdot A - P_0 \\cdot A$$\n","\n","Tomando el aire como gas ideal, se puede utilizar la ecuación de los gases ideales ($PV = m_a R T$ con R la constante de los gases ideales para el aire seco) para hallar la presión interna $P(x)$:\n","\n","$$P(x) = \\frac{m_a R T}{V}$$\n","\n","Si la longitud del cilindro es: $L=\\frac{V_{0}}{A}$, el $V$ para cualquier instante será: $V=(L+x)\\cdot A$\n","\n","Sustituyendo, se tiene que:\n","\n","$$P(x) = \\frac{m_a R T}{(L+x)\\cdot A}$$\n","\n","En la situación de equilibrio ($x=0$) el pistón está en reposo, es decir, la fuerza interna iguala a la fuerza atmosférica, por lo que:\n","\n","$$P_0 = \\frac{m_a R T}{L\\cdot A}$$\n","\n","Llevando estas expresiones a la fuerza neta:\n","\n","$$F_{neta} = \\frac{m_a R T}{(L+x)\\cdot A} \\cdot A - \\frac{m_a R T}{L\\cdot A} \\cdot A = \\frac{m_a R T}{L+x} - \\frac{m_a R T}{L}=m_a R T \\left(\\frac{1}{L+x}-\\frac{1}{L}\\right)=-m_a R T\\frac{x}{L(L+x)}$$\n","\n","Cuando el pistón se mueve, la fuerza neta no depende directamente de la presión atmosférica $P_0$, sino de la diferencia en la presión entre el gas y la atmósfera. Para pequeños desplazamientos $x$, la diferencia en la presión se vuelve pequeña y aproximadamente lineal. En otras palabras, la fuerza neta es aproximadamente proporcional a $x$ cuando $x$ es pequeño.\n","\n","Esto indica que:\n","\n","$$F_{neta} \\approx -\\frac{m_a R T}{L^2} x$$\n","\n","Aplicando la segunda Ley de Newton ($\\sum F=m_p·\\ddot{x}$) se obtiene que:\n","\n","$$-\\frac{m_a R T}{L^2} x = m_p \\ddot{x}$$\n","\n","Por tanto, la ecuación del movimiento es la ecuación diferencial del oscilador armónico simple:\n","$$\\ddot{x} + \\omega^2 x = 0$$\n","\n","donde la frecuencia angular es:\n","$$\\omega^2 = \\frac{m_a R T}{m_p L^2}$$\n","$$\\omega=\\sqrt\\frac{m_a R T}{m_p L^2}=\\sqrt\\frac{m_a R T}{m_p}·\\frac{1}{L}$$\n","\n","Siendo R la constante de los gases ideales para el aire seco, un valor conocido de $R=287\\frac{J}{kgK}$."],"metadata":{"id":"aDaNBQw8uwAs"}},{"cell_type":"markdown","source":["## Diagrama de cuerpo libre\n","\n","A continuación se muestra el diagrama de cuerpo libre del pistón con las fuerzas involucradas:\n","\n","- $ P(x)A $: presión del gas actuando hacia la izquierda.\n","- $ P_0A $: presión atmosférica actuando hacia la derecha."],"metadata":{"id":"szJvsSILejEj"}},{"cell_type":"code","source":["# Representación del diagrama de cuerpo libre\n","fig, ax = plt.subplots(figsize=(8, 3))  # se abre una figura vacía de dimesiones 8·3\n","\n","# Dibujo del pistón (se ha necesitado importar la librería patches para añadir los rectángulos)\n","#  para representar la masa del aire:\n","ax.add_patch(patches.Rectangle((3.9, 1.25), 1, 0.5, edgecolor='k', facecolor='lightgreen'))\n","#  para representar el pistón:\n","ax.add_patch(patches.Rectangle((3.7, 1.25), 0.2, 0.5, edgecolor='k', facecolor='k'))\n","ax.add_patch(patches.Rectangle((2.7, 1.43), 1, 0.13, edgecolor='k', facecolor='k'))\n","ax.text(3.6, 1.9, 'PISTÓN')\n","\n","# Flecha hacia la derecha (presión atmosférica)\n","ax.arrow(3, 1.65, 0.6, 0, head_width=0.1, head_length=0.1, fc='b', ec='b')  # coordenadas x y de inicio, vector dirección de la flecha, ancho de la punta, largo de la punta y colores\n","ax.text(2.9, 1.75, r'$P_0 A$', color='b') # coordenadas del texto de la flecha, texto y color\n","\n","# Flecha hacia la izquierda (presión del gas)\n","ax.arrow(4.62, 1.5, -0.6, 0, head_width=0.1, head_length=0.1, fc='r', ec='r')  # coordenadas x y de inicio, vector dirección de la flecha, ancho de la punta, largo de la punta y colores\n","ax.text(4.5, 1.6, r'$P(x) A$', color='r') # coordenadas del texto de la flecha, texto y color\n","\n","# Se establecen unos límites para que la imagen quede centrada\n","ax.set_xlim(1.5, 6)\n","ax.set_ylim(0.8, 2.2)\n","\n","# Se quitan los ejes\n","ax.axis('off')\n","\n","ax.set_title('DIAGRAMA DE CUERPO LIBRE DEL PISTÓN')\n","plt.show()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":290},"id":"HDN3leSFa_O6","outputId":"da8a2dd9-6e5e-4a32-f379-f914e9835922"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 800x300 with 1 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\n"},"metadata":{}}]},{"cell_type":"markdown","source":["### EJEMPLO 1: aprender a dibujar una gráfica de la posición frente al tiempo de un movimiento armónico simple para un valor de omega dado"],"metadata":{"id":"9_P6mMata36p"}},{"cell_type":"code","source":["import numpy as np\n","import matplotlib.pyplot as plt\n","import matplotlib.patches as patches\n","from scipy.integrate import odeint"],"metadata":{"id":"aJxNynopcqKe"},"execution_count":null,"outputs":[]},{"cell_type":"code","execution_count":null,"metadata":{"id":"nOr13uBFbTem"},"outputs":[],"source":["def rhs(X, t, omega): #Esto es el lado derecho de la ecuación, que equivale a la derivada temporal de X\n","    xdot, x = X\n","    return [-omega**2 * x, xdot] #omega es velocidad angular, x es posición y xdot es velocidad"]},{"cell_type":"markdown","source":["Vamos a definir un vector de tiempos en el que resolver la ecuación:"],"metadata":{"id":"RgS5KdxVb7Gp"}},{"cell_type":"code","source":["dt = 0.1 #paso de tiempo para la integración temporal, cuanto más pequeño mejor resolución\n","tiempo_final=12.0 #tiempo final para resolver el sistema\n","ts = np.arange(0, tiempo_final, dt)"],"metadata":{"id":"XxHSt1Uub6n-"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["Y a añadir las condiciones iniciales:"],"metadata":{"id":"Rhl8AnsdcM-R"}},{"cell_type":"code","source":["X0 = [0, 1] #donde la primera componente es xdot y la segunda x: en este caso hacemos que comience con velocidad cero y posición x=1"],"metadata":{"id":"UqewDl1rcPh5"},"execution_count":null,"outputs":[]},{"cell_type":"markdown","source":["Y finalmente se resuelve la ecuación utilizando un integrador temporal predefinido ```odeint```"],"metadata":{"id":"Qv67uG7ycaUi"}},{"cell_type":"code","source":["omega = 2\n","scipysol = odeint(rhs, X0, ts, args=(omega,)) #esta función sirve para obtener la solución mediante integración numérica (como hace Matlab y Simulink) en los instantes definidos en el vector ts.\n","#La solución se almacena en scipysol, que será un array de 2 dimensiones\n","plt.plot(ts, scipysol[:, 1]); #esto realiza una representación de la segunda componente del vector X, es decir, de la posición, frente al tiempo"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":430},"id":"DkktwRO_cjha","outputId":"b61bf424-6ad9-405e-d8ef-27442f7ff08e"},"execution_count":null,"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 Axes>"],"image/png":"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\n"},"metadata":{}}]},{"cell_type":"markdown","source":["### EJEMPLO 2: aprender, a partir de los valores de los parámetros físicos, a calcular omega y dibujar con ella una gráfica de la posición frente al tiempo de un movimiento armónico simple"],"metadata":{"id":"Rq0mYpSLbuuC"}},{"cell_type":"code","source":["# Se estiman valores para los parámetros físicos\n","mp = 0.1       # kg\n","ma = 0.01      # kg\n","A = 0.01       # m^2\n","V0 = 0.001     # m^3\n","R = 287        # J/kg·K\n","T = 300        # K\n","L= 0.5         # m        Se elige con idea de que sea mucho mayor que los desplazamientos de x\n","\n","# Cálculo de omega\n","omega = np.sqrt((ma * R * T) / (mp * L**2))\n","print(f\"Frecuencia angular ω = {omega:.2f} rad/s\")\n","\n","# Se define la ecuación\n","def rhs(X, t, omega): #Esto es el lado derecho de la ecuación, que equivale a la derivada temporal de X\n","    xdot, x = X\n","    return [-omega**2 * x, xdot] #omega es velocidad angular, x es posición y xdot es velocidad\n","\n","# Se define el vector de tiempos\n","dt = 0.1 #paso de tiempo para la integración temporal, cuanto más pequeño mejor resolución\n","tiempo_final=12.0 #tiempo final para resolver el sistema\n","ts = np.arange(0, tiempo_final, dt)\n","\n","# Condiciones iniciales: velocidad 0, desplazamiento 1 mm (para que sea lo suficientemente más pequeño que L)\n","X0 = [0, 0.001] #donde la primera componente es xdot y la segunda x: en este caso hacemos que comience con velocidad cero y posición x=0.001m\n","scipysol = odeint(rhs, X0, ts, args=(omega,)) #esta función sirve para obtener la solución mediante integración numérica (como hace Matlab y Simulink) en los instantes definidos en el vector ts.\n","#La solución se almacena en scipysol, que será un array de 2 dimensiones\n","\n","# Graficar desplazamiento\n","plt.plot(ts, scipysol[:, 1]*1000)  #esto realiza una representación de la segunda componente del vector X, es decir, de la posición, frente al tiempo. Se multiplica por 1000 para representarlo en mm.\n","plt.title(\"Desplazamiento del pistón (Movimiento Armónico Simple)\")\n","plt.xlabel(\"Tiempo [s]\")\n","plt.ylabel(\"Desplazamiento [mm]\")\n","plt.grid()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":489},"id":"QNmfPP0RXzr5","outputId":"248ff880-6886-43f4-bc4a-72a456e12161"},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Frecuencia angular ω = 185.58 rad/s\n"]},{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 Axes>"],"image/png":"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\n"},"metadata":{}}]},{"cell_type":"markdown","source":["## Conclusión\n","\n","El pistón realiza un movimiento armónico simple para pequeños desplazamientos. Su frecuencia angular depende de:\n","\n","- Masa del aire encerrada $m_a$\n","- Constante de los gases ideales para el aire seco $R=287\\frac{J}{kgK}$\n","- Temperatura del aire $T=cte$\n","- Masa del pistón $m_p$\n","- Longitud del pistón $L$\n","\n","El análisis es válido bajo la suposición de condiciones isotérmicas y amplitudes pequeñas."],"metadata":{"id":"-Bj9e1sampXN"}},{"cell_type":"markdown","source":["##Bibliografía\n","\n","**Para llegar a la ecuación del movimiento:**\n","\n","Pistón oscilante. (s. f.). http://tesla.us.es/wiki/index.php/Pist%C3%B3n_oscilante (Este enlace proporciona el estudio del pistón en vertical)\n","\n","**Para representar el diagrama de cuerpo libre:**\n","\n","matplotlib.patches.Rectangle — Matplotlib 3.10.1 documentation. (s. f.). https://matplotlib.org/stable/api/_as_gen/matplotlib.patches.Rectangle.html\n","\n","matplotlib.patches.Arrow — Matplotlib 3.10.1 documentation. (s. f.). https://matplotlib.org/stable/api/_as_gen/matplotlib.patches.Arrow.html\n"],"metadata":{"id":"-8LAiZgVhCT8"}}]}