{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Beispiel 18.2: Einfluss des gasseitigen Stoffübergangs auf Reaktionen 2. Ordnung \n", "\n", "Bearbeitet von Franz Braun\n", "\n", "Dieses Beispiel befindet sich im Lehrbuch auf den Seiten 275 - 276. Die Nummerierung\n", "der verwendeten Gleichungen entspricht der Nummerierung im Lehrbuch. Das hier angewendete\n", "Vorgehen entspricht dem im Lehrbuch vorgestellten Lösungsweg.\n", "\n", "Zunächst werden die benötigten Pakete importiert." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "### Import\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import solve_bvp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Anschließend werden die dimensionslosen Materialbilanzen (Gleichung 18.15a) und die dazugehörigen Randbedingungen (Tabelle 18.1) in eine Funktion implementiert." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def material(X,y):\n", " '''\n", " Dimensionslose Materialbilanz für die Reaktion 2.Ordnung (Gleichung 18.15a)\n", " y[0] : Restanteil von A1\n", " y[1] : Restanteil von A2\n", " y[2] : Restanteil von A3\n", " y[3] : erste Ableitung des Restanteils von A1 nach der dimensionslosen Ortskoordinate\n", " y[4] : erste Ableitung des Restanteils von A2 nach der dimensionslosen Ortskoordinate\n", " y[5] : erste Ableitung des Restanteils von A3 nach der dimensionslosen Ortskoordinate\n", " dy2dX2 : zweite Ableitung der Restanteile von nach der dimensionslosen Ortskoordinate (Vektor der Größe 3)\n", " nu : Stöchiometrische Koeffizienten (Vektor der Größe 3)\n", " omega : dimensionslose Reaktionsgeschwindigkeit\n", " X : Ortskoordinate\n", " '''\n", "\n", " omega = omega_f(y[:3])\n", " \n", " dy2dX2 = np.empty_like(y[3:])\n", " \n", " dy2dX2[0] = - Ha**2 * nu[0] * omega\n", " dy2dX2[1] = - Ha**2 * nu[1] * omega\n", " dy2dX2[2] = - Ha**2 * nu[2] * omega\n", " \n", "\n", " return np.vstack((y[3:],dy2dX2))\n", "\n", "\n", "\n", "def bc_material(y0,y1):\n", " '''\n", " Randbedingungen der Materialbilanz (Tabelle 18.1)\n", " y0 : Randbedingungen bei X = 0\n", " y1 : Randbedingungen bei X = 1\n", " '''\n", " BC = np.empty(nu.size *2)\n", " # A1\n", " BC[0] = y0[3] - Bi * (y0[0] - f_e[0]) # df_1,L = Bi_i,m * (f_i,L - f_1,G,b)\n", " BC[1] = y1[0] # f_1,L = 0 \n", " # A2\n", " BC[2] = y0[4] # df_2,L/dX = 0\n", " BC[3] = y1[1] - f_e[1] # f_2,L = f_2,L,b\n", " # A3\n", " BC[4] = y0[5] # df_3,L/dX = 0\n", " BC[5] = y1[2] - f_e[2] # f_3,L = f_3,L,b\n", " \n", " return BC" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Danach werden die stöchiometrischen Koeffizienten gemäß der Reaktionsgleichung (18.1) und die Hatta-Zahl parametriert. Die dimensionslose Reaktionsgeschwindigkeit 2. Ordnung ergibt sich aus Gleichung (18.12e) für eine einzelne Reaktion wie folgt:\n", "\n", "\\begin{align*}\n", " \\omega_\\mathrm{L} &= \\frac{r_\\mathrm{1,L}}{r_\\mathrm{1,e}} = \\frac{k_1\\,c_\\mathrm{1,L}}{k_1\\,c_\\mathrm{1,e,L}}\\frac{c_\\mathrm{2,L}}{c_\\mathrm{2,e,L}}\n", "\\end{align*}\n", "\n", "Durch Umformung erhalt man einen Ausdruck auf Basis des Restanteils und des Einsatzverhältnisses.\n", "\n", "\\begin{align*}\n", " \\omega_\\mathrm{L}\n", " &=\\frac{c_\\mathrm{1,L}}{c_\\mathrm{1,e,L}}\\frac{c_\\mathrm{2,L}}{c_\\mathrm{2,e,L}}\\frac{c_\\mathrm{1,e,L}}{c_\\mathrm{1,e,L}} \n", " = \\frac{c_\\mathrm{1,L}}{c_\\mathrm{1,e,L}}\\frac{c_\\mathrm{2,L}}{c_\\mathrm{1,e,L}}\\frac{c_\\mathrm{1,e,L}}{c_\\mathrm{2,e,L}}\\\\\n", " &=f_1\\,f_2\\,\\kappa_{2}^{-1}\n", "\\end{align*}\n", "\n", "Diese Gleichung für die dimensionslose Reaktionsgeschwindigkeit wird in eine Funktion implementiert." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "nu = np.array((-1,-1,1)) # Stöchiometrische Koeffizienten für A1, A2, A3 \n", "f_e = np.array((1,2,0)) # Restanteile am Eintritt\n", "Ha = 2 # Hatta - Zahl\n", "kappa_2 = 1 # Einsatzverhältnis\n", "\n", "def omega_f(f):\n", " '''\n", " Dimensionslose Reaktionsgeschwindigkeit für eine Reaktion 2. Ordnung\n", " f : Vektor der Restanteile \n", " '''\n", " return f[0] * f[1] / kappa_2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Da der Einfluss der Biot-Zahl $(Bi)$ betrachtet werden soll, erfolgt die Variation von $Bi$ in einer For-Schleife." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "Bi_vec = np.array((1,10,100,1000)) # Vektor mit Biot - Zahlen für Beispiel 18.3\n", "\n", "Lösungen = [] # Leere Liste zum Speichern der Lösungen\n", "N = 101 # Diskretisierung\n", "X = np.linspace(0,1,N) # Diskretisierung der Ortskoordinate\n", "init_f = np.ones((3,N)) # Startwerte für Restanteile\n", "init_df = np.ones((3,N))*1e-5 # Startwerte für die Ableitungen der Restanteile\n", "init = np.vstack((init_f,init_df)) # Zusammengefügte Startwerte für die Iterationen des Solvers\n", "\n", "for BiBi in Bi_vec:\n", " Bi = BiBi\n", " sol = solve_bvp(material, bc_material, X,init , max_nodes = 1e10, tol = 1e-10)\n", " if sol.success == False:\n", " print(sol)\n", " Lösungen.append(sol)\n", "\n", "Lösungen_3 = np.array((Lösungen))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Abschließend werden die Ergebnisse grafisch dargestellt." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "colors = ['black','gray','blue','red']\n", "\n", "fig, ax = plt.subplots(1, 1, figsize = (5, 5))\n", "for Lösung, Bi, color in zip(Lösungen_3,Bi_vec,colors):\n", " ax.plot(Lösung.x, Lösung.y[0], label = str(Bi), color = color)\n", " ax.plot(Lösung.x, Lösung.y[1], color = color, linestyle = '--')\n", "\n", "ax.set_xlim(0,1)\n", "ax.set_ylim(0,2)\n", "ax.tick_params(axis=\"y\",direction=\"in\", right = True)\n", "ax.tick_params(axis=\"x\",direction=\"in\", top = True)\n", "ax.set_ylabel(r'$f_{i,\\mathrm{L}}\\,/\\,1$')\n", "ax.set_xlabel(r'$\\chi \\,/\\,1$')\n", "ax.legend(title = '$Bi_\\mathrm{1,m}$ =',frameon = False, alignment = 'left')\n", "\n", "plt.tight_layout()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.4" } }, "nbformat": 4, "nbformat_minor": 2 }