{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Continuous Reactor Example \n", "### Simulation of a CSTR/PSR/WSR \n", "\n", "In this example we will illustrate how Cantera can be used to simulate a Continuously Stirred Tank Reactor (CSTR), also interchangeably referred to as a Perfectly Stirred Reactor or a Well Stirred Reactor, a Jet Stirred Reactor or a Longwell Reactor (there may well be more \"aliases\"). A cartoon of such a reactor is shown below\n", "\n", "\"Cartoon\n", "\n", "As the figure illustrates, this is an open system (unlike a Batch Reactor which is isolated). P, V and T are the reactor's pressure, volume and temperature respectively. The mass flow rate at which reactants come in is the same as that of the products which exit; and these stay in the reactor for a characteristic time $\\tau$, called the *residence time*. This is a key quantity in sizing the reactor and is defined as follows:\n", "\n", "\\begin{equation*}\n", "\\tau = \\frac{m}{\\dot{m}}\n", "\\end{equation*}\n", "\n", "where $m$ is the mass of the gas" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Running Cantera version: 2.3.0a2\n" ] } ], "source": [ "from __future__ import division\n", "from __future__ import print_function\n", "\n", "import pandas as pd\n", "import numpy as np\n", "import time\n", "import cantera as ct\n", "\n", "print(\"Running Cantera version: {}\".format(ct.__version__))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define the gas\n", "In this example, we will work with $nC\n", "_{7}H_{16}$/$O_{2}$/$He$ mixtures, for which experimental data can be found in the paper by [Zhang et al.](http://dx.doi.org/10.1016/j.combustflame.2015.08.001). We will use the same mechanism reported in the paper. It consists of 1268 species and 5336 reactions" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\n", "**** WARNING ****\n", "For species OHV, discontinuity in h/RT detected at Tmid = 1000\n", "\tValue computed using low-temperature polynomial: 53.6206\n", "\tValue computed using high-temperature polynomial: 53.5842\n", "\n", "\n", "**** WARNING ****\n", "For species CHV, discontinuity in h/RT detected at Tmid = 1000\n", "\tValue computed using low-temperature polynomial: 107.505\n", "\tValue computed using high-temperature polynomial: 107.348\n", "\n", "\n", "**** WARNING ****\n", "For species CH2CO, discontinuity in cp/R detected at Tmid = 1000\n", "\tValue computed using low-temperature polynomial: 10.0876\n", "\tValue computed using high-temperature polynomial: 10.1013\n", "\n", "\n", "**** WARNING ****\n", "For species C5H9B-A,COOH, discontinuity in cp/R detected at Tmid = 1675\n", "\tValue computed using low-temperature polynomial: 47.645\n", "\tValue computed using high-temperature polynomial: 47.5845\n", "\n", "\n", "**** WARNING ****\n", "For species C5H9B-C,DOOH, discontinuity in cp/R detected at Tmid = 1675\n", "\tValue computed using low-temperature polynomial: 47.645\n", "\tValue computed using high-temperature polynomial: 47.5845\n", "\n", "\n", "**** WARNING ****\n", "For species C5H9C-A,AOOH, discontinuity in cp/R detected at Tmid = 1681\n", "\tValue computed using low-temperature polynomial: 48.5491\n", "\tValue computed using high-temperature polynomial: 48.4914\n", "\n", "\n", "**** WARNING ****\n", "For species C5H9C-A,DOOH, discontinuity in cp/R detected at Tmid = 1681\n", "\tValue computed using low-temperature polynomial: 48.5491\n", "\tValue computed using high-temperature polynomial: 48.4914\n" ] } ], "source": [ "gas = ct.Solution('data/galway.cti')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define initial conditions\n", "#### Inlet conditions for the gas and reactor parameters" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Inlet gas conditions\n", "reactorTemperature = 925 #Kelvin\n", "reactorPressure = 1.046138*ct.one_atm #in atm. This equals 1.06 bars\n", "concentrations = {'NC7H16': 0.005, 'O2': 0.0275, 'HE': 0.9675}\n", "gas.TPX = reactorTemperature, reactorPressure, concentrations \n", "\n", "# Reactor parameters\n", "residenceTime = 2 #s\n", "reactorVolume = 30.5*(1e-2)**3 #m3\n", "\n", "# Instrument parameters\n", "\n", "# This is the \"conductance\" of the pressure valve and will determine its efficiency in \n", "# holding the reactor pressure to the desired conditions. \n", "pressureValveCoefficient = 0.01\n", "\n", "# This parameter will allow you to decide if the valve's conductance is acceptable. If there\n", "# is a pressure rise in the reactor beyond this tolerance, you will get a warning\n", "maxPressureRiseAllowed = 0.01" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Simulation parameters" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Simulation termination criterion\n", "maxSimulationTime = 50 # seconds" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Reactor arrangement\n", "\n", "We showed a cartoon of the reactor in the first figure in this notebook; but to actually simulate that, we need a few peripherals. A mass-flow controller upstream of the stirred reactor will allow us to flow gases in, and in-turn, a \"reservoir\" which simulates a gas tank is required to supply gases to the mass flow controller. Downstream of the reactor, we install a pressure regulator which allows the reactor pressure to stay within. Downstream of the regulator we will need another reservoir which acts like a \"sink\" or capture tank to capture all exhaust gases (even our simulations are environmentally friendly !). This arrangment is illustrated below\n", "\n", "\"Cartoon" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Initialize the stirred reactor and connect all peripherals" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "fuelAirMixtureTank = ct.Reservoir(gas)\n", "exhaust = ct.Reservoir(gas)\n", "\n", "stirredReactor = ct.IdealGasReactor(gas, energy='off', volume=reactorVolume)\n", "\n", "massFlowController = ct.MassFlowController(upstream=fuelAirMixtureTank,\n", " downstream=stirredReactor,\n", " mdot=stirredReactor.mass/residenceTime)\n", "\n", "pressureRegulator = ct.Valve(upstream=stirredReactor,\n", " downstream=exhaust,\n", " K=pressureValveCoefficient)\n", "\n", "reactorNetwork = ct.ReactorNet([stirredReactor])" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# now compile a list of all variables for which we will store data\n", "columnNames = [stirredReactor.component_name(item) for item in range(stirredReactor.n_vars)]\n", "columnNames = ['pressure'] + columnNames\n", "\n", "# use the above list to create a DataFrame\n", "timeHistory = pd.DataFrame(columns=columnNames)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Simulation Took 80.92s to compute, with 1264 steps\n" ] } ], "source": [ "# Start the stopwatch\n", "tic = time.time()\n", "\n", "# Set simulation start time to zero\n", "t = 0\n", "counter = 1\n", "while t < maxSimulationTime:\n", " t = reactorNetwork.step()\n", "\n", " # We will store only every 10th value. Remember, we have 1200+ species, so there will be\n", " # 1200 columns for us to work with\n", " if(counter%10 == 0):\n", " #Extract the state of the reactor\n", " state = np.hstack([stirredReactor.thermo.P, stirredReactor.mass, \n", " stirredReactor.volume, stirredReactor.T, stirredReactor.thermo.X])\n", " \n", " #Update the dataframe\n", " timeHistory.loc[t] = state\n", " \n", " counter += 1\n", "\n", "# Stop the stopwatch\n", "toc = time.time()\n", "\n", "print('Simulation Took {:3.2f}s to compute, with {} steps'.format(toc-tic, counter))\n", "\n", "# We now check to see if the pressure rise during the simulation, a.k.a the pressure valve\n", "# was okay\n", "pressureDifferential = timeHistory['pressure'].max()-timeHistory['pressure'].min()\n", "if(abs(pressureDifferential/reactorPressure) > maxPressureRiseAllowed):\n", " print(\"WARNING: Non-trivial pressure rise in the reactor. Adjust K value in valve\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot the results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Import modules and set plotting defaults" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import matplotlib as mpl\n", "%matplotlib notebook\n", "\n", "plt.style.use('ggplot')\n", "plt.style.use('seaborn-pastel')\n", "\n", "plt.rcParams['axes.labelsize'] = 18\n", "plt.rcParams['xtick.labelsize'] = 14\n", "plt.rcParams['ytick.labelsize'] = 14\n", "plt.rcParams['figure.autolayout'] = True" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a test, we plot the mole fraction of $CO$ and see if the simulation has converged. If not, go back and adjust max. number of steps and/or simulation time" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "application/javascript": [ "/* Put everything inside the global mpl namespace */\n", "window.mpl = {};\n", "\n", "mpl.get_websocket_type = function() {\n", " if (typeof(WebSocket) !== 'undefined') {\n", " return WebSocket;\n", " } else if (typeof(MozWebSocket) !== 'undefined') {\n", " return MozWebSocket;\n", " } else {\n", " alert('Your browser does not have WebSocket support.' +\n", " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", " 'Firefox 4 and 5 are also supported but you ' +\n", " 'have to enable WebSockets in about:config.');\n", " };\n", "}\n", "\n", "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", " this.id = figure_id;\n", "\n", " this.ws = websocket;\n", "\n", " this.supports_binary = (this.ws.binaryType != undefined);\n", "\n", " if (!this.supports_binary) {\n", " var warnings = document.getElementById(\"mpl-warnings\");\n", " if (warnings) {\n", " warnings.style.display = 'block';\n", " warnings.textContent = (\n", " \"This browser does not support binary websocket messages. \" +\n", " \"Performance may be slow.\");\n", " }\n", " }\n", "\n", " this.imageObj = new Image();\n", "\n", " this.context = undefined;\n", " this.message = undefined;\n", " this.canvas = undefined;\n", " this.rubberband_canvas = undefined;\n", " this.rubberband_context = undefined;\n", " this.format_dropdown = undefined;\n", "\n", " this.image_mode = 'full';\n", "\n", " this.root = $('
');\n", " this._root_extra_style(this.root)\n", " this.root.attr('style', 'display: inline-block');\n", "\n", " $(parent_element).append(this.root);\n", "\n", " this._init_header(this);\n", " this._init_canvas(this);\n", " this._init_toolbar(this);\n", "\n", " var fig = this;\n", "\n", " this.waiting = false;\n", "\n", " this.ws.onopen = function () {\n", " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", " fig.send_message(\"send_image_mode\", {});\n", " fig.send_message(\"refresh\", {});\n", " }\n", "\n", " this.imageObj.onload = function() {\n", " if (fig.image_mode == 'full') {\n", " // Full images could contain transparency (where diff images\n", " // almost always do), so we need to clear the canvas so that\n", " // there is no ghosting.\n", " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", " }\n", " fig.context.drawImage(fig.imageObj, 0, 0);\n", " };\n", "\n", " this.imageObj.onunload = function() {\n", " this.ws.close();\n", " }\n", "\n", " this.ws.onmessage = this._make_on_message_function(this);\n", "\n", " this.ondownload = ondownload;\n", "}\n", "\n", "mpl.figure.prototype._init_header = function() {\n", " var titlebar = $(\n", " '
');\n", " var titletext = $(\n", " '
');\n", " titlebar.append(titletext)\n", " this.root.append(titlebar);\n", " this.header = titletext[0];\n", "}\n", "\n", "\n", "\n", "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n", "\n", "}\n", "\n", "\n", "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n", "\n", "}\n", "\n", "mpl.figure.prototype._init_canvas = function() {\n", " var fig = this;\n", "\n", " var canvas_div = $('
');\n", "\n", " canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n", "\n", " function canvas_keyboard_event(event) {\n", " return fig.key_event(event, event['data']);\n", " }\n", "\n", " canvas_div.keydown('key_press', canvas_keyboard_event);\n", " canvas_div.keyup('key_release', canvas_keyboard_event);\n", " this.canvas_div = canvas_div\n", " this._canvas_extra_style(canvas_div)\n", " this.root.append(canvas_div);\n", "\n", " var canvas = $('');\n", " canvas.addClass('mpl-canvas');\n", " canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n", "\n", " this.canvas = canvas[0];\n", " this.context = canvas[0].getContext(\"2d\");\n", "\n", " var rubberband = $('');\n", " rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n", "\n", " var pass_mouse_events = true;\n", "\n", " canvas_div.resizable({\n", " start: function(event, ui) {\n", " pass_mouse_events = false;\n", " },\n", " resize: function(event, ui) {\n", " fig.request_resize(ui.size.width, ui.size.height);\n", " },\n", " stop: function(event, ui) {\n", " pass_mouse_events = true;\n", " fig.request_resize(ui.size.width, ui.size.height);\n", " },\n", " });\n", "\n", " function mouse_event_fn(event) {\n", " if (pass_mouse_events)\n", " return fig.mouse_event(event, event['data']);\n", " }\n", "\n", " rubberband.mousedown('button_press', mouse_event_fn);\n", " rubberband.mouseup('button_release', mouse_event_fn);\n", " // Throttle sequential mouse events to 1 every 20ms.\n", " rubberband.mousemove('motion_notify', mouse_event_fn);\n", "\n", " rubberband.mouseenter('figure_enter', mouse_event_fn);\n", " rubberband.mouseleave('figure_leave', mouse_event_fn);\n", "\n", " canvas_div.on(\"wheel\", function (event) {\n", " event = event.originalEvent;\n", " event['data'] = 'scroll'\n", " if (event.deltaY < 0) {\n", " event.step = 1;\n", " } else {\n", " event.step = -1;\n", " }\n", " mouse_event_fn(event);\n", " });\n", "\n", " canvas_div.append(canvas);\n", " canvas_div.append(rubberband);\n", "\n", " this.rubberband = rubberband;\n", " this.rubberband_canvas = rubberband[0];\n", " this.rubberband_context = rubberband[0].getContext(\"2d\");\n", " this.rubberband_context.strokeStyle = \"#000000\";\n", "\n", " this._resize_canvas = function(width, height) {\n", " // Keep the size of the canvas, canvas container, and rubber band\n", " // canvas in synch.\n", " canvas_div.css('width', width)\n", " canvas_div.css('height', height)\n", "\n", " canvas.attr('width', width);\n", " canvas.attr('height', height);\n", "\n", " rubberband.attr('width', width);\n", " rubberband.attr('height', height);\n", " }\n", "\n", " // Set the figure to an initial 600x600px, this will subsequently be updated\n", " // upon first draw.\n", " this._resize_canvas(600, 600);\n", "\n", " // Disable right mouse context menu.\n", " $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n", " return false;\n", " });\n", "\n", " function set_focus () {\n", " canvas.focus();\n", " canvas_div.focus();\n", " }\n", "\n", " window.setTimeout(set_focus, 100);\n", "}\n", "\n", "mpl.figure.prototype._init_toolbar = function() {\n", " var fig = this;\n", "\n", " var nav_element = $('
')\n", " nav_element.attr('style', 'width: 100%');\n", " this.root.append(nav_element);\n", "\n", " // Define a callback function for later on.\n", " function toolbar_event(event) {\n", " return fig.toolbar_button_onclick(event['data']);\n", " }\n", " function toolbar_mouse_event(event) {\n", " return fig.toolbar_button_onmouseover(event['data']);\n", " }\n", "\n", " for(var toolbar_ind in mpl.toolbar_items) {\n", " var name = mpl.toolbar_items[toolbar_ind][0];\n", " var tooltip = mpl.toolbar_items[toolbar_ind][1];\n", " var image = mpl.toolbar_items[toolbar_ind][2];\n", " var method_name = mpl.toolbar_items[toolbar_ind][3];\n", "\n", " if (!name) {\n", " // put a spacer in here.\n", " continue;\n", " }\n", " var button = $('');\n", " button.click(method_name, toolbar_event);\n", " button.mouseover(tooltip, toolbar_mouse_event);\n", " nav_element.append(button);\n", " }\n", "\n", " // Add the status bar.\n", " var status_bar = $('');\n", " nav_element.append(status_bar);\n", " this.message = status_bar[0];\n", "\n", " // Add the close button to the window.\n", " var buttongrp = $('
');\n", " var button = $('');\n", " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", " buttongrp.append(button);\n", " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", " titlebar.prepend(buttongrp);\n", "}\n", "\n", "mpl.figure.prototype._root_extra_style = function(el){\n", " var fig = this\n", " el.on(\"remove\", function(){\n", "\tfig.close_ws(fig, {});\n", " });\n", "}\n", "\n", "mpl.figure.prototype._canvas_extra_style = function(el){\n", " // this is important to make the div 'focusable\n", " el.attr('tabindex', 0)\n", " // reach out to IPython and tell the keyboard manager to turn it's self\n", " // off when our div gets focus\n", "\n", " // location in version 3\n", " if (IPython.notebook.keyboard_manager) {\n", " IPython.notebook.keyboard_manager.register_events(el);\n", " }\n", " else {\n", " // location in version 2\n", " IPython.keyboard_manager.register_events(el);\n", " }\n", "\n", "}\n", "\n", "mpl.figure.prototype._key_event_extra = function(event, name) {\n", " var manager = IPython.notebook.keyboard_manager;\n", " if (!manager)\n", " manager = IPython.keyboard_manager;\n", "\n", " // Check for shift+enter\n", " if (event.shiftKey && event.which == 13) {\n", " this.canvas_div.blur();\n", " event.shiftKey = false;\n", " // Send a \"J\" for go to next cell\n", " event.which = 74;\n", " event.keyCode = 74;\n", " manager.command_mode();\n", " manager.handle_keydown(event);\n", " }\n", "}\n", "\n", "mpl.figure.prototype.handle_save = function(fig, msg) {\n", " fig.ondownload(fig, null);\n", "}\n", "\n", "\n", "mpl.find_output_cell = function(html_output) {\n", " // Return the cell and output element which can be found *uniquely* in the notebook.\n", " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", " // IPython event is triggered only after the cells have been serialised, which for\n", " // our purposes (turning an active figure into a static one), is too late.\n", " var cells = IPython.notebook.get_cells();\n", " var ncells = cells.length;\n", " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", " data = data.data;\n", " }\n", " if (data['text/html'] == html_output) {\n", " return [cell, data, j];\n", " }\n", " }\n", " }\n", " }\n", "}\n", "\n", "// Register the function which deals with the matplotlib target/channel.\n", "// The kernel may be null if the page has been refreshed.\n", "if (IPython.notebook.kernel != null) {\n", " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", "}\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.plot(tempDependence.index, tempDependence['NC7H16'], 'r-', label=r'$nC_{7}H_{16}$')\n", "plt.plot(tempDependence.index, tempDependence['CO'], 'b-', label='CO')\n", "plt.plot(tempDependence.index, tempDependence['O2'], 'k-', label='O$_{2}$')\n", "\n", "plt.plot(expData['T'], expData['NC7H16'],'ro', label=r'$nC_{7}H_{16} (exp)$')\n", "plt.plot(expData['T'], expData['CO'],'b^', label='CO (exp)')\n", "plt.plot(expData['T'], expData['O2'],'ks', label='O$_{2}$ (exp)')\n", "\n", "plt.xlabel('Temperature (K)')\n", "plt.ylabel(r'Mole Fractions')\n", "\n", "plt.xlim([650, 1100])\n", "plt.legend(loc=1);" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }