reactors/batch_reactor_ignition_delay_NTC.ipynb

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   "source": [
    "# Ignition delay computation\n",
    "In this example, we will illustrate how to setup and use a constant volume batch reactor. This reactor will then be used to compute the ignition delay of a gas at any temperature and pressure.\n",
    "\n",
    "The reactor (system) is simply an insulated box."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Runnning Cantera version: 3.0.0\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import time\n",
    "\n",
    "import cantera as ct\n",
    "\n",
    "print(f\"Runnning Cantera version: {ct.__version__}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import modules and set plotting defaults"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_formats = [\"svg\"]\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.rcParams[\"axes.labelsize\"] = 18\n",
    "plt.rcParams[\"xtick.labelsize\"] = 12\n",
    "plt.rcParams[\"ytick.labelsize\"] = 12\n",
    "plt.rcParams[\"figure.autolayout\"] = True\n",
    "plt.rcParams[\"figure.dpi\"] = 120\n",
    "\n",
    "plt.style.use(\"ggplot\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the gas\n",
    "In this example we will choose n-heptane as the gas. For a representative kinetic model, we use the 160 species [mechanism](https://combustion.llnl.gov/archived-mechanisms/alkanes/heptane-reduced-mechanism) by [Seier et al. 2000, Proc. Comb. Inst](http://dx.doi.org/10.1016/S0082-0784&#40;00&#41;80610-4). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Niclas\\AppData\\Local\\Temp\\ipykernel_2336\\3597652223.py:1: UserWarning: NasaPoly2::validate: \n",
      "For species c7h15o-1, discontinuity in h/RT detected at Tmid = 1391\n",
      "\tValue computed using low-temperature polynomial:  21.83428060093267\n",
      "\tValue computed using high-temperature polynomial: 21.76699500201913\n",
      "\n",
      "  gas = ct.Solution(\"../data/seiser.yaml\")\n"
     ]
    }
   ],
   "source": [
    "gas = ct.Solution(\"../data/seiser.yaml\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define reactor conditions : temperature, pressure, fuel, stoichiometry"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the reactor temperature and pressure\n",
    "reactor_temperature = 1000  # Kelvin\n",
    "reactor_pressure = 101325  # Pascals\n",
    "\n",
    "gas.TP = reactor_temperature, reactor_pressure\n",
    "\n",
    "# Define the fuel, oxidizer and set the stoichiometry\n",
    "gas.set_equivalence_ratio(phi=1.0, fuel=\"nc7h16\", oxidizer={\"o2\": 1.0, \"n2\": 3.76})\n",
    "\n",
    "# Create a batch reactor object and add it to a reactor network\n",
    "# In this example, the batch reactor will be the only reactor\n",
    "# in the network\n",
    "r = ct.IdealGasReactor(contents=gas, name=\"Batch Reactor\")\n",
    "reactor_network = ct.ReactorNet([r])\n",
    "\n",
    "# use the above list to create a DataFrame\n",
    "time_history = ct.SolutionArray(gas, extra=\"t\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define useful functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ignition_delay(states, species):\n",
    "    \"\"\"\n",
    "    This function computes the ignition delay from the occurence of the\n",
    "    peak in species' concentration.\n",
    "    \"\"\"\n",
    "    i_ign = states(species).Y.argmax()\n",
    "    return states.t[i_ign]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computed Ignition Delay: 3.248e-02 seconds. Took 0.88s to compute\n"
     ]
    }
   ],
   "source": [
    "reference_species = \"oh\"\n",
    "\n",
    "# Tic\n",
    "t0 = time.time()\n",
    "\n",
    "# This is a starting estimate. If you do not get an ignition within this time, increase it\n",
    "estimated_ignition_delay_time = 0.1\n",
    "t = 0\n",
    "\n",
    "counter = 1\n",
    "while t < estimated_ignition_delay_time:\n",
    "    t = reactor_network.step()\n",
    "    if not counter % 10:\n",
    "        # We will save only every 10th value. Otherwise, this takes too long\n",
    "        # Note that the species concentrations are mass fractions\n",
    "        time_history.append(r.thermo.state, t=t)\n",
    "    counter += 1\n",
    "\n",
    "# We will use the 'oh' species to compute the ignition delay\n",
    "tau = ignition_delay(time_history, reference_species)\n",
    "\n",
    "# Toc\n",
    "t1 = time.time()\n",
    "\n",
    "print(f\"Computed Ignition Delay: {tau:.3e} seconds. Took {t1-t0:3.2f}s to compute\")\n",
    "\n",
    "# If you want to save all the data - molefractions, temperature, pressure, etc\n",
    "# uncomment the next line\n",
    "# time_history.to_csv(\"time_history.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot the result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Figure illustrating the definition of ignition delay"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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    "plt.figure()\n",
    "plt.plot(time_history.t, time_history(reference_species).Y, \"-o\")\n",
    "plt.xlabel(\"Time (s)\")\n",
    "plt.ylabel(\"$Y_{OH}$\")\n",
    "\n",
    "plt.xlim([0, 0.05])\n",
    "plt.arrow(\n",
    "    0,\n",
    "    0.008,\n",
    "    tau,\n",
    "    0,\n",
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    "plt.annotate(\n",
    "    r\"$Ignition Delay: \\tau_{ign}$\", xy=(0, 0), xytext=(0.01, 0.0082), fontsize=16\n",
    ");"
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   "source": [
    "## Illustration : NTC behavior\n",
    "\n",
    "A common benchmark for a reaction mechanism is its ability to reproduce the **N**egative **T**emperature **C**oefficient behavior. Intuitively, as the temperature of an explosive mixture increases, it should ignite faster. But, under certain conditions, we observe the opposite. This is referred to as NTC behavior. Reproducing experimentally observed NTC behavior is thus an important test for any mechanism. We will do this now by computing and visualizing the ignition delay for a wide range of temperatures"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the temperatures for which we will run the simulations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Make a list of all the temperatures we would like to run simulations at\n",
    "T = np.hstack((np.arange(1800, 900, -100), np.arange(975, 475, -25)))\n",
    "\n",
    "estimated_ignition_delay_times = np.ones_like(T, dtype=float)\n",
    "\n",
    "# Make time adjustments for the highest and lowest temperatures. This we do empirically\n",
    "estimated_ignition_delay_times[:6] = 6 * [0.1]\n",
    "estimated_ignition_delay_times[-4:-2] = 10\n",
    "estimated_ignition_delay_times[-2:] = 100\n",
    "\n",
    "# Now create a SolutionArray out of these\n",
    "ignition_delays = ct.SolutionArray(\n",
    "    gas, shape=T.shape, extra={\"tau\": estimated_ignition_delay_times}\n",
    ")\n",
    "ignition_delays.set_equivalence_ratio(\n",
    "    1.0, fuel=\"nc7h16\", oxidizer={\"o2\": 1.0, \"n2\": 3.76}\n",
    ")\n",
    "ignition_delays.TP = T, reactor_pressure"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, what we will do is simply run the code above the plots for each temperature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computed Ignition Delay: 2.943e-05 seconds for T=3048.1371968673066K. Took 0.62s to compute\n",
      "Computed Ignition Delay: 3.085e-05 seconds for T=3023.4796537279385K. Took 0.67s to compute\n",
      "Computed Ignition Delay: 4.082e-05 seconds for T=2998.3778591617374K. Took 0.63s to compute\n",
      "Computed Ignition Delay: 7.172e-05 seconds for T=2972.8347419918496K. Took 0.60s to compute\n",
      "Computed Ignition Delay: 1.646e-04 seconds for T=2946.858633180261K. Took 0.62s to compute\n",
      "Computed Ignition Delay: 4.748e-04 seconds for T=2920.4702945235736K. Took 0.71s to compute\n",
      "Computed Ignition Delay: 1.632e-03 seconds for T=2893.7088208401537K. Took 0.67s to compute\n",
      "Computed Ignition Delay: 6.443e-03 seconds for T=2866.624960561075K. Took 0.74s to compute\n",
      "Computed Ignition Delay: 3.248e-02 seconds for T=2839.2914558923862K. Took 0.78s to compute\n",
      "Computed Ignition Delay: 5.040e-02 seconds for T=2832.430978134923K. Took 0.85s to compute\n",
      "Computed Ignition Delay: 7.909e-02 seconds for T=2825.566934469486K. Took 0.84s to compute\n",
      "Computed Ignition Delay: 1.252e-01 seconds for T=2818.7047474963733K. Took 0.85s to compute\n",
      "Computed Ignition Delay: 1.983e-01 seconds for T=2811.849413329189K. Took 0.86s to compute\n",
      "Computed Ignition Delay: 3.057e-01 seconds for T=2805.0055341133316K. Took 0.93s to compute\n",
      "Computed Ignition Delay: 4.266e-01 seconds for T=2798.177351132977K. Took 0.95s to compute\n",
      "Computed Ignition Delay: 4.726e-01 seconds for T=2791.3687801293227K. Took 0.95s to compute\n",
      "Computed Ignition Delay: 3.795e-01 seconds for T=2784.5834564797206K. Took 0.99s to compute\n",
      "Computed Ignition Delay: 2.443e-01 seconds for T=2777.8247752274706K. Took 1.06s to compute\n",
      "Computed Ignition Delay: 1.462e-01 seconds for T=2771.0959422413275K. Took 1.10s to compute\n",
      "Computed Ignition Delay: 9.154e-02 seconds for T=2764.4000290839094K. Took 1.13s to compute\n",
      "Computed Ignition Delay: 6.427e-02 seconds for T=2757.7400327239848K. Took 1.17s to compute\n",
      "Computed Ignition Delay: 5.791e-02 seconds for T=2751.118942923986K. Took 1.14s to compute\n",
      "Computed Ignition Delay: 7.723e-02 seconds for T=2744.5398203117347K. Took 1.19s to compute\n",
      "Computed Ignition Delay: 1.503e-01 seconds for T=2738.005879744561K. Took 1.16s to compute\n",
      "Computed Ignition Delay: 3.754e-01 seconds for T=2731.520590755388K. Took 1.38s to compute\n",
      "Computed Ignition Delay: 1.106e+00 seconds for T=2725.087789024315K. Took 1.34s to compute\n",
      "Computed Ignition Delay: 3.746e+00 seconds for T=2718.7118087665854K. Took 1.36s to compute\n",
      "Computed Ignition Delay: 1.474e+01 seconds for T=2712.3976334047347K. Took 1.47s to compute\n",
      "Computed Ignition Delay: 6.945e+01 seconds for T=2706.1510725024746K. Took 1.37s to compute\n"
     ]
    }
   ],
   "source": [
    "for i, state in enumerate(ignition_delays):\n",
    "    # Setup the gas and reactor\n",
    "    gas.TPX = state.TPX\n",
    "    r = ct.IdealGasReactor(contents=gas, name=\"Batch Reactor\")\n",
    "    reactor_network = ct.ReactorNet([r])\n",
    "\n",
    "    reference_species_history = []\n",
    "    time_history = []\n",
    "\n",
    "    t0 = time.time()\n",
    "\n",
    "    t = 0\n",
    "    while t < estimated_ignition_delay_times[i]:\n",
    "        t = reactor_network.step()\n",
    "        time_history.append(t)\n",
    "        reference_species_history.append(gas[reference_species].X[0])\n",
    "\n",
    "    i_ign = np.array(reference_species_history).argmax()\n",
    "    tau = time_history[i_ign]\n",
    "    t1 = time.time()\n",
    "\n",
    "    print(\n",
    "        f\"Computed Ignition Delay: {tau:.3e} seconds for T={state.T}K. Took {t1 - t0:3.2f}s to compute\"\n",
    "    )\n",
    "\n",
    "    ignition_delays[i].tau = tau"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Figure: ignition delay ($\\tau$) vs. the inverse of temperature ($\\frac{1000}{T}$). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
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   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.semilogy(1000 / ignition_delays.T, ignition_delays.tau, \"o-\")\n",
    "ax.set_ylabel(\"Ignition Delay (s)\")\n",
    "ax.set_xlabel(r\"$\\frac{1000}{T (K)}$\", fontsize=18)\n",
    "\n",
    "# Add a second axis on top to plot the temperature for better readability\n",
    "ax2 = ax.twiny()\n",
    "ticks = ax.get_xticks()\n",
    "ax2.set_xticks(ticks)\n",
    "ax2.set_xticklabels((1000 / ticks).round(1))\n",
    "ax2.set_xlim(ax.get_xlim())\n",
    "ax2.set_xlabel(\"Temperature: $T(K)$\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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