demo/validate_AbInitio.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Valication of the implementation of _ab-Initio_  collision model in dsmcFoamPluxs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using matplotlib backend: Qt5Agg\n",
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab\n",
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "\n",
    "pd.set_option('precision', 8)\n",
    "pd.set_option('display.float_format', lambda x: '%.4e' % x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $^4$He Couttte flow at $\\delta = 1$\n",
    "\n",
    "Reproduce the results in `Ref:sharipovModelingTransportPhenomena2018`\n",
    "\n",
    "First find the vicosity from `Ref:bichInitioPotentialEnergy2007`, but finnaly use the value give by Sharipov. \n",
    "The viscosities are used to determin the number densities for each case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>T0</th>\n",
       "      <th>mu</th>\n",
       "      <th>n0</th>\n",
       "      <th>FNUM</th>\n",
       "      <th>Uw/2</th>\n",
       "      <th>dt</th>\n",
       "      <th>Pxy</th>\n",
       "      <th>PI</th>\n",
       "      <th>PI_Sharipov</th>\n",
       "      <th>PI_diff(%)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0000e+00</td>\n",
       "      <td>3.2885e-07</td>\n",
       "      <td>1.5352e+21</td>\n",
       "      <td>1.4993e+01</td>\n",
       "      <td>6.4456e+01</td>\n",
       "      <td>3.1029e-08</td>\n",
       "      <td>1.4660e-02</td>\n",
       "      <td>3.4582e-01</td>\n",
       "      <td>3.4564e-01</td>\n",
       "      <td>5.0973e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.2000e+00</td>\n",
       "      <td>3.4024e-07</td>\n",
       "      <td>1.4500e+21</td>\n",
       "      <td>1.4160e+01</td>\n",
       "      <td>7.0608e+01</td>\n",
       "      <td>2.8326e-08</td>\n",
       "      <td>1.7026e-02</td>\n",
       "      <td>3.5435e-01</td>\n",
       "      <td>3.5421e-01</td>\n",
       "      <td>4.0258e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.4000e+00</td>\n",
       "      <td>3.5804e-07</td>\n",
       "      <td>1.4127e+21</td>\n",
       "      <td>1.3796e+01</td>\n",
       "      <td>7.6265e+01</td>\n",
       "      <td>2.6224e-08</td>\n",
       "      <td>1.9823e-02</td>\n",
       "      <td>3.6298e-01</td>\n",
       "      <td>3.6314e-01</td>\n",
       "      <td>-4.4998e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.0000e+00</td>\n",
       "      <td>4.5832e-07</td>\n",
       "      <td>1.5130e+21</td>\n",
       "      <td>1.4775e+01</td>\n",
       "      <td>9.1154e+01</td>\n",
       "      <td>2.1941e-08</td>\n",
       "      <td>3.1636e-02</td>\n",
       "      <td>3.7863e-01</td>\n",
       "      <td>3.7883e-01</td>\n",
       "      <td>-5.3072e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.5000e+00</td>\n",
       "      <td>5.7879e-07</td>\n",
       "      <td>1.7089e+21</td>\n",
       "      <td>1.6689e+01</td>\n",
       "      <td>1.0191e+02</td>\n",
       "      <td>1.9625e-08</td>\n",
       "      <td>4.5029e-02</td>\n",
       "      <td>3.8169e-01</td>\n",
       "      <td>3.8162e-01</td>\n",
       "      <td>1.8271e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5.0000e+00</td>\n",
       "      <td>1.2234e-06</td>\n",
       "      <td>2.5543e+21</td>\n",
       "      <td>2.4945e+01</td>\n",
       "      <td>1.4413e+02</td>\n",
       "      <td>1.3877e-08</td>\n",
       "      <td>1.3014e-01</td>\n",
       "      <td>3.6902e-01</td>\n",
       "      <td>3.6896e-01</td>\n",
       "      <td>1.5999e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.0000e+01</td>\n",
       "      <td>2.1019e-06</td>\n",
       "      <td>3.1030e+21</td>\n",
       "      <td>3.0303e+01</td>\n",
       "      <td>2.0383e+02</td>\n",
       "      <td>9.8123e-09</td>\n",
       "      <td>3.1008e-01</td>\n",
       "      <td>3.6189e-01</td>\n",
       "      <td>3.6195e-01</td>\n",
       "      <td>-1.7273e-02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3.0000e+03</td>\n",
       "      <td>1.0517e-04</td>\n",
       "      <td>8.9643e+21</td>\n",
       "      <td>8.7542e+01</td>\n",
       "      <td>3.5304e+03</td>\n",
       "      <td>5.6651e-10</td>\n",
       "      <td>2.7105e+02</td>\n",
       "      <td>3.6501e-01</td>\n",
       "      <td>3.6495e-01</td>\n",
       "      <td>1.6486e-02</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      "text/plain": [
       "          T0         mu         n0       FNUM       Uw/2         dt  \\\n",
       "0 1.0000e+00 3.2885e-07 1.5352e+21 1.4993e+01 6.4456e+01 3.1029e-08   \n",
       "1 1.2000e+00 3.4024e-07 1.4500e+21 1.4160e+01 7.0608e+01 2.8326e-08   \n",
       "2 1.4000e+00 3.5804e-07 1.4127e+21 1.3796e+01 7.6265e+01 2.6224e-08   \n",
       "3 2.0000e+00 4.5832e-07 1.5130e+21 1.4775e+01 9.1154e+01 2.1941e-08   \n",
       "4 2.5000e+00 5.7879e-07 1.7089e+21 1.6689e+01 1.0191e+02 1.9625e-08   \n",
       "5 5.0000e+00 1.2234e-06 2.5543e+21 2.4945e+01 1.4413e+02 1.3877e-08   \n",
       "6 1.0000e+01 2.1019e-06 3.1030e+21 3.0303e+01 2.0383e+02 9.8123e-09   \n",
       "7 3.0000e+03 1.0517e-04 8.9643e+21 8.7542e+01 3.5304e+03 5.6651e-10   \n",
       "\n",
       "         Pxy         PI  PI_Sharipov  PI_diff(%)  \n",
       "0 1.4660e-02 3.4582e-01   3.4564e-01  5.0973e-02  \n",
       "1 1.7026e-02 3.5435e-01   3.5421e-01  4.0258e-02  \n",
       "2 1.9823e-02 3.6298e-01   3.6314e-01 -4.4998e-02  \n",
       "3 3.1636e-02 3.7863e-01   3.7883e-01 -5.3072e-02  \n",
       "4 4.5029e-02 3.8169e-01   3.8162e-01  1.8271e-02  \n",
       "5 1.3014e-01 3.6902e-01   3.6896e-01  1.5999e-02  \n",
       "6 3.1008e-01 3.6189e-01   3.6195e-01 -1.7273e-02  \n",
       "7 2.7105e+02 3.6501e-01   3.6495e-01  1.6486e-02  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = 1.38064852e-23 \n",
    "m = 4.002602/6.02214086e26\n",
    "H = 1e-3 # domain legth\n",
    "NX = 800 # cell size\n",
    "delta = 1\n",
    "# We consider the low temperatures where the non-dimensional shear stress varis more clearly with T\n",
    "T0 = array([1, 1.2, 1.4, 2.0, 2.5, 5.0, 10.0, 3000.0])\n",
    "# Viscosities from `Ref:bichInitioPotentialEnergy2007`\n",
    "#df['mu'] = {0.32875e-6, 0.34015e-6, 0.35796e-6, 0.45824e-6,0.57869e-6, 1.2234e-6,2.1018e-6, 118.52e-6}\n",
    "# Viscosities give by Professor Shaipov\n",
    "mu = array([0.32885, 0.34024, 0.35804, 0.45832, 0.57879, 1.22345, 2.10186, 105.17144])*1e-6\n",
    "v0 = sqrt(2*k/m*T0)\n",
    "p0 = delta * mu * v0/H # Equlibrium pressure \n",
    "n0 = p0/k/T0 # Number densities\n",
    "dx = H/NX #Cell size, NOTE, Using cubic cell in dsmcFoam\n",
    "# Number of equivlent moleculues per dsmc particles\n",
    "FNUM = n0*(dx**3)/200\n",
    "# Wall velocity should be Uw/2 and -Uw/2\n",
    "Uw = 2.0*v0\n",
    "# Time step size\n",
    "dt = 0.002*H/v0\n",
    "# NOTE, run 10,000 steps to steady state, then run 99,000 steps for sampling.\n",
    "\n",
    "# Table summarizing paremters and to compare the predicted non-dimensional shear stress\n",
    "df = pd.DataFrame({'T0':T0, 'mu':mu, 'n0':n0, 'FNUM':FNUM, 'Uw/2':Uw/2, 'dt':dt, 'Pxy':nan, 'PI':nan})\n",
    "\n",
    "# Reference data from `Ref:sharipovModelingTransportPhenomena2018` summplementary table.\n",
    "df['PI_Sharipov'] = {0.34564, 0.35421, 0.36314,0.37883, \n",
    "                     0.38162, 0.36896, 0.36195, 0.36495}\n",
    "\n",
    "# dsmcFoamPlus predicted dimensional shear stress\n",
    "df.loc[0,'Pxy'] = 0.01466\n",
    "df.loc[1,'Pxy'] = 0.0170256\n",
    "df.loc[2,'Pxy'] = 0.0198228\n",
    "df.loc[3,'Pxy'] = 0.0316365\n",
    "df.loc[4,'Pxy'] = 0.045029\n",
    "df.loc[5,'Pxy'] = 0.13014\n",
    "df.loc[6,'Pxy'] = 0.310076\n",
    "df.loc[7,'Pxy'] = 271.053\n",
    "\n",
    "# Non-dimensional shear stress\n",
    "df.PI= df.Pxy*v0/p0/Uw\n",
    "# Relative difference gagins Sharipov's paper data\n",
    "df['PI_diff(%)'] =  (df.PI - df.PI_Sharipov)/df.PI_Sharipov*100\n",
    "df"
   ]
  }
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