aae439Hw6.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Justin Butler\n",
    "## AAE 439 - HW 7\n",
    "\n",
    "File created in Jupyter Notebook and formatted using \\LaTeX"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "// Making sure the outputs display correctly\n",
       "IPython.OutputArea.prototype._should_scroll = function(lines) {\n",
       "    return false;\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%javascript\n",
    "// Making sure the outputs display correctly\n",
    "IPython.OutputArea.prototype._should_scroll = function(lines) {\n",
    "    return false;\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing required packages for this homework\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import os\n",
    "import sys\n",
    "import subprocess\n",
    "import shutil\n",
    "import sympy as sym\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.20\n",
    "The question was solved using NASA CEA online. This was done using ratios between 1 and 2 in increments of 0.05. I downloaded the .html file and input it line by line. You will see that in code file 1 below, I then searched for the molar masses, temperatures, and Isp values and converted them to float values to input into the graphs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.27\n",
    "Code file 2 is the location for the scripts created for this problem.\n",
    "\n",
    "### a)\n",
    "The code below presents my method for determining the chamber temperature using $K_p$. This process had me following the procedure laid out in class - guessing a $T_c$ and iterating.\n",
    "\n",
    "To find where $Q_12$ was zero, I utilized a trapezoid method of numerical integration to find $\\int Cp dT$ for the enthalpy terms.\n",
    "\n",
    "Equilibrium composition:\n",
    "$$ N_2H_4 \\to 0.998 N_2 + 1.994 H_2 + 0.004 NH_3$$\n",
    "\n",
    "Chamber Temperature:\n",
    "$$T_c = 870.4 \\text{ K}$$\n",
    "\n",
    "### b)\n",
    "The resulting $c^*$ of the decomposition gases was found using the equation given in chapter 4 of the text.\n",
    "\n",
    "$$c^* = 1004.532 \\text{ m/s}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.28\n",
    "The calculations are given in Code file 3 below which come from the CEA output file. As teh gasses expand out of the nozzle, more ammonia will most likely form as the enthalpy of formation for ammonia is negative while the enthalpy of formations for both $N_2$ and $H_2$ are zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "##############################\n",
    "#####    CODE FILE 1    ######\n",
    "##############################\n",
    "\n",
    "## IMPORT CEA OUTPUT ##\n",
    "cwd = os.getcwd()\n",
    "file_path = os.path.join(cwd, 'ceaOutput.txt')\n",
    "ceaFile = open(file_path, 'r')\n",
    "lines = []\n",
    "i = 0\n",
    "for line in ceaFile:\n",
    "    if i == 0 or i==1:\n",
    "        i=i+1\n",
    "    else:\n",
    "        lines.append([line])\n",
    "temp = []\n",
    "mol = []\n",
    "Isp = []\n",
    "for line in lines:\n",
    "    #print(line)\n",
    "    tCheck = line[0].startswith(' T, K')\n",
    "    iCheck = line[0].startswith(' Ivac,')\n",
    "    mCheck = line[0].startswith(' M,')\n",
    "    if tCheck:\n",
    "        temp.append(line[0])\n",
    "    if iCheck:\n",
    "        Isp.append(line[0])\n",
    "    if mCheck:\n",
    "        mol.append(line[0])\n",
    "\n",
    "temp = [float(item[18:-11]) for item in temp]\n",
    "mol = [float(item[19:-11]) for item in mol]\n",
    "Isp = [float(item[28:-2]) for item in Isp]\n",
    "r = np.linspace(1,2,len(temp))\n",
    "\n",
    "####### PLOT ########\n",
    "def plot(x,y,title):\n",
    "    plt.figure(figsize=(10,5))\n",
    "    plt.rc('xtick', labelsize=16)\n",
    "    plt.rc('ytick', labelsize=16)\n",
    "    #\n",
    "    plt.plot(x,y,'-')\n",
    "    #\n",
    "    plt.title(title, fontsize=18)\n",
    "    #plt.xlim(0,0.05)\n",
    "    #plt.ylim(0,0.1)\n",
    "    plt.xlabel('r (1 to 2)',fontsize=18)\n",
    "    #plt.legend(loc=2, fontsize=16)\n",
    "    #\n",
    "    #plt.savefig('figure')\n",
    "    #\n",
    "    plt.show()\n",
    "    plt.close()\n",
    "    return(None)\n",
    "titles = ['Chamber Temperature','Molar Mass',\n",
    "          'Chamber Temp/Molar Mass', \"Specific Impluse\"]\n",
    "ys = [temp,mol,[temp[i]/mol[i] for i in range(len(temp))],Isp]\n",
    "for i in range(4):\n",
    "    plot(r,ys[i],titles[i])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.27\n",
    "Hydrazine ($N_2H_4$) is a monopropleeant commmonly used in space propulsion application. This fluid decomposes into nitrogen gas, hydrogen gas, and ammonia ($NH_3$) depending on the pressure level. Assuming the hydrazine enters the reaction at room temperature and a decomposition at 10 atmospheres, determine:\n",
    "\n",
    "### a)\n",
    "The code below presents my method for determining the chamber temperature using $K_p$. This process had me following the procedure laid out in class - guessing a $T_c$ and iterating.\n",
    "\n",
    "To find where $Q_12$ was zero, I utilized a trapezoid method of numerical integration to find $\\int Cp dT$ for the enthalpy terms.\n",
    "\n",
    "Equilibrium composition:\n",
    "$$ N_2H_4 \\to 0.998 N_2 + 1.994 H_2 + 0.004 NH_3$$\n",
    "\n",
    "Chamber Temperature:\n",
    "$$T_c = 870.4 \\text{ K}$$\n",
    "\n",
    "### b)\n",
    "The resulting $c^*$ of the decomposition gases was found using the equation given in chapter 4 of the text.\n",
    "\n",
    "$$c^* = 1004.532 \\text{ m/s}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "##############################\n",
    "#####    CODE FILE 2    ######\n",
    "##############################\n",
    "\n",
    "\n",
    "# rounding function #\n",
    "def rounds(number):\n",
    "    trunc = float('%.3f'% (number * 1000/1000))\n",
    "    return(trunc)\n",
    "#Kp_16\n",
    "def Kp16(T):\n",
    "    if T>=600 and T<=2000:\n",
    "        Kp = 10**(1.0847*10**(-12) * T**4 -7.015*10**(-9)*T**3 +\n",
    "          1.7592*10**(-5)*T**2 - 2.14*10**(-2)*T + 6.4824)\n",
    "    elif T>2000:\n",
    "        Kp = 10**(-4.4574*10**(-11)*2000**(3)+5.2571*10**(-7)*2000**(2)\n",
    "              -2.2*10**(-3)*2000 -1.9461)\n",
    "    else:\n",
    "        print(\"Invalid Temperature. Give something larger than 600K\")\n",
    "        Kp = False\n",
    "    return Kp\n",
    "#Solving for #mols from Kp\n",
    "def molSolver(Kp):\n",
    "    # First c\n",
    "    c1 = 0\n",
    "    KpTest = 0\n",
    "    while KpTest < Kp:\n",
    "        KpTest = (c1 / (\n",
    "                 ((2-c1)/2)**(1/2) *\n",
    "                 ((4-3*c1)/2)**(3/2))\n",
    "                 )\n",
    "        c1+=0.0001\n",
    "        if c1 > 10:\n",
    "            c1 = 'null'\n",
    "            break\n",
    "    # Second c (possibly)\n",
    "    c2 = 1\n",
    "    KpTest = 1\n",
    "    while KpTest > Kp:\n",
    "        KpTest = (c2 / (\n",
    "                 ((2-c2)/2)**(1/2) *\n",
    "                 ((4-3*c2)/2)**(3/2))\n",
    "                 )\n",
    "        c2-=0.0001\n",
    "        if c2 < 0:\n",
    "            c2 = 'null'\n",
    "            break\n",
    "    try:\n",
    "        if np.abs(c1-c2) < 0.01:\n",
    "            return rounds(c1)\n",
    "        else:\n",
    "            return [rounds(c1),rounds(c2)]\n",
    "    except:\n",
    "        if type(c1)!='string':\n",
    "            return(c1)\n",
    "        elif type(c2)!='string':\n",
    "            return(c2)\n",
    "        else:\n",
    "            return(0)\n",
    "# Cp Equations as given in the book\n",
    "def CpSolver(T):\n",
    "    cpN = 27.336+6.23*(T/1000)-0.95082*(T/1000)*2\n",
    "    cpH = 26.896+4.3501*(T/1000)-0.32674*(T/1000)**2\n",
    "    cpAm = 27.578+25.665*(T/1000)+9.9072*(T/1000)**2-6.6909*(T/1000)**3\n",
    "    return([cpN,cpH,cpAm])\n",
    "# Trapezoid method for Approximate Integral\n",
    "def Trapezoid(data):\n",
    "    #Assuming evenly spaced points\n",
    "    delX = np.abs(data[0][0]-data[1][0])\n",
    "    yVal = [item[1] for item in data]\n",
    "    trap = (delX/2)*(data[0][1]+data[-1][1] +\n",
    "                    sum(2*yVal[1:-1]))\n",
    "    return(trap)\n",
    "\n",
    "T = np.linspace(600,4000,2000)       \n",
    "Kp = [Kp16(item) for item in T]\n",
    "c = [molSolver(item) for item in Kp]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[870.4352176088044]\n"
     ]
    }
   ],
   "source": [
    "Q12 = []\n",
    "for i in range(len(c)):\n",
    "    a = (2-c[i])/2\n",
    "    b = (4-3*c[i])/2\n",
    "    tRange = np.linspace(298,T[i],1000)\n",
    "    cpVals = [CpSolver(item) for item in tRange]\n",
    "    pointsN = [[tRange[i],cpVals[i][0]] for i in range(len(tRange))]\n",
    "    intN = Trapezoid(pointsN)\n",
    "    pointsH = [[tRange[i],cpVals[i][1]] for i in range(len(tRange))]\n",
    "    intH = Trapezoid(pointsH)\n",
    "    pointsAm = [[tRange[i],cpVals[i][2]] for i in range(len(tRange))]\n",
    "    intAm = Trapezoid(pointsAm)\n",
    "    # 2 -> 2B\n",
    "    H2H2b = a*intN + b*intH + c[i]*intN\n",
    "    delHb = (-11.04*4184 * c[i]) - (12.05 * 4184)\n",
    "    Q12.append(H2H2b + delHb)\n",
    "correct_Temp = []\n",
    "for item in Q12:\n",
    "    if np.abs(item)<50:\n",
    "        correct_Temp.append(Q12.index(item))\n",
    "print([T[i] for i in correct_Temp])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-8.733924464031588]\n",
      "[0.004]\n"
     ]
    }
   ],
   "source": [
    "print([Q12[item] for item in correct_Temp])\n",
    "print([c[item] for item in correct_Temp])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a:  0.998 , b:  1.994 , c:  0.004\n",
      "1004.532  m/s\n"
     ]
    }
   ],
   "source": [
    "T_c = T[correct_Temp[0]]\n",
    "M_N2 = 14.0067 #g/mol\n",
    "M_H2 = 2.01588 #g/mol\n",
    "M_Am = 17.031 #g/mol\n",
    "c_m = c[correct_Temp[0]]\n",
    "a_m = (2-c_m)/2\n",
    "b_m = (4-3*c_m)/2\n",
    "print('a: ',a_m,', b: ',b_m,', c: ',c_m)\n",
    "moles = sum([a_m,b_m,c_m])\n",
    "totMass = a_m*M_N2 + b_m*M_H2 + c_m*M_Am\n",
    "CpVal = CpSolver(T_c)\n",
    "Cp_N2,Cp_H2,Cp_Am = CpVal[0],CpVal[1],CpVal[2]\n",
    "g_N2= (Cp_N2/(Cp_N2-(8.134/M_N2)))\n",
    "g_H2 = (Cp_H2/(Cp_H2-(8.134/M_H2)))\n",
    "g_Am = (Cp_Am/(Cp_Am-(8.134/M_Am)))\n",
    "# Mass Average of gamma values\n",
    "gamma = (a_m/moles)*g_N2 + (b_m/moles)*g_H2 + (c_m/moles)*g_Am\n",
    "cStar = np.sqrt((8314*T_c)/(gamma*totMass))*(2/(gamma+1))**((-gamma -1)/(2*(gamma-1)))\n",
    "print(rounds(cStar),\" m/s\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.28\n",
    "The calculations are given in a table below from the CEA output file. As teh gasses expand out of the nozzle, more ammonia will most likely form as the enthalpy of formation for ammonia is negative while the enthalpy of formations for both $N_2$ and $H_2$ are zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 CHAMBER   THROAT\n",
      "\n",
      " Pinf/P            1.0000   1.8638\n",
      "\n",
      " P, BAR            10.133   5.4366\n",
      "\n",
      " T, K              873.44   743.91\n",
      "\n",
      " RHO, KG/CU M    1.4975 0 9.4753-1\n",
      "\n",
      " H, KJ/KG         1571.69  1183.44\n",
      "\n",
      " U, KJ/KG          895.05   609.68\n",
      "\n",
      " G, KJ/KG        -12205.6 -10550.6\n",
      "\n",
      " S, KJ/(KG)(K)    15.7735  15.7735\n",
      "\n",
      "\n",
      "\n",
      " M, (1/n)          10.733   10.780\n",
      "\n",
      " (dLV/dLP)t      -1.00471 -1.00895\n",
      "\n",
      " (dLV/dLT)p        1.0352   1.0769\n",
      "\n",
      " Cp, KJ/(KG)(K)    3.0566   3.3123\n",
      "\n",
      " GAMMAs            1.3641   1.3534\n",
      "\n",
      " SON VEL,M/SEC      960.7    881.2\n",
      "\n",
      " MACH NUMBER        0.000    1.000\n",
      "\n",
      "\n",
      "\n",
      " PERFORMANCE PARAMETERS\n",
      "\n",
      "\n",
      "\n",
      " Ae/At                      1.0000\n",
      "\n",
      " CSTAR, M/SEC               1213.5\n",
      "\n",
      " CF                         0.7261\n",
      "\n",
      " Ivac, M/SEC                1532.3\n",
      "\n",
      " Isp, M/SEC                  881.2\n",
      "\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "##############################\n",
    "#####    CODE FILE 3    ######\n",
    "##############################\n",
    "\n",
    "## IMPORT CEA OUTPUT ##\n",
    "cwd = os.getcwd()\n",
    "file_path = os.path.join(cwd, 'ceaOutput7_3.txt')\n",
    "ceaFile = open(file_path, 'r')\n",
    "lines = []\n",
    "i = 0\n",
    "for line in ceaFile:\n",
    "    if i > 47 and i < 74:\n",
    "        i+=1\n",
    "        lines.append([line])\n",
    "    else:\n",
    "        i+=1\n",
    "for item in lines:\n",
    "    print(item[0])"
   ]
  }
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