{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Diesel Cycle Example\n", "\n", "## Imports" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "from thermostate import State, Q_, units\n", "from thermostate.plotting import IdealGas\n", "\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "from numpy import arange" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "## Definitions" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "substance = \"air\"\n", "T_1 = Q_(25.0, \"degC\")\n", "p_1 = Q_(95.0, \"kPa\")\n", "V_1 = Q_(3.0, \"L\")\n", "r = Q_(18.0, \"dimensionless\")\n", "r_c = Q_(3.0, \"dimensionless\")\n", "rpm = Q_(1700.0, \"rpm\")\n", "n_C = Q_(4, \"dimensionless\")\n", "units.define(\"cycle = 2*revolution\") # Define a four-stroke cycle\n", "r_c_low = Q_(1.1, \"dimensionless\")\n", "r_c_high = Q_(4.5, \"dimensionless\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "## Problem Statement" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A four-cylinder Diesel engine has a BDC volume of 3.0 L per cylinder. The engine operates on the air-standard Diesel cycle with a compression ratio of 18.0 and a cutoff ratio of 3.0 . Air is at 25.0 celsius and 95.0 kPa at the beginning of the compression process. Determine\n", "\n", "1. the amount of power delivered by the engine, in kW, at 1700.0 rpm\n", "2. the thermal efficiency\n", "3. plot the power output as a function of the cutoff ratio, with values for $r_c$ from 1.1 to 4.5 , holding all other given values constant\n", "4. plot the thermal efficiency as a function of the cutoff ratio, with values for $r_c$ from 1.1 to 4.5 , holding all other given values constant" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "## Solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1. the power delivered" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "The power output can be found by taking the product of the net work per cylinder, the number of cylinders, and the net work per revolution\n", "\n", "$$\\dot{W}_{net} = n_C \\frac{N}{2} W_{net}$$\n", "\n", "First, we need to fix the four states. State 1 uses $p$ and $T$, state 2 uses $s$ and $v$, state 3 uses $p$ and $v$, and state 4 uses $v$ and $s$. We need to calculate the mass of air in one cylinder using the ideal gas law\n", "\n", "$$m = \\frac{pV}{RT}$$\n", "\n", "where $R=\\overline{R}/MW$ is the gas-specific constant.\n", "\n", "The Diesel cycle is made of 4 processes:\n", "\n", " 1. Isentropic compression\n", " 2. Isobaric heat input\n", " 3. Isentropic expansion \n", " 4. Isochoric heat rejection\n", "\n", "The following properties are used to fix the four states:\n", "\n", "State | Property 1 | Property 2 \n", ":-----:|:-----:|:-----:\n", "1|$$p_1 $$|$$T_1 $$\n", "2|$$v_2 = v_1/r $$|$$s_2=s_1 $$\n", "3|$$p_3=p_2 $$|$$v_3=r_c*v_2 $$\n", "4|$$v_4=v_1 $$|$$s_4=s_3 $$\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "MW_air = Q_(28.97, \"kg/kmol\")\n", "R = units.molar_gas_constant / MW_air\n", "m = (p_1 * V_1 / (R * T_1)).to(\"mg\")\n", "\n", "v_1 = (V_1 / m).to(\"m**3/kg\")\n", "st_1 = State(substance, p=p_1, T=T_1)\n", "s_1 = st_1.s.to(\"kJ/(kg*K)\")\n", "u_1 = st_1.u.to(\"kJ/kg\")\n", "\n", "v_2 = v_1 / r\n", "s_2 = s_1\n", "st_2 = State(substance, v=v_2, s=s_2)\n", "T_2 = st_2.T\n", "p_2 = st_2.p.to(\"kPa\")\n", "u_2 = st_2.u.to(\"kJ/kg\")\n", "\n", "v_3 = r_c * v_2\n", "p_3 = p_2\n", "st_3 = State(substance, p=p_3, v=v_3)\n", "T_3 = st_3.T\n", "s_3 = st_3.s.to(\"kJ/(kg*K)\")\n", "u_3 = st_3.u.to(\"kJ/kg\")\n", "\n", "s_4 = s_3\n", "v_4 = st_1.v\n", "st_4 = State(substance, v=v_4, s=s_4)\n", "T_4 = st_4.T\n", "p_4 = st_4.p.to(\"kPa\")\n", "u_4 = st_4.u.to(\"kJ/kg\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting the p-v and T-s diagrams of the cycle," ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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NqCS9roSaWhoWSvmg8UJi495UolNCPV2amqU0LJTyIUP9doqPWCHRayd1VQQb70/TkFDTTsNCKR8w2DdM8RsNFB1y9UmkrHSFREyqhoSaGRoWSnmxgd5hig7VU3y4nqEBB2lrIsndo4eb1MzTsFDKC/V3D3H2YD3njjQwPOggY10UG/akase18hgNC6W8SM+VQc4eqOP8sUbsdidLN0STe18qEQk6BFZ51qTCQkSigE8Dqe7rGGP+eHrKUmpu6bL1U/h6LRfebsY4YXleDOt3pejJdMprTHbP4jfAMeAg4Ji+cpSaWzqaeil8rZby062IH+TcHs+6ncmERuq0HOrGlB17g6EKGw77ML9+6tvc+djHyb7znil7/cmGxXxjzOen7F2VmuNaq69S8IcaqosuExDkx+ptiay7N1kn+FM3pezYG7z+7Pe4M/yDGAzdl228/uz3AKYsMCYbFr8TkT3GmFem5F2VmoOMMTSUXaHgtVoaL15h3vwAcvemsvqeREIWBnm6POXDjr3wPEMOB4XzWzBWm31okGMvPD/jYfEXwN+KyCAwDAhgjDE6fk+pCTidhqozNgpfq8VW182CsCBu/9BSVtwZT1CwjjFRt8bpdNLugMGMlfT5dZPYOw+D60O6u/3ylL3PpH5TjTE6Xk+pG2QfdnDh7RbOHqijy9ZPWFQIWz+6nKxNcXr5UjUlGhsb+f3vf89gbAr+vVeZ11JH59AAI1dQXxQROWXvdd2wEJEsY8wFEVk/3vPGmMIpq0SpWWKgd5iSo40Uv9FA/9UholMWsevTK0lfF4Wfn0z8AkpNoL+/n0OHDpGfn8/ChQvZvCKbsv0v4RgaHF0mIGgedz728Sl7z4n2LP4KeBL453GeM8C2KatEKR/X3TFA0eF6So81MTzoIHlFOOt2ppCwbDEiGhLq1jmdToqLi3n99dfp7+8nLy+Pe+65h+DgYJJjozn2wvN0t19mUUTklI+GEmPMxEv5mNzcXJOfn+/pMtQcYavr5syBOioL2gBYuiGa9buSiUzUo7dq6jQ1NfHKK6/Q0NBAYmIie/fuJS4ubkrfQ0QKjDG54z032ZPyioGfAS8ZYy5Ncp3ngPuBNmPMSqvtK7hO7rNZi/3tyAgrEfkC8Elc53H8uTHmNat9N/BdwB/4gTHmmcm8v1LTyRhDXWkHZ16vo/HiFQLn+bN6WyJrtiWxKDzY0+WpWaSvr49Dhw5RUFDAggUL2LdvH2vWrMHPb2b7vSY7FOMB4FHgJRFxAi/iCo6666zzQ+B7wPNj2r9tjPkn9wYRyQEeA1YA8cBBEVlmPf2vwA6gATgtIvuNMaWTrFupKWUfdlB+qpWiQ/V0NPWyICyIzQ9lsOLOeObND/R0eWoWcTqdFBQUcOjQIQYHB9m0aRNbt24lONgzX0YmOxqqFvgG8A0RyQT+HvhHXN/2r7XOURFJnWQd+4AXjDGDQLWIVAK3Wc9VGmOqAETkBWtZDQs1o/q7hyg52si5Iw30dw8TkbCQ7Y9nk7kxBv8AHdmkplZtbS2vvvoqLS0tpKamsmfPHqKjoz1a06QHeYtICq69i0dxHSr6m5t8z8+IyMeBfOCvjTFXgATgpNsyDVYbQP2Y9rxr1Pckrs54kpOTb7I0pd6ro6mXosP1XDzZgsPuJGVlBGvuTSJx+RLttFZTrrOzk4MHD1JSUkJoaCgPP/wwK1as8Irftcn2WbwDBAI/Bz488k3/Jnwf+BqukVRfwzXKakomIzTGPAs8C64O7ql4TTU3GaerP6L4cD11pR34B/qRtTmWNduTdGI/NS2GhoY4ceIEJ06cAOCuu+5iy5YtBAV5z5n9k92z+Lgx5uKtvpkxpnXkvoj8B/A762EjkOS2aKLVxnXalZpSw4MOLp5spuhwA52tfcwPCyLvA2msuCtBp+NQ08IYw7lz5zh48CBXr15lxYoV7Nixg8WLF3u6tPeZ6KS8v3K7v3fs88aYb93Im4lInDGm2Xr4EFBi3d8P/FREvoWrgzsTOIXrjPVMEUnDFRKPAR+5kfdUaiJX2/spOdJI6YkmBvvsRKcs4t4ncli6IVr7I9S0aWxs5NVXX6WhoYG4uDg+9KEPkZKS4umyrmmiPYubHiguIj8DtgKRItIAfBnYKiJrcR2GqgH+BMAYc15EXsLVcW0HnjLGOKzX+QzwGq7O9OeMMedvtialRhhjaCzv5NwbDVQX2UCE9LVRrNmeRGx6qFccI1azU2dnJ4cPH6a4uNijQ2FvlJ6Up+aU4UEH5adaKH6jgY6mXoIXBJKzJZ6Vdyfo+RFqWg0MDHD8+HFOnnSN5dm0aRNbtmzx2FDY8UzFSXnLcHVOxxhjVorIauADxph/mMI6lZo2XbY+St5spOytZgb77EQmLeSej2WxbGMMAUHXHAGu1C1zOBwUFhZy5MgRent7WbVqFdu3b/fKfonrmWwH938AnwP+HcAYUywiPwU0LJTXMk5D7fl2St5spPZ8O2Idalq9LZG4jDA91KSmlTGGiooKDhw4gM1mIzk5mY985CMkJCRMvLIXupEr5Z0a88dln4Z6lLplA73DlL3VTMmbDVy9PMD80CA27kllxZ0JeiU6NSOampo4cOAA1dXVhIeH8+ijj5KVleXTX1AmGxaXRSQDV8c0IvIw0Hz9VZSaOcYY2mq6KTnaQEV+G45hJ3FLw9j0YAbpa6N0VJOaER0dHRw+fJiSkhLmz5/Pfffdx4YNGwgI8P2LXE32X/BlXIegskSkEajGNT+UUh41POSg4nQrJW82YqvrJmCeP1mbYll5d4LO+qpmTG9vL2+++Sb5+fn4+/tz1113cfvtt3tV5/WtmmxY/BvwOFAF+OGaTfazwL9MT1lKXV9HUy/njzVy4WQLQ/12wuMXcNdjy1ieF0tQiO9/i1O+YWhoiJMnT3L8+HGGh4dZv349W7duZdGi2fdFZbJ/VQ/jmurjI8CdwMeBndNVlFLjsQ87uFRo4/yxRporu/ALEDLWRbPy7gTtsFYzym63U1BQwNGjR+nt7SUrK4vt27cTFRXl6dKmzWRnna0SkT8Cfg3UAbuMMf3TWZhSI6609HL+eBMX3m5msNdOWHQIt39wKVm3x+o0HGpGjVyp7siRI3R2dpKSksKjjz46JyYvnWi6j3NYndqWcFxnUr8jIhhjVk9ncWrusg85uHTGRunxJpoqOvHzE9LWRrHyrngSli1B9FrWagYZY7hw4QKHDx/GZrMRFxfH/fffT0ZGxpzZo51oz+L+GalCKUt7Yw/njzdR/k4Lg312wqJC2PxQBlmb45gfqnsRamYZY6iqquLw4cM0NjYSERHBhz/8YbKzs71+eo6pdt2wsC56pNS0GhqwU5nfRumJJlqrr7r6ItZGkbNF9yKU59TW1nL48GFqa2sJDQ3lgQceYO3atfj7z80z/nXYiPIIYwwtVVcpPdFEZUEb9kEHS2Lnc8fDS1m+SfsilOc0NDRw+PBhqqqqWLBgAbt372bDhg0EBs7ty+ZqWKgZ1Xd1iIvvtFB2ookrLX0EzPMnMzeanDviiUnT2V6V5zQ3N/PGG29QXl5OSEgIO3bsYOPGjV51ASJP0rBQ087hcFJ7rp2yt5qpK2nH6TTEpodxz8eyWLohmqBg/TVUntPS0sKbb75JWVkZwcHBbNu2jby8PObN06lh3OlfqZo27Y09lL3dTPk7LfR3DzM/NIg19yaRtTmO8Di9PKnyrObmZt58800uXLjAvHnzuOuuu9i8eTMhISGeLs0raVioKdXfM0TF6VYuvN2Cra4bP38hdXUk2bfHkZwTjp//3BpBorzP2JC4++672bRpk4bEBDQs1C0bOcx08WQLNecu43QYIpMWsuXDmSzLi9HOauUVmpqaOHr06GhIbN26lby8PA2JSdKwUDfFGIOtrpuLJ1uoyG+lv3uYkEWBrLonkaxNcUQmLvR0iUoBUF9fz9GjR6moqNCQuAUaFuqGdHcMUH6qhYsnW7jS0odfgJC2KpKszXEkrQjHXw8zKS9gjKGmpoajR49SXV3N/Pnz2b59Oxs3bpxVM8HOJA0LNaGhfjuXzrRx8Z1WGsuvgIG4pWFs/ehyMtZHE7xgbo8/V97DGENlZSVHjx6lvr6ehQsXsnPnTnJzc3UI7C3SsFDjctid1JV2UP5OC9XFl3EMOwmNCmHj3jSW58UQFjXf0yUqNcrpdFJWVsbx48dpbm4mNDSUPXv2sG7dujl/Mt1U0bBQo4zT0FLVRfmpVioL2hjoHSZ4YSA5d8Sz7LYYPWlOeR273U5xcTEnTpygvb2diIgIPvCBD7B69epZcXU6b6JbU9He2EP5qVYqTrfS3TGAf6Af6WsiWZYXS1KO9kMo7zM4OEhBQQFvv/023d3dxMXFzdkJ/maKhsUc1WXrpyLfFRAdTb2In5CUHU7evnTS1kTqWdXKK/X09HDq1ClOnz5Nf38/qamp7Nu3b05NFe4p+okwh/R2DlJZ0EZFfiut1VcBiMsI467HlrF0QzQhi7QDUHmn9vZ23n77bc6ePYvdbicrK4s77riDpKQkT5c2Z2hYzHL9PUNcKrRRmd9KY0UnGIhMWsjmhzJYuiGa0Egda668V0NDA2+99RalpaX4+/uzZs0abr/9diIjIz1d2pyjYTELDfQOU3XWRmVBGw0XrmCchsUx89m4N43M3GiWxOq8TMp7OZ1OKioqeOutt6itrSU4OJg777yT2267jUWLFnm6vDlLw2KWGOwbprroMhX5bTSUdeB0GkIjg1m3M5mlG6KJTFyox3SVVxsaGqKoqIi3336bjo4OwsLC2LVrF+vXr9cZYL2AhoUPG+gdprrIRmWBjYYLHTgdhkURway5N4mlG6KJSl6kAaG8Xnd3N6dOnSI/P5/+/n7i4+N5+OGHyc7OnrNXpfNGGhY+ZqBnmKoiG5cK22gou4LTaVgUHszqbUksXR9NdKoGhPINzc3NnDx5kpKSEhwOB1lZWWzevJnk5GT9HfZCGhY+oO/qEFVnXQHRWN6JcVp7ENuTyNgQTXSKBoTyDU6nkwsXLnDy5Enq6uoIDAxk/fr1bNq0iYiICE+Xp65Dw8JLdXcMUF1k41KhjabKTjAQFhXCuh3JZKyP0kNMyqf09/dTWFjIqVOn6OrqYvHixezcuZN169bp7K8+YtrCQkSeA+4H2owxK622cOBFIBWoAR4xxlwR16fed4E9QB/wCWNMobXO48DfWS/7D8aYH01XzZ7W2drn2oM4Y6OtxnUeRHj8AnL3pJKxLpqIhAUaEMqntLW1cerUKYqKihgeHiYlJYXdu3ezfPlyPdPax0znnsUPge8Bz7u1PQ0cMsY8IyJPW48/D9wHZFq3POD7QJ4VLl8GcgEDFIjIfmPMlWmse8YYY7hc30PVWRtVZ210NPUCEJ2yiE0PppO+NkqHuSqf43A4KC8v59SpU1RXV+Pv78+qVavIy8sjLi7O0+WpmzRtYWGMOSoiqWOa9wFbrfs/Ao7gCot9wPPGGAOcFJHFIhJnLXvAGNMBICIHgN3Az6ar7unmdDhpquyi+qyNqiIbPR2DiEB85mK2PJJJ+tooFoXrfPvK9/T29nLmzBlOnz5NV1cXoaGhbN++nfXr17NggX7p8XUz3WcRY4xptu63ADHW/QSg3m25BqvtWu3vIyJPAk8CJCcnT2HJt25owE59aQfVxZepOXeZwV47/oF+JOeEc9v96aSujtBLjyqfZIyhoaGB/Pz80VFNqamp7N69m2XLlunQ11nEYx3cxhgjImYKX+9Z4FmA3NzcKXvdm9XbOUh18WWqiy7TcLEDp90wb0EAqSsjSV8bRVJOOIHz9A9J+aahoSHOnTvH6dOnaWlpISgoiPXr15Obm0tMTMzEL6B8zkyHRauIxBljmq3DTG1WeyPgPiNYotXWyLuHrUbaj8xAnTfMGMPlhh5qii9TU3yZttpuAEIjg1l1dyJpayKJywjDT6f7Vj7MZrORn5/P2bNnGRwcJDo6mr1797J69Wo9y3qWm+mw2A88Djxj/fyNW/tnROQFXB3cXVagvAb8HxFZYi23E/jCDNd8TfZhB43lnaMB0XNlEARiUkNHp/oOj9MRTMq3DQ8PU1ZWRn5+PnV1dfj7+5OTk8PGjRtJSkrS3+85YjqHzv4M115BpIg04BrV9Azwkoh8EqgFHrEWfwXXsNlKXENnnwAwxnSIyNeA09ZyXx3p7PaU3s5BakvaqTl3mfqyDuxDTgKC/EjKDmfj/Wmkropkfqj2PyjfZ7PZKCgooKioiP7+fsLDw9mxYwdr1qxh4cKFni5PzTBxDUCaXXJzc01+fv6Nr1j8Ehz6KnQ1QFgibP8SZuWHaavtpqbkMrXn2rHVuQ4vLQyfR+qqSFJWRpCYtYSAQO1/UL5vZC+ioKCA2tpa/Pz8yMrKIjc3l9TUVD03YpYTkQJjTO54z+kZ3COKX4Lf/jkM9zPgXEB9Swq1Pyyjzhyiv98PEYhND2PTg+mkrookPF4PL6nZo6WlhcLCQoqLixkYGGDJkiVs376ddevW6V6EAjQs3nXoq/QMzOe5nq/g178UwY9guUrywgJSPvk4ydkRBC8M9HSVSk2ZgYEBSkpKKCwspKmpCX9/f7Kzs9mwYQMpKSm6F6HeQ8NiRFcDIX5+9PkJ3TGv8r+GjxIdWImfGNj4eU9Xp9SUcDqd1NbWcubMGUpLS7Hb7URHR7N7925Wr17N/PnzPV2i8lIaFiPCEvHvqudi5j8BENtijeoN02v8Kt/X2dlJUVERZ86cobOzk3nz5rFmzRrWrVtHQkKCHlJVE9KwGLH9S64+C3eBIa52pXzQ0NAQFy5c4OzZs1RVVQGQlpbGtm3byMrKIihIR+2pydOwGLHaGsV76qtgH3TtUWz/0rvtSvkAYwy1tbUUFRVx/vx5hoaGWLx4MXfffTdr165lyZIlE7+IUuPQsHC3+hFoetV1f/d/ebYWpW5AR0cHRUVFFBUV0dnZSVBQEDk5Oaxdu5bk5GTtrFa3TMNCKR/V19fH+fPnKSoqoqGhAYD09HTuuecesrOz9TCTmlIaFkr5kOHhYcrLyykuLqaiogKn00l0dDT33nsvq1atIiwszNMlqllKw0IpL+d0OqmpqaG4uJiysjIGBwdZuHAheXl5rF69mtjYWB3NpKadhoVSXsgYQ1NTE+fOnaOkpISenh6CgoLIzs5m1apVpKenaz+EmlEaFkp5kba2NkpKSigpKaGjowN/f38yMzNZtWoVy5YtIzBQZxFQnqFhoZSHtbe3jwaEzWZDREhLS2PLli1kZ2cTEhLi6RKV0rBQyhM6OjooLS3l/PnzNDe7rjScnJzMnj17yMnJ0cn7lNfRsFBqhowXEPHx8ezcuZMVK1boSCbl1TQslJpG7e3tlJaWUlpa+p6A2LFjBzk5OXpGtfIZGhZKTSFjDDabjdLSUsrKymhtbQU0IJTv07BQ6haNDHMtKyujrKyM9vZ2wNUHsWvXLrKzs1m8eLFni1TqFmlYKHUTHA4HtbW1XLhwgQsXLnD16lVEhNTUVPLy8sjOzmbRokWeLlOpKaNhodQkDQ4OcunSJS5evEh5eTn9/f0EBASQkZHBtm3bWLZsmV48SM1aGhZKXUd3dzcXL17k4sWLVFVV4XA4CA4OZtmyZWRlZbF06VKdsE/NCRoWSrkxxtDa2jq699DY2AjA4sWLyc3NJSsri+TkZPz9/T1cqVIzS8NCzXnDw8PU1NSMBsTVq1cBSEhI4J577iErK4vo6GidrE/NaRoWak7q7OykoqKCiooKqqurGR4eJjAwkIyMDLZu3UpmZqZ2UCvlRsNCzQkOh4P6+vrRgGhrawNch5fWrVtHZmYmqampOlGfUtegYaFmra6uLiorK6moqKCqqoqhoSH8/PxISUlh586dZGZmEhkZqYeXlJoEDQs1awwPD1NbW8ulS5eorKzEZrMBEBoaysqVK8nMzCQtLY3g4GAPV6qU79GwUD5rZGqNyspKLl26RG1tLXa7HX9/f5KTk1m7di2ZmZlERUXp3oNSt0jDQvmUq1evUl1dzaVLl6iqqqKnpweAyMhINmzYwNKlS0lJSdFzH5SaYhoWyqsNDAxQW1tLVVUVVVVVo4eW5s+fT1paGunp6WRkZOjcS0pNMw0L5VWGh4epr6+nurqa6upqGhsbMcYQEBAwemgpPT2dmJgYvQa1UjPII2EhIjVAN+AA7MaYXBEJB14EUoEa4BFjzBVxHWz+LrAH6AM+YYwp9ETdaurZ7XYaGxuprq6mpqaG+vp6HA4HIkJCQgJbtmwhPT2dxMREHdaqlAd5cs/iHmPMZbfHTwOHjDHPiMjT1uPPA/cBmdYtD/i+9VP5oJFwqKmpGQ0Hu90OQGxsLBs3biQtLY2UlBQdtaSUF/Gmw1D7gK3W/R8BR3CFxT7geWOMAU6KyGIRiTPGNHukSnVDhoaGaGhooLa2ltraWhoaGkbDISYmhg0bNpCamkpKSorO2KqUF/NUWBjgdRExwL8bY54FYtwCoAWIse4nAPVu6zZYbRoWXqivr4/6+npqa2upq6ujqakJp9OJiBAbG0tubi6pqakkJydrOCjlQzwVFluMMY0iEg0cEJEL7k8aY4wVJJMmIk8CT4LrCmVq+hlj6OzspK6ujvr6eurq6kan0fDz8yMhIYHNmzeTkpJCcnKyHlZSyod5JCyMMY3WzzYR+RVwG9A6cnhJROKANmvxRiDJbfVEq23saz4LPAuQm5t7Q0GjJsdut9PS0kJ9ff1oOIyc5xAUFERSUhIrVqwgJSWFhIQE7ZBWahaZ8bAQkQWAnzGm27q/E/gqsB94HHjG+vkba5X9wGdE5AVcHdtd2l8xM3p6ekaDoaGhgaamptH+hrCwMNLS0khKSiI5OZno6GgdyqrULOaJPYsY4FfW9AsBwE+NMX8QkdPASyLySaAWeMRa/hVcw2YrcQ2dfWLmS579hoeHaWlpoaGhYfTW1dUFgL+/P3FxceTm5pKUlERSUhKhoaEerlgpNZNmPCyMMVXAmnHa24Ht47Qb4KkZKG3OcDqdtLe309jYOHpraWnB6XQCrr2GhIQE8vLySExMJC4uTg8pKTXHedPQWTUNRjqhm5qa3nMbHBwEXH0N8fHxbN68mcTERBISEnSvQSn1PhoWs4gxhq6uLpqammhubh4Nhv7+fsA1QikmJoZVq1aRkJBAQkICkZGR2teglJqQhoWPcjqdXLlyhebmZlpaWkYDYiQYRITo6GiysrKIj48nPj6emJgYAgL0v1wpdeP0k8MH2O122traaG1tHQ2HlpYWhoaGANceg3swxMXFERMTo/0MSqkpo2HhZXp6emhtbR0NhNbWVi5fvjza+RwYGEhsbCxr1qwhLi6O2NhYoqOjdY9BKTWt9BPGQ4aGhrh8+TKtra2jew2tra309vaOLrNo0SJiY2NZvnw5sbGxxMTEEB4ern0MSqkZp2ExzRwOB+3t7dhsttFQaGtro6OjY3SZgIAAoqOjWbZsGTExMcTExBAdHc2CBQs8WLlSSr1Lw2KK2O12Ojo6sNlso8Fgs9lob28fPYQkIoSHhxMTE8Pq1auJjo4mOjpa9xaUUl5Pw8LNr880cqaukyG7gzueOczndi3nwXUJ71lmcHCQy5cvj95GwqGjowPX+YMuS5YsITo6muXLlxMdHU1UVBSRkZHa6ayU8kkaFpZfn2nkCy+fgzgHGOjs7OQ7Lx/DVrWE+GD76KGk7u7u0XVEhIiICKKiosjJySEqKoqoqCgiIiIICgry4L9GKaWmloaF5ZuvXYThfna1Z7PQMY+A4GIAGs/B5XnziIiIID09ncjIyNHbkiVLdBSSUmpO0E86S1NnP0IAPSI0B/XT0buCq85grppgSr+8D2viQ6WUmpM0LCzxi0No7OznYM+d72lPWByiQaGUmvN0CI7lc7uWExLo/562kEB/PrdruYcqUkop76F7FpaRUU/ffO0iTZ39xC8OGXc0lFJKzUUaFm4eXJeg4aCUUuPQw1BKKaUmpGGhlFJqQhoWSim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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Diesel = IdealGas(substance, (\"s\", \"T\"), (\"v\", \"p\"))\n", "\n", "Diesel.add_process(st_1, st_2, \"isentropic\")\n", "Diesel.add_process(st_2, st_3, \"isobaric\")\n", "Diesel.add_process(st_3, st_4, \"isentropic\")\n", "Diesel.add_process(st_4, st_1, \"isochoric\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The mass of air in one cylinder is $m =$ 3330.61 mg. Summarizing the states:\n", "\n", "| State | T | p | u | v | s |\n", "|-------|---------------------------|---------------------------|---------------------------|---------------------------|---------------------------|\n", "| 1 | 298.15 K | 95.00 kPa | 338.89 kJ/kg | 0.90 m3/kg | 3.90 kJ/(K kg) |\n", "| 2 | 900.45 K | 5256.76 kPa | 799.36 kJ/kg | 0.05 m3/kg | 3.90 kJ/(K kg) |\n", "| 3 | 2730.75 K | 5256.76 kPa | 2522.03 kJ/kg | 0.15 m3/kg | 5.25 kJ/(K kg) |\n", "| 4 | 1602.36 K | 511.21 kPa | 1426.75 kJ/kg | 0.90 m3/kg | 5.25 kJ/(K kg) |\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "W_12 = (m * (u_1 - u_2)).to(\"kJ\")\n", "W_23 = (m * p_2 * (v_3 - v_2)).to(\"kJ\")\n", "W_34 = (m * (u_3 - u_4)).to(\"kJ\")\n", "\n", "W_net = W_12 + W_23 + W_34\n", "\n", "Q_23 = (m * (u_3 - u_2) + W_23).to(\"kJ\")\n", "Q_41 = (m * (u_1 - u_4)).to(\"kJ\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Summarizing the energy transfers,\n", "\n", "| Process | Work | Heat Transfer |\n", "|-------------------|----------------------------|----------------------------|\n", "| 1 $\\rightarrow$ 2 | -1.53 kJ | 0.0 kJ |\n", "| 2 $\\rightarrow$ 3 | 1.75 kJ | 7.49 kJ |\n", "| 3 $\\rightarrow$ 4 | 3.65 kJ | 0.0 kJ |\n", "| 4 $\\rightarrow$ 1 | 0.0 kJ | -3.62 kJ |\n", "\n", "and the net work output per cylinder per cycle is $W_{net} =$ 3.87 kJ. Then, calculating the power output" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "Wdot_net = (n_C * rpm * W_net / units.cycle).to(\"kW\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "**Answer:** The net power output is $\\dot{W}_{net} =$ 219.10 kW\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2. the thermal efficiency" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "eta = W_net / Q_23" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "**Answer:** The thermal efficiency is $\\eta =$ 0.52 = 51.62% \n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3. plot the net power output as a function of $r_c$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For this part (and the next one), only states 3 and 4 are changed by changing the cutoff ratio. Therefore, we only re-compute those states, and the associated work and heat transfer values, in the following loop." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "eta_l = []\n", "Wdot_net_l = []\n", "r_c_l = arange(r_c_low.magnitude, r_c_high.magnitude + 0.1, 0.1)\n", "for r_c in r_c_l:\n", " v_3 = r_c * v_2\n", " p_3 = p_2\n", " st_3 = State(substance, p=p_3, v=v_3)\n", " s_3 = st_3.s.to(\"kJ/(kg*K)\")\n", " u_3 = st_3.u.to(\"kJ/kg\")\n", "\n", " s_4 = s_3\n", " v_4 = v_1\n", " st_4 = State(substance, v=v_4, s=s_4)\n", " u_4 = st_4.u.to(\"kJ/kg\")\n", "\n", " W_23 = (m * p_2 * (v_3 - v_2)).to(\"kJ\")\n", " W_34 = (m * (u_3 - u_4)).to(\"kJ\")\n", "\n", " W_net = W_12 + W_23 + W_34\n", " Wdot_net = (n_C * rpm * W_net / units.cycle).to(\"kW\")\n", " Wdot_net_l.append(Wdot_net.magnitude)\n", "\n", " Q_23 = (m * (u_3 - u_2) + W_23).to(\"kJ\")\n", " eta = W_net / Q_23\n", " eta_l.append(eta.magnitude)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.plot(r_c_l, Wdot_net_l, label=\"$\\dot{W}_{net}$\")\n", "plt.legend(loc=\"best\")\n", "plt.title(\"$\\dot{W}_{net}$ vs. $r_c$\")\n", "plt.xlabel(\"$r_c$ ($v_3/v_2$)\")\n", "plt.ylabel(\"$\\dot{W}_{net}$ (kW)\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4. plot $\\eta$ vs. $r_c$" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.plot(r_c_l, eta_l, label=\"$\\eta$\")\n", "plt.legend(loc=\"best\")\n", "plt.title(\"$\\eta$ vs. $r_c$\")\n", "plt.xlabel(\"$r_c$ ($v_3/v_2$)\")\n", "plt.ylabel(\"$\\eta$\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From these graphs, we note that as the cutoff ratio increases, the power delivered increases but the thermal efficiency decreases." ] } ], "metadata": { "anaconda-cloud": {}, "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": "3.9.2" }, "metadata": { "interpreter": { "hash": "6fd8de4baeba3334380c8c86eecee99239ef8fae7b6688e064a58f7fbba95a46" } } }, "nbformat": 4, "nbformat_minor": 2 }