{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 211 オットーサイクル\n",
"\n",
"Example: Spark-Ignition. Four-Stroke Engine\n",
"\n",
"## 読み込み"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import math\n",
"\n",
"import sys\n",
"sys.path.append(r'~\\Lib\\site-packages') # Path to library directory\n",
"import CoolProp\n",
"import CoolProp.CoolProp as CP \n",
"from CoolProp.Plots import PropertyPlot\n",
"\n",
"import matplotlib.pyplot as plt \n",
"%matplotlib inline\n",
"import warnings\n",
"warnings.filterwarnings(\"ignore\")\n",
"\n",
"import numpy as np\n",
"import pandas as pd"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## パラメータ定義"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"WF = 'air'\n",
"K = 273.15\n",
"bore = 0.1 # m\n",
"stroke = 0.09 #m\n",
"CR = 8.3 # Compression ratio\n",
"N_cyl = 4 # number of cylinder\n",
"N = 60 # engine speed 1/s\n",
"AF = 16 # air-fuel ratio\n",
"HC = 44*10**6 # heat of combusion J/kg\n",
"T_amb = 32 + K # outdoor air temperature\n",
"P_atm = 100*10**3 # atomospheric air temperature Pa\n",
"\n",
"Vol_dis_cyl = math.pi*bore**2 *stroke/4 # Displacement of each cylinder\n",
"Vol_cl = Vol_dis_cyl/(CR-1) # clearance volume\n",
"Vol_BDC = Vol_dis_cyl+Vol_cl #bottom dead center volume\n",
"Vol_TDC = Vol_cl # top dead center volume"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### データフレーム用意"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"index = list(range(1,4+1))\n",
"states = pd.DataFrame(columns=['T', 'P', 's', 'v', 'Vol', 'u', 'm'], index=index)#K, Pa, J/kg/K, m3/kg, m3/mol?, J/kg, kg/mol"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Point 1"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"states.ix[1, 'T'] = T_amb\n",
"states.ix[1, 'P'] = P_atm\n",
"states.ix[1, 's'] = CP.PropsSI('S', 'T', states.ix[1, 'T'], 'P', states.ix[1, 'P'], WF)\n",
"states.ix[1, 'u'] = CP.PropsSI('U', 'T', states.ix[1, 'T'], 'P', states.ix[1, 'P'], WF)\n",
"states.ix[1, 'v'] = 1/CP.PropsSI('D', 'T', states.ix[1, 'T'], 'P', states.ix[1, 'P'], WF)\n",
"states.ix[1, 'Vol'] = Vol_BDC\n",
"states.ix[1, 'm'] = states.ix[1, 'Vol'] / states.ix[1, 'v']"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Point 2"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"states.ix[2, 'm'] = states.ix[1, 'm']\n",
"states.ix[2, 'Vol'] = Vol_TDC\n",
"states.ix[2, 'v'] = states.ix[2, 'Vol'] / states.ix[2, 'm']\n",
"states.ix[2, 's'] = states.ix[1, 's']\n",
"states.ix[2, 'u'] = CP.PropsSI('U', 'D', 1/states.ix[2, 'v'], 'S', states.ix[2, 's'], WF)\n",
"states.ix[2, 'T'] = CP.PropsSI('T', 'D', 1/states.ix[2, 'v'], 'S', states.ix[2, 's'], WF)\n",
"states.ix[2, 'P'] = CP.PropsSI('P', 'D', 1/states.ix[2, 'v'], 'S', states.ix[2, 's'], WF)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Work etc."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"m_in:8.07E-04\n",
"m_f:4.75E-05\n"
]
}
],
"source": [
"W_comp = states.ix[2, 'm'] * states.ix[2, 'u'] - states.ix[1, 'm'] * states.ix[1, 'u'] #Compression work\n",
"m_in = (Vol_BDC - Vol_TDC) / (1/CP.PropsSI('D', 'T', T_amb, 'P', P_atm, WF)) #mass of incoming air\n",
"m_f = m_in / (AF+1) # mass of fuel\n",
"print('m_in:{:.02E}'.format(m_in))\n",
"print('m_f:{:.02E}'.format(m_f))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## State 3"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"states.ix[3, 'm'] = states.ix[2, 'm']\n",
"states.ix[3, 'Vol'] = Vol_TDC\n",
"states.ix[3, 'v'] = states.ix[3, 'Vol'] / states.ix[3, 'm']\n",
"states.ix[3, 'u'] = (m_f * HC - states.ix[2, 'm'] * states.ix[2, 'u']) / states.ix[3, 'm'] # from Energy balance\n",
"states.ix[3, 'T'] = CP.PropsSI('T', 'U', states.ix[3, 'u'], 'D', 1/states.ix[3, 'v'], WF)\n",
"states.ix[3, 'P'] = CP.PropsSI('P', 'U', states.ix[3, 'u'], 'D', 1/states.ix[3, 'v'], WF)\n",
"states.ix[3, 's'] = CP.PropsSI('S', 'U', states.ix[3, 'u'], 'D', 1/states.ix[3, 'v'], WF)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## State 4"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def find_P_from_v_s(WF, v, s, Pstart, Pstop, eps=1e-6):\n",
" v1 = 1/CP.PropsSI('D','P',Pstart,'S', s, WF)\n",
" v2 = 1/CP.PropsSI('D','P',Pstop,'S', s, WF)\n",
" while abs(v2-v1)/v > eps:\n",
" Pm = (Pstart+Pstop)/2.0\n",
" vm = 1/CP.PropsSI('D','P',Pm,'S',s,WF)\n",
" if (vm-v)*(v2-v) < 0: Pstart,v1 = Pm,vm\n",
" else: Pstop,v2 = Pm,vm\n",
" return Pm\n",
"\n",
"states.ix[4, 'm'] = states.ix[3, 'm']\n",
"states.ix[4, 'Vol'] = Vol_BDC\n",
"states.ix[4, 'v'] = states.ix[4, 'Vol'] / states.ix[4, 'm']\n",
"states.ix[4, 's'] = states.ix[3, 's']\n",
"\n",
"#states.ix[4, 'P'] = CP.PropsSI('P', 'D', 1/states.ix[4, 'v'], 'S', 1/states.ix[4, 's'], WF)\n",
"states.ix[4, 'P'] = find_P_from_v_s(WF, states.ix[4, 'v'], states.ix[4, 's'], states.ix[1, 'P'], states.ix[3, 'P'])\n",
"\n",
"#states.ix[4, 'T'] = CP.PropsSI('T', 'D', 1/states.ix[4, 'v'], 'S', 1/states.ix[4, 's'], WF)\n",
"states.ix[4, 'T'] = CP.PropsSI('T', 'D', 1/states.ix[4, 'v'], 'P', states.ix[4, 'P'], WF)\n",
"\n",
"#states.ix[4, 'u'] = CP.PropsSI('U', 'D', 1/states.ix[4, 'v'], 'S', 1/states.ix[4, 's'], WF)\n",
"states.ix[4, 'u'] = states.ix[3, 'u'] - states.ix[2, 'u']"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 結果テーブルの表示"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"W_net -848.25 = W_exp -581.94 - W_comp 266.31\n",
"eta: -0.41\n"
]
},
{
"data": {
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"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" T | \n",
" P | \n",
" s | \n",
" v | \n",
" Vol | \n",
" u | \n",
" m | \n",
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\n",
" \n",
" \n",
" \n",
" | 1 | \n",
" 305.15 | \n",
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" 0.000803688 | \n",
" 343914 | \n",
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\n",
" \n",
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" 695.502 | \n",
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" 634085 | \n",
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\n",
" \n",
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" 1831.19 | \n",
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" 1.64231e+06 | \n",
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\n",
" \n",
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