{
"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": {
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\n",
"image/svg+xml": [
"\r\n",
"\r\n",
"\r\n"
],
"text/plain": [
"