{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Engines and fuels" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Otto cycle\n", "* Gasoline engines\n", "* 4-stroke cycle\n", " 1. Intake\n", " 2. Compression\n", " 1. *Combustion at the top*\n", " 3. Expansion/power\n", " 4. Exhaust " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Idealized cycle\n", "\n", "\n", "* 1$\\rightarrow$ 2: ideal compression\n", " * Adiabatic, PV work required by the engine.\n", "* 2$\\rightarrow$ 3: sensible energy added through burning of the fuel/air mixture\n", " * Combustion assumed to occur quickly, at constant volume. Pressure rises. \n", "* 3$\\rightarrow$ 4: ideal expansion\n", " * Adiabatic, PV work produced by the engine.\n", "* 4$\\rightarrow$ 1: heat rejection\n", " * drop in pressure as the valve is opened at the bottom of the stroke.\n", " * exhaust and intake are the horizontal blue and green lines.\n", "\n", "#### Net work\n", "* The net work produced is the area under curve 3$\\rightarrow$4 minus the area under curve 1$\\rightarrow$2.\n", "* Since the compression and expansion are adiabatic, the work is equal to differences in internal energy $u$.\n", "* Work required for compression: $W_c=u_2-u_1$.\n", "* Work done by expansion: $W_e = u_3-u_4$.\n", "* Net work performed by the engine = $W_e-W_c = (u_3-u_4)-(u_2-u_1)$.\n", "\n", "**Note** that $u_2=u_3$ since process 2$\\rightarrow$3 is adiabatic and constant volume. \n", "The \"heat added\" step is really sensible energy generated by combustion. But the internal energy of the mixture remains fixed.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adiabatic compression and expansion.\n", "\n", "* Assume ideal gas and adiabatic compression/expansion.\n", "\n", "$$du = dW = -PdV$$\n", "\n", "* $du = c_vdT$\n", "$$c_vdT = -PdV$$\n", "\n", "* $P = RT/V$, rearrange\n", "\n", "$$\\frac{dT}{T} = -\\frac{R}{c_v}\\frac{dV}{V}$$\n", "\n", "* $R = c_p-c_v$, $\\gamma = c_p/c_v$.\n", "* $\\rightarrow$ $R/c_v = \\gamma -1$.\n", "\n", "$$\\frac{dT}{T} = -(\\gamma-1)\\frac{dV}{V}$$\n", "* Assume $\\gamma$ is constant. Then integrate to\n", "\n", "$$\\ln\\frac{T_2}{T_1} = -(\\gamma-1)\\ln\\frac{V_2}{V_1}$$\n", "* Rewrite as\n", "\n", "$$\\frac{T_2}{T_1} = \\left(\\frac{V_1}{V_2}\\right)^{\\gamma-1}$$\n", "\n", "\n", "* Using $P=RT/V$, and expressions for $\\gamma$ above, we have\n", "\n", "$$\\frac{T_2}{T_1} = \\left(\\frac{P_2}{P_1}\\right)^{(\\gamma-1)/\\gamma}$$\n", "\n", "\n", "* Similarly\n", "\n", "$$P_1V_1^\\gamma = P_2V_2^\\gamma$$\n", "\n", "\n", "* If we relax the assumption that $\\gamma$ is constant, we have\n", "\n", "$$\\ln\\frac{V_2}{V_1} = -\\int_{T_1}^{T_2}\\frac{c_v(T)}{RT}dT$$\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example\n", "* Compute the work and efficiency on a lower heating value basis for an Otto cycle with a stoichiometric methane-air mixture. \n", "* Use a compression ratio (CR) of 10. That is $V_1/V_2 = V_4/V_3 = 10$\n", "* **code below requires [streams.py](http://ignite.byu.edu/che633/lectureNotes/streams.py) and cantera**\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "NO = 7249.681704\n", "1581.0497304280145 541668.9741244189\n", "1834.455938236 619897.2037123365\n", "NO = 193.1\n", "η = 0.43\n", "P1 = 1.00 atm, T1 = 300 K\n", "P2 = 23.02 atm, T2 = 691 K\n", "P3 = 96.24 atm, T3 = 2846 K\n", "P4 = 5.35 atm, T4 = 1581 K\n" ] } ], "source": [ "from streams import streams\n", "\n", "strm = streams({\"O2\":1,\"N2\":3.76}, {\"CH4\":1}, 300, 300, 101325, \"gri30.yaml\")\n", "CR = 10\n", "\n", "#----------- state 1: cold, atmospheric reactants\n", "strm.set_gas_mixing_state(strm.ξst)\n", "P1 = strm.gas.P\n", "T1 = strm.gas.T\n", "u1 = strm.gas.int_energy_mass\n", "\n", "#----------- state 2: compress reactants\n", "strm.set_gas_state_adiabatic_compression_expansion(1/CR)\n", "P2 = strm.gas.P\n", "T2 = strm.gas.T\n", "u2 = strm.gas.int_energy_mass\n", "\n", "#----------- state 3: burnt products\n", "strm.gas.equilibrate(\"UV\")\n", "P3 = strm.gas.P\n", "T3 = strm.gas.T\n", "u3 = strm.gas.int_energy_mass\n", "\n", "print(f'NO = {strm.gas.Y[strm.gas.species_index(\"NO\")]*1000000:0f}')\n", "\n", "#----------- state 4: expanded products\n", "strm.set_gas_state_adiabatic_compression_expansion(CR)\n", "P4 = strm.gas.P\n", "T4 = strm.gas.T\n", "u4 = strm.gas.int_energy_mass\n", "print(T4, P4)\n", "\n", "strm.gas.equilibrate(\"UV\")\n", "print(strm.gas.T, strm.gas.P)\n", "print(f'NO = {strm.gas.Y[strm.gas.species_index(\"NO\")]*1000000:.1f}')\n", "\n", "#----------- work and efficiency\n", "\n", "W = (u3-u4) - (u2-u1) # J/kg mixture\n", "LHV = strm.get_LHV_pCC() # J/kg fuel\n", "\n", "η = W/strm.ξst/LHV # efficiency; ξst is used to convert W from J/kg mix to J/kg fuel\n", "\n", "print(f\"η = {η:.2f}\")\n", "\n", "print(f'P1 = {P1/101325:.2f} atm, T1 = {T1:.0f} K')\n", "print(f'P2 = {P2/101325:.2f} atm, T2 = {T2:.0f} K')\n", "print(f'P3 = {P3/101325:.2f} atm, T3 = {T3:.0f} K')\n", "print(f'P4 = {P4/101325:.2f} atm, T4 = {T4:.0f} K')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* A compression ratio of 5 gives $\\eta=0.33$\n", " * $P_2=9$ atm, $T_2=546$ K\n", "* A compression ratio of 10 gives $\\eta=0.43$\n", " * $P_2=23$ atm, $T_2=690$ K\n", "* At high CR, the high $T_2$ can lead to auto-ignition and engine knock, which can cause damage.\n", "* For methane-air, $\\gamma=1.37$\n", "\n", "### Octane rating\n", "* See [Wikipedia](https://en.wikipedia.org/wiki/Octane_rating) for lots of information\n", "* The octane number is the percent of iso-octane (by volume) in a mixture of iso-octane and n-heptane, that has the same knock characteristics as the given fuel. \n", "* A higher octane number indicates a fuel that is more resistant to knock.\n", "* There are several different measurement methods, including the \"Research Octane Number\" and the \"Motor Octane Number\", an average of which is used in the U.S.\n", "* It is possible to have an octane number [greater than 100](https://chemistry.stackexchange.com/questions/133487/how-is-octane-rating-defined-for-negative-values-and-those-over-100).\n", "* Higher octane numbers can tolerate higher compression ratios.\n", "* Elevation matters.\n", "\n", "#### [Review article on impact of fuel molecular structure on auto-ignition](https://doi.org/10.1016/j.pecs.2016.12.001)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Diesel cycle\n", "\n", "\n", "https://en.wikipedia.org/wiki/Diesel_cycle#/media/File:DieselCycle_PV.svg\n", "\n", "* 4 strokes\n", "* Compress only air $\\rightarrow$ hot\n", "* Then inject fuel $\\rightarrow$ autoignition, but the injection timing is controlled.\n", "* No knock issue, allows cheaper fuels.\n", "* High compression radio gives higher efficiency.\n", " * CR = 12-24.\n", "* In the diagram above, the combustion step 2$\\rightarrow$ 3 occurs with some piston travel $\\approx$ constant pressure.\n", "* Heat steps $Q$ again refer to release of sensible energy, and exhaust/intake.\n", "* In the code above, change the ```equilibrate(\"UV\")``` to ```equilibrate(\"HP\")```\n", "\n", "### Other cycles\n", "* Brayton cycle (gas turbines)\n", "* Rankine cycle (steam cycle, e.g., coal plants)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fuels\n", "* Compare diesel fuel and gasoline\n", "* Diesel: about 25% aromatics, $C_{12}H_{23}$, ($C_{10}H_{20}$ - $C_{15}H_{28}$)\n", "* Gasoline: about 35% aromatics, $C_8H_{18}$, ($C_4$ - $C_{12}$)\n", "* $\\rho_D\\approx 0.85$ kg/L, versus $\\rho_G\\approx 0.72$ kg/L\n", "* Heating value: $HV_D\\approx 38.6$ MJ/L versus $HV_G\\approx 34.9$ MJ/L\n", "* Heating value: $HV_D\\approx 45.4$ MJ/kg versus $HV_G\\approx 48.5$ MJ/kg\n", "\n", "* On an equal mass basis, the large differences in efficiency are due to diesel having higher compression ratios.\n", "\n", "* Ethanol additives reduces hydrocarbon emissions (volatile organic compounds, VOCs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exhaust gas recirculation (EGR)\n", "\n", "* $NO_x$ is a pollutant formed at high temperatures.\n", "* To reduce $NO_x$, reduce peak flame temperatures. \n", "* One way to do this is by recirculating cool exhaust gases into the reaction mixture. This increases the heat capacity and reduces the flame temperature. \n", " * Also reduces efficiency.\n", "* Very common in diesel engines.\n", " * Up to 50% EGR\n", "* In SI engines, only 5-15% EGR\n", "\n", "## Recuperation/Regeneration\n", "\n", "* Raise flame temperatures by preheating reactants (air).\n", "* Exchange heat with hot combustion products.\n", "* High temperature applications, glass furnaces.\n", "\n", "\n", "https://www.glassonweb.com/news/nsg-cold-repair-float-glass-furnace-us" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.405768344464696" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "1-(T1/T2)*(T4/T1-1)/(T3/T2-1)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "hide_input": false, "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.13.1" } }, "nbformat": 4, "nbformat_minor": 4 }