{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Air-Standard Brayton Cycle Example\n", "\n", "## Imports" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from thermostate import State, Q_, units\n", "from thermostate.plotting import IdealGas\n", "import numpy as np\n", "\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "## Definitions" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "substance = \"air\"\n", "p_1 = Q_(1.0, \"bar\")\n", "T_1 = Q_(300.0, \"K\")\n", "T_3 = Q_(1700.0, \"K\")\n", "p2_p1 = Q_(8.0, \"dimensionless\")\n", "p_low = Q_(2.0, \"dimensionless\")\n", "p_high = Q_(50.0, \"dimensionless\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "## Problem Statement" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An ideal air-standard Brayton cycle operates at steady state with compressor inlet conditions of 300.0 K and 1.0 bar and a fixed turbine inlet temperature of 1700.0 K and a compressor pressure ratio of 8.0. For the cycle,\n", "\n", "1. determine the net work developed per unit mass flowing, in kJ/kg\n", "2. determine the thermal efficiency\n", "3. plot the net work developed per unit mass flowing, in kJ/kg, as a function of the compressor pressure ratio from 2.0 to 50.0\n", "4. plot the thermal efficiency as a function of the compressor pressure ratio from 2.0 to 50.0\n", "5. Discuss any trends you find in parts 3 and 4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "## Solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1. the net work developed per unit mass flowing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The ideal Brayton cycle is made of 4 processes:\n", "\n", " 1. Isentropic compression\n", " 2. Isobaric heat input\n", " 3. Isentropic expansion \n", " 4. Isobaric heat rejection\n", "\n", "The following properties are used to fix the four states:\n", "\n", "State | Property 1 | Property 2 \n", ":-----:|:-----:|:-----:\n", "1|$$T_1$$|$$p_1$$\n", "2|$$p_2$$|$$s_2=s_1$$\n", "3|$$p_3=p_2$$|$$T_3$$\n", "4|$$s_4=s_3$$|$$p_4=p_1$$\n", "\n", "In the ideal Brayton cycle, work occurs in the isentropic compression and expansion. Therefore, the works are\n", "\n", "$$\n", "\\begin{aligned}\n", "\\frac{\\dot{W}_c}{\\dot{m}} &= h_1 - h_2 & \\frac{\\dot{W}_t}{\\dot{m}} &= h_3 - h_4\n", "\\end{aligned}\n", "$$\n", "\n", "First, fixing the four states" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "st_1 = State(substance, T=T_1, p=p_1)\n", "h_1 = st_1.h.to(\"kJ/kg\")\n", "s_1 = st_1.s.to(\"kJ/(kg*K)\")\n", "\n", "s_2 = s_1\n", "p_2 = p_1 * p2_p1\n", "st_2 = State(substance, p=p_2, s=s_2)\n", "h_2 = st_2.h.to(\"kJ/kg\")\n", "T_2 = st_2.T\n", "\n", "p_3 = p_2\n", "st_3 = State(substance, p=p_3, T=T_3)\n", "h_3 = st_3.h.to(\"kJ/kg\")\n", "s_3 = st_3.s.to(\"kJ/(kg*K)\")\n", "\n", "s_4 = s_3\n", "p_4 = p_1\n", "st_4 = State(substance, p=p_4, s=s_4)\n", "h_4 = st_4.h.to(\"kJ/kg\")\n", "T_4 = st_4.T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Summarizing the states,\n", "\n", "| State | T | p | h | s |\n", "|-------|---------------------------|---------------------------|---------------------------|---------------------------|\n", "| 1 | 300.00 K | 1.00 bar | 426.30 kJ/kg | 3.89 kJ/(K kg) |\n", "| 2 | 540.13 K | 8.00 bar | 670.65 kJ/kg | 3.89 kJ/(K kg) |\n", "| 3 | 1700.00 K | 8.00 bar | 2007.09 kJ/kg | 5.19 kJ/(K kg) |\n", "| 4 | 1029.42 K | 1.00 bar | 1206.17 kJ/kg | 5.19 kJ/(K kg) |\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting the p-v and T-s diagrams of the cycle," ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Brayton = IdealGas(substance, (\"s\", \"T\"), (\"v\", \"p\"))\n", "\n", "Brayton.add_process(st_1, st_2, \"isentropic\")\n", "Brayton.add_process(st_2, st_3, \"isobaric\")\n", "Brayton.add_process(st_3, st_4, \"isentropic\")\n", "Brayton.add_process(st_4, st_1, \"isobaric\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then, the net work is calculated by" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "W_c = h_1 - h_2\n", "W_t = h_3 - h_4\n", "W_net = W_c + W_t" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "**Answer:** The works are $\\dot{W}_c/\\dot{m} =$ -244.35 kJ/kg, $\\dot{W}_t/\\dot{m} =$ 800.92 kJ/kg, and $\\dot{W}_{net}/\\dot{m} =$ 556.57 kJ/kg\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2. the thermal efficiency" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "Q_23 = h_3 - h_2\n", "eta = W_net / Q_23" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "**Answer:** The thermal efficiency is $\\eta =$ 0.42 = 41.65%\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3. and 4. plot the net work per unit mass flowing and thermal efficiency" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "p_range = np.linspace(p_low, p_high, 50)\n", "eta_l = np.zeros(shape=p_range.shape) * units.dimensionless\n", "W_net_l = np.zeros(shape=p_range.shape) * units.kJ / units.kg\n", "for i, p_ratio in enumerate(p_range):\n", " s_2 = s_1\n", " p_2 = p_1 * p_ratio\n", " st_2 = State(substance, p=p_2, s=s_2)\n", " h_2 = st_2.h.to(\"kJ/kg\")\n", " T_2 = st_2.T\n", "\n", " p_3 = p_2\n", " st_3 = State(substance, p=p_3, T=T_3)\n", " h_3 = st_3.h.to(\"kJ/kg\")\n", " s_3 = st_3.s.to(\"kJ/(kg*K)\")\n", "\n", " s_4 = s_3\n", " p_4 = p_1\n", " st_4 = State(substance, p=p_4, s=s_4)\n", " h_4 = st_4.h.to(\"kJ/kg\")\n", " T_4 = st_4.T\n", "\n", " W_c = h_1 - h_2\n", " W_t = h_3 - h_4\n", " W_net = W_c + W_t\n", " W_net_l[i] = W_net\n", "\n", " Q_23 = h_3 - h_2\n", " eta = W_net / Q_23\n", " eta_l[i] = eta" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, work_ax = plt.subplots()\n", "work_ax.plot(p_range, W_net_l, label=\"Net work per unit mass flowing\", color=\"C0\")\n", "eta_ax = work_ax.twinx()\n", "eta_ax.plot(p_range, eta_l, label=\"Thermal efficiency\", color=\"C1\")\n", "work_ax.set_xlabel(\"Pressure ratio $p_2/p_1$\")\n", "work_ax.set_ylabel(\"Net work per unit mass flowing (kJ/kg)\")\n", "eta_ax.set_ylabel(\"Thermal efficiency\")\n", "lines, labels = work_ax.get_legend_handles_labels()\n", "lines2, labels2 = eta_ax.get_legend_handles_labels()\n", "work_ax.legend(lines + lines2, labels + labels2, loc=\"best\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We note from this graph that the thermal efficiency of the cycle increases continuously as the pressure ratio increases. However, because there is a fixed turbine inlet temperature, the work per unit mass flowing has a maximum around $p_2/p_1$ = 20." ] } ], "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": "3.7.10" }, "metadata": { "interpreter": { "hash": "6fd8de4baeba3334380c8c86eecee99239ef8fae7b6688e064a58f7fbba95a46" } } }, "nbformat": 4, "nbformat_minor": 2 }