{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Dimensional Analysis\n", "\n", "**Reading: 7.1, 7.4.1, 7.5-7.8, 7.9.2, 7.10**\n", " \n", "Working with students in my research lab, I have found that some of the **most neglected** or misunderstood principles are those related to dimensional analysis and dynamic similarity. We will talk more about what dynamic similarity is and how to apply it in class, but to get started let's look at a motivating example. Understanding the code is not necessary to understanding the concepts, but it would be useful to explore on your own." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Wind Turbine Example\n", "\n", "We are going to look at an example of a simulation (or experiment) predicting the power output of a wind turbine as a function of the wind speed and the rotation speed of the rotor. \n", "\n", "First, we need to do some setup. You can completely ignore this next code block—its details are not important to our discussion. It just imports some modules, sets a plot style, and defines a very simple power calculation function. It's basically a look-up table with numbers that come from pre-running my full turbine analysis code (https://github.com/wisdem/ccblade). The important point is that you now have a method ``power`` that computes the wind turbine's power output for a specified wind speed $U_\\infty$ and turbine rotation speed $\\Omega$ (for some pre-selected geometry). In addition, I've added a little random Gaussian noise in case you want to think of the outputs as experimental data. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "from math import pi\n", "import matplotlib.pyplot as plt\n", "\n", "# setup plot style\n", "plt.style.use('ggplot')\n", "plt.rcParams['font.size'] = 18.0\n", "plt.rcParams['figure.figsize'] = '7.0, 5.2'\n", "plt.rcParams['lines.markersize'] = 8.0\n", "\n", "def power(Uinf, Omega):\n", " Rtip = 63.0\n", " rho = 1.225\n", " tsr = Omega*pi/30.0*Rtip/Uinf\n", " \n", " tsrV = np.linspace(1, 18, 50)\n", " CPV = np.array([0.0051582969252168265, 0.0078368606973244839, 0.013165552495878379, 0.025127527586220052, 0.045944561271158105, 0.074525830251031017, 0.10855095748435095, 0.14580969059900983, 0.18492236877346321, 0.22601552590539764, 0.26994898861654087, 0.31656353230581302, 0.36160006778421366, 0.39860111624800532, 0.424349912982949, 0.44115672062700917, 0.45219160365421102, 0.45926496268053218, 0.46334909648965472, 0.46495676519844836, 0.46440618292238589, 0.46195433684911774, 0.45782637190152536, 0.45227437793771447, 0.44556705415118902, 0.43794643800210098, 0.42955698106676804, 0.42041151934919924, 0.41047515135334811, 0.39971776136796933, 0.3881151227580602, 0.37563728366652888, 0.36224867466992822, 0.34791525639561632, 0.33260462373502292, 0.31628695819045533, 0.29893738026716216, 0.28054069643667945, 0.26110471808240104, 0.24066522063541104, 0.21923002382015289, 0.19680854209630785, 0.17348393269700382, 0.14935107809913706, 0.1244265247555085, 0.098695924717879385, 0.072144631367803844, 0.044771616959821792, 0.016680229959477631, 0.0])\n", " CP = np.interp(tsr, tsrV, CPV)\n", " P = CP * (0.5*rho*Uinf**3 * pi*Rtip**2)\n", " \n", " error = np.random.randn(len(P))* 0.03*P\n", " P += error\n", "\n", " return P" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's run this funciton for a bunch of different wind speeds and turbine rotation speeds (you could think of running these cases experimentally). To begin with, we will just choose these operational points randomly from uniform probability distributions\n", "$$ U_\\infty \\in [5.0, 15.0] \\text{ m/s}$$\n", "$$ \\Omega \\in [1.0, 30.0] \\text{ rpm}$$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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hqpCCt25eTdbZnTB///vf45FHHkFtbS22bNmC9evXY/DgwRg1ahQiIiLcESMR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\nmYmXXnpJnzQbGhpw9OhRpxIm0L5W9K677sK///1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0adNw00034fvvv0d1dTX69u2Lnj17YsSIEVyjSUQ+1SM1DVWlFSzGTz7hdNA8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\nIpqnq8X40u1YlP8w1Gq1v5t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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# number of pts to evaluate\n", "n = 100\n", "\n", "# random inputs\n", "Uinf = 5.0 + (15.0-5.0)*np.random.rand(n) # m/s\n", "Omega = 1.0 + (30.0-1.0)*np.random.rand(n) # rpm\n", "\n", "# evaluate power\n", "P = power(Uinf, Omega)\n", "\n", "# generate some plots\n", "plt.figure()\n", "plt.plot(Uinf, P/1e6, 'o')\n", "plt.xlabel('$U_\\infty$ (m/s)')\n", "plt.ylabel('Power (MW)')\n", "\n", "plt.figure()\n", "plt.plot(Omega, P/1e6, 'o')\n", "plt.xlabel('$\\Omega$ (rpm)')\n", "plt.ylabel('Power (MW)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There appears to be very little structure in this data. In other words, if I gave you a wind speed, you'd wouldn't be able to predict the power output (although it appears as if we could define a maximum power, which is true). The same conclusion applies for the rotation speed. From 7.1 you learned that appropriately chosen nondimensional parameters can simplify the relationships between variables. The important parameters in this case are the tip-speed ratio\n", "$$\\lambda = \\frac{\\Omega R}{U_\\infty}$$\n", "and the power coefficient\n", "$$ C_P = \\frac{P}{\\frac{1}{2} \\rho U_\\infty^3 (\\pi R^2)}$$\n", "Instead of our current function\n", "$$ P = f(U_\\infty, \\Omega)$$\n", "we expect that by nondimensionalizing we can achieve a simplifed functional form of\n", "$$ C_P = f(\\lambda)$$\n", "\n", "Let's take our same data, normalize it approprirately, then replot." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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WiMhLURL3u/Eorp7nXshkxSBLROQli2qq2/Pmq0lVuO6brBhkiYi8NHdxPpoH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\nFuz5TI/XW7vxaG46lDIpt77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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# normalize (this comes from our known geometry and operational point)\n", "Rtip = 63.0\n", "rho = 1.225\n", "\n", "tsr = Omega*pi/30.0*Rtip/Uinf # with conversion from RPM to Hz\n", "CP = P / (0.5*rho*Uinf**3 * pi*Rtip**2)\n", "\n", "plt.figure()\n", "plt.plot(tsr, CP, 'o')\n", "plt.xlim([0.0, 20.0])\n", "plt.xlabel('$\\lambda$')\n", "plt.ylabel('$C_P$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, the structure in the data is clearly visible. If I gave you a freestream velocity, and a rotation rate, you could predict the power coefficient without running any additional experiments. Additionally, if you were trying to build a predictive computational model, you could now do so easily.\n", "\n", "Of course, most people don't run purely random input points. A scenario that I see more frequently looks like the one below. In this case we are going to ramp up the wind speed from 5 to 15 m/s (e.g., in a wind tunnel), and we are going to repeat that for 4 discrete fixed rotation speeds ($\\Omega = 3, 10, 20, 30$ rpm). The variation in power for all four rotation speeds is shown in the plot below." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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iY2NNvRUhhHgk5nlLhfxHPDVpiX4mqZtFAkBVdTGOnVmP+PhEuEPPS+aZSnDa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\n+5F8AQWU5Yexc9cnk6JTYZ6prKqqwh1LLPcqmbNK9hLskH4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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# sets of rotation speeds\n", "Omegavec = [3.0, 10.0, 20.0, 30.0]\n", "nspeeds = len(Omegavec)\n", "Uinf = np.linspace(5.0, 15.0, n) # m/s\n", "\n", "# evaluate power curve for each rotation speed\n", "P = np.zeros((nspeeds, n))\n", "for i in range(nspeeds):\n", " P[i, :] = power(Uinf, Omegavec[i]*np.ones(n))\n", "\n", "plt.figure()\n", "for i in range(nspeeds):\n", " plt.plot(Uinf, P[i, :]/1e6, 'o')\n", "plt.xlabel('$U_\\infty$')\n", "plt.ylabel('Power (MW)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is clearly some well-defined relationships. Although, it appears that there is a separate relationship for each rotation speed. Let's normalize the data, in the same manner we did previously, and replot." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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oYyONJylWBqPO89SvQacGLzS8+gvurWnH5lI28W75+oDCgxXzZkxF+Jmdbr9j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\naNVYkD4I1yXE4MmjlWhzyHA4naz0REQA2lN6Ks8c7DJzQ6/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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# normalize\n", "tsr = np.zeros((nspeeds, n))\n", "for i in range(nspeeds):\n", " tsr[i, :] = Omegavec[i]*pi/30.0*Rtip/Uinf\n", "\n", "CP = P / (0.5*rho*Uinf**3 * pi*Rtip**2)\n", "\n", "plt.figure()\n", "for i in range(nspeeds):\n", " plt.plot(tsr[i, :], CP[i, :], 'o')\n", "plt.xlim([0.0, 20.0])\n", "plt.xlabel('$\\lambda$')\n", "plt.ylabel('$C_P$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, it is apparent that we weren't really generating separate data relationships, but rather evaluating different portions of one underlying data relationship. This simple example highlights the importance, and the power of proper nondimensional analysis." ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.8" } }, "nbformat": 4, "nbformat_minor": 0 }