{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "###### Content provided under a Creative Commons Attribution license, CC-BY 4.0; code under BSD 3-Clause license. (c)2014 Lorena A. Barba, Olivier Mesnard. Thanks: NSF for support via CAREER award #1149784." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Doublet" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Welcome to the third lesson of *AeroPython*! We created some very interesting potential flows in lessons 1 and 2, with our [Source & Sink](01_Lesson01_sourceSink.ipynb) notebook, and our [Source & Sink in a Freestream](02_Lesson02_sourceSinkFreestream.ipynb) notebook.\n", "\n", "Think about the Source & Sink again, and now imagine that you are looking at this flow pattern from very far away. The streamlines that are between the source and the sink will be very short, from this vantage point. And the other streamlines will start looking like two groups of circles, tangent at the origin. If you look from far enough away, the distance between source and sink approaches zero, and the pattern you see is called a *doublet*.\n", "\n", "Let's see what this looks like. First, load our favorite libraries." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import math\n", "import numpy\n", "from matplotlib import pyplot\n", "# embed figures into the notebook\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the previous notebook, we saw that a source-sink pair in a uniform flow can be used to represent the streamlines around a particular shape, named a Rankine oval. In this notebook, we will turn that source-sink pair into a doublet.\n", "\n", "First, consider a source of strength $\\sigma$ at $\\left(-\\frac{l}{2},0\\right)$ and a sink of opposite strength located at $\\left(\\frac{l}{2},0\\right)$. Here is a sketch to help you visualize the situation:\n", "\n", "