{ "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)2015 L.A. Barba, Pi-Yueh Chuang." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 2D Multi-element airfoil" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is your [_AeroPython_](https://github.com/barbagroup/AeroPython) assignment for the fourth course module, titled **\"Vortex-panel method for lifting bodies.\"** You will investigate a 2D multi-element airfoil, or wing section with extended flap, adapting the source-vortex panel method of [Lesson 11](11_Lesson11_vortexSourcePanelMethod.ipynb) to compute the flow around two airfoils. \n", "\n", "The key concepts for using the vortex-source panel method with a multi-element airfoil are:\n", "\n", "1. each airfoil has its own vortex strength, and\n", "2. the trailing edge at each airfoil must follow the Kutta condition.\n", "\n", "In the first part of the assignment, you will use a test for which we have a theoretical solution, due to Williams (1973). Have a look at the reference, and get a feel for its mathematical genius! In the second part, you will use a more popular airfoil (the NACA 23012) for both the main wing section and the flap. For this case, there is an old classic NACA report by Wenzinger (1938) giving data from experiments in a wind tunnel. This exercise will get you wondering about some very interesting aerodynamical questions!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Part 1: Williams' test case" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Your task is to calculate the pressure coefficient on a multi-element wing section, consisting of a *main airfoil* and an *external-airfoil flap*. This test is from Williams (1973), who obtained a beautiful theoretical solution using the techniques of conformal mapping.\n", "\n", "The profile of the wing section looks like this, with flap extended:\n", "