#!/usr/bin/env python
# coding: utf-8

# ###### Content provided under a Creative Commons Attribution license, CC-BY 4.0; code under BSD 3-Clause license. (c)2014 Lorena A. Barba, Pi-Yueh Chuang. Thanks: NSF for support via CAREER award #1149784.

# # Source Distribution on an Airfoil

# In [Lesson 3](03_Lesson03_doublet.ipynb) of *AeroPython*, you learned that it is possible to represent potential flow around a circular cylinder using the superposition of a doublet singularity and a free stream. But potential flow is even more powerful: you can represent the flow around *any* shape. How is it possible, you might ask?
# 
# For non-lifting bodies, you can use a source distribution on the body surface, superposed with a free stream. In this assignment, you will build the flow around a NACA0012 airfoil, using a set of sources.
# 
# Before you start, take a moment to think: in flow around a symmetric airfoil at $0^{\circ}$ angle of attack,
# 
# * Where is the point of maximum pressure?
# * What do we call that point?
# * Will the airfoil generate any lift?
# 
# At the end of this assignment, come back to these questions, and see if it all makes sense.

# ## Problem Setup

# You will read data files containing information about the location and the strength of a set of sources located on the surface of a NACA0012 airfoil. 
# 
# There are three data files: NACA0012_x.txt, NACA0012_y.txt, and NACA0012_sigma.txt. To load each file into a NumPy array, you need the function [`numpy.loadtxt`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.loadtxt.html). The files should be found in the `resources` folder of the `lessons`. 

# Using 51 mesh points in each direction, and a domain $[-1, 2]\times[-0.5, 0.5]$, compute the velocity due to the set of sources plus a free stream in the $x$-direction with $U_{\infty}=1$. Also compute the coefficient of pressure on your grid points.

# ## Questions:

# 1. What is the value of maximum pressure coefficient, $C_p$?
# 2. What are the array indices for the maximum value of $C_p$?
# 
# Make the following plots to visualize and inspect the resulting flow pattern:
# 
# * Stream lines in the domain and the profile of our NACA0012 airfoil, in one plot
# * Distribution of the pressure coefficient and a single marker on the location of the maximum pressure

# **Hint**: You might use the following NumPy functions: [`numpy.unravel_index`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.unravel_index.html) and [`numpy.argmax`](http://docs.scipy.org/doc/numpy/reference/generated/numpy.argmax.html)

# ##### Think

# 1. Do the stream lines look like you expected?
# 2. What does the distribution of pressure tell you about lift generated by the airfoil?
# 3. Does the location of the point of maximum pressure seem right to you?

# In[1]:


from IPython.core.display import HTML
def css_styling(filepath):
    styles = open(filepath, 'r').read()
    return HTML(styles)
css_styling('../styles/custom.css')