{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 1 - Introduction\n", "\n", "Code used to generate figures and examples from Chapter 1 of [*Introduction to Fluid Dynamics*, by Joseph D. MacMillan](https://josephmacmillan.github.io/IntroductionToFluidDynamics/). This work is licensed under a [Creative Commons Attribution-ShareAlike 4.0\n", "International License.](https://creativecommons.org/licenses/by-sa/4.0/)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import matplotlib.pyplot as plt\n", "from matplotlib import rc\n", "import numpy as np\n", "\n", "rc('text.latex',preamble='\\\\usepackage{libertine}\\n\\\\usepackage[libertine]{newtxmath}')\n", "rc('font',**{'family':'serif','serif':['Linux Libertine O']}, size=18)\n", "rc('text', usetex=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Figure 1.2: A vector plot for flow about a stagnation point" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The velocity field is given by\n", "$$\n", "u = \\alpha x, \\quad v = -\\alpha y, \\quad w = 0.\n", "$$\n", "The code below plots a vector field for this flow." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-2, 2, 11)\n", "y = np.linspace(-2, 2, 11)\n", "x, y = np.meshgrid(x, y)\n", "\n", "alpha = 1.0\n", "u = alpha * x\n", "v = -alpha * y\n", "\n", "uu = np.sqrt(u*u + v*v)\n", "\n", "fig = plt.figure(figsize=(4, 4))\n", "ax = fig.add_subplot(1,1,1)\n", "ax.set_xlabel('$x$')\n", "ax.set_ylabel('$y$')\n", "ax.set_aspect('equal')\n", "ax.quiver(x, y, u, v, pivot='middle')\n", "\n", "plt.savefig('fig_vector_plot.pdf', bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Figure 1.3: Plotting Streamlines" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As an example of calculating and then plotting streamlines, consider the flow given by\n", "$$\n", "\\mathbf{u} = [\\alpha x, -\\alpha y].\n", "$$\n", "Note that this is two dimensional, steady flow.\n", "\n", "Streamlines are found from \n", "$$\n", "\\frac{dx/ds}{u} = \\frac{dy/ds}{v},\n", "$$\n", "or, plugging in $u$ and $v$ from above (and removing the parameter for simplicity)\n", "$$\n", "\\frac{dx}{\\alpha x} = -\\frac{dy}{\\alpha y}.\n", "$$\n", "Rearranging, integrating both sides, and then solving for $y$ gives the function\n", "$$\n", "y(x) = \\frac{c}{x}.\n", "$$\n", "That's our answer; $c$ is the integration constant, which will vary from streamline to streamline." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# here's the streamline function y(x). Try your own!\n", "def streamline_function(x, c):\n", " return c / x\n", "\n", "# the rest of the code computes the lines ...\n", "x = np.linspace(-2, 2, 100)\n", "y = streamline_function(x, 0.0)\n", "c = np.linspace(-2, 2, 9)\n", "\n", "# ... and plots them.\n", "fig = plt.figure(figsize=(4, 4))\n", "ax = fig.add_subplot(1,1,1)\n", "ax.set_xlabel('$x$')\n", "ax.set_ylabel('$y$')\n", "ax.set_aspect('equal')\n", "ax.set_xlim(-2, 2)\n", "ax.set_ylim(-2, 2)\n", "for i in range(len(c)):\n", " y = streamline_function(x, c[i])\n", " ax.plot(x, y, color='black')\n", "\n", "plt.savefig('fig_streamline_example.pdf', bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Figure 1.5: A shear flow\n", "\n", "The flow is given by\n", "$$\n", "\\mathbf{u} = [\\beta y , 0, 0],\n", "$$\n", "where $\\beta = 1$ in this case." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x=np.linspace(0, 2, 8)\n", "y=np.linspace(0, 2, 8)\n", "x, y=np.meshgrid(x, y)\n", "\n", "beta = 1.0\n", "u = beta * y\n", "v = 0.0\n", "\n", "uu = np.sqrt(u*u + v*v)\n", "\n", "fig = plt.figure(figsize=(4, 4))\n", "ax = fig.add_subplot(1,1,1)\n", "ax.set_xlabel('$x$')\n", "ax.set_ylabel('$y$')\n", "ax.set_aspect('equal')\n", "plt.quiver(x, y, u, v, pivot='tail')\n", "\n", "plt.savefig(\"fig_shear_vector.pdf\", bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Figure 1.6: Line vortex\n", "\n", "The line vortex flow is given by\n", "$$\n", "\\mathbf{u} = \\frac{k}{s} \\, \\hat{\\phi},\n", "$$\n", "where $k = 1$ in this case. Since this is flow given in cylindrical coordinates, the plot below is done in the polar coordinate projection." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "radii = np.linspace(0.3, 2, 10)\n", "thetas = np.linspace(0,2*np.pi,20)\n", "theta, r = np.meshgrid(thetas, radii)\n", "\n", "k = 1.0\n", "u_r = 0.0\n", "u_theta = k / r\n", "\n", "fig = plt.figure(figsize=(4, 4))\n", "ax = fig.add_subplot(111, projection='polar')\n", "ax.set_yticklabels([])\n", "ax.set_xticklabels([])\n", "ax.axis(False)\n", "ax.quiver(theta, r, u_r * np.cos(theta) - u_theta * np.sin(theta), u_r*np.sin(theta) + u_theta * np.cos(theta), pivot='tail')\n", "\n", "plt.savefig(\"fig_line_vortex_vector.pdf\")" ] } ], "metadata": { "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": "3.10.6" } }, "nbformat": 4, "nbformat_minor": 1 }