{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorial 2 - Fluid Visualization\n", "\n", "This second tutorial for [*Introduction to Fluid Dynamics*](https://josephmacmillan.github.io/IntroductionToFluidDynamics/) will cover the basics of visualizing fluid flow -- using vector plots and streamlines, mostly. \n", "\n", "Now, an ideal fluid has two main properties -- the velocity at each point, and the pressure at each point. So this tutorial will work up to the following visualization:\n", "![Flow around a cylinder, with pressure](fig_cylinder_pressure.png)\n", "\n", "That shows an ideal flow around a cylinder, with streamlines shown as the faint lines and the colours representing pressure (with pink as regions of highest pressure). We'll build up to this slowly, learning how to visualize fluids along the way.\n", "\n", "## 2.1 Vector Plots\n", "\n", "If we're only interested in velocity, a vector plot makes sense. Consider, for example, the flow given by\n", "$$\n", "\\mathbf{u} = [x, -y].\n", "$$\n", "Let's look at just the first quadrant:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "x = np.linspace(0, 5, 10)\n", "y = np.linspace(0, 5, 10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we're importing NumPy and creating an array of values for horizontal and vertical positions. But we actually need more than two arrays -- we need a *mesh* of values, or a grid. That's a little confusing, but here's what I mean:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Here's the original array:\n", " [0. 0.55555556 1.11111111 1.66666667 2.22222222 2.77777778\n", " 3.33333333 3.88888889 4.44444444 5. ]\n", "\n", "And here's the mesh:\n", " [[0. 0.55555556 1.11111111 1.66666667 2.22222222 2.77777778\n", " 3.33333333 3.88888889 4.44444444 5. ]\n", " [0. 0.55555556 1.11111111 1.66666667 2.22222222 2.77777778\n", " 3.33333333 3.88888889 4.44444444 5. ]\n", " [0. 0.55555556 1.11111111 1.66666667 2.22222222 2.77777778\n", " 3.33333333 3.88888889 4.44444444 5. ]\n", " [0. 0.55555556 1.11111111 1.66666667 2.22222222 2.77777778\n", " 3.33333333 3.88888889 4.44444444 5. ]\n", " [0. 0.55555556 1.11111111 1.66666667 2.22222222 2.77777778\n", " 3.33333333 3.88888889 4.44444444 5. ]\n", " [0. 0.55555556 1.11111111 1.66666667 2.22222222 2.77777778\n", " 3.33333333 3.88888889 4.44444444 5. ]\n", " [0. 0.55555556 1.11111111 1.66666667 2.22222222 2.77777778\n", " 3.33333333 3.88888889 4.44444444 5. ]\n", " [0. 0.55555556 1.11111111 1.66666667 2.22222222 2.77777778\n", " 3.33333333 3.88888889 4.44444444 5. ]\n", " [0. 0.55555556 1.11111111 1.66666667 2.22222222 2.77777778\n", " 3.33333333 3.88888889 4.44444444 5. ]\n", " [0. 0.55555556 1.11111111 1.66666667 2.22222222 2.77777778\n", " 3.33333333 3.88888889 4.44444444 5. ]]\n" ] } ], "source": [ "print(\"Here's the original array:\\n\", x)\n", "xx, yy = np.meshgrid(x, y)\n", "print(\"\\nAnd here's the mesh:\\n\", xx)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So now we have a 10x10 matrix, with each row the original x array. What's the point of that? Together with the y matrix, we have a series of (x,y) pairs that represent each point within the region. MatPlotLib has various functions that can draw something at these points; if, for example, we calculate the speed of the fluid at each point ..." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "uu = xx\n", "vv = -yy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "... then we can use matplotlib to plot vectors at each:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "fig = plt.figure()\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(xx, yy, uu, vv, pivot='middle')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There's 100 (10x10) little arrows in the plot; we can adjust the size by changing the size of our original arrays:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 5, 20)\n", "y = np.linspace(0, 5, 20)\n", "xx, yy = np.meshgrid(x, y)\n", "uu = xx\n", "vv = -yy\n", "\n", "fig = plt.figure()\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(xx, yy, uu, vv, pivot='middle')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That might be too many, though, so use your judgement." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 2.2 Streamlines\n", "\n", "An alternative to visualizing the flow is with streamlines, which are a little less cluttering than vector plots but still carry lots of info. Technically, a streamline is a curve in the fluid where, at each point, the curve has the same direction as the fluid velocity. There are two ways to find streamlines, either directly or through the stream function. \n", "\n", "For example, the streamlines for the flow above are given by\n", "$$\n", "y(x) = \\frac{c}{x},\n", "$$\n", "where $c$ is a constant -- different values will give you different streamlines. Let's give it a try; we'll start by setting up the x axis and the constants, and then loop over the constants and plot each line. I'll make the constant $c$ go from 0.3 to 23, since that makes the lines span the full region I'm plotting, and I'll plot 10 streamlines." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = np.linspace(0.001, 5, 100)\n", "c = np.linspace(0.3, 23, 10)\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.set_xlim(0, 5)\n", "ax.set_ylim(0, 5)\n", "\n", "for k in c:\n", " y = k / x\n", " ax.plot(x, y, color='black')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That's not bad, but we don't always have the function that gives streamlines, and it can be a pain to derive. But we have two other options.\n", "\n", "First, MatPlotLib has a built-in stream plot function that works just like a vector plot -- it takes the velocity components as input and makes a streamline plot instead of a bunch of vectors. Here's what it looks like:" ] }, { "cell_type": "code", "execution_count": 84, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = np.linspace(0.001, 5, 100)\n", "y = np.linspace(0.001, 5, 100)\n", "xx, yy = np.meshgrid(x, y)\n", "uu = xx\n", "vv = -yy\n", "\n", "fig = plt.figure()\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.streamplot(xx, yy, uu, vv)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But, to be honest, I'm not too keen on this plot. I expect streamlines to go to infinity (unless there's an object or line source present), but these sometimes randomly stop and start. The second method uses the *stream function* $\\psi$, which is constant on streamlines.\n", "\n", "For our example flow, the stream function is\n", "$$\n", "\\psi = xy.\n", "$$\n", "To use this in plotting, we'll have to follow a method similar to the vector plot and streamplot, but use MatPlotLib's contour function. Here's how." ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 85, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "xx, yy = np.meshgrid(x, y)\n", "psi = xx * yy\n", "\n", "fig = plt.figure()\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.contour(xx, yy, psi, 11, colors='black')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.3 Heat Maps\n", "\n", "As a third visualization method, we could also plot a property of the fluid as a *heat map*, meaning that each point in the fluid is coloured according to the value of that property. As a first example, we can do this for velocity and use MatPlotLib's imshow to display the meshgrid as an image." ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 86, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "u = np.sqrt(uu**2 + vv**2)\n", "\n", "fig = plt.figure()\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.imshow(u, extent=[0, 5, 0, 5], origin='lower', cmap='viridis')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can overlay streamlines just for fun:" ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 89, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\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.imshow(u, extent=[0, 5, 0, 5], origin='lower', cmap='viridis')\n", "ax.contour(xx, yy, psi, 11, colors='white')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.4 Adding Objects\n", "\n", "Finally, we want to reproduce that figure at the top -- but it has a big grey circle in the middle, representing the cylinder the fluid surrounds. We can add in a circle by creating one with the Circle function and then adding it to the axes with add_patch. \n", "\n", "This example is a little different than above -- the stream function is\n", "$$\n", "\\psi = U \\left( s - \\frac{a^2}{s} \\right) \\sin \\phi,\n", "$$\n", "and the pressure is given by\n", "$$\n", "p = p_\\infty + \\frac{1}{2} \\rho U^2 \\frac{a^2}{s^2} \\left( 2 \\cos 2 \\phi - \\frac{a^2}{s^2} \\right).\n", "$$\n", "That's in cylindrical coordinates, if we convert to Cartesian, it becomes\n", "$$\n", "p = p_\\infty + \\frac{1}{2} \\rho a^2 U^2 \\left( \\frac{2x^2 - 2y^2 - a^2}{(x^2 + y^2)^2} \\right).\n", "$$\n", "I'll use $p_\\infty = 0$ in the code for simplicity, and adjusted the vmin and vmax parameters in the imshow function to make sure that the image looks good (the pressure spikes to infinity inside the cylinder, but that's okay since there isn't any fluid there)." ] }, { "cell_type": "code", "execution_count": 170, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-0.00024691 -0.0003103 -0.00037493 ... -0.00037493 -0.0003103\n", " -0.00024691]\n", " [-0.00019018 -0.00025363 -0.00031835 ... -0.00031835 -0.00025363\n", " -0.00019018]\n", " [-0.00013229 -0.00019579 -0.00026058 ... -0.00026058 -0.00019579\n", " -0.00013229]\n", " ...\n", " [-0.00013229 -0.00019579 -0.00026058 ... -0.00026058 -0.00019579\n", " -0.00013229]\n", " [-0.00019018 -0.00025363 -0.00031835 ... -0.00031835 -0.00025363\n", " -0.00019018]\n", " [-0.00024691 -0.0003103 -0.00037493 ... -0.00037493 -0.0003103\n", " -0.00024691]] -1973466.3706174644 0.07995252964855698\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 170, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "rho = 1.0\n", "a = 1.0\n", "U = 0.4\n", "\n", "x = np.linspace(-3, 3, 300)\n", "y = np.linspace(-3, 3, 300)\n", "\n", "xx, yy = np.meshgrid(x, y)\n", "pp = 0.5 * rho * a**2 * U**2 * (2*xx**2 - 2*yy**2 - a**2) / (xx**2 + yy**2)**2\n", "s = np.sqrt(xx**2 + yy**2)\n", "sin_phi = yy / s \n", "psi = U * (s - a**2 / s) * sin_phi\n", "\n", "fig = plt.figure(figsize = (8, 8))\n", "ax = fig.add_subplot(1, 1, 1)\n", "\n", "plt.imshow(pp, extent=[-3, 3, -3, 3], origin='lower', cmap='coolwarm', vmin = -0.2, vmax = 0.08)\n", "\n", "plt.axis('off')\n", "\n", "circ = plt.Circle((0,0),radius=a, fc='lightgrey', fill=True, alpha=1, zorder=3, color=\"black\")\n", "ax.add_patch(circ)\n", "\n", "import matplotlib\n", "matplotlib.rcParams['contour.negative_linestyle'] = 'solid'\n", "plt.contour(xx, yy, psi, colors='white', levels = 400, alpha=1, linewidths = 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That's not exactly the same as the image above, but it's pretty close. Go ahead and change parameters, colormaps, etc, to make an image you like." ] } ], "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": 4 }