{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 2 - Viscous Fluids\n", "\n", "Code used to generate figures and examples from Chapter 2 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": 2, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import matplotlib\n", "from mpl_toolkits.mplot3d import Axes3D\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 2.2: Poiseuille flow slowing down over time\n", "\n", "The fluid velocity is given by\n", "$$\n", "u(y, t) = \\frac{4Ph^2}{\\pi^3 \\nu \\rho} \\sum_{n=1, 3, 5 \\dots}^\\infty \\frac{1}{n^3} \\sin(n \\pi y / h) \\, e^{-n^2 \\pi^2 \\nu t / h^2},\n", "$$\n", "plotted for three times ($t = 0$, $t = 0.5$, and $t=1.5$). I've set the physical constants to one." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P = 1.0\n", "nu = 1.0\n", "rho = 1.0\n", "h = 1.0\n", "n_max = 30\n", "\n", "y = np.linspace(0, h, 1000)\n", "u0 = np.zeros(1000)\n", "u1 = np.zeros(1000)\n", "u2 = np.zeros(1000)\n", "t0 = 0.0\n", "t1 = 0.5\n", "t2 = 1.5\n", "for n in range(1, n_max, 2):\n", " u0 += 1 / n**3 * np.sin(n * np.pi * y / h) * np.exp(-n**2 * t0)\n", " u1 += 1 / n**3 * np.sin(n * np.pi * y / h) * np.exp(-n**2 * t1)\n", " u2 += 1 / n**3 * np.sin(n * np.pi * y / h) * np.exp(-n**2 * t2)\n", " \n", "#u_init = 0.5 * (y - y**2)\n", "\n", "fig = plt.figure(figsize=(6, 4))\n", "plt.plot(u0, y, color=\"black\")\n", "plt.plot(u1, y, color=\"black\")\n", "plt.plot(u2, y, color=\"black\")\n", "plt.xlabel(\"$u(y, t)$\")\n", "plt.ylabel(\"$y/h$\")\n", "plt.text(0.8, 0.8, \"$t=0$\")\n", "plt.text(0.6, 0.61, \"$t=0.5$\")\n", "plt.text(0.2, 0.25, \"$t=1.5$\")\n", "plt.savefig(\"fig_poise_time.pdf\", bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Figure 2.3: An impulsively moved boudary\n", "\n", "The fluid velocity in this case is \n", "$$\n", "u(y, t) = U \\left[ 1 - \\frac{y}{h} - \\frac{2}{\\pi} \\sum_{n=1}^\\infty \\frac{1}{n} \\sin(n \\pi y / h) \\, e^{-n^2 \\pi^2 \\nu t / h^2} \\right].\n", "$$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "U = 1.0\n", "nu = 1.0\n", "h = 1.0\n", "n_max = 10\n", "\n", "y = np.linspace(0, h, 1000)\n", "u1 = np.zeros(1000)\n", "u2 = np.zeros(1000)\n", "t1 = 0.1\n", "t2 = 0.8\n", "for n in range(1, n_max, 1):\n", " u1 += 2.0 / np.pi / n * np.sin(n * np.pi * y / h) * np.exp(-n**2 * t1)\n", " u2 += 2.0 / np.pi / n * np.sin(n * np.pi * y / h) * np.exp(-n**2 * t2)\n", "u1 = U * (1 - y/h - u1)\n", "u2 = U * (1 - y/h - u2)\n", " \n", "u_ss = U * (1.0 - y/h)\n", "\n", "fig = plt.figure(figsize=(6, 4))\n", "plt.plot(u_ss, y, color=\"red\")\n", "plt.plot(u1, y, color=\"black\")\n", "plt.plot(u2, y, color=\"black\")\n", "plt.xlabel(\"$u/U$\")\n", "plt.ylabel(\"$y/h$\")\n", "plt.text(0.0, 0.1, \"$t=0.1$\")\n", "plt.text(0.35, 0.4, \"$t=0.8$\")\n", "plt.text(0.7, 0.35, \"steady-state\", color=\"red\")\n", "plt.savefig(\"fig_poise_imp.pdf\", bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Figure 2.7: Self similar flow\n", "\n", "The fluid velocity is \n", "$$\n", "u(y, t) = f(\\eta) = U\\left[ 1 - \\frac{1}{\\sqrt{\\pi}} \\int_0^\\eta e^{-\\tfrac{1}{4} \\eta'^2} d\\eta' \\right],\n", "$$\n", "where \n", "$$\n", "\\eta = \\frac{y}{\\sqrt{\\nu t}},\n", "$$\n", "and I've plotted the velocity at two different times -- and with two different scales, to show off the self-similar nature of the solution." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy import integrate\n", "\n", "U = 1.0\n", "nu = 1.0\n", "\n", "y = np.linspace(0, 10.0*np.sqrt(nu * 10), 1000)\n", "u1 = np.zeros(1000)\n", "u2 = np.zeros(1000)\n", "t1 = 1.0\n", "t2 = 10.0\n", "\n", "for i in range(len(y)):\n", " eta1 = y[i] / np.sqrt(nu * t1)\n", " eta2 = y[i] / np.sqrt(nu * t2)\n", " u1[i] = U * ( 1.0 - 1.0 / np.sqrt(np.pi) * integrate.quad(lambda x: np.exp(-0.25 * x**2), 0, eta1)[0] )\n", " u2[i] = U * ( 1.0 - 1.0 / np.sqrt(np.pi) * integrate.quad(lambda x: np.exp(-0.25 * x**2), 0, eta2)[0] )\n", "\n", "\n", "fig = plt.figure(figsize=(8, 4))\n", "ax = fig.add_subplot(1,2,1)\n", "ax.plot(u1, y, color=\"black\")\n", "ax.set_ylim(0, 10)\n", "\n", "ax.text(0.7, 8, \"$t=1$\")\n", "ax.set_xlabel(\"$u/U$\")\n", "ax.set_ylabel(\"y\")\n", "\n", "ax = fig.add_subplot(1,2,2)\n", "ax.plot(u2, y, color=\"black\")\n", "\n", "ax.set_ylim(0, 10)\n", "ax.text(0.7, 8, \"$t=10$\")\n", "ax.set_xlabel(\"$u/U$\")\n", "\n", "plt.savefig(\"fig_ss_vel1.pdf\", bbox_inches='tight')" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(8, 4))\n", "ax = fig.add_subplot(1,2,1)\n", "ax.plot(u1, y, color=\"black\")\n", "ax.set_ylim(0, 10)\n", "\n", "ax.text(0.7, 8, \"$t=1$\")\n", "ax.set_xlabel(\"$u/U$\")\n", "ax.set_ylabel(\"y\")\n", "\n", "ax = fig.add_subplot(1,2,2)\n", "ax.plot(u2, y, color=\"black\")\n", "\n", "ax.set_ylim(0, 10*np.sqrt(10))\n", "ax.text(0.7, 25, \"$t=10$\")\n", "ax.set_xlabel(\"$u/U$\")\n", "\n", "plt.savefig(\"fig_ss_vel2.pdf\", bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Figure 2.10: Bessel functions\n", "\n", "Here I plot the Bessel functions of the first and second kinds, along with printing the zeros of each." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "J_1 zeros: [ 3.83170597 7.01558667 10.17346814 13.32369194 16.47063005]\n", "Y_1 zeros: [ 2.19714133 5.42968104 8.59600587 11.74915483 14.89744213]\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.special import j1, y1, jn_zeros, yn_zeros\n", "\n", "x = np.linspace(0, 20, 1000)\n", "J = j1(x)\n", "Y = y1(x)\n", "\n", "fig = plt.figure(figsize=(6, 4))\n", "ax = fig.add_subplot(1,1,1)\n", "ax.grid(True)\n", "\n", "ax.plot(x, J, color=\"black\")\n", "ax.plot(x, Y, color=\"red\")\n", "ax.set_ylim(-2, 1)\n", "ax.set_xlabel(\"$x$\")\n", "\n", "plt.savefig(\"fig_bessel.pdf\", bbox_inches='tight')\n", "\n", "print(\"J_1 zeros: \", jn_zeros(1, 5))\n", "print(\"Y_1 zeros: \", yn_zeros(1, 5))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Figure 2.11: Spin down\n", "\n", "The fluid velocity is\n", "$$\n", "u_\\phi(s, t) = 2\\Omega a \\sum_{n=1}^\\infty \\frac{J_1(\\lambda_n s/a)}{\\lambda_n J_2(\\lambda_n)} \\, e^{-\\lambda_n^2 \\nu t / a^2}.\n", "$$\n", "It's plotted at three different times." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.special import jv\n", "\n", "Omega = 1.0\n", "a = 4.0\n", "nu = 0.01\n", "n_zeros = 100000\n", "\n", "r = np.linspace(0, 0.999*a, 1000)\n", "z = jn_zeros(1, n_zeros)\n", "\n", "t1= 0\n", "u1= 0\n", "t2 = 30\n", "t3 = 110\n", "u2 = 0\n", "u3 = 0\n", "for n in range(0,n_zeros):\n", " u1 += 2.0 * j1(z[n] * r / a) / z[n] / jv(2, z[n]) * np.exp(- z[n]**2 * nu * t1 / a**2)\n", " u2 += 2.0 * j1(z[n] * r / a) / z[n] / jv(2, z[n]) * np.exp(- z[n]**2 * nu * t2 / a**2)\n", " u3 += 2.0 * j1(z[n] * r / a) / z[n] / jv(2, z[n]) * np.exp(- z[n]**2 * nu * t3 / a**2)\n", " \n", " \n", "fig = plt.figure(figsize=(6, 4))\n", "ax = fig.add_subplot(1,1,1)\n", "\n", "ax.plot(r, u1, color=\"black\")\n", "ax.plot(r, u2, color=\"black\")\n", "ax.plot(r, u3, color=\"black\")\n", "\n", "ax.text(2.8, 0.9, \"$t=0$ s\")\n", "ax.text(3.3, 0.5, \"$t=30$ s\")\n", "ax.text(2.5, 0.05, \"$t=110$ s\")\n", "ax.set_xlabel(\"$s$ (cm)\")\n", "ax.set_ylabel(r\"$u_{\\theta} / \\Omega a$\")\n", "\n", "plt.savefig(\"fig_spin_vel.pdf\", bbox_inches='tight')\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Figure 2.13: Decay of a line vortex\n", "\n", "The fluid velocity is\n", "$$\n", "u_\\phi(s, t) = \\frac{\\Gamma_0}{2\\pi s} \\left( 1- e^{-s^2 / 4 \\nu t} \\right).\n", "$$\n", "I've also plotted the small- and large- radii behaviour of the fluid." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Gamma0 = 1.0\n", "nu = 1.0\n", "\n", "t0 = 0.0\n", "t1 = 0.1\n", "t2 = 0.7\n", "\n", "r = np.linspace(0.001, 8, 1000)\n", "u0 = Gamma0 / (2.0*np.pi * r)\n", "u1 = Gamma0 / (2.0*np.pi * r) * (1.0 - np.exp(-r**2 / (4.0 * nu * t1)))\n", "u2 = Gamma0 / (2.0*np.pi * r) * (1.0 - np.exp(-r**2 / (4.0 * nu * t2)))\n", "u_small1 = Gamma0 / (8*np.pi * nu * t1) * r\n", "u_small2 = Gamma0 / (8*np.pi * nu * t2) * r\n", "\n", "fig = plt.figure(figsize=(8, 4))\n", "\n", "ax = fig.add_subplot(1,2,1)\n", "\n", "ax.plot(r, u1, color=\"black\")\n", "ax.plot(r, u2, color=\"black\")\n", "ax.set_xlabel(\"$s$\")\n", "ax.set_ylabel(r\"$u_{\\theta}$\")\n", "\n", "ax.text(2, 0.12, \"$t=0.1$\")\n", "ax.text(2, 0.02, \"$t=0.7$\")\n", "\n", "ax = fig.add_subplot(1,2,2)\n", "ax.plot(r, u2, color=\"black\")\n", "ax.plot(r, u0, color=\"black\", ls=\"--\")\n", "ax.plot(r, u_small2, color=\"black\", ls=\"--\")\n", "ax.set_ylim(0, 0.1)\n", "ax.set_xlim(0, 5)\n", "ax.set_xlabel(\"$s$\")\n", "ax.set_ylabel(r\"$u_{\\theta}$\")\n", "\n", "fig.subplots_adjust(wspace=0.5)\n", "\n", "plt.savefig(\"fig_line_vortex.pdf\", bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Figure 2.14: Vorticity transport\n", "\n", "The vorticity for the impulsively moved boundary and the line vortex at different times, showing their evolution from infinity." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Gamma0 = 1.0\n", "nu = 1.0\n", "U = 1.0\n", "\n", "def vorticity_imp(y, t):\n", " return U / np.sqrt(np.pi * nu * t) * np.exp(-y**2 / 4.0 / nu / t)\n", "\n", "def vorticity_vortex(r, t):\n", " return Gamma0 / (4.0 * np.pi * nu * t) * np.exp(-r**2 / 4.0 / nu / t)\n", "\n", "y = np.linspace(0.001, 4, 1000)\n", "\n", "fig = plt.figure(figsize=(8, 4))\n", "\n", "ax = fig.add_subplot(1,2,1)\n", "\n", "ax.plot(y, vorticity_imp(y, 0.01), color=\"black\")\n", "ax.plot(y, vorticity_imp(y, 0.2), color=\"black\")\n", "ax.plot(y, vorticity_imp(y, 1.0), color=\"black\")\n", "ax.set_xlabel(\"$y$\")\n", "ax.set_ylabel(\"$\\omega$\")\n", "ax.set_ylim(-0.1, 2)\n", "ax.set_xlim(0, 3)\n", "\n", "ax.text(0.4, 1.7, \"$t=0.01$\")\n", "ax.text(0.8, 0.9, \"$t=0.2$\")\n", "ax.text(2.0, 0.3, \"$t=1.0$\")\n", "\n", "ax = fig.add_subplot(1,2,2)\n", "\n", "ax.plot(y, vorticity_vortex(y, 0.01), color=\"black\")\n", "ax.plot(y, vorticity_vortex(y, 0.2), color=\"black\")\n", "ax.plot(y, vorticity_vortex(y, 1.0), color=\"black\")\n", "ax.set_xlabel(\"$s$\")\n", "ax.set_ylabel(\"$\\omega$\")\n", "ax.set_ylim(-0.06, 0.7)\n", "ax.set_xlim(0, 3)\n", "\n", "ax.text(0.5, 0.6, \"$t=0.01$\")\n", "ax.text(0.8, 0.2, \"$t=0.2$\")\n", "ax.text(2.0, 0.1, \"$t=1.0$\")\n", "\n", "\n", "fig.subplots_adjust(wspace=0.5)\n", "\n", "plt.savefig(\"fig_vorticity_transport.pdf\", bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Figures 2.16: Boundary layers\n", "\n", "Here I'm solving the ODE\n", "$$\n", "f''' + ff'' - f'^2 + 1 = 0\n", "$$\n", "with boundary conditions\n", "$$\n", "f(0) = 0; \\quad f'(0) = 0; \\quad \\text{and} \\quad f'(\\infty) = 1.\n", "$$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "d_eta = 0.001\n", "eta = np.arange(0.0, 7.0, d_eta)\n", "\n", "# Here f = f, g = f', and h = f''.\n", "# h0 is the initial condition for f'' -- we have to guess the value that makes the\n", "# value of f' at infinity come out correct (it should be one). I just did it by brute force.\n", "def run_solution(h0): \n", "\n", " f = np.zeros(len(eta))\n", " g = np.zeros(len(eta))\n", " h = np.zeros(len(eta))\n", " h[0] = h0\n", "\n", " for i in range(len(eta)-1):\n", " f[i+1] = f[i] + g[i] * d_eta\n", " g[i+1] = g[i] + h[i] * d_eta\n", " h[i+1] = h[i] + (g[i]**2 - f[i] * h[i] - 1.0) * d_eta\n", " \n", " return f, g\n", "\n", "f, g = run_solution(1.2324)\n", "\n", "fig = plt.figure(figsize=(4, 4))\n", "ax = fig.add_subplot(1,1,1)\n", "ax.plot(eta, f, color='black')\n", "ax.plot(eta, g, color='red')\n", "\n", "ax.set_xlabel('$\\eta$')\n", "ax.set_ylim(-0.2, 3)\n", "ax.text(5.7, 1.2, \"$f\\'(\\eta)$\", color='red')\n", "ax.text(1.7, 2.5, \"$f(\\eta)$\")\n", "\n", "plt.savefig('fig_boundary_result1.pdf', bbox_inches='tight')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Figure 2.17: Boundary Layers\n", "\n", "Using the solution above to create a nice vector/heatmap plot to see the boundary layer." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-3, 3, 101)\n", "y = np.linspace(0, 5.0, 101)\n", "x, y = np.meshgrid(x, y)\n", "\n", "u = x * np.interp(y, eta, g)\n", "v = -np.interp(y, eta, f)\n", "\n", "U = np.sqrt(u**2 + v**2)\n", "\n", "fig = plt.figure(figsize=(8, 6))\n", "ax1 = fig.add_subplot(1,2,2)\n", "ax1.set_xlabel('$x$')\n", "ax1.set_ylabel('$y$')\n", "ax1.set_aspect('equal')\n", "#ax.quiver(x, y, u, v, pivot='middle')\n", "plt.imshow(U, extent=[-3, 3, 0, 5], origin='lower', cmap='gist_rainbow', alpha=1)\n", "#plt.colorbar(shrink=0.5)\n", "\n", "ax2 = fig.add_subplot(1,2,1)\n", "ax2.set_xlabel('$x$')\n", "ax2.set_ylabel('$y$')\n", "ax2.set_aspect('equal')\n", "#ax.quiver(x, y, x, -y, pivot='middle')\n", "plt.imshow(np.sqrt(x**2 + y**2), extent=[-3, 3, 0, 5], origin='lower', cmap='gist_rainbow', alpha=1)\n", "\n", "x = np.linspace(-3, 3, 11)\n", "y = np.linspace(0, 5.0, 11)\n", "x, y = np.meshgrid(x, y)\n", "\n", "u = x * np.interp(y, eta, g)\n", "v = -np.interp(y, eta, f)\n", "ax1.quiver(x, y, u, v, pivot='middle')\n", "ax2.quiver(x, y, x, -y, pivot='middle')\n", "\n", "\n", "plt.savefig(\"fig_boundary_result2.pdf\", bbox_inches='tight')\n" ] } ], "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": 2 }