From 3b13e56b9118e293fa3b44eb998ffccaeccf9ff8 Mon Sep 17 00:00:00 2001 From: Amiya Date: Mon, 14 Dec 2015 20:36:32 -0500 Subject: [PATCH 01/14] update 1 --- .../Rayleigh Benard Convection.ipynb | 165 ++++++++++++++++++ 1 file changed, 165 insertions(+) create mode 100644 Amiya Project/Rayleigh Benard Convection.ipynb diff --git a/Amiya Project/Rayleigh Benard Convection.ipynb b/Amiya Project/Rayleigh Benard Convection.ipynb new file mode 100644 index 0000000..e97db3b --- /dev/null +++ b/Amiya Project/Rayleigh Benard Convection.ipynb @@ -0,0 +1,165 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "from matplotlib import rcParams\n", + "rcParams['font.family'] = 'serif'\n", + "rcParams['font.size'] = 16" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "18.6070972831627 38.6070972831627\n" + ] + } + ], + "source": [ + "H = 0.25\n", + "L = 1\n", + "\n", + "alpha = 207 #Volume expansion coefficient of water @ 20 C\n", + "k = 0.6 #Thermal conductivity of water @ 20 C\n", + "v = 0.894 # viscosity of water change to matrix\n", + "\n", + "ReC = 1100.65 #Critical Rayleigh number for one free and one rigid boundary condition\n", + "g = 9.81\n", + "D = 0.143E-6 #Thermal diffusivity of water\n", + "rho_i = 1.105 #Density of water @ 20 C\n", + "R = 287 #Cp - Cv for water change later\n", + "\n", + "delT = (ReC*v*k)/(alpha*g*H**3)\n", + "nxy = 101\n", + "nt = 500\n", + "\n", + "dxy = L/(nxy-1)\n", + "\n", + "#Change to Kelivin?\n", + "To = 20\n", + "Ti = np.ones((nxy, nxy))*To\n", + "Ti[0,:] = 20 + delT\n", + "\n", + "rho = np.ones((nxy,nxy), dtype=float)*rho_i\n", + "rho[0,:] = rho_i*(1-alpha*(Ti[0,:] - To))\n", + "\n", + "pi = np.zeros((nxy,nxy), dtype=float)\n", + "pi[:,:] = Ti[:,:]*rho_i[0:,0:] * R\n", + "\n", + "ui = np.zeros((nxy,nxy), dtype=float)\n", + "\n", + "print(delT, 20+delT)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.03496503496503497\n" + ] + } + ], + "source": [ + "# stability\n", + "sigma = 0.00005\n", + "dt = sigma*min(dxy,dxy)**2/D\n", + "\n", + "print(dt)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.01\n" + ] + } + ], + "source": [ + "print(dxy)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def ftcs(T, To, u, p, rho, rho_i, alpha, k, R, nt, dt, dxy):\n", + " \n", + " for n in range(nt):\n", + " un = u.copy()\n", + " Tn = T.copy()\n", + " Pn = p.copy\n", + " \n", + " T[1:-1,1:-1] = Tn[1:-1,1:-1] + dt*((un[1:-1,1:-1]/dxy)*(Tn[2:,1:-1]\\\n", + " + Tn[1:-1,2:] - (2*Tn[1:-1,1:-1])) + \n", + " (k/dxy**2)*(Tn[2:,1:-1] + Tn[:-2,1:-1] + Tn[1:-1,2:]\\\n", + " + Tn[1:-1,:-2] - (4*Tn[1:-1,1:-1])))\n", + " \n", + " rho[1:-1,1:-1] = rho_i*(1- alpha*(T[1:-1,1:-1] - 20))\n", + " p[1:-1,1:-1] = rho[1:-1,1:-1]*T[1:-1,1:-1] * R\n", + " \n", + " \n", + " u[1:-1,1:-1] = un[1:-1,1:-1] + dt*((un[1:-1,1:-1]/dxy)*(un[2:,1:-1]\\\n", + " + un[1:-1,2:] - (2*un[1:-1,1:-1])) + \n", + " (u[1:-1,1:-1])*(un[2:,1:-1] + un[:-2,1:-1] + un[1:-1,2:]\\\n", + " + un[1:-1,:-2] - (4*un[1:-1,1:-1])) - \\\n", + " ((1/rho_i)*P[1:-1,1:-1]) + ((rho[1:-1,1:-1]/rho_i)*g))" + ] + } + ], + "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": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} From 42d37e97974781d498f44c12315d5d8d312a2340 Mon Sep 17 00:00:00 2001 From: Amiya Date: Mon, 14 Dec 2015 21:08:28 -0500 Subject: [PATCH 02/14] final project fixed equation u --- Amiya Project/Rayleigh Benard Convection.ipynb | 9 ++++----- 1 file changed, 4 insertions(+), 5 deletions(-) diff --git a/Amiya Project/Rayleigh Benard Convection.ipynb b/Amiya Project/Rayleigh Benard Convection.ipynb index e97db3b..16e0044 100644 --- a/Amiya Project/Rayleigh Benard Convection.ipynb +++ b/Amiya Project/Rayleigh Benard Convection.ipynb @@ -133,11 +133,10 @@ " p[1:-1,1:-1] = rho[1:-1,1:-1]*T[1:-1,1:-1] * R\n", " \n", " \n", - " u[1:-1,1:-1] = un[1:-1,1:-1] + dt*((un[1:-1,1:-1]/dxy)*(un[2:,1:-1]\\\n", - " + un[1:-1,2:] - (2*un[1:-1,1:-1])) + \n", - " (u[1:-1,1:-1])*(un[2:,1:-1] + un[:-2,1:-1] + un[1:-1,2:]\\\n", - " + un[1:-1,:-2] - (4*un[1:-1,1:-1])) - \\\n", - " ((1/rho_i)*P[1:-1,1:-1]) + ((rho[1:-1,1:-1]/rho_i)*g))" + " u[1:-1,1:-1] = un[1:-1,1:-1] + dt*(-(1/rho_i)*(p[2:,1:-1] + p[1:-1,2:] - 2*p[1:-1,1:-1]) + (rho[1:-1,1:-1]*g/rho_i)\\\n", + " + (u[1:-1,1:-1]/dxy)*(0.5*(u[2:,1:-1] - u[:-2,1:-1] \\\n", + " + u[1:-1,2:] - u[1:-1,:-2]) \\\n", + " + (1/dxy)*(u[2:,1:-1] + u[:-2,1:-1] + u[1:-1,2:] + u[1:-1,:-2] - 4*u[1:-1,1:-1]))" ] } ], From 82426fc45e1a0ebdf6dcdc2906c11b91d8ff158b Mon Sep 17 00:00:00 2001 From: Amiya Date: Mon, 14 Dec 2015 21:39:46 -0500 Subject: [PATCH 03/14] update pressure eqt --- .../Rayleigh Benard Convection.ipynb | 67 +++++++++++++++---- 1 file changed, 55 insertions(+), 12 deletions(-) diff --git a/Amiya Project/Rayleigh Benard Convection.ipynb b/Amiya Project/Rayleigh Benard Convection.ipynb index 16e0044..dd20831 100644 --- a/Amiya Project/Rayleigh Benard Convection.ipynb +++ b/Amiya Project/Rayleigh Benard Convection.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 3, + "execution_count": 6, "metadata": { "collapsed": false }, @@ -18,7 +18,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 11, "metadata": { "collapsed": false }, @@ -27,7 +27,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "18.6070972831627 38.6070972831627\n" + "To = 18.6070972831627 Tl = 38.6070972831627\n" ] } ], @@ -46,11 +46,18 @@ "R = 287 #Cp - Cv for water change later\n", "\n", "delT = (ReC*v*k)/(alpha*g*H**3)\n", + "\n", + "L = 1\n", + "H = 0.001\n", + "\n", "nxy = 101\n", "nt = 500\n", "\n", "dxy = L/(nxy-1)\n", "\n", + "x = np.linspace(0,L,nxy)\n", + "y = np.linspace(0,H,nxy)\n", + "\n", "#Change to Kelivin?\n", "To = 20\n", "Ti = np.ones((nxy, nxy))*To\n", @@ -60,16 +67,17 @@ "rho[0,:] = rho_i*(1-alpha*(Ti[0,:] - To))\n", "\n", "pi = np.zeros((nxy,nxy), dtype=float)\n", - "pi[:,:] = Ti[:,:]*rho_i[0:,0:] * R\n", + "pi[:,:] = Ti[:,:]*rho[0:,0:] * R\n", "\n", "ui = np.zeros((nxy,nxy), dtype=float)\n", "\n", - "print(delT, 20+delT)" + "print('To =',delT, 'Tl =',20+delT)\n", + "#print('x =', x, 'y =', y)" ] }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 12, "metadata": { "collapsed": false }, @@ -92,7 +100,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 13, "metadata": { "collapsed": false }, @@ -111,13 +119,13 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 16, "metadata": { - "collapsed": true + "collapsed": false }, "outputs": [], "source": [ - "def ftcs(T, To, u, p, rho, rho_i, alpha, k, R, nt, dt, dxy):\n", + "def ftcs(T, To, u, p, rho, rho_i, alpha, k, g, y, nt, dt, dxy):\n", " \n", " for n in range(nt):\n", " un = u.copy()\n", @@ -130,14 +138,49 @@ " + Tn[1:-1,:-2] - (4*Tn[1:-1,1:-1])))\n", " \n", " rho[1:-1,1:-1] = rho_i*(1- alpha*(T[1:-1,1:-1] - 20))\n", - " p[1:-1,1:-1] = rho[1:-1,1:-1]*T[1:-1,1:-1] * R\n", + " p[1:-1,1:-1] = rho[1:-1,1:-1]*y[1:-1,1:-1] * g\n", " \n", " \n", " u[1:-1,1:-1] = un[1:-1,1:-1] + dt*(-(1/rho_i)*(p[2:,1:-1] + p[1:-1,2:] - 2*p[1:-1,1:-1]) + (rho[1:-1,1:-1]*g/rho_i)\\\n", " + (u[1:-1,1:-1]/dxy)*(0.5*(u[2:,1:-1] - u[:-2,1:-1] \\\n", " + u[1:-1,2:] - u[1:-1,:-2]) \\\n", - " + (1/dxy)*(u[2:,1:-1] + u[:-2,1:-1] + u[1:-1,2:] + u[1:-1,:-2] - 4*u[1:-1,1:-1]))" + " + (1/dxy)*(u[2:,1:-1] + u[:-2,1:-1] + u[1:-1,2:] + u[1:-1,:-2] - 4*u[1:-1,1:-1])))\n", + " \n", + " return T" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "ename": "IndexError", + "evalue": "too many indices for array", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mIndexError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mT\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mftcs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mTi\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mTo\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mui\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mpi\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mrho\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mrho_i\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0malpha\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mg\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mnt\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mdt\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mdxy\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[1;32m\u001b[0m in \u001b[0;36mftcs\u001b[1;34m(T, To, u, p, rho, rho_i, alpha, k, g, y, nt, dt, dxy)\u001b[0m\n\u001b[0;32m 11\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 12\u001b[0m \u001b[0mrho\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mrho_i\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m-\u001b[0m \u001b[0malpha\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m-\u001b[0m \u001b[1;36m20\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 13\u001b[1;33m \u001b[0mp\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mrho\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mg\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 14\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 15\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mIndexError\u001b[0m: too many indices for array" + ] + } + ], + "source": [ + "T = ftcs(Ti,To,ui,pi,rho,rho_i,alpha,k,g,y,nt,dt,dxy)" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] } ], "metadata": { From 88609371d7c2599be146cb8633e127163c739a0f Mon Sep 17 00:00:00 2001 From: Amiya Date: Mon, 14 Dec 2015 21:52:01 -0500 Subject: [PATCH 04/14] time loop done --- .../Rayleigh Benard Convection.ipynb | 64 ++++++++++++++----- 1 file changed, 47 insertions(+), 17 deletions(-) diff --git a/Amiya Project/Rayleigh Benard Convection.ipynb b/Amiya Project/Rayleigh Benard Convection.ipynb index dd20831..cdd9fbe 100644 --- a/Amiya Project/Rayleigh Benard Convection.ipynb +++ b/Amiya Project/Rayleigh Benard Convection.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 6, + "execution_count": 8, "metadata": { "collapsed": false }, @@ -11,14 +11,14 @@ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", - "from matplotlib import rcParams\n", + "from matplotlib import rcParams, cm\n", "rcParams['font.family'] = 'serif'\n", "rcParams['font.size'] = 16" ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 9, "metadata": { "collapsed": false }, @@ -77,7 +77,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 10, "metadata": { "collapsed": false }, @@ -100,7 +100,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 11, "metadata": { "collapsed": false }, @@ -119,7 +119,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 12, "metadata": { "collapsed": false }, @@ -138,7 +138,7 @@ " + Tn[1:-1,:-2] - (4*Tn[1:-1,1:-1])))\n", " \n", " rho[1:-1,1:-1] = rho_i*(1- alpha*(T[1:-1,1:-1] - 20))\n", - " p[1:-1,1:-1] = rho[1:-1,1:-1]*y[1:-1,1:-1] * g\n", + " p[1:-1,1:-1] = rho[1:-1,1:-1]*y[1:-1] * g\n", " \n", " \n", " u[1:-1,1:-1] = un[1:-1,1:-1] + dt*(-(1/rho_i)*(p[2:,1:-1] + p[1:-1,2:] - 2*p[1:-1,1:-1]) + (rho[1:-1,1:-1]*g/rho_i)\\\n", @@ -151,21 +151,25 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { - "ename": "IndexError", - "evalue": "too many indices for array", - "output_type": "error", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[1;31mIndexError\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mT\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mftcs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mTi\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mTo\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mui\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mpi\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mrho\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mrho_i\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0malpha\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mg\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mnt\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mdt\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mdxy\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", - "\u001b[1;32m\u001b[0m in \u001b[0;36mftcs\u001b[1;34m(T, To, u, p, rho, rho_i, alpha, k, g, y, nt, dt, dxy)\u001b[0m\n\u001b[0;32m 11\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 12\u001b[0m \u001b[0mrho\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mrho_i\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m-\u001b[0m \u001b[0malpha\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m-\u001b[0m \u001b[1;36m20\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 13\u001b[1;33m \u001b[0mp\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mrho\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mg\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 14\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 15\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;31mIndexError\u001b[0m: too many indices for array" + "name": "stderr", + "output_type": "stream", + "text": [ + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:8: RuntimeWarning: overflow encountered in multiply\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:16: RuntimeWarning: invalid value encountered in add\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:16: RuntimeWarning: invalid value encountered in subtract\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:16: RuntimeWarning: overflow encountered in multiply\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:8: RuntimeWarning: invalid value encountered in add\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:8: RuntimeWarning: invalid value encountered in subtract\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:8: RuntimeWarning: invalid value encountered in multiply\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:10: RuntimeWarning: invalid value encountered in add\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:10: RuntimeWarning: invalid value encountered in subtract\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:12: RuntimeWarning: overflow encountered in multiply\n" ] } ], @@ -173,6 +177,32 @@ "T = ftcs(Ti,To,ui,pi,rho,rho_i,alpha,k,g,y,nt,dt,dxy)" ] }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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2Bz4LFHZGt15E5CTAzMysDUlaMyJeq/HVTOAAYHdgIXBTfrW9gA1yzMWSXgYmR8RP6tXh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\nlJMAMzOzkvr/WvLbO/LWIbsAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(8,5))\n", + "plt.contourf(x,y,T,20,cmap=cm.viridis)\n", + "plt.xlabel('$x$')\n", + "plt.ylabel('$y$')\n", + "plt.colorbar();\n" + ] + }, { "cell_type": "code", "execution_count": null, From 5db7707a6f1a2b159b068de8d794de6233c554d8 Mon Sep 17 00:00:00 2001 From: Amiya Date: Mon, 14 Dec 2015 23:20:03 -0500 Subject: [PATCH 05/14] update changed viscosity --- .../Rayleigh Benard Convection.ipynb | 99 +++++++++++++------ 1 file changed, 70 insertions(+), 29 deletions(-) diff --git a/Amiya Project/Rayleigh Benard Convection.ipynb b/Amiya Project/Rayleigh Benard Convection.ipynb index cdd9fbe..f3413a9 100644 --- a/Amiya Project/Rayleigh Benard Convection.ipynb +++ b/Amiya Project/Rayleigh Benard Convection.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 8, + "execution_count": 32, "metadata": { "collapsed": false }, @@ -18,7 +18,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 33, "metadata": { "collapsed": false }, @@ -27,7 +27,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "To = 18.6070972831627 Tl = 38.6070972831627\n" + "To = 326968.748019503 Tl = 326988.748019503\n" ] } ], @@ -37,7 +37,6 @@ "\n", "alpha = 207 #Volume expansion coefficient of water @ 20 C\n", "k = 0.6 #Thermal conductivity of water @ 20 C\n", - "v = 0.894 # viscosity of water change to matrix\n", "\n", "ReC = 1100.65 #Critical Rayleigh number for one free and one rigid boundary condition\n", "g = 9.81\n", @@ -45,8 +44,6 @@ "rho_i = 1.105 #Density of water @ 20 C\n", "R = 287 #Cp - Cv for water change later\n", "\n", - "delT = (ReC*v*k)/(alpha*g*H**3)\n", - "\n", "L = 1\n", "H = 0.001\n", "\n", @@ -60,9 +57,13 @@ "\n", "#Change to Kelivin?\n", "To = 20\n", + "vo = 2.414*10**(-5) * 10**(247.8/(To + 273 - 140)) #initial kinematic viscosity of water\n", + "delT = (ReC*vo*k)/(alpha*g*H**3)\n", "Ti = np.ones((nxy, nxy))*To\n", "Ti[0,:] = 20 + delT\n", "\n", + "v = np.ones((nxy,nxy))*2.414*10**(-5) * 10**(247.8/(Ti + 273 - 140)) #viscosity of water\n", + "\n", "rho = np.ones((nxy,nxy), dtype=float)*rho_i\n", "rho[0,:] = rho_i*(1-alpha*(Ti[0,:] - To))\n", "\n", @@ -77,7 +78,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 34, "metadata": { "collapsed": false }, @@ -100,7 +101,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 35, "metadata": { "collapsed": false }, @@ -119,19 +120,26 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [], "source": [ - "def ftcs(T, To, u, p, rho, rho_i, alpha, k, g, y, nt, dt, dxy):\n", + "def ftcs(T, To, u, p, rho, rho_i, alpha, v, k, g, y, delT, nt, dt, dxy):\n", " \n", " for n in range(nt):\n", + " \n", + " # Boundary conditions\n", + " u[-1,:] = 0 #Top Boundary\n", + " u[0,:] = 0 #Bottom Boundary\n", + " T[0,:] = To + delT #Top Boundary\n", + " T[-1,:] = To #Bottom Boundary\n", + "\n", " un = u.copy()\n", " Tn = T.copy()\n", - " Pn = p.copy\n", - " \n", + " pn = p.copy()\n", + " vn = v.copy()\n", " T[1:-1,1:-1] = Tn[1:-1,1:-1] + dt*((un[1:-1,1:-1]/dxy)*(Tn[2:,1:-1]\\\n", " + Tn[1:-1,2:] - (2*Tn[1:-1,1:-1])) + \n", " (k/dxy**2)*(Tn[2:,1:-1] + Tn[:-2,1:-1] + Tn[1:-1,2:]\\\n", @@ -142,16 +150,17 @@ " \n", " \n", " u[1:-1,1:-1] = un[1:-1,1:-1] + dt*(-(1/rho_i)*(p[2:,1:-1] + p[1:-1,2:] - 2*p[1:-1,1:-1]) + (rho[1:-1,1:-1]*g/rho_i)\\\n", - " + (u[1:-1,1:-1]/dxy)*(0.5*(u[2:,1:-1] - u[:-2,1:-1] \\\n", + " + (1/dxy)*(u[1:-1,1:-1]*0.5*(u[2:,1:-1] - u[:-2,1:-1] \\\n", " + u[1:-1,2:] - u[1:-1,:-2]) \\\n", - " + (1/dxy)*(u[2:,1:-1] + u[:-2,1:-1] + u[1:-1,2:] + u[1:-1,:-2] - 4*u[1:-1,1:-1])))\n", + " + (v[1:-1,1:-1]/dxy)*(u[2:,1:-1] + u[:-2,1:-1] + u[1:-1,2:] + u[1:-1,:-2] - 4*u[1:-1,1:-1])))\n", + "\n", " \n", " return T" ] }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 37, "metadata": { "collapsed": false }, @@ -160,35 +169,36 @@ "name": "stderr", "output_type": "stream", "text": [ - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:8: RuntimeWarning: overflow encountered in multiply\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:16: RuntimeWarning: invalid value encountered in add\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:16: RuntimeWarning: invalid value encountered in subtract\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:16: RuntimeWarning: overflow encountered in multiply\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:8: RuntimeWarning: invalid value encountered in add\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:8: RuntimeWarning: invalid value encountered in subtract\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:8: RuntimeWarning: invalid value encountered in multiply\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:10: RuntimeWarning: invalid value encountered in add\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:10: RuntimeWarning: invalid value encountered in subtract\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:12: RuntimeWarning: overflow encountered in multiply\n" + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:15: RuntimeWarning: overflow encountered in multiply\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:23: RuntimeWarning: invalid value encountered in subtract\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:23: RuntimeWarning: overflow encountered in multiply\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:23: RuntimeWarning: invalid value encountered in add\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:15: RuntimeWarning: invalid value encountered in subtract\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:17: RuntimeWarning: invalid value encountered in add\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:17: RuntimeWarning: invalid value encountered in subtract\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:15: RuntimeWarning: invalid value encountered in add\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:15: RuntimeWarning: invalid value encountered in multiply\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:19: RuntimeWarning: overflow encountered in multiply\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:17: RuntimeWarning: overflow encountered in multiply\n" ] } ], "source": [ - "T = ftcs(Ti,To,ui,pi,rho,rho_i,alpha,k,g,y,nt,dt,dxy)" + "T = ftcs(Ti,To,ui,pi,rho,rho_i,alpha,v,k,g,y,delT,nt,dt,dxy)" ] }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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2Bz4LFHZGt15E5CTAzMysDUlaMyJeq/HVTOAAYHdgIXBTfrW9gA1yzMWSXgYmR8RP6tXh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\nlJMAMzOzkvr/WvLbO/LWIbsAAAAASUVORK5CYII=\n", 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sh/VqC83MzDZDko4BfgLsA0QX2Q5JMyQ9IOkXkuZKOr2UGSBpqqTH8uv3SRrd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\nEXFUfr5jPt7lEXFBIXc7sHc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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -203,6 +213,37 @@ "plt.colorbar();\n" ] }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 3.26988748e+05 3.26988748e+05 3.26988748e+05 ..., 3.26988748e+05\n", + " 3.26988748e+05 3.26988748e+05]\n", + " [ 2.00000000e+01 nan nan ..., nan\n", + " nan 2.00000000e+01]\n", + " [ 2.00000000e+01 nan nan ..., nan\n", + " nan 2.00000000e+01]\n", + " ..., \n", + " [ 2.00000000e+01 nan nan ..., nan\n", + " nan 2.00000000e+01]\n", + " [ 2.00000000e+01 nan nan ..., nan\n", + " nan 2.00000000e+01]\n", + " [ 2.00000000e+01 2.00000000e+01 2.00000000e+01 ..., 2.00000000e+01\n", + " 2.00000000e+01 2.00000000e+01]]\n" + ] + } + ], + "source": [ + "print(T)" + ] + }, { "cell_type": "code", "execution_count": null, From 41b91798618a8d683e0aba6247a66c9223d7a583 Mon Sep 17 00:00:00 2001 From: Amiya Date: Mon, 14 Dec 2015 23:50:04 -0500 Subject: [PATCH 06/14] fixed viscosity eqtn --- .../Rayleigh Benard Convection.ipynb | 75 +++++++++---------- 1 file changed, 37 insertions(+), 38 deletions(-) diff --git a/Amiya Project/Rayleigh Benard Convection.ipynb b/Amiya Project/Rayleigh Benard Convection.ipynb index f3413a9..5534628 100644 --- a/Amiya Project/Rayleigh Benard Convection.ipynb +++ b/Amiya Project/Rayleigh Benard Convection.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 32, + "execution_count": 31, "metadata": { "collapsed": false }, @@ -18,7 +18,7 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 32, "metadata": { "collapsed": false }, @@ -27,7 +27,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "To = 326968.748019503 Tl = 326988.748019503\n" + "delT = 0.0001209287767702047 Tl = 20.00012092877677\n", + "1.0054144180571545e-06\n" ] } ], @@ -38,11 +39,11 @@ "alpha = 207 #Volume expansion coefficient of water @ 20 C\n", "k = 0.6 #Thermal conductivity of water @ 20 C\n", "\n", - "ReC = 1100.65 #Critical Rayleigh number for one free and one rigid boundary condition\n", + "#ReC = 1100.65 #Critical Rayleigh number for one free and one rigid boundary condition\n", + "ReC = 1708 #Critical Rayleigh number for two rigid body boundary condition\n", "g = 9.81\n", "D = 0.143E-6 #Thermal diffusivity of water\n", - "rho_i = 1.105 #Density of water @ 20 C\n", - "R = 287 #Cp - Cv for water change later\n", + "rho_i = 1000 #Density of water @ 20 C\n", "\n", "L = 1\n", "H = 0.001\n", @@ -57,28 +58,29 @@ "\n", "#Change to Kelivin?\n", "To = 20\n", - "vo = 2.414*10**(-5) * 10**(247.8/(To + 273 - 140)) #initial kinematic viscosity of water\n", - "delT = (ReC*vo*k)/(alpha*g*H**3)\n", + "vo = 2.414*10**(-5) * 10**(247.8/(To + 273 - 140)) / rho_i #initial kinematic viscosity of water\n", + "delT = (ReC*vo*1.43*10**(-7))/(alpha*g*H**3)\n", "Ti = np.ones((nxy, nxy))*To\n", "Ti[0,:] = 20 + delT\n", "\n", - "v = np.ones((nxy,nxy))*2.414*10**(-5) * 10**(247.8/(Ti + 273 - 140)) #viscosity of water\n", - "\n", "rho = np.ones((nxy,nxy), dtype=float)*rho_i\n", "rho[0,:] = rho_i*(1-alpha*(Ti[0,:] - To))\n", "\n", + "v = np.ones((nxy,nxy))*2.414*10**(-5) * 10**(247.8/(Ti + 273 - 140)) / rho #kinematic viscosity of water\n", + "\n", "pi = np.zeros((nxy,nxy), dtype=float)\n", "pi[:,:] = Ti[:,:]*rho[0:,0:] * R\n", "\n", "ui = np.zeros((nxy,nxy), dtype=float)\n", "\n", - "print('To =',delT, 'Tl =',20+delT)\n", + "print('delT =',delT, 'Tl =',20+delT)\n", + "print(vo)\n", "#print('x =', x, 'y =', y)" ] }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 33, "metadata": { "collapsed": false }, @@ -101,7 +103,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 34, "metadata": { "collapsed": false }, @@ -120,7 +122,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 35, "metadata": { "collapsed": false }, @@ -160,7 +162,7 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 36, "metadata": { "collapsed": false }, @@ -169,17 +171,15 @@ "name": "stderr", "output_type": "stream", "text": [ - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:15: RuntimeWarning: overflow encountered in multiply\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:23: RuntimeWarning: invalid value encountered in subtract\n", "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:23: RuntimeWarning: overflow encountered in multiply\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:15: RuntimeWarning: overflow encountered in multiply\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:15: RuntimeWarning: invalid value encountered in multiply\n", "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:23: RuntimeWarning: invalid value encountered in add\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:23: RuntimeWarning: invalid value encountered in subtract\n", + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:15: RuntimeWarning: invalid value encountered in add\n", "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:15: RuntimeWarning: invalid value encountered in subtract\n", "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:17: RuntimeWarning: invalid value encountered in add\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:17: RuntimeWarning: invalid value encountered in subtract\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:15: RuntimeWarning: invalid value encountered in add\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:15: RuntimeWarning: invalid value encountered in multiply\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:19: RuntimeWarning: overflow encountered in multiply\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:17: RuntimeWarning: overflow encountered in multiply\n" + "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:17: RuntimeWarning: invalid value encountered in subtract\n" ] } ], @@ -189,16 +189,16 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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sh/VqC83MzDZDko4BfgLsA0QX2Q5JMyQ9IOkXkuZKOr2UGSBpqqTH8uv3SRrd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\nA6uBWyQ9LOlnwFfya5/L287t1ZZWoyd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NiCPy521ye9+JiHMLcbcC/XOSgiQB84A7IuL4Qtwk4HPAuyNimaQDclsfK/XnbmBIRGxb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\nm9apu7jKPaCF+b1vIY4qx1lI+sU0Eld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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -215,7 +215,7 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 38, "metadata": { "collapsed": false }, @@ -224,19 +224,18 @@ "name": "stdout", "output_type": "stream", "text": [ - "[[ 3.26988748e+05 3.26988748e+05 3.26988748e+05 ..., 3.26988748e+05\n", - " 3.26988748e+05 3.26988748e+05]\n", - " [ 2.00000000e+01 nan nan ..., nan\n", - " nan 2.00000000e+01]\n", - " [ 2.00000000e+01 nan nan ..., nan\n", - " nan 2.00000000e+01]\n", + "[[ 20.00012093 20.00012093 20.00012093 ..., 20.00012093 20.00012093\n", + " 20.00012093]\n", + " [ 20. nan nan ..., nan nan\n", + " 20. ]\n", + " [ 20. nan nan ..., nan nan\n", + " 20. ]\n", " ..., \n", - " [ 2.00000000e+01 nan nan ..., nan\n", - " nan 2.00000000e+01]\n", - " [ 2.00000000e+01 nan nan ..., nan\n", - " nan 2.00000000e+01]\n", - " [ 2.00000000e+01 2.00000000e+01 2.00000000e+01 ..., 2.00000000e+01\n", - " 2.00000000e+01 2.00000000e+01]]\n" + " [ 20. nan nan ..., nan nan\n", + " 20. ]\n", + " [ 20. nan nan ..., nan nan\n", + " 20. ]\n", + " [ 20. 20. 20. ..., 20. 20. 20. ]]\n" ] } ], From 5ad2a211a4fbe1778d9ee6c6575e1711308d7660 Mon Sep 17 00:00:00 2001 From: Amiya Date: Tue, 15 Dec 2015 00:26:22 -0500 Subject: [PATCH 07/14] fixed alpha --- .../Rayleigh Benard Convection.ipynb | 76 +++++++------------ 1 file changed, 29 insertions(+), 47 deletions(-) diff --git a/Amiya Project/Rayleigh Benard Convection.ipynb b/Amiya Project/Rayleigh Benard Convection.ipynb index 5534628..319820c 100644 --- a/Amiya Project/Rayleigh Benard Convection.ipynb +++ b/Amiya Project/Rayleigh Benard Convection.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 31, + "execution_count": 69, "metadata": { "collapsed": false }, @@ -18,7 +18,7 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 70, "metadata": { "collapsed": false }, @@ -27,7 +27,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "delT = 0.0001209287767702047 Tl = 20.00012092877677\n", + "delT = 1.209287767702047e-07 Tl = 20.000000120928778\n", "1.0054144180571545e-06\n" ] } @@ -36,7 +36,7 @@ "H = 0.25\n", "L = 1\n", "\n", - "alpha = 207 #Volume expansion coefficient of water @ 20 C\n", + "alpha = 207*10**(-6) #Volume expansion coefficient of water @ 20 C\n", "k = 0.6 #Thermal conductivity of water @ 20 C\n", "\n", "#ReC = 1100.65 #Critical Rayleigh number for one free and one rigid boundary condition\n", @@ -45,8 +45,8 @@ "D = 0.143E-6 #Thermal diffusivity of water\n", "rho_i = 1000 #Density of water @ 20 C\n", "\n", - "L = 1\n", - "H = 0.001\n", + "L = 10\n", + "H = 1\n", "\n", "nxy = 101\n", "nt = 500\n", @@ -61,7 +61,7 @@ "vo = 2.414*10**(-5) * 10**(247.8/(To + 273 - 140)) / rho_i #initial kinematic viscosity of water\n", "delT = (ReC*vo*1.43*10**(-7))/(alpha*g*H**3)\n", "Ti = np.ones((nxy, nxy))*To\n", - "Ti[0,:] = 20 + delT\n", + "Ti[-1,:] = To + 30\n", "\n", "rho = np.ones((nxy,nxy), dtype=float)*rho_i\n", "rho[0,:] = rho_i*(1-alpha*(Ti[0,:] - To))\n", @@ -69,7 +69,7 @@ "v = np.ones((nxy,nxy))*2.414*10**(-5) * 10**(247.8/(Ti + 273 - 140)) / rho #kinematic viscosity of water\n", "\n", "pi = np.zeros((nxy,nxy), dtype=float)\n", - "pi[:,:] = Ti[:,:]*rho[0:,0:] * R\n", + "pi[:,:] = rho[:,:] * y[:] * g\n", "\n", "ui = np.zeros((nxy,nxy), dtype=float)\n", "\n", @@ -80,7 +80,7 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 71, "metadata": { "collapsed": false }, @@ -89,21 +89,22 @@ "name": "stdout", "output_type": "stream", "text": [ - "0.03496503496503497\n" + "0.001\n" ] } ], "source": [ "# stability\n", "sigma = 0.00005\n", - "dt = sigma*min(dxy,dxy)**2/D\n", + "#dt = sigma*min(dxy,dxy)**2/D\n", + "dt = 0.001\n", "\n", "print(dt)" ] }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 72, "metadata": { "collapsed": false }, @@ -112,7 +113,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "0.01\n" + "0.1\n" ] } ], @@ -122,7 +123,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 73, "metadata": { "collapsed": false }, @@ -135,8 +136,8 @@ " # Boundary conditions\n", " u[-1,:] = 0 #Top Boundary\n", " u[0,:] = 0 #Bottom Boundary\n", - " T[0,:] = To + delT #Top Boundary\n", - " T[-1,:] = To #Bottom Boundary\n", + " T[-1,:] = To + 30 #Bottom Boundary\n", + " T[0,:] = To #top Boundary\n", "\n", " un = u.copy()\n", " Tn = T.copy()\n", @@ -162,43 +163,27 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 74, "metadata": { "collapsed": false }, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:23: RuntimeWarning: overflow encountered in multiply\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:15: RuntimeWarning: overflow encountered in multiply\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:15: RuntimeWarning: invalid value encountered in multiply\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:23: RuntimeWarning: invalid value encountered in add\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:23: RuntimeWarning: invalid value encountered in subtract\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:15: RuntimeWarning: invalid value encountered in add\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:15: RuntimeWarning: invalid value encountered in subtract\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:17: RuntimeWarning: invalid value encountered in add\n", - "C:\\Users\\amiya\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:17: RuntimeWarning: invalid value encountered in subtract\n" - ] - } - ], + "outputs": [], "source": [ "T = ftcs(Ti,To,ui,pi,rho,rho_i,alpha,v,k,g,y,delT,nt,dt,dxy)" ] }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 75, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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NiCPy521ye9+JiHMLcbcC/XOSgiQB84A7IuL4Qtwk4HPAuyNimaQDclsfK/XnbmBIRGxb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\nm9apu7jKPaCF+b1vIY4qx1lI+sU0Eld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qBfqw51scyA56s4lttGFc+HUKhHZNs/CGxgEOEyfEJ3pvfBRqoTH0hxMRv5X0I+ATkq6P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\nFeYgNzMzqzAHuZmZWYU5yM3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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -215,7 +200,7 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 76, "metadata": { "collapsed": false }, @@ -224,18 +209,15 @@ "name": "stdout", "output_type": "stream", "text": [ - "[[ 20.00012093 20.00012093 20.00012093 ..., 20.00012093 20.00012093\n", - " 20.00012093]\n", - " [ 20. nan nan ..., nan nan\n", - " 20. ]\n", - " [ 20. nan nan ..., nan nan\n", - " 20. ]\n", + "[[ 20. 20. 20. ..., 20. 20. 20. ]\n", + " [ 20. 20. 20. ..., 20. 20. 20. ]\n", + " [ 20. 20. 20. ..., 20. 20. 20. ]\n", " ..., \n", - " [ 20. nan nan ..., nan nan\n", + " [ 20. 34.04182049 41.00887689 ..., 34.97558313 28.83395561\n", " 20. ]\n", - " [ 20. nan nan ..., nan nan\n", + " [ 20. 38.13235576 44.41729127 ..., 41.14160358 34.99409619\n", " 20. ]\n", - " [ 20. 20. 20. ..., 20. 20. 20. ]]\n" + " [ 50. 50. 50. ..., 50. 50. 50. ]]\n" ] } ], From 7a6b32ea4e4f75b0440f3b367a710eaddfcf3d33 Mon Sep 17 00:00:00 2001 From: Amiya Date: Tue, 15 Dec 2015 01:36:00 -0500 Subject: [PATCH 08/14] Fixed BCs --- .../Rayleigh Benard Convection.ipynb | 182 +++++++++++++++--- 1 file changed, 157 insertions(+), 25 deletions(-) diff --git a/Amiya Project/Rayleigh Benard Convection.ipynb b/Amiya Project/Rayleigh Benard Convection.ipynb index 319820c..e706e21 100644 --- a/Amiya Project/Rayleigh Benard Convection.ipynb +++ b/Amiya Project/Rayleigh Benard Convection.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 69, + "execution_count": 238, "metadata": { "collapsed": false }, @@ -18,7 +18,7 @@ }, { "cell_type": "code", - "execution_count": 70, + "execution_count": 239, "metadata": { "collapsed": false }, @@ -27,7 +27,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "delT = 1.209287767702047e-07 Tl = 20.000000120928778\n", + "delT = 0.12092877677020468 Tl = 20.120928776770203\n", "1.0054144180571545e-06\n" ] } @@ -46,7 +46,7 @@ "rho_i = 1000 #Density of water @ 20 C\n", "\n", "L = 10\n", - "H = 1\n", + "H = 0.01\n", "\n", "nxy = 101\n", "nt = 500\n", @@ -55,7 +55,9 @@ "\n", "x = np.linspace(0,L,nxy)\n", "y = np.linspace(0,H,nxy)\n", - "\n", + "ya = np.ones((nxy,nxy))\n", + "for i in range(nxy):\n", + " ya[:,i] = y\n", "#Change to Kelivin?\n", "To = 20\n", "vo = 2.414*10**(-5) * 10**(247.8/(To + 273 - 140)) / rho_i #initial kinematic viscosity of water\n", @@ -69,7 +71,7 @@ "v = np.ones((nxy,nxy))*2.414*10**(-5) * 10**(247.8/(Ti + 273 - 140)) / rho #kinematic viscosity of water\n", "\n", "pi = np.zeros((nxy,nxy), dtype=float)\n", - "pi[:,:] = rho[:,:] * y[:] * g\n", + "pi[:,:] = rho[:,:] * ya[:,:] * g\n", "\n", "ui = np.zeros((nxy,nxy), dtype=float)\n", "\n", @@ -80,7 +82,7 @@ }, { "cell_type": "code", - "execution_count": 71, + "execution_count": 240, "metadata": { "collapsed": false }, @@ -104,7 +106,7 @@ }, { "cell_type": "code", - "execution_count": 72, + "execution_count": 241, "metadata": { "collapsed": false }, @@ -123,7 +125,7 @@ }, { "cell_type": "code", - "execution_count": 73, + "execution_count": 242, "metadata": { "collapsed": false }, @@ -136,8 +138,8 @@ " # Boundary conditions\n", " u[-1,:] = 0 #Top Boundary\n", " u[0,:] = 0 #Bottom Boundary\n", - " T[-1,:] = To + 30 #Bottom Boundary\n", - " T[0,:] = To #top Boundary\n", + " T[0,:] = To + 30 #Bottom Boundary\n", + " T[-1,:] = To #top Boundary\n", "\n", " un = u.copy()\n", " Tn = T.copy()\n", @@ -149,8 +151,9 @@ " + Tn[1:-1,:-2] - (4*Tn[1:-1,1:-1])))\n", " \n", " rho[1:-1,1:-1] = rho_i*(1- alpha*(T[1:-1,1:-1] - 20))\n", - " p[1:-1,1:-1] = rho[1:-1,1:-1]*y[1:-1] * g\n", + " p[1:-1,1:-1] = rho[1:-1,1:-1]*ya[1:-1,1:-1] * g\n", " \n", + " v[1:-1,1:-1] = 2.414*10**(-5) * 10**(247.8/(T[1:-1,1:-1] + 273 - 140)) / rho[1:-1,1:-1]\n", " \n", " u[1:-1,1:-1] = un[1:-1,1:-1] + dt*(-(1/rho_i)*(p[2:,1:-1] + p[1:-1,2:] - 2*p[1:-1,1:-1]) + (rho[1:-1,1:-1]*g/rho_i)\\\n", " + (1/dxy)*(u[1:-1,1:-1]*0.5*(u[2:,1:-1] - u[:-2,1:-1] \\\n", @@ -163,7 +166,7 @@ }, { "cell_type": "code", - "execution_count": 74, + "execution_count": 243, "metadata": { "collapsed": false }, @@ -174,16 +177,16 @@ }, { "cell_type": "code", - "execution_count": 75, + "execution_count": 244, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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yMzOzCnOQm5mZVZiD3MzMrMIc5GZmZhXmIDczM6swryM3M7OeM7Ci5SXKe4Z7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\nrkJggg==\n", 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zMytUehMlMzOzdcHgl6PqJnSNewzMzMys4MTAzMzMCk4MzMzMrODEwMzMzApO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\nZmZmhf8fspCfXfWGFQ4AAAAASUVORK5CYII=\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -192,7 +195,7 @@ ], "source": [ "plt.figure(figsize=(8,5))\n", - "plt.contourf(x,y,T,20,cmap=cm.viridis)\n", + "plt.contourf(x,y,Ti,20,cmap=cm.viridis)\n", "plt.xlabel('$x$')\n", "plt.ylabel('$y$')\n", "plt.colorbar();\n" @@ -200,7 +203,7 @@ }, { "cell_type": "code", - "execution_count": 76, + "execution_count": 245, "metadata": { "collapsed": false }, @@ -209,15 +212,15 @@ "name": "stdout", "output_type": "stream", "text": [ - "[[ 20. 20. 20. ..., 20. 20. 20. ]\n", - " [ 20. 20. 20. ..., 20. 20. 20. ]\n", - " [ 20. 20. 20. ..., 20. 20. 20. ]\n", - " ..., \n", - " [ 20. 34.04182049 41.00887689 ..., 34.97558313 28.83395561\n", + "[[ 50. 50. 50. ..., 50. 50. 50. ]\n", + " [ 20. 31.24606041 35.92810255 ..., 35.63953431 31.71920868\n", " 20. ]\n", - " [ 20. 38.13235576 44.41729127 ..., 41.14160358 34.99409619\n", + " [ 20. 25.96178197 28.87450968 ..., 28.46203708 25.33425292\n", " 20. ]\n", - " [ 50. 50. 50. ..., 50. 50. 50. ]]\n" + " ..., \n", + " [ 20. 20. 20. ..., 20. 20. 20. ]\n", + " [ 20. 20. 20. ..., 20. 20. 20. ]\n", + " [ 20. 20. 20. ..., 20. 20. 20. ]]\n" ] } ], @@ -225,6 +228,135 @@ "print(T)" ] }, + { + "cell_type": "code", + "execution_count": 246, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "102\n" + ] + } + ], + "source": [ + "print(ui.argmax())" + ] + }, + { + "cell_type": "code", + "execution_count": 247, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "61.216268941\n" + ] + } + ], + "source": [ + "print(ui[1,3])" + ] + }, + { + "cell_type": "code", + "execution_count": 248, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "102\n" + ] + } + ], + "source": [ + "def find_nearest(array,value):\n", + " idx = (np.abs(array-value)).argmin()\n", + " return idx\n", + "\n", + "value = 900\n", + "\n", + "loc = find_nearest(ui, value)\n", + "print(loc)" + ] + }, + { + "cell_type": "code", + "execution_count": 249, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "830.033812255\n" + ] + } + ], + "source": [ + "print(np.abs(ui-900).min())" + ] + }, + { + "cell_type": "code", + "execution_count": 250, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(array([1], dtype=int64), array([1], dtype=int64))\n" + ] + } + ], + "source": [ + "print(np.where(ui==900-np.abs(ui-900).min()))" + ] + }, + { + "cell_type": "code", + "execution_count": 251, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0. 0. 0. ..., 0. 0. 0. ]\n", + " [ 0. 69.96618775 0.35068574 ..., 2.53918912 1.3582699 0. ]\n", + " [ 0. 0.35718329 2.76598709 ..., 1.53694795 1.09842556\n", + " 0. ]\n", + " ..., \n", + " [ 0. 2.54165246 1.53732047 ..., 1.5593685 1.0969332 0. ]\n", + " [ 0. 1.35954534 1.09874381 ..., 1.0969332 0.89407909\n", + " 0. ]\n", + " [ 0. 0. 0. ..., 0. 0. 0. ]]\n" + ] + } + ], + "source": [ + "print(ui)" + ] + }, { "cell_type": "code", "execution_count": null, From 512603cac1f89716de531a9b7e06bddc7ed0b2f5 Mon Sep 17 00:00:00 2001 From: Amiya Date: Tue, 15 Dec 2015 03:13:18 -0500 Subject: [PATCH 09/14] notebook --- .../Rayleigh Benard Convection-Notebook.ipynb | 472 ++++++++++++++++++ .../Rayleigh Benard Convection.ipynb | 82 +-- Amiya Project/images/Benard cells 3D.PNG | Bin 0 -> 721930 bytes .../B\303\251nard_cells_convection.ogv.jpg" | Bin 0 -> 13470 bytes Amiya Project/images/Set-up.PNG | Bin 0 -> 16247 bytes 5 files changed, 515 insertions(+), 39 deletions(-) create mode 100644 Amiya Project/Rayleigh Benard Convection-Notebook.ipynb create mode 100644 Amiya Project/images/Benard cells 3D.PNG create mode 100644 "Amiya Project/images/B\303\251nard_cells_convection.ogv.jpg" create mode 100644 Amiya Project/images/Set-up.PNG diff --git a/Amiya Project/Rayleigh Benard Convection-Notebook.ipynb b/Amiya Project/Rayleigh Benard Convection-Notebook.ipynb new file mode 100644 index 0000000..22a0717 --- /dev/null +++ b/Amiya Project/Rayleigh Benard Convection-Notebook.ipynb @@ -0,0 +1,472 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Rayleigh-Benard Convection" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Natural convection is a mechanism where motion is induced in a fluid, not \n", + "through artificial means but by the effects of bouyancy. One of the most commonly studied convection phenomenon, is the Rayleigh-Benard convection. When a thin layer of fluid is heated from below, once the temperature difference, between the top and bottom fluid layers, grows large enough, convection cells, also called Benard cells, form within the fluid. As a result, some interesting patterns can be observed in the fluid.\n", + "\n", + "![alt text](images/Bénard_cells_convection.ogv.jpg)\n", + "\n", + "In the 1900s, Henri Benard studied convection by heating a thin layer of fluid from below. Benard's experiments attempted to emulate a layer of fluid that was infinitely long.\n", + "\n", + "Inspired by Benard's experiments, in 1916, Lord Rayleigh.....Rayleigh was more interested in the stability aspect of Benard's problem. He showed that when the temperature gradient was high enough to make the Rayleigh number exceed a critical value, instability would occur, leading to the formation of Benard cells.\n", + "\n", + "$$Ra = \\frac{\\alpha \\Delta Tgh^3}{\\nu \\kappa }$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Problem Setup" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For this case, we will be considering a layer of fluid placed between to rigid plates.\n", + "\n", + "![alt text](images/Set-up.png)\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Governing Equations" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The governing equations for this case, are derived by applying the Boussinesq approximation to the Navier-Stokes equations. The Boussinesq approximation neglects all density changes in the momentum equation, except for the gravity term. The assumption is, that the density changes are small compared to the velocity gradients. The gravitational constant is, however, strong enough to make it relevant." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\\frac{Du}{Dt} = -\\frac{1}{\\rho_{o}}\\nabla p + \\frac{\\rho}{\\rho_{o}}g + \\nu\\nabla^2u$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Under the same assumption, the density can be shown to have a linear dependancy on the temperature.\n", + "\n", + "$$\\rho = \\rho_{o}(1-\\alpha(T-T_{o})$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And finally, the thermal energy equation can be approximated to a familiar form.\n", + "\n", + "$$\\frac{DT}{Dt} = D\\nabla^2T$$\n", + "\n", + "Where the thermal diffusivity, $$D = \\frac{k}{\\rho c}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 238, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "from matplotlib import rcParams, cm\n", + "rcParams['font.family'] = 'serif'\n", + "rcParams['font.size'] = 16" + ] + }, + { + "cell_type": "code", + "execution_count": 239, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "delT = 0.12092877677020468 Tl = 20.120928776770203\n", + "1.0054144180571545e-06\n" + ] + } + ], + "source": [ + "H = 0.25\n", + "L = 1\n", + "\n", + "alpha = 207*10**(-6) #Volume expansion coefficient of water @ 20 C\n", + "k = 0.6 #Thermal conductivity of water @ 20 C\n", + "\n", + "#ReC = 1100.65 #Critical Rayleigh number for one free and one rigid boundary condition\n", + "ReC = 1708 #Critical Rayleigh number for two rigid body boundary condition\n", + "g = 9.81\n", + "D = 0.143E-6 #Thermal diffusivity of water\n", + "rho_i = 1000 #Density of water @ 20 C\n", + "\n", + "L = 10\n", + "H = 0.01\n", + "\n", + "nxy = 101\n", + "nt = 500\n", + "\n", + "dxy = L/(nxy-1)\n", + "\n", + "x = np.linspace(0,L,nxy)\n", + "y = np.linspace(0,H,nxy)\n", + "ya = np.ones((nxy,nxy))\n", + "for i in range(nxy):\n", + " ya[:,i] = y\n", + "#Change to Kelivin?\n", + "To = 20\n", + "vo = 2.414*10**(-5) * 10**(247.8/(To + 273 - 140)) / rho_i #initial kinematic viscosity of water\n", + "delT = (ReC*vo*1.43*10**(-7))/(alpha*g*H**3)\n", + "Ti = np.ones((nxy, nxy))*To\n", + "Ti[-1,:] = To + 30\n", + "\n", + "rho = np.ones((nxy,nxy), dtype=float)*rho_i\n", + "rho[0,:] = rho_i*(1-alpha*(Ti[0,:] - To))\n", + "\n", + "v = np.ones((nxy,nxy))*2.414*10**(-5) * 10**(247.8/(Ti + 273 - 140)) / rho #kinematic viscosity of water\n", + "\n", + "pi = np.zeros((nxy,nxy), dtype=float)\n", + "pi[:,:] = rho[:,:] * ya[:,:] * g\n", + "\n", + "ui = np.zeros((nxy,nxy), dtype=float)\n", + "\n", + "print('delT =',delT, 'Tl =',20+delT)\n", + "print(vo)\n", + "#print('x =', x, 'y =', y)" + ] + }, + { + "cell_type": "code", + "execution_count": 240, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.001\n" + ] + } + ], + "source": [ + "# stability\n", + "sigma = 0.00005\n", + "#dt = sigma*min(dxy,dxy)**2/D\n", + "dt = 0.001\n", + "\n", + "print(dt)" + ] + }, + { + "cell_type": "code", + "execution_count": 241, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.1\n" + ] + } + ], + "source": [ + "print(dxy)" + ] + }, + { + "cell_type": "code", + "execution_count": 242, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def ftcs(T, To, u, p, rho, rho_i, alpha, v, k, g, y, delT, nt, dt, dxy):\n", + " \n", + " for n in range(nt):\n", + " \n", + " # Boundary conditions\n", + " u[-1,:] = 0 #Top Boundary\n", + " u[0,:] = 0 #Bottom Boundary\n", + " T[0,:] = To + 30 #Bottom Boundary\n", + " T[-1,:] = To #top Boundary\n", + "\n", + " un = u.copy()\n", + " Tn = T.copy()\n", + " pn = p.copy()\n", + " vn = v.copy()\n", + " T[1:-1,1:-1] = Tn[1:-1,1:-1] + dt*((un[1:-1,1:-1]/dxy)*(Tn[2:,1:-1]\\\n", + " + Tn[1:-1,2:] - (2*Tn[1:-1,1:-1])) + \n", + " (k/dxy**2)*(Tn[2:,1:-1] + Tn[:-2,1:-1] + Tn[1:-1,2:]\\\n", + " + Tn[1:-1,:-2] - (4*Tn[1:-1,1:-1])))\n", + " \n", + " rho[1:-1,1:-1] = rho_i*(1- alpha*(T[1:-1,1:-1] - 20))\n", + " p[1:-1,1:-1] = rho[1:-1,1:-1]*ya[1:-1,1:-1] * g\n", + " \n", + " v[1:-1,1:-1] = 2.414*10**(-5) * 10**(247.8/(T[1:-1,1:-1] + 273 - 140)) / rho[1:-1,1:-1]\n", + " \n", + " u[1:-1,1:-1] = un[1:-1,1:-1] + dt*(-(1/rho_i)*(p[2:,1:-1] + p[1:-1,2:] - 2*p[1:-1,1:-1]) + (rho[1:-1,1:-1]*g/rho_i)\\\n", + " + (1/dxy)*(u[1:-1,1:-1]*0.5*(u[2:,1:-1] - u[:-2,1:-1] \\\n", + " + u[1:-1,2:] - u[1:-1,:-2]) \\\n", + " + (v[1:-1,1:-1]/dxy)*(u[2:,1:-1] + u[:-2,1:-1] + u[1:-1,2:] + u[1:-1,:-2] - 4*u[1:-1,1:-1])))\n", + "\n", + " \n", + " return T" + ] + }, + { + "cell_type": "code", + "execution_count": 243, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "T = ftcs(Ti,To,ui,pi,rho,rho_i,alpha,v,k,g,y,delT,nt,dt,dxy)" + ] + }, + { + "cell_type": "code", + "execution_count": 244, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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zMytUehMlMzOzdcHgl6PqJnSNewzMzMys4MTAzMzMCk4MzMzMrODEwMzMzApO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\nZmZmhf8fspCfXfWGFQ4AAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(8,5))\n", + "plt.contourf(x,y,Ti,20,cmap=cm.viridis)\n", + "plt.xlabel('$x$')\n", + "plt.ylabel('$y$')\n", + "plt.colorbar();\n" + ] + }, + { + "cell_type": "code", + "execution_count": 245, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 50. 50. 50. ..., 50. 50. 50. ]\n", + " [ 20. 31.24606041 35.92810255 ..., 35.63953431 31.71920868\n", + " 20. ]\n", + " [ 20. 25.96178197 28.87450968 ..., 28.46203708 25.33425292\n", + " 20. ]\n", + " ..., \n", + " [ 20. 20. 20. ..., 20. 20. 20. ]\n", + " [ 20. 20. 20. ..., 20. 20. 20. ]\n", + " [ 20. 20. 20. ..., 20. 20. 20. ]]\n" + ] + } + ], + "source": [ + "print(T)" + ] + }, + { + "cell_type": "code", + "execution_count": 246, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "102\n" + ] + } + ], + "source": [ + "print(ui.argmax())" + ] + }, + { + "cell_type": "code", + "execution_count": 247, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "61.216268941\n" + ] + } + ], + "source": [ + "print(ui[1,3])" + ] + }, + { + "cell_type": "code", + "execution_count": 248, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "102\n" + ] + } + ], + "source": [ + "def find_nearest(array,value):\n", + " idx = (np.abs(array-value)).argmin()\n", + " return idx\n", + "\n", + "value = 900\n", + "\n", + "loc = find_nearest(ui, value)\n", + "print(loc)" + ] + }, + { + "cell_type": "code", + "execution_count": 249, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "830.033812255\n" + ] + } + ], + "source": [ + "print(np.abs(ui-900).min())" + ] + }, + { + "cell_type": "code", + "execution_count": 250, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(array([1], dtype=int64), array([1], dtype=int64))\n" + ] + } + ], + "source": [ + "print(np.where(ui==900-np.abs(ui-900).min()))" + ] + }, + { + "cell_type": "code", + "execution_count": 251, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 0. 0. 0. ..., 0. 0. 0. ]\n", + " [ 0. 69.96618775 0.35068574 ..., 2.53918912 1.3582699 0. ]\n", + " [ 0. 0.35718329 2.76598709 ..., 1.53694795 1.09842556\n", + " 0. ]\n", + " ..., \n", + " [ 0. 2.54165246 1.53732047 ..., 1.5593685 1.0969332 0. ]\n", + " [ 0. 1.35954534 1.09874381 ..., 1.0969332 0.89407909\n", + " 0. ]\n", + " [ 0. 0. 0. ..., 0. 0. 0. ]]\n" + ] + } + ], + "source": [ + "print(ui)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "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": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Amiya Project/Rayleigh Benard Convection.ipynb b/Amiya Project/Rayleigh Benard Convection.ipynb index e706e21..b3ad7a3 100644 --- a/Amiya Project/Rayleigh Benard Convection.ipynb +++ b/Amiya Project/Rayleigh Benard Convection.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 238, + "execution_count": 295, "metadata": { "collapsed": false }, @@ -18,7 +18,7 @@ }, { "cell_type": "code", - "execution_count": 239, + "execution_count": 296, "metadata": { "collapsed": false }, @@ -27,7 +27,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "delT = 0.12092877677020468 Tl = 20.120928776770203\n", + "delT = 120.36236563779158 Tl = 140.36236563779158\n", "1.0054144180571545e-06\n" ] } @@ -45,11 +45,11 @@ "D = 0.143E-6 #Thermal diffusivity of water\n", "rho_i = 1000 #Density of water @ 20 C\n", "\n", - "L = 10\n", - "H = 0.01\n", + "L = 100\n", + "H = 0.001\n", "\n", "nxy = 101\n", - "nt = 500\n", + "nt = 4000\n", "\n", "dxy = L/(nxy-1)\n", "\n", @@ -61,9 +61,9 @@ "#Change to Kelivin?\n", "To = 20\n", "vo = 2.414*10**(-5) * 10**(247.8/(To + 273 - 140)) / rho_i #initial kinematic viscosity of water\n", - "delT = (ReC*vo*1.43*10**(-7))/(alpha*g*H**3)\n", + "delT = (1700*vo*1.43*10**(-7))/(alpha*g*H**3)\n", "Ti = np.ones((nxy, nxy))*To\n", - "Ti[-1,:] = To + 30\n", + "Ti[-1,:] = To + 50\n", "\n", "rho = np.ones((nxy,nxy), dtype=float)*rho_i\n", "rho[0,:] = rho_i*(1-alpha*(Ti[0,:] - To))\n", @@ -82,7 +82,7 @@ }, { "cell_type": "code", - "execution_count": 240, + "execution_count": 297, "metadata": { "collapsed": false }, @@ -106,7 +106,7 @@ }, { "cell_type": "code", - "execution_count": 241, + "execution_count": 298, "metadata": { "collapsed": false }, @@ -115,7 +115,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "0.1\n" + "1.0\n" ] } ], @@ -125,7 +125,7 @@ }, { "cell_type": "code", - "execution_count": 242, + "execution_count": 299, "metadata": { "collapsed": false }, @@ -138,7 +138,7 @@ " # Boundary conditions\n", " u[-1,:] = 0 #Top Boundary\n", " u[0,:] = 0 #Bottom Boundary\n", - " T[0,:] = To + 30 #Bottom Boundary\n", + " T[0,:] = To + 50 #Bottom Boundary\n", " T[-1,:] = To #top Boundary\n", "\n", " un = u.copy()\n", @@ -166,7 +166,7 @@ }, { "cell_type": "code", - "execution_count": 243, + "execution_count": 300, "metadata": { "collapsed": false }, @@ -177,16 +177,16 @@ }, { "cell_type": "code", - "execution_count": 244, + "execution_count": 301, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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zMytUehMlMzOzdcHgl6PqJnSNewzMzMys4MTAzMzMCk4MzMzMrODEwMzMzApO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\nAvCnBuWzgclt6o4nXW95okH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ZmZmV4iTCzMzMSnESYWZmZqU4iTAzM7NSnESYmZlZKU4izMzMrBQnEWZmZlaKkwgzMzMr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\nKX46w8zMrAVJ2gf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"stream", "text": [ - "61.216268941\n" + "862.236960737\n" ] } ], @@ -268,7 +268,7 @@ }, { "cell_type": "code", - "execution_count": 248, + "execution_count": 305, "metadata": { "collapsed": false }, @@ -277,7 +277,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "102\n" + "304\n" ] } ], @@ -294,7 +294,7 @@ }, { "cell_type": "code", - "execution_count": 249, + "execution_count": 306, "metadata": { "collapsed": false }, @@ -303,7 +303,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "830.033812255\n" + "37.7130942726\n" ] } ], @@ -313,7 +313,7 @@ }, { "cell_type": "code", - "execution_count": 250, + "execution_count": 307, "metadata": { "collapsed": false }, @@ -322,7 +322,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "(array([1], dtype=int64), array([1], dtype=int64))\n" + "(array([3], dtype=int64), array([1], dtype=int64))\n" ] } ], @@ -332,7 +332,7 @@ }, { "cell_type": "code", - "execution_count": 251, + "execution_count": 308, "metadata": { 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