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diff --git a/Fluidization_Engineering/ch11.ipynb b/Fluidization_Engineering/ch11.ipynb new file mode 100644 index 00000000..b665def9 --- /dev/null +++ b/Fluidization_Engineering/ch11.ipynb @@ -0,0 +1,359 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 11 : Particle to Gas Mass and Heat Transfer" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "%pylab inline" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n", + "For more information, type 'help(pylab)'.\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 1, Page 265\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Fitting Reported Mass Transfer Data with the Bubbling Bed Model\n", + "\n", + "#Variable declaration\n", + "db=0.37; #Equilibrium bubble size in cm\n", + "dp=0.028; #Particle size in cm\n", + "rhos=1.06; #Density of solids in g/cc\n", + "ephsilonmf=0.5; #Void fraction at minimum fluidization condition\n", + "phis=0.4; #Sphericity of solids\n", + "gammab=0.005; #Ratio of volume of dispersed solids to that of bubble phase\n", + "rhog=1.18E-3; #Density of air in g/cc\n", + "myu=1.8E-4; #Viscosity of gas in g/cm s\n", + "D=0.065; #Diffusion coefficient of gas in cm**2/s\n", + "Sc=2.35; #Schmidt number\n", + "etad=1; #Adsorption efficiency factor\n", + "y=1;\n", + "umf=1.21; #Velocity at minimum fluidization condition in cm/s\n", + "ut=69; #Terminal velocity in cm/s\n", + "g=980; #Acceleration due to gravity in square cm/s**2\n", + "uo=[10,20,30,40,50];#Superficial gas velocity in cm/s\n", + "\n", + "#CALCULATION\n", + "n=len(uo);\n", + "i=0;\n", + "Rept=(dp*ut*rhog)/myu;\n", + "Shstar=2+(0.6*(Rept**0.5)*(Sc**(1/3)));#Sherwood no. from Eqn.(1)\n", + "Kbc=4.5*(umf/db)+5.85*((D**0.5*g**0.25)/db**(5/4));#Gas interchange coefficient between bubble and cloud from Eqn.(10.27)\n", + "ubr=0.711*(g*db)**0.5;#Rise velocity of the bubble\n", + "x = [0,0,0,0,0]\n", + "Shbed = [0,0,0,0,0]\n", + "Rep = [0,0,0,0,0]\n", + "while i<n:\n", + " x[i]=(uo[i]-umf)/(ubr*(1-ephsilonmf));#The term delta/(1-epshilonf) after simplification\n", + " Shbed[i]=x[i]*((gammab*Shstar*etad)+((phis*dp**2*y)/(6*D))*Kbc);#Sherwood no. from Eqn.(11)\n", + " Rep[i]=(dp*uo[i]*rhog)/myu;#Reynolds of the particle\n", + " i=i+1;\n", + "\n", + "#OUTPUT\n", + "print 'The desired result is the relationship between Shbed and Rep The points gives a straight line of the form y=mx+c'\n", + "print 'Rep',\n", + "print '\\t\\tShbed'\n", + "i=0;\n", + "while i<n:\n", + " print '%f'%Rep[i],\n", + " print '\\t%f'%Shbed[i]\n", + " i=i+1;\n", + "import matplotlib.pyplot as plt\n", + "plt.plot(Rep,Shbed);\n", + "plt.xlabel(\"Rep\");\n", + "plt.ylabel(\"Shbed\");\n", + "\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n", + "The desired result is the relationship between Shbed and Rep The points gives a straight line of the form y=mx+c\n", + "Rep \t\tShbed\n", + "1.835556 \t0.065762\n", + "3.671111 \t0.140576\n", + "5.506667 \t0.215391\n", + "7.342222 \t0.290206\n", + "9.177778 \t0.365020\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "<matplotlib.figure.Figure at 0x2b26690>" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 2, Page 267" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from scipy.optimize import fsolve \n", + "import math \n", + "\n", + "#INPUT\n", + "umf=0.12 #Velocity at minimum fluidization condition in cm/s\n", + "uo=40.; #Superficial gas velocity in cm/s\n", + "ub=120; #Velocity of the bubble in cm/s\n", + "D=0.7; #Diffusion coefficient of gas in cm**2/s\n", + "abkbe1=1.; #Bubble-emuslion interchange coefficient for non absorbing particles(m=0)\n", + "abkbe2=18.; #Bubble-emuslion interchange coefficient for highly absorbing particles(m=infinity)\n", + "g=980.; #Acceleration due to gravity in square cm/s**2\n", + "\n", + "#CALCULATION\n", + "#For non absorbing particles m=0,etad=0\n", + "Kbc=(ub/uo)*(abkbe1);\n", + "dbguess=2;#Guess value of db\n", + "def solver_func(db): #Function defined for solving the system\n", + " return abkbe1-(uo/ub)*(4.5*(umf/db)+5.85*(D**0.5*g**0.25)/(db**(5/4.)));#Eqn.(10.27)\n", + "\n", + "d=fsolve(solver_func,dbguess)\n", + "#For highly absorbing particles m=infinity, etad=1\n", + "M=abkbe2-(uo/ub)*Kbc;\n", + "#For intermediate condition\n", + "alpha=100.;\n", + "m=10.;\n", + "etad=1./(1+(alpha/m));#Fitted adsorption efficiency factor from Eqn.(23)\n", + "abkbe3=M*etad+(uo/ub)*Kbc;\n", + "\n", + "#OUTPUT\n", + "print 'For non absorbing particles:\\tDiameter of bubble=%fcm\\tBubble-cloud interchange coefficient=%fs**-1'%(d,Kbc);\n", + "print 'For highly absorbing partilces:\\tM=%f'%(M);\n", + "print 'For intermediate condition:\\tFitted adsorption efficiency factor:%f\\tBubble-emuslion interchange coefficient:%fs**-1'%(etad,abkbe3);\n", + "\n", + "#====================================END OF PROGRAM ======================================================" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "For non absorbing particles:\tDiameter of bubble=6.010032cm\tBubble-cloud interchange coefficient=3.000000s**-1\n", + "For highly absorbing partilces:\tM=17.000000\n", + "For intermediate condition:\tFitted adsorption efficiency factor:0.090909\tBubble-emuslion interchange coefficient:2.545455s**-1\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 3, Page 273\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Fitting Reported Heat Transfer Data with the Bubbling Bed Model\n", + "\n", + "#Variable declaration\n", + "rhos=1.3; #Density of solids in g/cc\n", + "phis=0.806; #Sphericity of solids\n", + "gammab=0.001; #Ratio of volume of dispersed solids to that of bubble phase\n", + "rhog=1.18E-3; #Density of air in g/cc\n", + "Pr=0.69; #Prandtl number\n", + "myu=1.8E-4; #Viscosity of gas in g/cm s\n", + "Cpg=1.00; #Specific heat capacity of gas in J/g K\n", + "ephsilonmf=0.45; #Void fraction at minimum fluidization condition\n", + "kg=2.61E-4; #Thermal concuctivity of gas in W/cm k\n", + "dp=0.036; #Particle size in cm\n", + "umf=6.5; #Velocity at minimum fluidization condition in cm/s\n", + "ut=150.; #Terminal velocity in cm/s\n", + "db=0.4; #Equilibrium bubble size in cm\n", + "etah=1; #Efficiency of heat transfer\n", + "uo=[10.,20.,30.,40.,50.];#Superficial gas velocity in cm/s\n", + "g=980.; #Acceleration due to gravity in square cm/s**2\n", + "\n", + "#CALCULATION\n", + "Nustar=2+(((dp*ut*rhog)/myu)**0.5*Pr**(1./3));#Nusselt no. from Eqn.(25)\n", + "Hbc=4.5*(umf*rhog*Cpg/db)+5.85*((kg*rhog*Cpg)**0.5*g**0.25/db**(5./4));#Total heat interchange across the bubble-cloud boundary from Eqn.(32)\n", + "ubr=0.711*(g*db)**0.5;#Rise velocity of the bubble from Eqn.(6.7)\n", + "n=len(uo);\n", + "i=0;\n", + "x = [0,0,0,0,0]\n", + "Nubed = [0,0,0,0,0]\n", + "Rep = [0,0,0,0,0]\n", + "\n", + "while i<n:\n", + " x[i]=(uo[i]-umf)/(ubr*(1-ephsilonmf));#The term delta/(1-epshilonf) after simplification\n", + " Nubed[i]=x[i]*(gammab*Nustar*etah+(phis*dp**2/(6*kg))*Hbc);#Nusselt no. from Eqn.(36)\n", + " Rep[i]=(dp*uo[i]*rhog)/myu;#Reynolds of the particle\n", + " i=i+1;\n", + "\n", + "#OUTPUT\n", + "print 'The desired result is the relationship between Nubed and Rep which is in the form of a straight line y=mx+c'\n", + "print 'Rep',\n", + "print '\\t\\tNubed'\n", + "i=0;\n", + "while i<n:\n", + " print '%f'%Rep[i],\n", + " print '\\t%f'%Nubed[i]\n", + " i=i+1;\n", + "import matplotlib.pyplot as plt\n", + "plt.plot(Rep,Nubed);\n", + "plt.xlabel(\"Rep\");\n", + "plt.ylabel(\"Nubed\");\n", + "plt.show()\n", + " " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The desired result is the relationship between Nubed and Rep which is in the form of a straight line y=mx+c\n", + "Rep \t\tNubed\n", + "2.360000 \t0.046518\n", + "4.720000 \t0.179427\n", + "7.080000 \t0.312335\n", + "9.440000 \t0.445244\n", + "11.800000 \t0.578152\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "<matplotlib.figure.Figure at 0x269c250>" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example 4, Page 274\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Heating a Particle in a Fluidized Bed\n", + "\n", + "import math\n", + "\n", + "#Variable declaration\n", + "rhog=1.2; #Density of air in kg/m**3\n", + "myu=1.8E-5; #Viscosity of gas in kg/m s\n", + "kg=2.6E-2; #Thermal concuctivity of gas in W/m k\n", + "dp=1E-4; #Particle size in m\n", + "rhos=8920; #Density of solids in kg/m**3\n", + "Cps=390; #Specific heat capacity of the solid in J/kg K\n", + "ephsilonf=0.5; #Void fraction of the fluidized bed\n", + "umf=0.1; #Velocity at minimum fluidization condition in m/s\n", + "uo=0.1; #Superficial gas velocity in m/s\n", + "pi=3.14\n", + "\n", + "#CALCULATION\n", + "to=0; #Initial temperature of the bed\n", + "T=100; #Temperature of the bed\n", + "t=0.99*T; #Particle temperature i.e. when it approaches 1% of the bed temperature\n", + "mp=(pi/6)*dp**3*rhos; #Mass of the particle\n", + "A=pi*dp**2; #Surface area of the particle\n", + "Rep=(dp*uo*rhog)/myu; #Reynold's no. of the particle\n", + "Nubed=0.0178; #Nusselt no. from Fig.(6)\n", + "hbed1=(Nubed*kg)/dp; #Heat transfer coefficient of the bed\n", + "t1=(mp*Cps/(hbed1*A))*math.log((T-to)/(T-t));#Time needed for the particle approach 1 percentage of the bed temperature in case(a)\n", + "hbed2=140*hbed1;#Since from Fig.(6) Nup is 140 times Nubed\n", + "t2=(mp*Cps/(hbed2*A))*math.log((T-to)/(T-t));#Time needed for the particle approach 1 percentage of the bed temperature in case(b)\n", + "\n", + "#OUTPUT\n", + "print 'Case(a):Using the whole bed coefficient from Fig.(6)'\n", + "print '\\tTime needed for the particle approach 1 percentage of the bed temperature is %.0fs'%t1\n", + "print 'Case(b):Uisng the single-particle coefficient of Eqn.(25),also shown in Fig.(6)'\n", + "print '\\tTime needed for the particle approach 1 percentage of the bed temperature is %.2fs'%t2" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Case(a):Using the whole bed coefficient from Fig.(6)\n", + "\tTime needed for the particle approach 1 percentage of the bed temperature is 58s\n", + "Case(b):Uisng the single-particle coefficient of Eqn.(25),also shown in Fig.(6)\n", + "\tTime needed for the particle approach 1 percentage of the bed temperature is 0.41s\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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