path: root/Fluidization_Engineering/ch11.ipynb

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  {
   "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": [
      "\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",
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RlJR0Rnn9weLFMHEijB5t3b+hXTu7E4mIPygsLKSwsPCMx3u9QDjOYjLck7HH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\niDRIBUJERBqkAiEiIg36/9fGcNvjU2I2AAAAAElFTkSuQmCC\n",
       "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": [
      "\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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TIhARCXBKBCIiAc4riSAvL4+oqCgiIyNJT0+vc8z9999PZGQkPXv2pKioyBth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\nEYiIBDglAhGRAKdEICIS4JQIREQC3P8HJOZBYJAptYQAAAAASUVORK5CYII=\n",
       "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": [
      "\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": {}
  }
 ]
}