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-{
- "metadata": {
- "name": ""
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 8 : High Velocity Fludization"
- ]
- },
- {
- "cell_type": "heading",
- "level": 3,
- "metadata": {},
- "source": [
- "Example 1, Page 206\n"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math \n",
- "from numpy import zeros\n",
- "from scipy.optimize import fsolve \n",
- "\n",
- "\n",
- "#INPUT\n",
- "Lmf=2.4; #Length of bed at minimum fluidized condition in m\n",
- "uo=[2.,4.,6.]; #Superficial gas velocity in m/s\n",
- "GsII=100.; #Solid circulation rate in kg/m**2 s for Mode II\n",
- "uoIII=4.; #Superficial gas velocity in m/s for Mode III\n",
- "GsIII=[42.,50.,100.,200.,400.]; #Solid circulation rate in kg/m**2 s for Mode III\n",
- "GsIV=[70.,100.,120.]; #Solid circulation rate in kg/m**2 s for Mode IV\n",
- "dt=0.4; #Column diamter in m\n",
- "Ht=10.; #Height of column in m\n",
- "rhos=1000.; #Density of solid in kg/m**3\n",
- "dpbar=55.; #Particle diameter in micrometer\n",
- "ephsilonmf=0.5; #Void fraction at minimum fluidization condition\n",
- "\n",
- "#CALCULATION\n",
- "#Mode I\n",
- "ephsilonstar=0.01; #Saturation carrying capacity of gas\n",
- "ephsilonsd=[0.2,0.16,0.14]; #Solid holdup in lower dense region from Fig.8(b) for various uo\n",
- "n=len(uo);\n",
- "i=0;\n",
- "Hfguess=2.; #Guess value of height\n",
- "a = zeros(n)\n",
- "Hf = zeros(n)\n",
- "Hd = zeros(n)\n",
- "ephsilonse = zeros(n)\n",
- "GsI = zeros(n)\n",
- "# endfunction\n",
- " \n",
- "while i<n:\n",
- " a[i]= 3./uo[i]; #Decay consmath.tant\n",
- " def solver_func(Hf): #Function defined for solving the system\n",
- " return Lmf*(1-ephsilonmf)-((ephsilonsd[i]-(ephsilonstar+(ephsilonsd[i]-ephsilonstar)*math.exp(-a[i]*Hf)))/a[i])-Ht*ephsilonsd[i]+Hf*(ephsilonsd[i]-ephsilonstar);\n",
- " \n",
- " Hf[i] = fsolve(solver_func,1E-6)\n",
- " Hd[i]=Ht-Hf[i];#Height of lower densce region\n",
- " ephsilonse[i]=ephsilonstar+(ephsilonsd[i]-ephsilonstar)*math.exp(-a[i]*Hf[i]);#Solid holdup at exit\n",
- " GsI[i]=rhos*uo[i]*ephsilonse[i];#Solid circulation rate from Eqn.(4)\n",
- " i=i+1;\n",
- "\n",
- "#Mode II\n",
- "i=0;\n",
- "Hfguess2=2;#Guess value of height\n",
- "ephsilonseII = zeros(n)\n",
- "HdII = zeros(n)\n",
- "LmfII = zeros(n)\n",
- "HfII = zeros(n)\n",
- "while i<n:\n",
- " ephsilonseII[i]=GsII/(rhos*uo[i]);#Solid holdup at exit\n",
- " def solver_func1(Hf): #Function defined for solving the system\n",
- " return ephsilonseII[i]-ephsilonstar-(ephsilonsd[i]-ephsilonstar)*math.exp(-a[i]*Hf);#From Eqn.(7)\n",
- " HfII[i] = fsolve(solver_func1,1E-6)\n",
- " HdII[i]=Ht-HfII[i];#Height of lower dense region\n",
- " #Length of bed minimum fluidization condtion\n",
- " LmfII[i]=(1-ephsilonmf)**-1*((ephsilonsd[i]-ephsilonseII[i])/a[i])+Ht*ephsilonsd[i]-HfII[i]*(ephsilonsd[i]-ephsilonstar);\n",
- " i=i+1;\n",
- "\n",
- "#Mode III\n",
- "aIII = 3./uoIII; #Decay consmath.tant\n",
- "ephsilonsdIII=0.16; #Solid holdup at lower dense region\n",
- "i=0;\n",
- "m=len(GsIII);\n",
- "Hfguess3=2;#Guess value of height \n",
- "ephsilonseIII = zeros(m)\n",
- "HdIII = zeros(m)\n",
- "ephsilonseIII = zeros(m)\n",
- "LmfIII = zeros(m)\n",
- "HfIII = zeros(m)\n",
- "while i<m:\n",
- " ephsilonseIII[i]=GsIII[i]/(rhos*uoIII);#Solid holdup at exit\n",
- " def solver_func2(Hf): #Function defined for solving the system\n",
- " return ephsilonseIII[i]-ephsilonstar-(ephsilonsdIII-ephsilonstar)*math.exp(-aIII*Hf);#From Eqn.(7)\n",
- "\n",
- " HfIII[i] = fsolve(solver_func2,1E-6)\n",
- " HdIII[i]=Ht-HfIII[i]; #Height of lower dense region\n",
- " #Length of bed at minimum fluidization condition\n",
- " LmfIII[i]=(1-ephsilonmf)**-1*(((ephsilonsdIII-ephsilonseIII[i])/aIII)+Ht*ephsilonsdIII-HfIII[i]*(ephsilonsdIII-ephsilonstar));\n",
- " i=i+1;\n",
- "\n",
- "#Mode IV\n",
- "i=0;\n",
- "Hfguess4=2;#Guess value of height\n",
- "aIV = zeros(n)\n",
- "ephsilonseIV = zeros(n)\n",
- "HdIV = zeros(n)\n",
- "HfIV = zeros(n)\n",
- "LmfIV = zeros(n)\n",
- "while i<n:\n",
- " aIV[i]=3./uo[i]; #Decay consmath.tant\n",
- " ephsilonseIV[i]=GsIV[i]/(rhos*uo[i]); #Solid holdup at exit\n",
- " def solver_func3(Hf): #Function defined for solving the system\n",
- " return ephsilonseIV[i]-ephsilonstar-(ephsilonsd[i]-ephsilonstar)*math.exp(-aIV[i]*Hf); #From Eqn.(7)\n",
- "\n",
- " HfIV[i] = fsolve(solver_func3,1E-6)\n",
- " HdIV[i]=Ht-HfIV[i];#Height of lower dense region\n",
- " #Length of bed at minimum fluidization condition\n",
- " LmfIV[i]=(1-ephsilonmf)**-1*(((ephsilonsd[i]-ephsilonseIV[i])/aIV[i])+Ht*ephsilonsd[i]-HfIV[i]*(ephsilonsd[i]-ephsilonstar));\n",
- " i=i+1;\n",
- "\n",
- "#OUTPUT\n",
- "print 'Mode I';\n",
- "print '\\tuom/s\\t\\tephsilonse-\\tHfm\\t\\tHdm\\t\\tGskg/m**2 s';\n",
- "i=0;\n",
- "while i<n:\n",
- " print '\\t%f\\t%f\\t%f\\t%f\\t%f'%(uo[i],ephsilonse[i],Hf[i],Hd[i],GsI[i]);\n",
- " i=i+1;\n",
- "\n",
- "print 'Mode II';\n",
- "print '\\tuom/s\\t\\tephsilonse-\\tHfm\\t\\tHdm\\t\\tLmfm';\n",
- "i=0;\n",
- "while i<n:\n",
- " print '\\t%f\\t%f\\t%f\\t%f\\t%f'%(uo[i],ephsilonseII[i],HfII[i],HdII[i],LmfII[i]);\n",
- " i=i+1;\n",
- "\n",
- "print 'Mode III';\n",
- "print '\\tGskg/m** s\\tephsilonse-\\tHfm\\t\\tHdm\\t\\tLmfm';\n",
- "i=0;\n",
- "while i<m:\n",
- " print '\\t%f\\t%f\\t%f\\t%f\\t%f'%(GsIII[i],ephsilonseIII[i],HfIII[i],HdIII[i],LmfIII[i]);\n",
- " i=i+1;\n",
- "\n",
- "print 'Mode IV';\n",
- "print '\\tuom/s\\t\\tGskg/m**2 s\\tephsilonse-\\tHfm\\t\\tLmfm';\n",
- "i=0;\n",
- "while i<n:\n",
- " print '\\t%f\\t%f\\t%f\\t%f\\t%f'%(uo[i],GsIV[i],ephsilonseIV[i],HfIV[i],LmfIV[i]);\n",
- " i=i+1;\n",
- "\n",
- "#====================================END OF PROGRAM ======================================================"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "Mode I\n",
- "\tuom/s\t\tephsilonse-\tHfm\t\tHdm\t\tGskg/m**2 s\n",
- "\t2.000000\t0.192856\t0.025551\t9.974449\t385.711493\n",
- "\t4.000000\t0.017870\t3.930041\t6.069959\t71.481458\n",
- "\t6.000000\t0.037349\t3.117707\t6.882293\t224.094133\n",
- "Mode II\n",
- "\tuom/s\t\tephsilonse-\tHfm\t\tHdm\t\tLmfm\n",
- "\t2.000000\t0.050000\t1.038763\t8.961237\t2.002635\n",
- "\t4.000000\t0.025000\t3.070113\t6.929887\t1.499483\n",
- "\t6.000000\t0.016667\t5.940829\t4.059171\t1.121026\n",
- "Mode III\n",
- "\tGskg/m** s\tephsilonse-\tHfm\t\tHdm\t\tLmfm\n",
- "\t42.000000\t0.010500\t7.605043\t2.394957\t1.317154\n",
- "\t50.000000\t0.012500\t5.459126\t4.540874\t1.955596\n",
- "\t100.000000\t0.025000\t3.070113\t6.929887\t2.638966\n",
- "\t200.000000\t0.050000\t1.762341\t8.237659\t2.964631\n",
- "\t400.000000\t0.100000\t0.681101\t9.318899\t3.155670\n",
- "Mode IV\n",
- "\tuom/s\t\tGskg/m**2 s\tephsilonse-\tHfm\t\tLmfm\n",
- "\t2.000000\t70.000000\t0.035000\t1.352099\t3.706202\n",
- "\t4.000000\t100.000000\t0.025000\t3.070113\t2.638966\n",
- "\t6.000000\t120.000000\t0.020000\t5.129899\t1.946226\n"
- ]
- },
- {
- "output_type": "stream",
- "stream": "stderr",
- "text": [
- "/usr/lib/python2.7/dist-packages/scipy/optimize/minpack.py:227: RuntimeWarning: The iteration is not making good progress, as measured by the \n",
- " improvement from the last ten iterations.\n",
- " warnings.warn(msg, RuntimeWarning)\n"
- ]
- }
- ],
- "prompt_number": 1
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [],
- "language": "python",
- "metadata": {},
- "outputs": []
- }
- ],
- "metadata": {}
- }
- ]
-} \ No newline at end of file
generated by cgit (git 2.34.1) at 2025-01-10 00:06:43 +0000