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"source": [
"Chapter 8 : High Velocity Fludization"
]
},
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"level": 3,
"metadata": {},
"source": [
"Example 1, Page 206\n"
]
},
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"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"
]
},
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"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"
]
}
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