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{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 9 : Solid Movement Mixing Segregation and Staging"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 1, Page 218\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"umf=0.015; #Velocity at minimum fluidization condition in m/s\n",
"ephsilonmf=0.5; #Void fraction at minimum fluidization condition\n",
"uo=0.1; #Superficial gas velocity in m/s\n",
"delta=0.2; #Bed fraction in bubbles\n",
"db=0.06; #Equilibrium bubble size in m\n",
"dt=[0.1,0.3,0.6,1.5]; #Various vessel sizes in m\n",
"ub=[0.4,0.75,0.85,1.1]; #Bubble velocity in m/s\n",
"Dsv=[0.03,0.11,0.14,0.23]; #Reported values of vertical dispersion coefficient\n",
"\n",
"#CALCULATION\n",
"n=len(ub);\n",
"i=0;\n",
"fw1=2;#Wake fraction from Hamilton et al.\n",
"fw2=0.32;#Wake fraction from Fig.(5.8)\n",
"fw=(fw1+fw2)*0.5;#Average value of wake fraction\n",
"Dsv1 = []\n",
"Dsv2 = []\n",
"while i<n:\n",
" Dsv1.append(12*((uo*100)**0.5)*((dt[i]*100)**0.9));#Vertical distribution coefficient from Eqn.(3)\n",
" Dsv2.append((fw**2*ephsilonmf*delta*db*ub[i]**2)/(3*umf));#Vertical distribution coefficient from Eqn.(12)\n",
" i=i+1;\n",
"\n",
"print Dsv1\n",
"\n",
"#OUTPUT\n",
"print '\\t\\tVertical dispersion coefficient(m**2/s)'\n",
"print 'Vessel Size(m)',\n",
"print '\\tFrom Experiment',\n",
"print '\\tFrom Eqn.(3)',\n",
"print '\\tFrom Eqn.(12)'\n",
"i=0;\n",
"while i<n:\n",
" print '%.2f'%dt[i],\n",
" print '\\t%.3f'%Dsv[i],\n",
" print '\\t%.2f'%(Dsv1[i]/10**4),\n",
" print '\\t%.2f'%Dsv2[i]\n",
" i=i+1; \n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[301.42637178114967, 810.1965234492834, 1511.8801720132121, 3448.7632274996104]\n",
"\t\tVertical dispersion coefficient(m**2/s)\n",
"Vessel Size(m) \tFrom Experiment \tFrom Eqn.(3) \tFrom Eqn.(12)\n",
"0.10 \t0.030 \t0.03 \t0.03\n",
"0.30 \t0.110 \t0.08 \t0.10\n",
"0.60 \t0.140 \t0.15 \t0.13\n",
"1.50 \t0.230 \t0.34 \t0.22\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2, Page 222\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"Lmf=0.83; #Length of bed at minimum fluidization condition in m\n",
"dp=450.0; #Average particle size in micrometer\n",
"ephsilonmf=0.42; #Void fraction at minimum fluidization condition\n",
"umf=0.17; #Velocity at minimum fluidization condition in m/s\n",
"uo=[0.37,0.47,0.57,0.67]; #Superficial gas velocity in m/s\n",
"Dsh=[0.0012,0.0018,0.0021,0.0025]; #Horizontal Drift Coefficient from Experiment in m**2/s\n",
"db=[0.10,0.14]; #Equilibrium bubble size in m\n",
"g=9.81; #Acceleration due to gravity in m/s**2\n",
"\n",
"\n",
"#CALCULATION\n",
"n=len(uo);\n",
"m=len(db);\n",
"k=0;\n",
"alpha=0.77;#Since we are not dealing with Geldart A or AB solids\n",
"uf=umf/ephsilonmf;\n",
"ubr = []\n",
"ub = []\n",
"delta = []\n",
"Dshc = []\n",
"for j in range(m):\n",
" for i in range(n):\n",
" ubr.append(0.711*(db[j]*g)**0.5);#Rise velocity of a single bubble in m/s\n",
" ub.append(uo[i]-umf+ubr[k]);#Rise velocity of bubbles in a bubbling bed\n",
" delta.append((uo[i]-umf)/(ub[k]+umf));#Bed fraction in bubbles\n",
" if ubr[i]>uf:\n",
" Dshc.append((3/16.0)*(delta[k]/(1-delta[k]))*((alpha**2*db[j]*ubr[k]*((((ubr[k]+2*uf)/(ubr[k]-uf))**(1.0/3))-1))));\n",
" #Horizontal Distribution coeff. from Eqn.(14)\n",
" else:\n",
" Dsh.append((3.0/16)*(delta/(1-delta))*(alpha**2*umf*db/ephsilonmf))\n",
" #Horizontal Distribution coeff. from Eqn.(15)\n",
" Dshc.append((3/16.0)*(delta[k]/(1-delta[k]))*((alpha**2*db[j]*ubr[k]*((((ubr[k]+2*uf)/(ubr[k]-uf))**(1/3.0))-1))));#Horizontal Distribution coeff. from Eqn.(14)\n",
" k=k+1;\n",
"i=0;\n",
"j=0;\n",
"k=0;\n",
"while k<m*n:\n",
" print 'Snce we do not have ub=%fm/s>>uf=%fm/s we use Eqn.(14).'%(ub[k],uf)\n",
" print 'Gas Velocity(m/s)'\n",
" print '\\tHorizontal Drift Coefficient Calculated(m**2/s)'\n",
" print '\\tHorizontal Drift Coefficient from Experiment(m**2/s)'\n",
" while j<m:\n",
" print 'db=%fm'%db[j]\n",
" while i<n:\n",
" print '%f'%uo[i],\n",
" print '\\t\\t%f'%Dshc[k],\n",
" print '\\t\\t\\t\\t\\t%f'%Dsh[i]\n",
" i=i+1; \n",
" k=k+1;\n",
" i=0;\n",
" j=j+1;\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Snce we do not have ub=0.904213m/s>>uf=0.404762m/s we use Eqn.(14).\n",
"Gas Velocity(m/s)\n",
"\tHorizontal Drift Coefficient Calculated(m**2/s)\n",
"\tHorizontal Drift Coefficient from Experiment(m**2/s)\n",
"db=0.100000m\n",
"0.370000 \t\t0.001283 \t\t\t\t\t0.001200\n",
"0.470000 \t\t0.001283 \t\t\t\t\t0.001800\n",
"0.570000 \t\t0.001924 \t\t\t\t\t0.002100\n",
"0.670000 \t\t0.001924 \t\t\t\t\t0.002500\n",
"db=0.140000m\n",
"0.370000 \t\t0.002566 \t\t\t\t\t0.001200\n",
"0.470000 \t\t0.002566 \t\t\t\t\t0.001800\n",
"0.570000 \t\t0.003207 \t\t\t\t\t0.002100\n",
"0.670000 \t\t0.003207 \t\t\t\t\t0.002500\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 3, Page 232\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\n",
"\n",
"#Variable declaration\n",
"Gsup=1.5; #Solid interchange rate in kg/m**2plate s\n",
"dor=19.1; #Orifice diameter in mm\n",
"dp=210; #Particle size in micrometer\n",
"uo=0.4; #Superficial gas velocity in m/s\n",
"fopen=[0.12,0.17,0.26]; #Open area fraction \n",
"pi=3.14;\n",
"\n",
"#CALCULATION\n",
"n=len(fopen);\n",
"uor = []\n",
"ls1 = []\n",
"i=0\n",
"while i<n:\n",
" uor.append(uo/fopen[i]); #Gas velocity through the orifice\n",
" ls1.append(Gsup/fopen[i]);#Flux of solids through the holes\n",
" i=i+1;\n",
"\n",
"ls2=[12,20,25]; #Flux of solids through holes from Fig.13(c) for different uor values\n",
"fopen1=0.12; #Open area fraction which gives reasonable fit\n",
"lor=math.sqrt(((math.pi/4)*dor**2)/fopen1);#Orifice spacing\n",
"\n",
"#OUTPUT\n",
"print 'fopen',\n",
"print '\\t\\tuor(m/s)',\n",
"print '\\tls from Eqn.(18)',\n",
"print '\\tls from Fig.13(c)'\n",
"i=0;\n",
"while i<n:\n",
" print '%f'%fopen[i],\n",
" print '\\t%f'%uor[i],\n",
" print '\\t%f'%ls1[i],\n",
" print '\\t\\t%f'%ls2[i]\n",
" i=i+1; \n",
"\n",
"print '\\nFor square pitch, the orifice spacing should be %fmm'%lor\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"fopen \t\tuor(m/s) \tls from Eqn.(18) \tls from Fig.13(c)\n",
"0.120000 \t3.333333 \t12.500000 \t\t12.000000\n",
"0.170000 \t2.352941 \t8.823529 \t\t20.000000\n",
"0.260000 \t1.538462 \t5.769231 \t\t25.000000\n",
"\n",
"For square pitch, the orifice spacing should be 48.863850mm\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}