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{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 3 : Fluidization and Mapping of Regimes"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1, Page 68\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"weight = [0,60,150,270,330,360.0]; # Weight in grams for the oversized particles\n",
"psize = [50,75,100,125,150,175]; #PSD in micrometers\n",
"\n",
"#CALCULATION\n",
"l = len(psize); # To obtain the size of input array\n",
"# Computation of sauter mean diameter for the given PSD\n",
"i = 0;\n",
"dpi = [0,0,0,0,0,0]\n",
"weightf = [0,0,0,0,0,0]\n",
"dp = [0,0,0,0,0,0]\n",
"while i<l-1:\n",
" dpi[i]=(psize[i]+ psize[i+1])/2.0;\n",
" weightf[i]=(weight[i+1]-weight[i])/weight[5]; \n",
" dp[i]=weightf[i]/float(dpi[i]); \n",
" i=i+1;\n",
"\n",
"dpbar=1/sum(dp); #Calculation of average particle daimeter Eq.(15)\n",
"\n",
"#OUTPUT\n",
"print '\\n The Sauter mean diameter of the material with the given particle size distribution = %.0f micrometer'%dpbar\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" The Sauter mean diameter of the material with the given particle size distribution = 98 micrometer\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2, Page 76\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Estimation of Minimum fluidizing velocity\n",
"\n",
"#INPUT\n",
"ephsilon=0.55; #Void fraction of bed\n",
"rhog=0.0012; #Density of gas in g/cc\n",
"myu=.00018; #Viscosity of gas in g/cm s\n",
"dpbar=0.016; #Mean diameter of solids in centimeter\n",
"phis=0.67; #Sphericity of solids\n",
"rhos=2.6; #Density of solids in g/cc\n",
"g=980; #Acceleration due to gravity in square cm/s**2\n",
"\n",
"#CALCULATION\n",
"#Computation of umf using the simplified equation for small particles\n",
"umf=((dpbar**2)*(rhos-rhog)*g*(ephsilon**3)*(phis**2))/(150*myu*(1-ephsilon));#Simplified equation to calculate minimum fluidizing velocity \n",
" #for small particles Eq.(21)\n",
"Re=(dpbar*umf*rhog)/myu;#To calculate Reynolds number for particle\n",
"\n",
"#Computation of umf if neither void fraction of bed nor sphericity is known\n",
"c1=28.7\n",
"c2=0.0494; #Value of constants from Table 4, page 70\n",
"umf1=(myu/(dpbar*rhog))*(((c1**2)+((c2*(dpbar**3)*rhog*(rhos-rhog)*g)/(myu**2)))**0.5-c1); #Equation to calculate minimum fluidizing velocity \n",
" #for coarse particles Eq.(25)\n",
"err=((umf-umf1)/umf)*100; #Calculation of error from experimental value\n",
"\n",
"#OUTPUT\n",
"if Re<20:\n",
"\tprint 'The particle Reynolds no = %f'%Re\n",
"\tprint 'The simplified equation used for calculating minimum fluidizing velocity is valid.'\n",
"\n",
"print 'The minimum fluidizing velocity by simplified equation for small particles = %.2fcm/s'%umf\n",
"print 'The minimum fluidizing velocity by equation for coarse partilces = %.2fcm/s'%umf1\n",
"print 'This value is %d percent below the experimentally reported value.'%err\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The particle Reynolds no = 0.427493\n",
"The simplified equation used for calculating minimum fluidizing velocity is valid.\n",
"The minimum fluidizing velocity by simplified equation for small particles = 4.01cm/s\n",
"The minimum fluidizing velocity by equation for coarse partilces = 3.10cm/s\n",
"This value is 22 percent below the experimentally reported value.\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 3, Page 82\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"rhog=1.2e-3; #Density of air in g/cc\n",
"myu=1.8e-4 #Viscosity of air in g/cm s\n",
"dpbar=0.016 #Mean diameter of solids in centimeter\n",
"phis=0.67; #Sphericity of solids\n",
"rhos=2.6; #Density of solids in g/cc\n",
"g=980 #Acceleration due to gravity in square cm/s**2\n",
"\n",
"#CALCULATION\n",
"dpstar=dpbar*((rhog*(rhos-rhog)*g)/myu**2)**(1/3.0); #Calculation of dimensionless particle size Eq.(31)\n",
"utstar=((18/(dpstar**2))+(2.335-(1.744*phis))/(dpstar**0.5))**-1; #Calculation of dimensionless gas velocity Eq.(33)\n",
"ut=utstar*((myu*(rhos-rhog)*g)/rhog**2)**(1/3.0); #Calculation of terminal velocity of falling particles Eq.(32)\n",
"\n",
"\n",
"#OUTPUT\n",
"print 'The dimensionless particle size = %.2f'%dpstar\n",
"print 'The dimensionless gas velocity = %.3f'%utstar\n",
"print 'The terminal velocity of falling particles = %d cm/s'%ut\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The dimensionless particle size = 7.28\n",
"The dimensionless gas velocity = 1.296\n",
"The terminal velocity of falling particles = 88 cm/s\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4, Page 91\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"rhos=1.5; #Density of Solid in g/cc\n",
"uo1=40; uo2=80; #Superficial gas velocity in cm/s\n",
"dp1=0.006; dp2=0.045; #Particle size in centimeter\n",
"rhog1=1.5E-3; rhog2=1E-3; #Density of gas in g/cc\n",
"myu1=2E-4; myu2=2.5E-4; #Viscosity of air in g/cm s\n",
"g=980; #Acceleration due to gravity in square cm/s**2\n",
"\n",
"#CALCULATION\n",
"#for smaller particles\n",
"dpstar1=dp1*((rhog1*(rhos-rhog1)*g)/myu1**2)**(1/3.0); #Calculation of dimensionless particle diamter Eq.(31)\n",
"uostar1=uo1*((rhog1**2)/((myu1)*(rhos-rhog1)*g))**(1/3.0);\n",
"uostar2=uo2*((rhog1**2)/((myu1)*(rhos-rhog1)*g))**(1/3.0); #Calculation of dimensionless superficial gas velocity Eq.(32)\n",
"\n",
"#for larger particles \n",
"dpstar2=dp2*((rhog2*(rhos-rhog2)*g)/myu2**2)**(1/3.0); #Calculation of dimensionless particle diamter Eq.(31)\n",
"uostar3=uo1*((rhog2**2)/((myu2)*(rhos-rhog2)*g))**(1/3.0);\n",
"uostar4=uo2*((rhog2**2)/((myu2)*(rhos-rhog2)*g))**(1/3.0); #Calculation of dimensionless superficial gas velocity Eq.(32)\n",
"\n",
"\n",
"#OUTPUT\n",
"print 'For particle of size %.3f centimeter'%dp1\n",
"print 'The dimensionless particle diameter = %.2f'%dpstar1\n",
"print 'The dimensionless superficial gas velocity = %.4fcm/s(for superficial gas velocity of %dcm/s)'%(uostar1,uo1)\n",
"print 'The dimensionless superficial gas velocity = %.3fcm/s(for superficial gas velocity of %dcm/s)'%(uostar2,uo2)\n",
"print 'From Fig.16(page 89)comparing u*=%.4f vs dp*=%.2f'%(uostar1,dpstar1)\n",
"print 'For Superficial gas velocity =%d Mode of Fluidization:Onset of turbulent fluidization in an ordinary bubbling bed'%(uo1)\n",
"print 'From Fig.16(page 89)comparing u* =%.3f vs dp* =%f'%(uostar2,dpstar1)\n",
"print 'For Superficial gas velocity =%f Mode of Fluidization:Fast fluidization(requires a circulating solid system)'%(uo2)\n",
"print 'For particle of size %f centimeter'%(dp2)\n",
"print 'The dimensionless particle diameter = %f'%(dpstar2)\n",
"print 'The dimensionless superficial gas velocity = %fcm/s(for superficial gas velocity of %fcm/s)'%(uostar3,uo1)\n",
"print 'The dimensionless superficial gas velocity = %fcm/s(for superficial gas velocity of %fcm/s)'%(uostar4,uo2)\n",
"print 'From Fig.16(page 89)comparing u*=%f vs dp*=%f'%(uostar3,dpstar2)\n",
"print 'For Superficial gas velocity =%f Mode of Fluidization:Bublling Fluidization'%(uo1)\n",
"print 'From Fig.16(page 89)comparing u* =%f vs dp* =%f'%(uostar4,dpstar2)\n",
"print 'For Superficial gas velocity =%f Mode of Fluidization:Bubbling Fluidization'%(uo2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"For particle of size 0.006 centimeter\n",
"The dimensionless particle diameter = 2.28\n",
"The dimensionless superficial gas velocity = 0.7885cm/s(for superficial gas velocity of 40cm/s)\n",
"The dimensionless superficial gas velocity = 1.577cm/s(for superficial gas velocity of 80cm/s)\n",
"From Fig.16(page 89)comparing u*=0.7885 vs dp*=2.28\n",
"For Superficial gas velocity =40 Mode of Fluidization:Onset of turbulent fluidization in an ordinary bubbling bed\n",
"From Fig.16(page 89)comparing u* =1.577 vs dp* =2.282737\n",
"For Superficial gas velocity =80.000000 Mode of Fluidization:Fast fluidization(requires a circulating solid system)\n",
"For particle of size 0.045000 centimeter\n",
"The dimensionless particle diameter = 12.890262\n",
"The dimensionless superficial gas velocity = 0.558561cm/s(for superficial gas velocity of 40.000000cm/s)\n",
"The dimensionless superficial gas velocity = 1.117122cm/s(for superficial gas velocity of 80.000000cm/s)\n",
"From Fig.16(page 89)comparing u*=0.558561 vs dp*=12.890262\n",
"For Superficial gas velocity =40.000000 Mode of Fluidization:Bublling Fluidization\n",
"From Fig.16(page 89)comparing u* =1.117122 vs dp* =12.890262\n",
"For Superficial gas velocity =80.000000 Mode of Fluidization:Bubbling Fluidization\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
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}
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