Chapter 8 : High Velocity Fludization

Example 1, Page 206

In [1]:
import math 
from numpy import zeros
from scipy.optimize import fsolve 

Lmf=2.4;            #Length of bed at minimum fluidized condition in m
uo=[2.,4.,6.];         #Superficial gas velocity in m/s
GsII=100.;          #Solid circulation rate in kg/m**2 s for Mode II
uoIII=4.;            #Superficial gas velocity in m/s for Mode III
GsIII=[42.,50.,100.,200.,400.];          #Solid circulation rate in kg/m**2 s for Mode III
GsIV=[70.,100.,120.];                  #Solid circulation rate in kg/m**2 s for Mode IV
dt=0.4;                             #Column diamter in m
Ht=10.;                              #Height of column in m
rhos=1000.;                         #Density of solid in kg/m**3
dpbar=55.;                          #Particle diameter in micrometer
ephsilonmf=0.5;                     #Void fraction at minimum fluidization condition

#Mode I
ephsilonstar=0.01;                  #Saturation carrying capacity of gas
ephsilonsd=[0.2,0.16,0.14];         #Solid holdup in lower dense region from Fig.8(b) for various uo
Hfguess=2.;          #Guess value of height
a = zeros(n)
Hf = zeros(n)
Hd = zeros(n)
ephsilonse = zeros(n)
GsI = zeros(n)
#    endfunction
while i<n:
    a[i]= 3./uo[i];         #Decay consmath.tant
    def solver_func(Hf):            #Function defined for solving the system
        return Lmf*(1-ephsilonmf)-((ephsilonsd[i]-(ephsilonstar+(ephsilonsd[i]-ephsilonstar)*math.exp(-a[i]*Hf)))/a[i])-Ht*ephsilonsd[i]+Hf*(ephsilonsd[i]-ephsilonstar);
    Hf[i] = fsolve(solver_func,1E-6)
    Hd[i]=Ht-Hf[i];#Height of lower densce region
    ephsilonse[i]=ephsilonstar+(ephsilonsd[i]-ephsilonstar)*math.exp(-a[i]*Hf[i]);#Solid holdup at exit
    GsI[i]=rhos*uo[i]*ephsilonse[i];#Solid circulation rate from Eqn.(4)

#Mode II
Hfguess2=2;#Guess value of height
ephsilonseII = zeros(n)
HdII = zeros(n)
LmfII = zeros(n)
HfII = zeros(n)
while i<n:
    ephsilonseII[i]=GsII/(rhos*uo[i]);#Solid holdup at exit
    def solver_func1(Hf):           #Function defined for solving the system
        return ephsilonseII[i]-ephsilonstar-(ephsilonsd[i]-ephsilonstar)*math.exp(-a[i]*Hf);#From Eqn.(7)
    HfII[i] = fsolve(solver_func1,1E-6)
    HdII[i]=Ht-HfII[i];#Height of lower dense region
    #Length of bed minimum fluidization condtion

#Mode III
aIII = 3./uoIII;            #Decay consmath.tant
ephsilonsdIII=0.16;         #Solid holdup at lower dense region
Hfguess3=2;#Guess value of height 
ephsilonseIII = zeros(m)
HdIII = zeros(m)
ephsilonseIII = zeros(m)
LmfIII = zeros(m)
HfIII = zeros(m)
while i<m:
    ephsilonseIII[i]=GsIII[i]/(rhos*uoIII);#Solid holdup at exit
    def solver_func2(Hf):       #Function defined for solving the system
        return ephsilonseIII[i]-ephsilonstar-(ephsilonsdIII-ephsilonstar)*math.exp(-aIII*Hf);#From Eqn.(7)

    HfIII[i] = fsolve(solver_func2,1E-6)
    HdIII[i]=Ht-HfIII[i];       #Height of lower dense region
    #Length of bed at minimum fluidization condition

#Mode IV
Hfguess4=2;#Guess value of height
aIV = zeros(n)
ephsilonseIV = zeros(n)
HdIV = zeros(n)
HfIV = zeros(n)
LmfIV = zeros(n)
while i<n:
    aIV[i]=3./uo[i];            #Decay consmath.tant
    ephsilonseIV[i]=GsIV[i]/(rhos*uo[i]);       #Solid holdup at exit
    def solver_func3(Hf):       #Function defined for solving the system
        return ephsilonseIV[i]-ephsilonstar-(ephsilonsd[i]-ephsilonstar)*math.exp(-aIV[i]*Hf);      #From Eqn.(7)

    HfIV[i] = fsolve(solver_func3,1E-6)
    HdIV[i]=Ht-HfIV[i];#Height of lower dense region
    #Length of bed at minimum fluidization condition

print 'Mode I';
print '\tuom/s\t\tephsilonse-\tHfm\t\tHdm\t\tGskg/m**2 s';
while i<n:
    print '\t%f\t%f\t%f\t%f\t%f'%(uo[i],ephsilonse[i],Hf[i],Hd[i],GsI[i]);

print 'Mode II';
print '\tuom/s\t\tephsilonse-\tHfm\t\tHdm\t\tLmfm';
while i<n:
    print '\t%f\t%f\t%f\t%f\t%f'%(uo[i],ephsilonseII[i],HfII[i],HdII[i],LmfII[i]);

print 'Mode III';
print '\tGskg/m** s\tephsilonse-\tHfm\t\tHdm\t\tLmfm';
while i<m:
    print '\t%f\t%f\t%f\t%f\t%f'%(GsIII[i],ephsilonseIII[i],HfIII[i],HdIII[i],LmfIII[i]);

print 'Mode IV';
print '\tuom/s\t\tGskg/m**2 s\tephsilonse-\tHfm\t\tLmfm';
while i<n:
    print '\t%f\t%f\t%f\t%f\t%f'%(uo[i],GsIV[i],ephsilonseIV[i],HfIV[i],LmfIV[i]);

#====================================END OF PROGRAM ======================================================
Mode I
	uom/s		ephsilonse-	Hfm		Hdm		Gskg/m**2 s
	2.000000	0.192856	0.025551	9.974449	385.711493
	4.000000	0.017870	3.930041	6.069959	71.481458
	6.000000	0.037349	3.117707	6.882293	224.094133
Mode II
	uom/s		ephsilonse-	Hfm		Hdm		Lmfm
	2.000000	0.050000	1.038763	8.961237	2.002635
	4.000000	0.025000	3.070113	6.929887	1.499483
	6.000000	0.016667	5.940829	4.059171	1.121026
Mode III
	Gskg/m** s	ephsilonse-	Hfm		Hdm		Lmfm
	42.000000	0.010500	7.605043	2.394957	1.317154
	50.000000	0.012500	5.459126	4.540874	1.955596
	100.000000	0.025000	3.070113	6.929887	2.638966
	200.000000	0.050000	1.762341	8.237659	2.964631
	400.000000	0.100000	0.681101	9.318899	3.155670
Mode IV
	uom/s		Gskg/m**2 s	ephsilonse-	Hfm		Lmfm
	2.000000	70.000000	0.035000	1.352099	3.706202
	4.000000	100.000000	0.025000	3.070113	2.638966
	6.000000	120.000000	0.020000	5.129899	1.946226
/usr/lib/python2.7/dist-packages/scipy/optimize/ RuntimeWarning: The iteration is not making good progress, as measured by the 
  improvement from the last ten iterations.
  warnings.warn(msg, RuntimeWarning)
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