Chapter3-Two-dimensional Cascades

Ex1-pg77

In [1]:
import math
#calculate the
a_l=0.5
alpha2=20.
theta=30.
##function to calculate m and delta
m = 0.23*(2*a_l)**2 + alpha2/500;
delta = m*theta;

##given data
alpha1_ = 50;## in deg
alpha2_ = 20;## in deg
a_l = 0.5;##percentage
s_l = 1.0;
eps = 21;##in deg

##Calculations
theta = alpha1_ - alpha2_;
alpha21 = 20;##in deg
alpha22 = 28.1;##in deg

alpha23 = 28.6;##in deg

alpha1 = eps + alpha23;
i = alpha1 - alpha1_;
alpham = (180./math.pi)*math.atan(0.5*(math.tan(alpha1*math.pi/180.) + math.tan(alpha23*math.pi/180.)));
CL = 2*(s_l)*math.cos(alpham*math.pi/180.)*(math.tan(alpha1*math.pi/180.) - math.tan(alpha23*math.pi/180.));

##Results
print'%s %.2f %s'%('The fluid deflection = ',eps,' deg.');
print'%s %.2f %s'%('\n The fluid deviation = ',i,' deg.');
print'%s %.2f %s'%('\n The ideal lift coefficient at the design point = ',CL,'');

The fluid deflection =  21.00  deg.

 The fluid deviation =  -0.40  deg.

 The ideal lift coefficient at the design point =  0.95

Ex2-pg78

In [3]:
import math
#calculate the

##given data
s_l = 1.0;
alpha1_ = 50.;##in deg
alpha2_ = 20.;##in deg
eps_ = 21.;##in deg
i_ = -0.4;##in deg
i = 3.8;##in deg
CD = 0.017;
eps = 1.15*eps_;

##Calculations
alpha1 = alpha1_+i;
alpha2 = alpha1-eps;
alpham = (180./math.pi)*math.atan(0.5*(math.tan(alpha1*math.pi/180.) + math.tan(alpha2*math.pi/180.)));
zeta = CD/((s_l)*(math.cos(alpham*math.pi/180.))**3);
Cf = 2.*(math.tan(alpha1*math.pi/180.) - math.tan(alpha2*math.pi/180.));
eff_D = 1 - zeta/(Cf*math.tan(alpham*math.pi/180.));

##Results
print'%s %.2f %s'%('The tangential lift force coefficient = ',Cf,'');
print'%s %.2f %s'%('\n The diffuser efficiency =  ',eff_D*100,'percentage.');

The tangential lift force coefficient =  1.59 

 The diffuser efficiency =   97.03 percentage.

Ex3-pg83

In [4]:
import math
import numpy
#calculate the
##given data
alpha1 = 58.;##in deg
alpha2 = 44.;##in deg
AVR = 1.0;

##Calculations
alpham = (180./math.pi)*math.atan(0.5*(math.tan(alpha1*math.pi/180.) + math.tan(alpha2*math.pi/180.)));
zetam = (180./math.pi)*math.atan(math.tan(alpham*math.pi/180.) - 0.213);
Cpi = 1.-(math.cos(alpha1*math.pi/180.)/math.cos(alpha2*math.pi/180.))**2;
s_l = 9.*(0.567-Cpi);
theta = ((zetam-alpha2+1.1*(s_l)**(1/3.))/(0.5-0.31*(s_l)**(1/3.)));
delta = alpha2-zetam-0.5*theta;
print round(theta,2)
print round(s_l,2)
##Results

21.08
0.99