Chapter 18 : Gas Compressors

Example 18.1 Page No : 723

In [7]:
import math 

# Variables
T2 = 488.
T1 = 298.; n = 1.3; R =8314./44;

# Calculation and Results
rp = (T2/T1)**(n/(n-1));
print "Pressure ratio is",round(rp,2)

b = 0.12; 			# Bore of compressor
L = 0.15; 			# Stroke of compressor
V1 = (math.pi/4)*(b)**2*L ; 
P1 = 120e03; 			# in kPa
W = ((n*P1*V1)/(n-1))*(((rp)**((n-1)/n))-1);
P = (W*1200*0.001)/60 ; 
print "Indicated power is",round(P,2),"kW"
print "Shaft power is",round((P/0.8),1),"kW"

V1_dot = V1*(1200./60);
m_dot = (P1*V1_dot)/(R*T1);
print "Mass flow rate is",round(m_dot,4),"kg/s"

rp_1 = rp**2;
print "Pressure ratio when second stage is added is",round(rp_1,1)

V2 = (1./rp)**(1./n)*V1;
print "Volume derived per cycle is V2",round(V2,5),"m3"

d = math.sqrt((V2*4)/(L*math.pi));
print "Second stage bore would be",round((d*1000),0),"mm"

Pressure ratio is 8.48
Indicated power is 11.25 kW
Shaft power is 14.1 kW
Mass flow rate is 0.0723 kg/s
Pressure ratio when second stage is added is 71.9
Volume derived per cycle is V2 0.00033 m3
Second stage bore would be 53.0 mm

Example 18.2 Page No : 724

In [2]:
import math 

# Variables
P1 = 101.3e03
P4 = P1; 			# in Pa
P2 = 8*P1
P3 = P2;
T1 = 288.
Vs = 2000.;
V3 = 100.
Vc = V3;

# Calculation and Results
V1 = Vs + Vc ;
n = 1.25
R = 287.;
V4 = ((P3/P4)**(1./n))*V3;
W = ((n*P1*(V1-V4)*1e-06)/(n-1))*(((P2/P1)**((n-1)/n))-1);
P = (W*800*0.001)/60 ; 
print "Indicated poer is",round(P,2),"kW"
print "Volumetric efficiency is",round((100*(V1-V4)/Vs),1),"%"

m = (P1*(V1-V4)*1e-06)/(R*T1);
m_dot = m*800;
print "Mass flow rate is",round(m_dot,2),"kg/min"

FAD = (V1-V4)*1e-06*800;
print "Free air delivery is",round(FAD,2),"m3/min"

Wt = P1*(V1-V4)*1e-06*math.log(P2/P1);
n_isothermal = (Wt*800*0.001)/(P*60);
print "Isothermal efficiency is",round(100*n_isothermal,1),"%"

ip = P/0.85;
print "Input power is",round(ip,2),"kW"

Indicated poer is 5.48 kW
Volumetric efficiency is 78.6 %
Mass flow rate is 1.54 kg/min
Free air delivery is 1.26 m3/min
Isothermal efficiency is 80.6 %
Input power is 6.44 kW

Example 18.3 Page No : 725

In [4]:
import math 

# Variables
P1 = 1.; 
P3 = 9.;

# Calculation
P2 = math.sqrt(P1*P3);
T1 = 300.; 
cp = 1.005;
R = 0.287; n = 1.3;
W = ((2*n*R*T1)/(n-1))*((P2/P1)**((n-1)/n)-1);
T2 = T1*(P2/P1)**((n-1)/n);
H = cp*(T2-T1);

# Results
print "Heat rejected to the intercooler is",round(H,2),"kJ/kg"

# rounding off error is there.

Heat rejected to the intercooler is 87.0 kJ/kg

Example 18.4 Page No : 726

In [11]:
import math 

# Variables
P1 = 1.013
P4 = 80.;
P2 = math.sqrt(P1*P4);
V_dot = 4./60; 			# in m3/s
n = 1.25;
n_mech = 0.75;

# Calculation
W_dot = ((2*n)/(n-1))*((P1*100*V_dot)/n_mech)*((P2/P1)**((n-1)/n)-1);
N = 250.;
L = (3*60.)/(2*N); 			# Stroke length of piston in m
Vlp = 4/N;
n_vol = 0.8;
Dlp = math.sqrt((Vlp*4)/(n_vol*L*math.pi));
Dhp = Dlp*math.sqrt(P1/P2);

# Results
print "Minimum power required is",round(W_dot,2),"kW"
print "Stroke of the compressor is",L*100,"cm"
print "Bore of high pressure compressure is",round((Dhp*100),2),"cm"
print "Bore of lo pressure compressure is",round((Dlp*100),1),"cm"

Minimum power required is 49.34 kW
Stroke of the compressor is 36.0 cm
Bore of high pressure compressure is 8.92 cm
Bore of lo pressure compressure is 26.6 cm

Example 18.5 Page No : 727

In [12]:
# Variables
V12 = 0.4; 			# V12 = V1./V2
T1 = 38.+273; 
n = 1.3; 
P3 = 112.; 			# back pressure
m = 1.25; R = 0.287;

# Calculation
T2 = ((V12)**(n-1))*T1;
P1 = 700.; 			# in kPa
P2 = P1*(V12)**n;
V2 = (m*R*T2)/P2;
v2 = V2/m ;
A = R*T1 + R*(T1-T2)/(n-1) - P3*v2; 			# Area of indicator diagram
IO = A*0.85*m;

# Results
print "Indicated output is",round(IO,2),"kJ"

Indicated output is 132.88 kJ

Example 18.6 Page No : 728

In [5]:
import math 

# Variables
P1 = 1.
P41 = 15.; 			# P41 = P4/P1
P21 = (P41)**(1./3);
P2 = P21*P1;
n = 1.3; 
R = 0.287;
P3 = P21*P2;
P11 = P2; P12 = P1;
b = 0.45
s = 0.3; 			# Bore and stroke of cylinder
Vs = (math.pi/4)*b**2*s; 			# Swept volume of the cylinder

# Calculation and Results
V11 = 0.05*Vs; 			# Clearance volume
V1 = V11+Vs;
V12 = V11*(P11/P12)**(1./n);
print "Effective swept volume of the LP cylinder is",round((V1-V12),5),"m3"

T1 = 291.
T3 = T1; 
T5 = T1;
P43 = P21; 			# P4/P3
T6 = T5*(P43)**((n-1)/n);
print "Delivery temperature is",round(T6,1),"K"

P4 = 15; 			# Delivery pressure
V6_7 = (P1/P4)*(T6/T1)*(V1-V12); 			# V6-V7
print "Volume of the air delivered",round(V6_7,5),"m3"

W = ((3*n*R*T1)/(n-1))*((P21)**((n-1)/n)-1);
print "Work done per kg of the air is",round(W,1),"kJ"

# rounding off error is there. please check.

Effective swept volume of the LP cylinder is 0.04532 m3
Delivery temperature is 358.4 K
Volume of the air delivered 0.00372 m3
Work done per kg of the air is 251.4 kJ

Example 18.7 Page No : 729

In [14]:
# Variables
P1 = 1.013;
P2 = 1.5*P1;
Vs = 0.03
Va = Vs;
WD = (P2-P1)*Vs*100.;
Pi = (P1+P2)/2;
g = 1.4;

# Calculation
Aa = ((g*P1*100*Vs)/(g-1))*((Pi/P1)**((g-1)/g)-1);
Vb = Va *(P1/Pi)**(1./g);
Ab = Vb*(P2-Pi)*100;
WR = Aa+Ab;

# Results
print "Work required is",round(WR,2),"kJ/rev"

Work required is 1.35 kJ/rev

Example 18.8 Page No : 730

In [9]:
# For Blower
import math 
m_dot = 1.; 
R = 0.287; 
T1 = 343.;
P1 = 100.; 
P2 = 2*P1; 
g = 1.4;

# Calculation and Results
V_dot = (m_dot*R*T1)/P1;
PRb = V_dot*(P2-P1);
print "Power required by the blower is",round(PRb,1),"kW"

# For van compressor
P1v = 1.
V21 = 0.7 			# V2/V1
P2v = P1v*(1./V12)**g;
V2_dot = 0.7;
V1_dot = 0.7*V_dot;
P3v = 2.;
PRv = (g/0.4)*P1*0.995*( (1.65/1)**(0.4/g) - 1) + 0.696*(2 - 1.65)*P1
print "Power Required by van compressor is",round(PRv),"kW"

Power required by the blower is 98.4 kW
Power Required by van compressor is 78.0 kW

Example 18.9 Page No : 731

In [13]:
# Variables
T1 = 283.
P21 = 2.5; 			# P2/P1
P32 = 2.1; 			# P3/P2
ns = 0.85
ma = 5.; 
cp = 1.005;

# Calculation
T2s = round(T1*(P21)**((g-1)/g),1);
T2 = round(T1 + (T2s-T1)/ns,2);
T3 = T2-50;
T4s = round(T3*(P32)**((g-1)/g),2);
T4 = T3 + (T4s-T3)/ns;
P = ma*cp*((T2-T1)+(T4-T3));

# Results
print "Total compressor power is",round(P,1),"kW"

# note : T4 is calculted wrongly in book. please check.

Total compressor power is 965.1 kW

Example 18.10 Page No : 732

In [15]:
# Variables
T1 = 278.
P21 = 2.5; 			# P2/P1
cp = 1.005
ns = 0.84; V2 = 120.;

# Calculation
T2s = T1*(P21)**((g-1)/g);
T2 = T1 + (T2s-T1)/ns;
mg = 0.04*(13+1);
P = mg*cp*(T2-T1);
T02 = T2 + V2**2/(2*cp*1000);
P1 = 0.6;
P2 = P21*0.6;
P02 = P2*(T02/T2)**(g/(g-1));

# Results
print "Power required to drive the compressor is",round(P,1),"kW"
print "Stagnation temperature is",round(T02,2),"K"
print "Stagnation pressure is",round(P02,3),"bar"

# note : rounding off error is there. please check.

Power required to drive the compressor is 55.7 kW
Stagnation temperature is 384.21 K
Stagnation pressure is 1.602 bar