1.
Compressor Data
Compressor inlet pressure, P01 = 101.325 kPa
Compressor inlet temperature, T01 = 288 K
Compressor inlet density, ρa = 1.225 kJ/kgK
Specific heat capacity of air, Cpa = 1.005 kJ/kgK
Gas constant, R = 287 J/kgK
Specific heat ratio of air, γa = 1.4
Isentropic efficiency, ηc = 0.85
Compressor slip factor, σc = 0.7
Specific speed of compressor, Ns = 1 rpm
Compressor pressure ratio, P02 / P01= 2.5
Compressor mass flow rate, m°
a = 0.3 kg/s
Compressor impeller diameter, D2 = 0.05 m
Compressor eye root diameter, dr = 0.015 m
Compressor eye tip diameter, dt = 0.03 m

2.
Compressor calculation
Compressor outlet pressor, P02 = 2.5 × P01
= 7 × 101.325
= 253.3125 kPa
Compressor outlet isentropic temperature, T02
′
= T01 ×
P02
P01
γa−1
γa
= 288 × 2.5
1.4−1
1.4
= 374.187808 K
Compressor outlet temperature, T02 =
T02
′ −T01
ηc
+ T01
=
374.187808−288
0.85
+ 288
= 389.397421 K

3.
Compressor work done, Wc = m°
a Cpa (T02 – T01)
= 0.3 × 1.005 × (389.397421 – 288)
= 30.5713224 kW
Enthalpy drop, Δh0,1-2 = Cpa (T02 – T01)
= 1.005 × (389.397421 – 288)
= 101.904408 kJ/kg
Impeller velocity, U2 =
∆h0,1−2
σc
=
101.904408 ×103
0.6
= 381.546492 m/s

4.
Eye impeller area, a =
π
4
× dt
2
− dr
2
=
π
4
× (0.032−0.0152)
= 0.0005301437 m3
C1 =
ma
°
ρ a
=
0.3
1.225×0.0005301437
= 461.94637 m/s
Assume C2r = C1 = 461.94637 m/s
C2w = σc × U2
= 0.7 × 381.546492
= 267.082544 m/s

5.
C2 = C2r
2
+ C2w
2
= 461.94637 2 + 267.082544 2
= 533.598663 m/s
Compressor exit temperature, T2 = T02 -
C2
2
2cp
= 398.397421 -
533.598663 2
2×1.005×103
= 247.741931

6.
Compressor exit pressure, P2 = P02 ×
T2
T02
γa
γa−1
= 253.3125 ×
247.741931
389.397421
1.4
1.4−1
= 52.033038 kPa
Compressor exit density, ρ2 =
P2
RT2
=
52.033038×103
287×247.741931
= 0.731809 kg/m3

7.
H =
m°
ρ2πD2×C2r
=
0.3
0.731809×π×0.05×461.94637
= 0.005649 m
Compressor exit area, A2 = πD2H
= π × 0.05 × 0.005649
= 0.00088734 m2
Cr2 =
m°
ρ2A2
=
0.3
0.731809×0.00088734
= 461.99092 m/s

8.
Compressor outlet volume flow rate, v2
°
=
1
ρ2
=
1
0.731809
= 1.366476 m3
Compressor speed, N =
60× Δh0,1−2
3
4×Ns
2π v2
°
=
60× 101.904408×103
3
4×1
2×π× 1.366476
= 46592.40256 rpm

9.
Eye mean diameter, dm =
dt+dr
2
=
0.03+0.015
2
= 0.0225 m
Eye mean impeller velocity, Um = πdmN/60
= π ×0.0225× 46592.40256/60
= 54.890381 m/s
Eye mean impeller angle, αm = tan-1(
C1
Um
)
= tan-1 461.94637
54.890381
= 83.223651 °

10.
Eye root diameter, dr = 0.015 m
Eye root impeller velocity, Uer = πdrN/60
= π × 0.015 × 46592.40256/60
= 36.593587 m/s
Eye root impeller angle, αer = tan-1 C1
Uer
= tan-1 461.94637
36.593587
= 85.470710 °
Eye tip diameter, dt = 0.03 m
Eye tip impeller velocity, Uet = πdtN/60
= π × 0.03 × 46592.40256 /60
= 73.187174 m/s

11.
Eye tip impeller angle, αet = tan−1 C1
Uet
= tan−1 461.94637
73.187174
= 80.997331 °
Compressor exit impeller angle, β2 = tan−1 C2r
C2w
= tan−1 461.990538
267.082544
= 59.967252 °
Number of blade of compressor, Z = 6.5×
D2+dm
D2−dm
× sin
β2+β1
2
= 6.5×
0.05+0.0225
0.05−0.0225
× sin
59.967252 +0
2
= 8.563940 ~ 8 blades

12.
Turbine Data
Turbine outlet pressure,P04 = P01 = 101.325 kPa
Turbine inlet temperature, T03 = 700 K
Specific heat capacity of gas, Cpg = 1.051 kJ/kgK
Gas constant, R = 287 J/kgK
Specific heat ratio of gas, γg = 1.33
Isentropic efficiency, ηt = 0.9
Turbine slip factor, σt = 0.9
Turbine speed, N = 46592.40256 rpm
Turbine expression ratio, P03 / P04 = 2
Turbine mass flow rate, m°
g = 0.2 kg/s
Turbine impeller diameter, D3 = 0.045 m
Turbine eye root diameter, d4r = 0.012 m
Turbine eye tip diameter, d4t = 0.032 m
Head, H = m

13.
Turbine calculation
Turbine inlet pressure, P03 = P04 × 2
= 101.325 × 2
= 202.65 kPa
Turbine outlet isentropic temperature, T04
′
=
T03
P03
P04
γg−1
γg
=
700
2
1.33−1
1.33
= 589.394918 K

14.
Turbine outlet temperature, T04 = T03 -
T03−T04
′
ηt
= 700 -
700−589.394918
0.9
= 577.105464 K
Turbine work done, Wt = mg
° Cpg T03 − T04
= 0.2 × 1.051 × (700 – 577.105464)
= 25.832431 kW
Enthalpy drop, Δh0,3-4 = Cpg (T03 – T04)
= 1.051 × (700 - 577.105464 )
= 129.162157 kW

15.
U3 =
Δh0,3−4
σt
=
129.162157×103
0.9
= 378.831767 m/s
Turbine impeller diameter, D3 =
U3×60
π×N
=
378.831767 ×60
π ×46592.40256
= 0.155286 m