DEPARTMENT OF AEROSPACE ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY, TECHNOLOGY, BOMBAY
PROPULSION LABORATORY REPORT
EXPERIMENT 11 NOZZLE THRUST AND EFFICIENCY MEASUREMENT
SUBMITTED BY: ARAVINDKUMAR Roll No.163010021
NOZZLE EFFCIENCY AND THRUST MEASUREMENT
Aim:
To study the performance characteristics of Convergent and Convergent-Divergent nozzles and measure the thrust and efficiency.
Apparatus Required:
F791 Nozzle performance test unit. Nozzles: Convergent Nozzle of throat diameter 2mm and four Convergent-Divergent with exit Area to throat area of 1.2, 1.4, 1.6 and 2. Two Pressure Gauges, 0 to 1100KN/ 2 Stainless Steel Chamber, 50mm diameter and 300mm long, end cover secured by bolts and sealed by ring. Hollow cantilever beam of 250mm length with impact head and nozzle adaptor, cantilever deflection approximately 4N/mm. Valves and Air regulators. Micrometer with least count 0.01mm with electrical contact, indicator Lamp and Volt meter.
The high velocity jet of fluid leaving a nozzle may be used in several ways: In a turbine, the kinetic energy stored in the fluid forms the energy available to the blades or the Rotor for conversion to shaft work. In rockets and jet propulsion, the change of momentum associated with the velocity changes in the nozzle provides most of the propulsion force. In ejectors and injectors, the changes of momentum of the jet, with its entrained fluid, is used to bring about the desired pressure changes. Compressible Flow through Nozzle is accompanied by shock waves inside the nozzle and can be carefully moved out of the nozzle by adjusting the inlet and exit pressure thus making the flow isentropic throughout. The presence of shocks inside the nozzle causes the viscous dissipation and reduction in total pressure long the length of the nozzle causing reduction in nozzle efficiency. The governing equation for nozzle in subsonic and supersonic flow is:
= (−) If the flow is subsonic, the area of the flow should be decreased to accelerate the flow. Subsequently if the for achieving supersonic flow, the area should be increased to accelerate up to higher Mach numbers above sonic.
F igur e 1. Convergent Nozzle
F igure 2. Convergent Divergent Nozzle
F igure 3. F791 Nozzle performance apparatus
F igure 4 . F791 Nozzle performance apparatus layout
Performance Parameters:
Due to the effects of friction, uncontrolled expansion, shocks etc., the velocity of the jet of fluid leaving a nozzle will be lower than that from an ideal nozzle.
The efficiency of a nozzle as a kinetic energy producer is the ratio:
Efficiency = Actual thrust =
̇V
real
This velocity V real can be calculated using experimental thrust and mass flow rate.
. .
Δ
Kinetic energy increase across the nozzle = Kinetic energy increase in an isentroic nozzle
=
Ideal thrust of the nozzle:
=
exit P √ = 2 Cp T01{1(Pinlet )^ }
Δ
.
. =
Where Cp = Specific heat at constant pressure T01 =Total Temperature
. Nozzle pressure ratio after choking F igure 4
Procedure: 1. The load versus the deflection curve of the thrust measuring device is found out and plotted, which basically comprises of a cantilever beam, whose deflection is measured using an electronic circuit. 2. By using the deflection we can find the thrust produced, which can be calculated by dividing the deflection by the slope of the load verses deflection curve. 3. The nozzle is then fixed on the tip of the cantilever beam, which is then fixed inside a canister that has a certain pressure inside corresponding to the back pressure. 4. The pressure ratio is varied by either keeping the inlet pressure constant or by keeping the exit pressure fixed. 5. The deflections are noted along with the mass flow rate from Rota-meter and inlet temperature from the digital thermometer. 6. Using the obtained data, the specific thrust and the nozzle efficiency are calculated. 7. The same steps are repeated for all the other nozzles.
Observations:
Deflection during loading
Deflection during unloading
Average
δ1
δ2
δ3
N
mm
mm
mm
0.5
12
6
9
1
26
18
22
1.5
40
33
36.5
2
50
46
48
2.5
64
59
61.5
3
76
71
73.5
3.5
90
83
86.5
4
104
104
104
Weight
Table1. Load and Deflection readings for calibration of the beam
Load vs Deflection 4.5 4 3.5 3 d 2.5 a o L 2
Load
1.5 1 0.5 0 0
20
40
60
80
100
120
Delection
F igur e 5. Slope of Load vs. deflection curve. Equation of the Load-deflection curve: Y = .04x + .02
Observation table for nozzles:
P1
P2
δ
Actual Thrust
Actual Velocity
m
To1
Ideal Velocity
Efficiency
Ideal thrust
Kpa
Kpa
mm
N
m/s
Kg/s
K
m/s
%
N
701.33
601.33
6.00
0.26
86.67
0.0030
0.83
302.00
161.64
28.75
0.48
701.33
501.33
16.00
0.66
169.23
0.0039
0.67
302.00
235.74
51.53
0.92
701.33
401.33
28.00
1.14
271.43
0.0042
0.50
302.00
299.28
82.25
1.26
701.33
301.33
39.00
1.58
316.00
0.0050
0.33
302.10
361.01
76.62
1.81
701.33
201.33
52.00
2.10
420.00
0.0050
0.17
302.10
426.94
96.77
2.13
Pr.Raio
Table2. Observation and calculated data for Nozzle 1 at P1= 701.325 KPa
P2
P1
T1
δ
Thrust
m
Actual Velocity
Ideal Velocity
Efficiency
Pr .ratio
Ideal thrust
Kpa
Kpa
K
mm
N
Kg/s
m/s
m/s
%
201.33
301.33
302.20
16.00
0.66
0.0020
330.00
287.59
75.95
0.67
0.58
201.33
401.33
302.30
25.00
1.02
0.0026
392.31
368.78
88.36
0.50
0.96
201.33
501.33
302.30
38.00
1.54
0.0035
440.00
417.66
90.10
0.40
1.46
201.33
601.33
302.30
46.00
1.86
0.0040
465.00
451.77
94.39
0.33
1.81
201.33
701.33
302.30
59.00
2.38
0.0051
466.67
477.49
104.69
0.29
2.44
Table2. Observation and calculated data for Nozzle 1 at P2= 201.325 KPa
P1
P2
T1
δ
m
Thrust
Actual Velocity
Ideal Velocity
Efficiency
Ideal Thrust
Kpa
Kpa
K
mm
kg/s
N
m/s
m/s
%
N
701.33
601.33
302.40
11.00
0.0036
0.46
127.78
161.75
62.41
0.58
701.33
501.33
302.40
18.00
0.0042
0.74
176.19
235.89
55.79
0.99
701.33
401.33
302.40
30.00
0.0048
1.22
254.17
299.48
72.03
1.44
701.33
301.33
302.50
39.00
0.0047
1.58
336.17
361.25
86.60
1.70
701.33
201.33
302.50
54.00
0.0050
2.18
436.00
427.23
104.15
2.14
Table3. Observation and calculated data for Nozzle 2 at P1= 701.325 KPa
P2
P1
T1
δ
m
Thrust
Actual Velocity
Ideal Velocity
Efficiency
Pr. Ratio
Ideal thrust
Kpa
Kpa
K
mm
kg/s
N
m/s
m/s
%
201.33
301.33
302.50
11.00
0.0020
0.46
230.00
257.36
79.87
0.67
0.51
201.33
401.33
302.50
19.00
0.0027
0.78
288.89
329.95
76.66
0.50
0.89
201.33
501.33
302.50
35.00
0.0036
1.42
394.44
373.69
111.42
0.40
1.35
201.33
601.33
302.50
42.00
0.0040
1.70
425.00
404.21
110.55
0.33
1.62
201.33
701.33
302.60
55.00
0.0050
2.22
444.00
427.30
107.97
0.29
2.14
Table 4. Observation and calculated data for Nozzle 2 at P2= 201.325 KPa
P1
P2
T1
δ
m
Thrust
Actual Velocity
Ideal Velocity
Efficiency
Ideal Thrust
Kpa
Kpa
K
mm
kg/s
N
m/s
m/s
%
N
701.33
601.33
302.60
12.00
0.0051
0.50
98.04
161.80
36.71
0.83
701.33
501.33
302.60
18.00
0.0050
0.74
148.00
235.97
39.34
1.18
701.33
401.33
302.60
24.00
0.0050
0.98
196.00
299.58
42.81
1.50
701.33
301.33
302.60
35.00
0.0049
1.42
289.80
361.31
64.33
1.77
701.33
201.33
302.70
50.00
0.0050
2.02
404.00
427.37
89.36
2.14
Table5. Observation and calculated data for Nozzle 3 at P1= 701.325 KPa
P2
P1
T1
δ
m
Thrust
Actual Velocity
Ideal Velocity
Efficiency
Pr. Ratio
Ideal thrust
Kpa
Kpa
K
mm
kg/s
N
m/s
m/s
%
201.33
301.33
302.70
6.00
0.0020
0.26
130.00
257.44
25.50
0.67
0.51
201.33
401.33
302.70
14.00
0.0026
0.58
223.08
330.06
45.68
0.50
0.86
201.33
501.33
302.70
20.00
0.0036
0.82
227.78
373.81
37.13
0.40
1.35
201.33
601.33
302.70
41.00
0.0045
1.66
368.89
404.34
83.23
0.33
1.82
201.33
701.33
302.70
51.00
0.0050
2.06
412.00
427.37
92.94
0.29
2.14
Table6. Observation and calculated data for Nozzle 3 at P2= 201.325 KPa
Sample Calculations:
Actual Thrust from equation Y = .04x + .02 obtained from load deflection plot. Actual Thrust: 0.26 N 2. Actual velocity = Actual Thrust / mass flow rate. Actual Velocity= 130 m/sec
* = √ 2 Cp T01{1(PPinletexit )^ } 3. Ideal Thrust =
Cp = 1005 J/KgK
= 201.33 KPa = 301.33 KPa T01 = 302 K
So
= 257.44 m/s
Ideal Thrust = m*Videal = .51 N Efficiency = Va2/Vi2 = 25.25 %
Graphs:
Mass flow rate vs Pressure ratio for consant P1 0.006
0.005
0.004 e t a r
w o 0.003 l f s s a M0.002
Mass flow rate (Nozzle1) Mass Flow rate (Nozzle 2) Mass flow rate ( Nozzle 3)
0.001
0 0
0.2
0.4
0.6
Pressure Ratio
0.8
1
Graph1. Mass flow rate vs. Pressure ratio for all nozzles at constant inlet pressure= 701.325kpa
Ideal Thrust vs Pressure Ratio for constant P1 2.5
2 t s 1.5 u r h T l a e 1 d I
Ideal thrust (Nozzle 1) Ideal Thrust (Nozzle 2) Ideal thrust (Nozzle 3)
0.5
0 0
0.2
0.4
0.6
0.8
1
Pressure ratio
Graph2. Ideal thrust vs Pressure ratio keeping inlet pressure constant = 701.325kpa
Specific thrust vs Pressure ratio for constant P1 500 450 400 t s u r 350 h t c i f i c 300 e p S 250
Specific thrust (Nozzle 1) Specific thrust (Nozzle 2) Specific thrust (Nozzle 3)
200 150 0
0.2
0.4
0.6
0.8
1
Pressure ratio
Graph3. Specific thrust vs Pressure ratio keeping inlet pressure constant = 701.325kpa
Efficiency Vs pressure ratio for const P1 120
100
80 y c n e i 60 c i f f E
Efficiency (Nozzle 1) Efficiency (Nozzle 2)
40
Eficiency (Nozzle3)
20
0 0
0.2
0.4
0.6
0.8
1
Pressure ratio
Graph4. Efficiency vs Pressure ratio keeping inlet pressure constant = 701.325kpa
Mass flow rate vs Pressure ratio for consant P2 0.006
0.005
0.004 e t a r w o 0.003 l f s s a M 0.002
Mass flow rate (Nozzle1) Mass Flow rate (Nozzle 2) Mass flow rate ( Nozzle 3)
0.001
0 0
0.2
0.4
0.6
Pressure Ratio
0.8
1
Graph5. Mass flow rate vs. Pressure ratio for all nozzles at constant exit pressure= 201.325kpa
Specific thrust vs Pressure ratio for constant P2 500 450 400 t s 350 u r h t c 300 i f i c e 250 p S
Specific thrust (Nozzle 1) Specific thrust (Nozzle 2) Specific thrust (Nozzle 3)
200 150 100 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Pressure ratio
Graph6. Specific thrust vs Pressure ratio keeping exit pressure constant = 201.325kpa
Conclusion:
The performance analysis of one convergent and two convergent divergent nozzles were done a different pressure ratios. The dependence of the performance parameters such as thrust, exit velocity, specific thrust and efficiency on different pressure ratios were measured and plotted. It has been observed that if the pressure ratio is more, the mass flow rate and exit velocity becomes more. This also in turn shows that the thrust is directly proportional to the pressure difference between the inlet ant the ex it within the choking limit. The Effect of pressure ratio is significant in increasing the mass flow rate and velocity hence improving the thrust output and also the efficiency of the nozzle.
