Nozzle Efficiency

Experimental Determination of Nozzle efficiency Sunil Kumar (09D01015) AIM To study the variation of o f nozzle efficiency with varying Inlet and Back pressures for three different nozzles

THEORY Flow through an Ideal nozzle is supposed to be isentropic, but in real life there are losses and hence it is important to study the effect of various parameters on efficiency of nozzle. Efficiency is a factor indicative of all losses that occur during the diffusion process inside the nozzle. In this experiment we will study the effect of variation of efficiency with total inlet pressure and back pressure for three nozzles having different exit area.

SETUP: For this experiment we have used the following setup by PA HILTON

PA HILTON MODEL

Sensors: 1. Rotameter – used for measuring mass flow rate 2. Dial Gauge – used for measuring thrust or jet reaction 3. Pressure Sensors 4. Temperature Sensors

FORMULAE: 

 

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− .  = _ 6. ̇ =0.985∗̇   =  ̇       = 0.5 ∗   where π = P2/P1 ∆=1       ɳ =   ⁄∆



 = √ 2 ∗∆

OBSERVATION: Calibration of Dial Gauge: To measure the nozzle exit velocity we use an impact head to kill the entire axial component of velocity. This change in momentum exerts a force on the impact head which is mounted on a cantilever arm. A Dial Gauge is used to measure the deflection of the Cantilever Arm. To calibrate dial gauge we have used the standard weights given by the manufacturer. Note: The dial gauge was not properly configured and hence we got high value of intercept during our calibration but since we is does not change the slope it will not affect the readings.

Weight 0.5 1 1.5 2 2.5 3 3.5 4

Dial Reading 23 35 48.5 61 75 85.5 103 116

Calibration 140 120

y = 26.571x + 8.5893

100

g n i d 80 a e R l 60 a i D

40 20 0 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Force

Hence the final relation between Force (F) and Dial Readings (D) is

F = (D-8.5893)/26.571

Sample Calculations: Sample calculation for one of the readings for nozzle 1 has been shown below. Upper mentioned formulae are directly used without stating here. P1 = 801 kPa

P2 = 151 kPa

̇ = 5.4 /

Mass flow rate

Corrected mass flow rate = 0.985*5.4 = 5.319 g/sec T1 = 29.1

℃ = 302.25 K

Dial Reading = 72 Force= (72-8.589)/26.571 = 2.386 N Pressure Ratio Pi = 151/801 = 0.19 Calculated Velocity = 2.386 / 5.319 = 448.67 m/s Specific Kinetic Energy = 0.5*448.67^2 = 100652.2 J/Kg

.)=115127.3 ∆=1004.5∗302.25∗(10.19.  = √2∗115127 =479.8 Efficiency = (100652.2/115127.3) =0.874

Tables: V calc = Velocity Calculated Specific KE = Specific Kinetic Energy Design Pressure Ratio for Nozzle 1 = 0.528 – 1 Design Pressure ratio for the nozzle 2 is ~ 0.26 Design Pressure ratio for the nozzle 5 is ~ 0.1 Correc = corrected

Nozzle 1 Case 1: Back Pressure Varied& Inlet Pressure is Constant

ṁ

pi (P2/P1)

ṁ

Force

V calc

Specific.KE

delta H

ɳ

correc

V ideal

29.1

0.19

5.319

2.386

448.67

100652.2

29.1

0.25

5.319

2.236

420.37

88354.4

5.4

58

29.1

0.38

5.319

1.860

349.61

61114.1

300

5.2

52

29.1

0.50

5.122

1.634

318.97

50871.5

700

400

4.8

42

29.1

0.63

4.728

1.257

265.95

35365.4

700

500

4

31

29.2

0.75

3.940

0.843

214.07

22913.1

700

600

3

20

29.2

0.88

2.955

0.429

145.33

10560.6

0.874 0.892 0.825 0.934 0.928 0.957 0.930

479.8

68

115127.3 99077.3 74064.6 54459.2 38095.1 23931.8 11354.0

P1 kPa

P2 kPa

Dial

g/s

700

50

5.4

72

700

100

5.4

700

200

700

T1

445.1 384.9 330.0 276.0 218.8 150.7

Nozzle 1 Case 2: Back Pressure is Constant & Inlet Pressure is varied

ṁ

P1

P2

kPa 200

kPa g/s 100 1.8

300

100

400

Dial

T1

pi

15

29.3

(P2/P1) 0.67

2.6

25

29.4

100

3.4

35

500

100

4

600

100

4.6

ṁ

Force

V calc

Specific.KE

delta H

ɳ

correc 1.773

V ideal

0.241

136.08

9259.5

33105.1

0.280

257.3

0.50

2.561

0.618

241.17

29080.7

54424.7

0.534

329.9

29.1

0.40

3.349

0.994

296.80

44044.7

69731.8

0.632

373.4

47

29.2

0.33

3.940

1.446

366.90

67309.0

81608.9

0.825

404.0

57

29.2

0.29

4.531

1.822

402.11

80845.2

91164.2

0.887

427.0

700

100

5.4

67

29.2

0.25

5.319

2.198

413.29

85405.0

99110.1

0.862

445.2


ṁ

P1

P2

Dial

kPa

kPa

g/s

700

50

5.7

74

700

100

5.7

700

200

700

T1

pi

ṁ

Force

V calc

Specific.KE

delta H

ɳ

V

(P2/P1)

correc

ideal

29.4

0.19

5.615

2.462

438.46

96124.4

115241

0.834

480.1

68

29.4

0.25

5.615

2.236

398.24

79298.6

99175.7

0.799

445.4

5.7

59

29.5

0.38

5.615

1.897

337.91

57093.0

74162.6

0.769

385.1

300

5.6

51

29.7

0.50

5.516

1.596

289.37

41866.1

54567.3

0.767

330.4

700

400

5.2

43

29.6

0.63

5.122

1.295

252.84

31964.6

38158.1

0.838

276.3

700

500

4.6

32

29.8

0.75

4.531

0.881

194.45

18906.3

23979.3

0.788

219.0

700

600

3.4

20

29.8

0.88

3.349

0.429

128.23

8221.9

11376.5

0.723

150.8


ṁ

Force

(P2/P1)

ṁ

correc

29.7

0.67

1.773

0.204

114.86

6596.2

33148.9

0.199

257.5

25

29.7

0.50

2.758

0.618

223.94

25074.7

54478.6

0.460

330.1

3.6

36

29.7

0.40

3.546

1.032

290.92

42318.1

69870.2

0.606

373.8

100

4.4

47

29.6

0.33

4.334

1.446

333.55

55627.3

81716.9

0.681

404.3

600

100

5

58

29.5

0.29

4.925

1.860

377.58

71283.5

91254.7

0.781

427.2

700

100

5.8

68

29.6

0.25

5.713

2.236

391.38

76587.8

99241.2

0.772

445.5

P1

P2

Dial

kPa

kPa

g/s

200

100

1.8

14

300

100

2.8

400

100

500

T1

pi

V calc

Specific.KE

delta H

ɳ

V ideal


ṁ

Force

(P2/P1)

ṁ

correc

29.9

0.19

5.713

2.386

417.73

87247.9

115432.0

0.756

480.5

65

29.9

0.25

5.713

2.123

371.61

69048.4

99339.6

0.695

445.7

5.8

54

29.9

0.38

5.713

1.709

299.15

44745.3

74260.6

0.603

385.4

300

5.8

44

29.9

0.50

5.713

1.333

233.27

27208.3

54603.3

0.498

330.5

700

400

5.8

36

30

0.63

5.713

1.032

180.57

16303.3

38208.5

0.427

276.4

700

500

5.8

31

30.1

0.75

5.713

0.843

147.63

10898.0

24003.0

0.454

219.1

700

600

5.4

25

30.1

0.88

5.319

0.618

116.12

6741.6

11387.8

0.592

150.9

P1

P2

Dial

kPa

kPa

g/s

700

50

5.8

72

700

100

5.8

700

200

700

T1

pi

V calc

Specific.KE

delta H

ɳ

V ideal


ṁ

Force

(P2/P1)

ṁ

correc

30

0.67

2.167

0.204

93.97

4415.6

33181.8

0.133

257.6

23

29.9

0.50

2.758

0.542

196.65

19335.4

54514.6

0.355

330.2

33

29.8

0.40

3.546

0.919

259.08

33562.0

69893.3

0.480

373.9

P1

P2

Dial

kPa

kPa

g/s

200

100

2.2

14

300

100

2.8

400

100

3.6

T1

pi

V calc

Specific.KE

delta H

ɳ

V ideal

500

100

4.5

43

29.8

0.33

4.433

1.295

292.17

42682.6

81770.9

0.522

404.4

600

100

5.2

54

29.8

0.29

5.122

1.709

333.67

55666.9

91345.1

0.609

427.4

700

100

5.8

66

29.9

0.25

5.713

2.161

378.20

71518.1

99339.6

0.720

445.7

PLOTS PI = C => Inlet Pressure is Constant PB = C => Back Pressure is Constant Mass flow rate v/s Inlet Pressure (Back Pressure = 201 kPa) 6.000 5.500 5.000 ) s / g 4.500 ( e t a 4.000 R w3.500 o l f s s 3.000 a M

Nozzle 1 Nozzle 2 Nozzle 5

2.500

2.000 1.500 280

380

480

580

680

780

Inlet Pressure (in kPa)

Mass Flow rate v/s Pressure Ratio’s

880

6.000 Nozzle 1 (PI=C)

5.500 5.000

Nozzle 2 (PI=C)

) c e s / 4.500 g ( e t a R4.000 w o l F s s 3.500 a M

Nozzle 5 (PI=C) Nozzle 1 (PB=C)

3.000

Nozzle 2 (PB=C)

2.500 Nozzle 5 (PB=C)

2.000 0.10

0.30

0.50

0.70

0.90

Pressure Ratio (pi)

Exit Velocity v/s Pressure Ratio

500.00

Nozzle 1 (PI=c)

450.00 400.00

Nozzle 2 (PI=c)

350.00 y t i 300.00 c o l e 250.00 V t i x 200.00 E

Nozzle 5 (PI=c) Nozzle 1 (PB =c )

150.00 Nozzle 2 (PB=C)

100.00 50.00 0.00 0.00

0.20

0.40

0.60

Pressure Ratio(pi)

0.80

1.00

Nozzle 5 (PB=C)

Efficiency v/s Pressure Ratio

1.200

Nozzle 1 (PI=C)

1.000

Nozzle 2 (PI=C)

0.800

Nozzle 5 (PI=C)

y c n e i 0.600 c e i f f E

Nozzle 1 (PB=C)

0.400

Nozzle 2 (PB=C)

0.200

Nozzle 5 (PB=C)

0.000 0.00

0.20

0.40

0.60

0.80

1.00

Pressure Ratio(pi)

Conclusions:  

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In Plot 1, we can that mass flow rate increases linearly with Inlet Pressure as expected In Plot 2, for the case Inlet pressure is held constant and back pressure is reduced choking occurs when P.R is less than 0.5. o Also for second case when Inlet Pressure is varied and Back pressure is held constant we can see that mass flow rate continuously increases with decrease in P.R and choking is not observed. Hence we can say that mass flow rate not only depends on pressure ratio but also on the value of Inlet pressure. For nozzle 1 and 2 choking occurs when pressure ratios are less than 0.5 but for nozzle 5 o mass flow rate is almost constant from P.R of 0.7 which shows that flow is chocked below P.R of 0.7. In Plot 3, we find that Velocity increases with decrease in P.R and we have found similar trend in all three nozzles and for both cases. In Plot 4 of efficiency v/s pressure ratios we found that, Efficiency for nozzle 1 is almost same for P.R greater than 0.5, which is justified from the fact o that nozzle 1 is convergent type of nozzle which is most efficient for subsonic flows and hence its efficiency decreases when operated below P.R of 0.5 o Efficiency for nozzle 2 increases once the flow turn supersonic, that is when P.R falls below 0.528, this is expected as the nozzle is designed for P.R of 0.26. But the efficiency does not change much as compared to nozzle 1 Trend of efficiency for nozzle 5 is little different from nozzle 2. The efficiency is maximum o when it is operated at very higher and very low P.R. The possible reason being the Exit to Throat area ratio being high, close to 2. This means that is can be efficiently operated at P.R



greater than 0.7 and P.R lower than 0.4. For the case when back pressure is held constant and inlet pressure is varied we can see o that the efficiency is continuously increasing with decrement in P.R for all the three nozzles. When nozzles are operated at P.R other than designed then they are either over expanded or under expanded which increases loss in the nozzle and hence gives lower efficiency than expected.

Nozzle Efficiency

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