Lab 4 - Converging Diverging Nozzle - Fluid Dynamics PDF

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Summary

Therefore, it can be concluded, that higher the back pressures lower will be the Mach number due to the decrease in mass flow. And, when the flow accelerates subsonically or supersonically the pressure drops....

Description

ENGI-3555 Objective: To study the different flow regimes of one- dimensional compressible flow in a converging- diverging nozzle. Apparatus: As specified in the lab manual. Procedure: As specified in the lab manual. Results and graphs: Table 1: Experimental Data Position @ Increment of 0.1 inch 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

80 psig 88.2 88.3 88.7 89.2 88.5 88.3 88.1 87.5 74.7 74.7 74.1 74.1 75 75 75.3 75.9 76.5 76.8 77.2 77.2 77.6 77.7 78.2 78.4 78.6 78.6 79.2 79.3 78.8 79

62 psig 88.5 89 89 88.4 88.3 88 88.1 84.7 53 51.2 46.5 45.2 46.2 48 49.8 52 53.7 54.9 56.3 57.3 58.3 59 59.9 60.8 61 62 62.4 62.5 62.4 62.3

50 psig 88.5 88.7 88.6 88.7 88.4 88.3 88.7 84.7 51 48.7 42 37 31.8 25.4 24.2 21.8 19.3 19.2 40.8 43.2 45 46.2 47.3 48.2 49 50.2 50.7 50.7 50.8 50.7

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10 psig 88.6 88.6 88.5 88.3 88.8 88.7 88.1 84.4 50.5 48.6 42 37.1 31.8 25.5 24.2 21.7 19.3 19.2 16.7 15 14.2 12.9 12.1 10.6 9.2 9.3 10.3 10.3 10.2 10.2

ENGI-3555 To

17.4

16.7

15.9

15.6

ºC

T2

16.4

15.6

15.1

14.9

ºC

P2

100.4

100.4

100.4

100.4

0.92

1.76

1.82

1.86

P1-P2

kPa in H2O

Table 2: Back Pressure Setting 80 PSIG

Back Pressure Setting (psig) 62 PSIG 50 PSIG 10 PSIG

Position

Units

1

709.08

711.14

711.14

711.83

kPa

2

709.77

714.59

712.52

711.83

kPa

3

712.52

714.59

711.83

711.14

kPa

4

715.97

710.46

712.52

709.77

kPa

5

711.14

709.77

710.46

713.21

kPa

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

709.77 708.39 704.25 615.97 615.97 611.83 611.83 618.04 618.04 620.11 624.25 628.39 630.46 633.21 633.21 635.97 636.66 640.11 641.49 642.87 642.87 647.01 647.70 644.25 645.63

707.70 708.39 684.94 466.32 453.90 421.49 412.52 419.42 431.83 444.25 459.42 471.14 479.42 489.08 495.97 502.87 507.70 513.90 520.11 521.49 528.39 531.14 531.83 531.14 530.46

709.77 712.52 684.94 452.52 436.66 390.46 355.97 320.11 275.97 267.70 251.14 233.90 233.21 382.18 398.73 411.14 419.42 427.01 433.21 438.73 447.01 450.46 450.46 451.14 450.46

712.52 708.39 682.87 449.08 435.97 390.46 356.66 320.11 276.66 267.70 250.46 233.90 233.21 215.97 204.25 198.73 189.77 184.25 173.90 164.25 164.94 171.83 171.83 171.14 171.14

kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa kPa

To

290.55

289.85

289.05

288.75

K

T2

289.55

288.75

288.25

288.05

K

P2

100.8

100.8

100.8

100.8

kPa

P1-P2

0.229

0.438

0.453

0.463

kPa

Table 3: P/Po Tabulation P/P0 Tabulation

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80 PSIG

Back Pressure Setting (psig) 62 50 10 PSIG PSIG PSIG

Position 1

1.0000

1.0000

1.0000

1.0000

2

1.0000

1.0048

1.0019

1.0000

3

1.0000

1.0048

1.0010

0.9990

4

1.0000

1.0000

1.0000

0.9971

5

1.0000

0.9981

1.0000

1.0000

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

1.0000 1.0000 0.9932 0.8687 0.8687 0.8629 0.8629 0.8716 0.8716 0.8745 0.8804 0.8862 0.8891 0.8930 0.8930 0.8969 0.8979 0.9027 0.9047 0.9066 0.9066 0.9125 0.9134 0.9086 0.9105

1.0000 0.9961 0.9631 0.6557 0.6383 0.5927 0.5801 0.5898 0.6072 0.6247 0.6460 0.6625 0.6742 0.6877 0.6974 0.7071 0.7139 0.7226 0.7314 0.7333 0.7430 0.7469 0.7479 0.7469 0.7459

1.0000 1.0019 0.9631 0.6363 0.6140 0.5491 0.5006 0.4501 0.3881 0.3764 0.3532 0.3289 0.3279 0.5374 0.5607 0.5781 0.5898 0.6004 0.6092 0.6169 0.6286 0.6334 0.6334 0.6344 0.6334

1.0000 0.9952 0.9593 0.6309 0.6125 0.5485 0.5010 0.4497 0.3887 0.3761 0.3518 0.3286 0.3276 0.3034 0.2869 0.2792 0.2666 0.2588 0.2443 0.2307 0.2317 0.2414 0.2414 0.2404 0.2404

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ENGI-3555

Table 4: Constants Discharge Coefficient (Cz)

Gas Constant (R)

0.623

J/kgK 287

Specific Heat Ratio (k)

Area (Nozzle Throat)

Area (Orifice)

1.4

m2 9.34019E-06

m2 0.000572

Table 5: Mach Numbers

80 PSIG

Mach Number Tabulation Back Pressure Setting (psig) 62 50 10 PSIG PSIG PSIG

Position 1

0.0000

0.0000

0.0000

0.0000

2

0.0000

0.0743

0.0000

0.0000

3

0.0000

0.0734

0.0000

0.0000

4

0.0000

0.0000

0.0000

0.0645

5

0.0000

0.0527

0.0000

0.0000

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

0.0000 0.0000 0.0000 0.4530 0.4530 0.4639 0.4639 0.4474 0.4474 0.4419 0.4306 0.4190 0.4132 0.4053 0.4053 0.3973 0.3953 0.3851 0.3810 0.3768 0.3768 0.3641 0.3620 0.3726 0.3684

0.0000 0.0745 0.2322 0.8005 0.8273 0.8978 0.9175 0.9023 0.8752 0.8482 0.8153 0.7900 0.7722 0.7513 0.7364 0.7214 0.7109 0.6973 0.6837 0.6807 0.6655 0.6594 0.6579 0.6594 0.6609

0.0000 0.0745 0.2322 0.8303 0.8646 0.9666 1.0455 1.1317 1.2461 1.2689 1.3159 1.3674 1.3695 0.9852 0.9481 0.9205 0.9023 0.8857 0.8722 0.8602 0.8422 0.8347 0.8347 0.8332 0.8347

0.0000 0.0833 0.2443 0.8387 0.8671 0.9674 1.0447 1.1325 1.2450 1.2696 1.3186 1.3681 1.3702 1.4248 1.4640 1.4830 1.5149 1.5351 1.5745 1.6131 1.6103 1.5826 1.5826 1.5853 1.5853

Table 6: Back Pressure Settings 4

Orifice Area / Pipeline Area b 0.1254

ENGI-3555

Description

Units

80

62

50

10

Back Pressure (PB) Pressure Downstream of Orifice (P2)

kPa

653.88

529.77

447.04

171.25

kPa

100.8

100.8

100.8

100.8

Pressure Difference P1-P2

kPa

0.229

0.438

0.453

0.463

Upstream Stagnation Air Pressure (P 0)

kPa

721.00

721.00

721.00

721.00

Pressure Ratio (PB/P0)

-

0.9069

0.7348

0.6200

0.2375

Stagnation Air Temperature (T0)

K

290.55

289.85

289.05

288.75

Temperature Downstream of Orifice (T2)

K

289.55

Actual Mass Flow Rate (m)

kg/s

8.466E-03

Choked Flow (m)

kg/s

1.597E-02

288.75 1.173E02 1.599E02

288.25 1.193E02 1.601E02

288.05 1.207E02 1.602E02

Figure 1: P/Po Versus Position

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Figure 2: Mass Flow vs. Pb/Po

Figure 3: Mach # vs. Position

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Discussion: Figure 1, shows that P/P0 decreases with the increase in the position. It can also be observed that P/P0 for the higher back pressure settings tends to decrease slower than the lower back pressure settings. This graph is very crucial for determining the mach numbers and shock. The pressure rises instantaneously across a shock Figure 2, on the other hand, shows how pressure ratio affects the mass flow. So, by analyzing the data and the graph, it can be determined that mass flow is reducing with the increase in the pressure ratio (Pb/P0). This also shows that mass flow reduces with the increase in back pressure settings. If the back pressure is lowered enough there’s a point where the flow rate stops increasing and it doesn't matter how much the back pressure is lowered there will not be any more mass flow out of the nozzle. When this occurs it is considered that the nozzle is choked. This behavior can not be changed by increasing the size of nozzle throat because this would take place eventually. The nozzle can become choked even if the throat is eliminated. This behavior has to do with the flows at Mach 1. When the nozzle isn't choked, the flow through it is subsonic. And, if the back pressure is lowered, the flow goes faster and the flow rate increases. Moreover, further lowering of back pressure causes the flow speed at the throat to reach the Mach 1, for example, the speed of sound. However, any further decrease in back pressure will not accelerate the flow through the nozzle. So, in other words, we can say that there is no change in mass flow rate when the nozzle is choked. Figure 3, mach # versus position, shows that lower back pressures have higher Mach number. So, by comparing the results for pressure ratios and Mach number, it is determined how the back pressure settings and flow rate affect the Mach number. The following figure 1 shows different flow patterns:

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Figure 4: Theory of Shockwaves

Sources of error: In this lab, it is assumed that the system is 1 dimensional with isotropic flow, frictionless and adiabatic. However, this is not true because the system can neither be frictionless nor adiabatic because during the process there is certainly a gain or loss of heat. Moreover, other errors could have occurred due to the mass flow taken downstream and fluctuation in pressure during the experiment. Furthermore, the search tube going down the nozzle adding more to the surface area causing more friction leading to small errors. Also, the normal shock is measured incorrectly because the search tube hole is larger than the normal shock. Constantly adjusting the pressure at 90 psi also causes continuous error. The CB runs on a central compressor system that incurs pressure losses when other items are connected and used in series. Other small errors could have occurred due to the pressure gauge, temperature gauge, fluctuation in manometer and orifice disturbance. Also, the equations that are being used for results is based on isentropic, adiabatic flow.

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ENGI-3555

Conclusion: Therefore, it can be concluded, that higher the back pressures lower will be the Mach number due to the decrease in mass flow. And, when the flow accelerates subsonically or supersonically the pressure drops.

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ENGI-3555 Sample Calculations:

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