FACULTY OF ENGINEERING AND THE BUILT ENVIRONMENT

DEPARTMENT OF MECHANICAL

ENGINEERING TECHNOLOGY

STEAM MECHANICAL PLANT 3 (SMP301)

NOZZLE LABORATORY REPORT

JASON BASSON

201020061

LECTURER: E. Bakaya-Kayahurwa

Statement of originality

This is to certify that to the best of my knowledge, the content of this report is my own work.

I certify that the content of this report is the product of my own work and that all the assistance received in preparing this report and sources have been acknowledged.

Jason Basson

Student number: 201020061

Acknowledgements.

I would like to thank the following individuals for their time, assistance and the use of their facilities:

Mr. E. Bakaya-Kayahurwa.

The lab technicians and my fellow students.

The Department of Mechanical Engineering Technology for kindly allowing us to conduct our experiment in their facility.

Abstract

The purpose of this experiment is to study the variation of pressure as steam flows through a converging-diverging nozzle, perhaps the most important and basic piece of engineering hardware associated with the propulsion and the high speed flow of gasses.

Table of Contents

Topic Page

1. Introduction 1

2. Objective 1

3. Apparatus and Experimental Procedure

1

4. Observations, Analysis and Results

2

5. Discussions 5

6. Conclusions 5

7. Recommendations 6

8. References 6

9. Appendices 6

1. Introduction

A nozzle is a duct of smoothly varying cross-sectional area in which a steadily flowing fluid can be made to accelerate by a pressure drop along the duct [1.]. There are several applications in practice that require a high velocity stream of fluid, and nozzles are the most efficient way of obtaining this. Some of these applications include steam and gas turbines, jet engines, rocket motors and many other applications.

This report will deal mainly with the flow of steam through a nozzle.

2. Objective

The aim of this report is to determine the mass flow rate of steam through a convergent-divergent nozzle as well as to determine the critical velocity and pressure of the nozzle.

3. Apparatus and Experimental Procedure

The atmospheric pressure was recorded using a mercury barometer located near the apparatus. The steam entered the nozzle dry saturated at 200 kPa gauge pressure. Pressure readings were recorded at even intervals of approximately 2.032mm throughout the length of the nozzle. The pressure drop across the nozzle was recorded. Finally, the back pressure of the nozzle was recorded.

1.

4. Observations, Analysis and Results

The barometric pressure was recorded at 720.25 mmHg, converted to kilopascals gives 96.025 kPa. Assuming the pressure probe is moved at even increments of 2.032 mm down the nozzle. It is assumed that the steam enters the nozzle dry saturated at inlet pressureP1; it is also assumed that flow is in equilibrium throughout expansion and that expansion is isentropic.

The absolute pressure is the sum of the gauge pressure and the barometric pressure calculated at each interval with the formula: Pabsolute=Pgauge+Pbarometric

It is assumed that the steam enters the nozzle dry saturated and the inlet velocity C1 is negligible. For convenience in calculation, the absolute pressure of the steam at each interval is rounded off to a value that is tabulated on the steam tables. The properties of the steam at inlet are read off the steam tables and the following values are obtained:

h1=hg at 300 kPa=2724 kJ /kg

s1=sg at 300 kPa=6.991kJ /kgK

T 1=T s at 300 kPa=133.5℃

The mass flow rate of the steam flowing through the nozzle is determined by employing the following formula:

m v t=A t C t

Where v t is the specific volume of steam at the throat, Atis the throat area and C tis the throat or critical velocity. The throat area is calculated as follows:

At=π d2

4=π × 0.00482

4=18.095× 10−6 m2

In order to determine the throat velocity C t the critical pressure Pt needs to be calculated. The properties of the steam at critical pressure are then read off the steam tables and the critical velocity is determined.

Pt

P1=¿

where k is the isentropic index for dry saturated steam=1.135 and P1 is the inlet pressure.

Pt=300 ׿

The properties of steam at 173.1 kPa are not tabulated on the steam tables, therefor it is rounded off to the closest tabulated value 170 kPa

s1=s t=6.991kJ /kgK

st<sg @170 kPa ¿ kJ/kgK) therefor the steam is wet at the throat.

2.

Since the expansion is isentropic, the dryness fraction of steam at the throat can be determined as follows:

st=sf + x sfg

x=s t−s f

sfg=6.991−1.475

7.181−1.475=0.967

Now the specific enthalpy of steam at the throat can be determined

ht=h f +x hfg=483+0.967 ×2216=2625.87 kJ /kg

The velocity at the throat is determined using the following the following formula:

C t=√2000(h1−ht)=44.72√2724−2625.87=443 m/ s

The specific volume of steam at the throat is now determined

v t=x v g=0.967 ×1.031=0.997 m3/kg

Now that all the variables have been determined, the mass flow rate of steam can be calculated

m=C t A t

v t=443 ×18.094 × 10−6

0.997=8.04 × 10−3 kg /s

¿8.04 g /s

The mass flow rate to throat area ratio can now be determined:

mA t

= 8.04 ×10−3

18.095× 10−6 =464.22 kg/m2 s

The mass flow rate to area ratio as well as the enthalpy, absolute pressure, dryness fraction, specific volume and velocity at each interval in the nozzle are determined by using the enthalpy/entropy chart (Mollier diagram). Once again, for convenience the recorded pressures are rounded off to the closest tabulated values in the steam tables. The results are tabulated on the following page.

Using the calculated values for mass flow rate to area ratios and the absolute pressures, a graph is plotted.

3.

Distance of probe

Pressure (gauge)kPa

Pressure (absolute)kPa

Enthalpy

kJ /kg

Specific Volume m3/kg

Dryness Fraction

Velocity

m /s

Mass/Area

kg /m2 s

2.032 200 296.25 2724 0.6056 1 0 0

4.064 200 296.25 2724 0.6056 1 0 0

6.096 200 296.25 2724 0.6056 1 0 0

8.128 200 296.25 2724 0.6056 1 0 0

10.16 200 296.25 2724 0.6056 1 0 0

12.192 200 296.25 2724 0.6056 1 0 0

14.224 200 296.25 2724 0.6056 1 0 0

16.256 200 296.25 2724 0.6056 1 0 0

18.288 200 296.25 2724 0.6056 1 0 0

20.32 180 276.25 2718 0.6421 0.994 109.5 170.5

22.352 175 271.25 2714 0.663 0.992 141.4 213.3

24.384 155 251.25 2700 0.7112 0.99 219.1 308

26.416 140 236.25 2668 0.7345 0.984 334.6 440.5

28.448 130 226.25 2660 0.7597 0.978 357.8 471

30.48 120 216.25 2654 0.7912 0.977 374.15 472.9

32.512 110 206.25 2648 0.8239 0.974 389.9 473.2

34.544 100 196.25 2642 0.834 0.972 404.9 485.5

36.576 100 196.25 2642 0.834 0.972 404.9 485.5

38.068 95 191.25 2640 0.902 0.971 409.9 454.4

40.64 80 176.25 2620 0.9459 0.968 456.1 482.2

42.672 80 176.25 2620 0.9459 0.968 456.1 482.2

44.704 75 171.25 2617 0.9949 0.965 462.6 465

46.742 60 156.25 2604 1.0463 0.959 489.9 468.2

48.78 60 156.25 2604 1.0463 0.959 489.9 468.2

50.812 58 154.25 2600 1.1092 0.957 498 448.97

4.

140 160 180 200 220 240 260 280 300 3200

100

200

300

400

500

600

Pressure (absolute) 𝑘𝑃𝑎

Mas

s/Ar

ea∕𝑘𝑔〖𝑚

^2 𝑠〗

5. Discussions

The first part of the report required that the mass flow rate through the nozzle be calculated. The mass flow rate at the throat was calculated as 8.04 × 10−3 kg /s. The corresponding critical pressure and velocity found to be as 173.1 kPa and 443 m / s respectively.

It can be observed from the schematic diagram of the nozzle that the throat is situated between 9.4mm from entry to 16.3 mm. The corresponding pressures at that region as tabulated are 200 kPa as opposed to the calculated throat or critical pressure of 173.1 kPa. It is seen on the table that the calculated critical pressure is situated between 42.672mm and 44.704mm in the nozzle cross section. This indicates an error in the recording the pressure readings. This discrepancy can be attributed to the following reasons:

1. There could have been possible errors made by students when the readings were recorded

2. There possibly may have been errors that went unnoticed in the lab with pressure gauges which could account for small errors.

3. The instructor noted to us that the equipment was not functioning properly before we used it. This may have caused deviations in the actual results.

It is also clear that the nozzle is under expanding, in other words flow through the nozzle is choked. This is because the exit pressure or back pressure 154.25 kPa is less than the critical pressure of 173.1 kPa. A correctly designed convergent-divergent nozzle is always choked [2.]

6. Conclusions

Following this experiment it is evident that the analysis of a seemingly simple device like the converging diverging nozzle is more challenging than originally expected. Using the methods set out above, the challenges involved in designing of such nozzles, for various environments

5.

that occur in such applications is made very apparent.

7. Recommendations

It is suggested that routine maintenance be conducted on the apparatus in accordance with the manufacturer’s specifications. It was observed that the floor of the laboratory was wet as a result of the steam condensing as it exits the apparatus. Therefor it is recommended that non-slip or slip resistant footwear is worn when conducting the experiment to avoid serious injury. The surfaces of the apparatus may become hot, it is for this reason that caution should be practised when conducting the experiment. The appropriate PPE should also be worn when conducting the experiment to ensure personal safety.

8. Referencing

Citations

[1.]-[2.] Eastop, T. D. and McConkey, A. (1993) Applied Thermodynamics for Enineering Technologists. 5th Edition. London: Pearson Education Limited

References

Moran, M. J. et al. (2011) Fundamentals of Engineering Thermodynamics. 7th Edition. Hoboken NJ: Wiley and Sons

Nag, P. K. (2013) Engineering Thermodynamics. 5th Edition. New Delhi: McGraw Hill Education

Rajput, R. K. (2010) A Textbook of Engineering Thermodynamics. 4th Edition. New Delhi: Laxmi Publications

9. Appendices

6.

7.