THE AMERICAN UNIVERSITY IN CAIROSchool of Sciences and EngineeringMechanical Engineering Department

MENG 3602-84: Applied Fluid Mechanics LabDr. Omar Huzayin

Eng. Shehaby

Lab Report # 5

Nozzle Pressure Distribution Unit

Due:

Wednesday, 3th December 2014

Submitted by:

Ahmed SabahFarah Sarhan

Abstract

In this experiment, we aim to study the behavior of pressurized air passing through De Laval nozzle. We will use the Hilton nozzle pressure distribution unit (F810) to investigate this behavior. A brief introduction about De Laval nozzle and the apparatus will be given. Then, we will explain how the machine works and the detailed procedures to follow. Also calculations and results that clarify more the behavior of the nozzle will be provided. At the end, we will conclude what we did in the experiment and our main purpose.

Table of ContentsList of Figures3Introduction4Nomenclature5Theory6Objectives9Apparatus10Nozzle geometry:12Procedures13Results14Discussion and Conclusion17References19

List of Figures

Figure 1 - Pressure against De Laval Nozzle shape7Figure 2 - Nozzle Pressure distribution unit11Figure 3 - Nozzle Geometry12Figure 4 - Pressure ratio with Length of Nozzle16Figure 5 - Mach number with length of nozzle16

Introduction

The Hilton nozzle pressure distribution unit made by P.A. Hilton has been designed for educational reasons. It can be used in conducting a large number of experiments. But it has been specifically designed to demonstrate the phenomena associated to fluxes through nozzles and to allow the students or researchers to investigate the pressure distribution through the different types of nozzles. Also, it allows the investigation of the mass flow rate in convergent-divergent and convergent nozzles. The main problem that the Hilton nozzle pressure distribution unit has overcame was that all the experimental equipment used before for the same demonstration used steam instead of air. The use of steam required a heavy demand of energy to be fired a while before the test is to start and also the presence of a condenser with a cooling water supply. This new unit used compressed air at a pressure and mass flow rate that can be provided from the type of compressor that is usually available in workshops and laboratories.Nozzles are vital components in many things like turbines, jet engines, rockets, ejectors, etc. the behavior of the nozzles in these machines have a remarkable effect on the effectiveness and efficiency of the machine. In this experiment we are interested in studying the behavior of De Laval nozzle (the pressure distribution across it). Swedish inventor Gustaf de Laval invented De Laval nozzle, for use on a steam turbine. The nozzle is designed in a way that when a pressurized gas pass through the pinched area, it accelerates its speed to reach supersonic speed and when it expands, the heat energy transforms into kinetic energy. This specification made it widely used in many machines like steam turbine, rocket engine nozzles and others.

Nomenclature

NameSymbolUnits

Mach NumberMa-

Velocityvm/s

Velocity of soundcm/s

DiameterDm

RadiusRm

PressurePPa

TemperatureTK

Theory

The flow in a pipe is characterized by the Mach number, which is evaluated using:

where v is the velocity of the flow and c is the speed of the sound at the flows temperature and pressure.The Mach number divides flow types into 3 categories:Subsonic where Ma1The relation between the area and the flow velocity from in subsonic differs from supersonic and is governed by the following relation:

where A is the area of the cross section. This relationship tells us that for subsonic flow, decreasing the area will increase the velocity but for supersonic flow, increasing the area will increase the velocity. In addition, we know that for a throat, the maximum Ma is 1. In the De Laval nozzle, the flow enters as subsonic flow, and then accelerates. If the reservoir pressure is enough (compared to the exit pressure) is sufficient, the flow will reach Ma=1 at the throat. If, however, the pressure is not enough, the flow continues subsonic. After the flow is chocked at the throat, there are several possible scenarios. 1. Isentropic: The flow continues with subsonic velocity till the exit. (Line B)2. Non-Isentropic: The flow continues with supersonic velocity till the exit. (Line D)3. Isentropic: The flow continues supersonic, experiences a normal shock wave and continues subsonic. (Line C)

D

Figure 1 - Pressure against De Laval Nozzle shapeFor Isentropic flow:The total pressure can be calculated from the pressure at a point using its Mach number as follows:

where k=1.4 for air. The total temperature can also be calculated from the temperature at a using its Mach number as follows:

The Mach number at a point can be calculated from the area to area of throat ratio. The equations yields two answers, the answer is selected as relevant to flow (subsonic or supersonic). This equation cant be used across shockwaves i.e.

For non-isentropic flow, we can calculate the Mach number after the shockwave (2) using the Mach number before the shockwave (1):

Objectives

This experiment aims at studying flow behaviors in a De Laval nozzle. It shows that the Mach number, along with other properties, is affected by the conditions at the nozzle exit (e.g. back pressure).1. The study and investigation of flow in a Laval nozzle2. Plotting the derived Mach number against nozzle length3. Plotting the ratio (Pressure/Total Pressure) against nozzle length4. Plotting the ratio (Pressure/Total Pressure) against the mass flow rate5. Observation of the effect that the changing of back pressure has on pressure and Mach number distributions

Apparatus

In order to study flow behaviors in Laval nozzles, we will use a nozzle distribution unit. This unit will help us understand the effect of the nozzle conditions: the exit and backpressure, will affect the flow behavior and Mach number. The apparatus consists of a nozzle, De Laval, which has air flowing inside at different flow rates which will change the exit pressure and consequently the behavior of the flow. Eight pressure meters are there to measure pressure in eight different sections of the nozzle. Two thermometers are there to measure the total temperature before and after the nozzle. To measure the flow rate, there is an air flow meter. Finally, we will have two valves which will control the back pressure hence the flow rate.

1

87654234

Figure 2 - Nozzle Pressure distribution unit1. Sections pressure meters from P1 to P8.2. Air inlet pressure.3. Thermometers.4. Inlet control valve.5. Air flow meter.6. Air outlet pressure.7. Nozzle.8. Outlet control valve.

Nozzle geometry:

Figure 3 - Nozzle Geometry

SectionDiameter (mm)

12.4

22

32.13

42.26

52.39

62.52

72.66

82.79

Table 1 - Nozzle DiametersProcedures

In order to start the experiment, we will need first to have a pressurized reservoir to provide us with the air flow then do the following:1. Fix the inlet pressure.2. Change the back-pressure (0, 200, 400, 550 and 650 KPa) using the outlet control valve.3. For each back-pressure get values for pressure in the 8 sections of the nozzle, get readings for the flow rate of the fluid as well as temperatures before and after the nozzle.4. Plot the derived Mach number against nozzle length. 5. Plot the ratio (Pressure/Total Pressure) against nozzle length. 6. Plot the ratio (Pressure/Total Pressure) against the mass flow rate.

Results

Pb=0Pb=200Pb=400Pb=550Pb=600

sectionPPPPP

1620620610660700

2400400400540700

3240240370540700

4180180330600700

5120160440603690

6110240480630720

790240480620700

8100260510640720

Pb=0 KPaPb=200 KPaPb=400 KPaPb=550 KPaPb=600 KPa

SectionP/Pt (0)P/Pt (200)P/Pt (400)P/Pt (550)P/Pt (600)

10.8857142860.8857142860.8714285710.9428571431

20.5714285710.5714285710.5714285710.7714285711

30.3428571430.3428571430.5285714290.7714285711

40.2571428570.2571428570.4714285710.8571428571

50.1714285710.2285714290.6285714290.8614285710.985714286

60.1571428570.3428571430.6857142860.91.028571429

70.1285714290.3428571430.6857142860.8857142861

80.1428571430.3714285710.7285714290.9142857141.028571429

Pb=0 KPaPb=200 KPaPb=400 KPaPb=550 KPaPb=600 KPa

SectionM (0)M (200)M (400)M (550)M (600)

10.4200160780.4200160780.447792770.2911501430

20.9310801690.9310801690.9310801690.6203389840

31.3374707371.3374707370.999530110.6203389840

41.5396132481.5396132481.0947155410.4744857420

51.8098823151.6194631080.8422002920.4665791890.143518812

61.8665447161.3374707370.7543975150.390900760

71.9961535891.3374707370.7543975150.4200160780

81.9282622151.2788016920.6881001510.3600976130

A/A*

1720720710760800

2500500500640800

3340340470640800

4280280430700800

5220260540703790

6210340580730820

7190340580720800

8200360610740820

Figure 4 Mach number with Length of Nozzle

Figure 5 Pressure ratio with length of nozzle

Discussion and Conclusion

Increasing the backpressure decreases the mass flow rate. As the mass flow rate increases, the velocity increases. By applying the energy conservation, when the velocity increases, the pressure of the flow decreases. When the backpressure reached 400kPa, further increase in the backpressure didnt increase the mass flow rate and the throat was chocked with Mach number equal to 1. Each flow (relative to backpressure) exhibits different pressure behavior. 1. Backpressure of 650kPa:*The flow was subsonic all through the nozzle since the backpressure was not enough to provide for a larger mass flow rate with larger velocity. *Measurements for this flow were incorrect, the absolute pressure at all points was larger than the total pressure, yielding a ratio more than one and consequently the Mach number wasnt calculated.2. Backpressure of 550kPa:*Similar analysis to previously explained one. *Measurements of flow were reasonable and the Mach number varied changed from 0.2 at entrance, increased, as area decreased, to 0.7 at throat and decreases again to 0.3 with increase in area.3. Backpressure of 400kPa:*The flow was chocked at the throat and continued as supersonic flow.*A normal shockwave occurred between sections 3 and 4. *The flow continued as a subsonic flow.*The maximum Mach number reached was 1.4338.4. Backpressure of 200kPa:*Similar analysis to the previous one.*A normal shockwave occurred between sections 5 and 6.*The maximum Mach number reached was 1.79.5. Backpressure of 0kPa:*The flow was supersonic through the nozzle.*The Mach number reached its maximum at the exit, 2.17. As the backpressure decreases, more air is pushed from the high-pressure reservoir to the low-pressure exit. The increasing mass flow rate means increasing velocity, which in accordance to the energy equation, decreases the local pressure to keep the total energy/pressure constant. Beyond a certain limit of backpressure to reservoir pressure difference, the mass flow rate cant increase, since the throat cant accommodate for more mass passing per unit time. At this condition, the Mach number at the throat is 1. As this seizes to happen, the flow continues subsonic since not enough energy is available for higher velocities. As the backpressure continues to decrease, thus allowing for more mass flow rate, the flow tries to continue supersonic but experiences shockwaves that decrease the pressure and force the flow back into subsonic state. When the backpressure is low enough, the flow passes through the whole nozzle with supersonic velocity.

References

http://en.wikipedia.org/wiki/De_Laval_nozzle

http://fichas.prodel.es/mecanica%20de%20fluidos%20hidraulica/F810.pdf

http://www.edibon.com/products/catalogues/en/units/thermodynamicsthermotechnics/nozzlessteam/TPT.pdf

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