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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