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December 2014
Thermodynamic
Processes
Student Guide
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Table of Contents
INTRODUCTION...................................................................................................................... 1
TLO 1 THERMODYNAMIC SYSTEMS AND PROCESSES............................................................ 2
Overview .......................................................................................................................... 2
ELO 1.1 Nozzle Characteristics ....................................................................................... 3
ELO 1.2 Turbines Design and Characteristics ............................................................... 10
ELO 1.3 Throttling Characteristics ................................................................................ 23
TLO 1 Summary ............................................................................................................ 28
TLO 2 COMPRESSION PROCESSES ....................................................................................... 30
Overview ........................................................................................................................ 30
ELO 2.1 Gas Laws ......................................................................................................... 32
ELO 2.2 Compression Process ....................................................................................... 39
TLO 2 Summary ............................................................................................................ 43
THERMODYNAMIC PROCESSES SUMMARY .......................................................................... 45
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Thermodynamic Processes
Revision History
Revision
Date
Version
Number
Purpose for Revision
Performed
By
11/6/2014
0
New Module
OGF Team
12/11/2014
1
Added signature of OGF
Working Group Chair
OGF Team
Introduction
Energy conversion in nozzles and the role nozzles play in plant equipment
operation such as turbines and flow-measuring devices is a major part of
your understanding both the design of the power plant and how the plant
functions. We have not yet discussed processes performed by gases as we
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1
have focused on the steam cycle, yet many applications of the use of gases
are occurring all the time during plant operation.
Importance
Plants incorporate nozzles extensively and throughout the facility. It is
important to understand how nozzles affect system flow dynamics and how
nozzle characteristics can be used to aid in the safety design of the plant.
Various instruments use the pressure differences created by nozzles to
display flow. The stages of turbines use nozzles. Nozzles can also limit or
choke fluid flow to acceptable levels.
The compression of a gas results in different final states than the
compression of a saturated vapor such as steam. Gases follow laws that
relate their volume, pressure, and temperature unlike steam, which
undergoes phase changes if temperature or pressure varies sufficiently.
These laws must be understood to ensure plant equipment is maintained
within design limits.
Thermodynamics Processes Objectives
At the completion of this training session, the trainee will demonstrate
mastery of this topic by passing a written exam with a grade of 80 percent
or higher on the following Terminal Learning Objectives (TLOs):
1. Explain thermodynamic systems and processes.
2. Explain compression processes and the laws associated with them.
TLO 1 Thermodynamic Systems and Processes
Overview
There are many thermodynamic processes occurring continuously as a plant
operates; many of these processes are invisible to the operator. The plant
equipment incorporates these processes in the plant design to ensure the
plant operates properly. For instance, the operator can monitor the steam
properties at the inlet to the main turbine and the properties of steam at the
main turbine exhaust, but cannot see the thermodynamic process that occurs
within the turbine. The turbine extracts work from the steam (converting
the thermal energy of the steam into mechanical energy). Nozzles play a
key role in this energy conversion. The operator monitors instrument air
header pressure but does not normally observe the operation of the air
compressors providing this air supply.
Importance
These thermodynamic processes are important in understanding the
operation and design of the complete power plant and this module will
explain the processes.
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Objectives
Upon completion of this lesson, you will be able to do the following:
1. Describe the operation of nozzles to include:
a. Functions of nozzles in flow restrictors
b. Functions of nozzles in air ejectors
2. Explain the design of turbines, including the functions of nozzles,
fixed blading, moving blading, and the reason turbines are multistage.
3. Determine exit conditions for a throttling process.
ELO 1.1 Nozzle Characteristics
Introduction
A nozzle is a mechanical device used to change the energy of a working
fluid from one form to another for a specific purpose. The cross-sectional
area in a nozzle varies to control the flowrate, speed, direction, mass, shape,
and/or the pressure of the stream that emerges from them. Depending on
the type of nozzle, the kinetic energy of the fluid will increase or decrease
as it moves through the device. The figure below shows three of the
common types of nozzles.
Figure: Typical Nozzle Types
There are two types of nozzles: convergent and divergent. The convergent
nozzle cross-section narrows from a wide diameter to a smaller diameter in
the direction of the flow and accelerates the fluid. In the divergent nozzle
cross-section, the diameter expands and slows the fluid upon exit. A
convergent-divergent nozzle has a convergent section followed by a
divergent section and is often called a De Laval nozzle.
Theory of Nozzle Operation
We will use the General Energy Equation, with several simplifications, to
explain nozzle operation.
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3
In a convergent nozzle, the piping at the exit is of a smaller diameter than
the entrance (A1 > A2).
Figure: Convergent Nozzle
The elevation change from entrance (1) to exit (2) is insignificant.
𝑃𝐸1 = 𝑃𝐸2
Inlet piping diameter is greater than outlet piping diameter. With steady
flow, outlet velocity is greater than inlet velocity.
𝐾𝐸2 > 𝐾𝐸1
There is no work done on or done by the fluid in the nozzle.
𝑊𝐼𝑁 = 𝑊𝑂𝑈𝑇 = 0
Assume that no heat transfers into or out of the fluid as it flows through the
nozzle.
𝑄𝐼𝑁 = 𝑄𝑂𝑈𝑇 = 0
Assume that there is no friction as the fluid flows through the nozzle.
𝑈1 = 𝑈2
𝑚̇1 = 𝑚̇2
𝐴𝑉
= 𝜌𝐴𝑉
𝜈
𝜌1 𝐴1 𝑉1 = 𝜌2 𝐴2 𝑉2 = 𝜌𝑥 𝐴𝑥 𝑉𝑥
𝑚̇ =
Where:
𝑚̇ = mass flow rate (lbm/sec)
A = cross-sectional flow area (ft2)
V = fluid velocity (ft/sec)
 = specific volume of fluid (ft3/lbm)
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Rev 1
ρ = density of fluid (lbm/ft3)
Note: some texts use the symbol V with an overbar to denote velocity or
average velocity; in this module, we will use V or Vel to denote velocity.
The last equation above is termed the continuity equation for steady flow
processes. If we assume that the specific volume (and therefore density) is
constant (incompressible fluid) the velocity must increase if the crosssectional flow area decreases and vice versa. A converging nozzle increases
a fluid's velocity and kinetic energy at the expense of decreasing its
enthalpy (pressure). A diverging nozzle decreases the velocity and
increases pressure at its exit.
Application of the first law of thermodynamics shows that the change in KE
must balance with an opposite change in another stored energy form. With
the assumptions given, we can see that the Pv energy must decrease if KE is
increased. If we also assume that the fluid is incompressible (𝜈1 = 𝑣2 ) we
can see that the change in pressure (ΔP) is proportional to the change in KE.
𝐾𝐸1 + 𝑃1 𝑣 = 𝐾𝐸2 + 𝑃2 𝑣
𝐾𝐸2 − 𝐾𝐸1 = 𝑃1 𝑣 − 𝑃2 𝑣
𝐾𝐸2 − 𝐾𝐸1 = (𝑃1 − 𝑃2 )𝑣
The above equations show that a nozzle can exchange kinetic energy and
pressure volume energy as desired. For a convergent nozzle, the velocity
and kinetic energy increase and pressure decreases. The opposite effect
takes place for a divergent nozzle - the kinetic energy decreases as fluid
velocity decreases and Pv energy increases.
If the working fluid is steam, the specific volume is not constant since the
fluid is compressible. In this case we leave the internal energy term in the
equation and the result is:
𝐾𝐸2 − 𝐾𝐸1 = (𝑃𝑉 + 𝑈)1 − (𝑃𝑉 + 𝑈)2
𝐾𝐸2 − 𝐾𝐸1 = 𝐻1 − 𝐻2
The thermodynamic process of an ideal nozzle is adiabatic with no loss of
energy. (As defined by Princeton University: “In thermodynamics, an
adiabatic process or an isocaloric process is a thermodynamic process in
which no heat is transferred to or from the working fluid. The term
‘adiabatic’ literally means impassable.”) In a real nozzle, entropy will
increase slightly due to turbulence and friction losses.
Convergent nozzles accelerate subsonic fluids. Fluid moves through a
nozzle as a function of the differential pressure from the nozzle inlet to
outlet. The design shape of the nozzle will determine the critical pressure,
which is the outlet pressure that will cause supersonic flow in the throat of
the nozzle. In a convergent nozzle, the sonic flow creates turbulence and
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backpressure that limits flow; this is termed choking flow. If the nozzle
critical pressure ratio (ratio of pressure that will cause sonic velocity to
pressure at inlet) is high enough, the flow will reach sonic velocity at the
narrowest point, the nozzle throat. In this situation, the nozzle is termed
choked. Increasing the nozzle pressure ratio above the critical pressure will
not increase the throat velocity. If the downstream flow is free to expand
smoothly as in a divergent nozzle, supersonic velocities can be reached.
Figure: Supersonic Flow through a Convergent-Divergent Nozzle
If the velocity reaches sonic conditions at the venturi, the increasing area of
the divergent nozzle causes the velocity to increase further and the pressure
to decrease further. If the velocity does not reach sonic conditions at the
venturi, then the velocity will begin decreasing and the pressure will begin
increasing.
Convergent-divergent nozzles can therefore accelerate fluids that have
choked in the convergent section to supersonic speeds. This convergentdivergent process is more efficient than allowing a convergent nozzle to
expand supersonically externally. The shape of the divergent section also
ensures that the direction of the escaping gases is directly backwards, as any
sideways component would not contribute to thrust.

6
Assume that the steam generator piping includes a convergentdivergent nozzle, as shown in the figure below. This provides a
method for measuring steam flow using the ΔP between the inlet and
the outlet of the convergent section. In case of a steam line break, the
nozzle serves as a flow restriction to limit the maximum amount of
steam escaping the steam generator, but nozzle design assumes
normal steaming rates during non-accident conditions.
Rev 1
Figure: Convergent-Divergent Venturi Tube for Flow Measurement

The inlet piping to the reactor coolant pumps' suction increases in
diameter (divergent nozzle). This raises the available suction pressure
for the pumps to aid in preventing cavitation.
 Within the turbine, nozzles (called "fixed blades") act to direct steam
flow onto the rotating blades and (in some cases) to increase velocity
to raise the force applied to the rotating blades.
Figure: Nozzle-Bucket Stage in Impulse Turbine
Steam Jet Air Ejectors
An air ejector is a pump-like device, with no moving parts that utilizes
high-pressure steam to compress vapors or gases as illustrated in the figure
below. High-pressure steam enters a convergent nozzle; the steam exits the
nozzle at increased velocity and decreased pressure. The nozzle creates a
low-pressure area that will draw in the fluids around it and mix those with
the high velocity fluid in the throat of the device. The mixture passes
through a divergent section to decrease the velocity of the mixture and
increase its discharge pressure. A jet pump works similarly, except water
functions as both the driving fluid and the entrained fluid. This allows the
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jet pump to increase the mass of liquid being pumped without additional
pumps or electrical power.
Figure: Simple Air Ejector (Jet Pump)
Steam enters a convergent-divergent nozzle at a relatively high pressure and
low velocity in a steam jet air ejector shown below. The convergent nozzle
increases the velocity of the steam to sonic velocity (1) and then to
supersonic velocity in the divergent section (2) as it enters into the suction
chamber. The supersonic velocity results in the lowest pressure of the
steam in the nozzle (2). The condenser feeds the suction chamber. The
low-pressure area will draw more fluid from around the nozzle into the
throat of the diffuser, entraining the drawn fluid with the driving fluid. The
decreasing area slows the supersonic velocity back to sonic and increases
the pressure (3) as the fluid moves through the convergent-divergent
diffuser section. The divergent section of the diffuser then drops the
velocity to subsonic and increases the pressure enough to discharge to
atmosphere or greater (4). Use of steam at a pressure between 200 psi and
300 psi as the high-pressure fluid enables a single-stage air ejector to draw a
vacuum of about 26 inches Hg.
The low-pressure area in the suction chamber draws air and noncondensable gases into the nozzle. Momentum transfers from the steam to
the air and non-condensable gases and they become "entrained" in the steam
flowing through the air ejector.
The mixture of steam and gas reaches sonic velocity in the suction chamber.
Sonic velocity is the speed of sound in that substance. The nozzle design
allows the steam to accelerate to super-sonic velocity resulting in a lower
pressure at the suction chamber. As the air and non-condensable gases exit
the suction chamber, the nozzle maintains the low-pressure suction area,
which allows more air and non-condensable gases to enter from the suction
line. As the mixture enters the diffuser section, the diverging nozzle slows
down the flow while increasing its pressure. The figure below shows a
cross-section of a steam jet air ejector with pressure and velocity levels
along the section.
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Rev 1
Figure: Steam Jet Air Ejector Operation
Vacuums of 29 inches Hg require two stages of air ejection.


First Stage - suction located on top of the condenser
Second Stage - suction comes from the first stage diffuser
The exhaust steam from the second stage passes through an air ejector
condenser cooled by condensate to condense the steam, as shown in the
figure below. The air ejector condenser also preheats the condensate
returning to the boiler.
Figure: Two-Stage Steam Jet Ejector
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9
Assume steady flow conditions from the entrance into the first stage air
ejector to the exit at the second stage air ejector, which means no mass is
lost or gained through the nozzle and mass flow rate is constant.
Knowledge Check
In what type of nozzle can supersonic speeds be
reached for incompressible fluids?
A.
Convergent
B.
Divergent
C.
Convergent-Divergent
D.
Divergent-Convergent
Knowledge Check
In what type of nozzle will flow be limited to sonic?
A.
Convergent
B.
Divergent
C.
Convergent-Divergent
D.
Divergent-Convergent
ELO 1.2 Turbines Design and Characteristics
Introduction
A turbine is a device used to convert the energy in high-pressure steam into
rotating kinetic energy. The two steps to accomplish this are as follow:
1. The P is the energy of the steam and is converted to kinetic energy
2. A portion of the steam's kinetic energy is imparted to the turbine rotor
giving it kinetic energy
Large turbines used in nuclear power plants generally have multiple turbine
components: one high-pressure turbine mounted on the same shaft as two or
three low-pressure turbines. The turbine is termed a "tandem" unit when all
turbine units share a common shaft. The generator is mounted at the end of
that shaft.
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Rev 1
Recall that a T-s or h-s diagram of a steam cycle can illustrate the work
performed by the turbine. On the h-s diagram below, real turbine work is
shown by the line from Point 2 to 3'.
There are two basic types of turbines:


impulse turbines
reaction turbines
The name impulse comes from the fact that high velocity steam strikes the
turbine blading (an impulse) and causes the turbine rotor to turn. Reaction
turbines use nozzle energy conversion in the moving blades to create
rotation force.
The figure below illustrates how steam enters at the steam chest in the
center of the turbine and flows axially in both directions through the turbine
multiple stages. Each turbine stage consists of a fixed nozzle block where
the steam gains kinetic energy before impinging on the moving blades. A
stage is comprised of one set of nozzles and moving blades. Because the
high kinetic energy of the steam strikes the moving blades and causes the
blades to rotate, this is termed an impulse turbine.
Figure: Impulse Turbine Components
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Theory of Operation
A steam turbine can be defined as a form of heat engine in which the input
energy of the steam is converted into useful work output in two distinct
steps:
1. The available thermal energy of steam is converted into kinetic
energy by expansion through a nozzle.
2. The resultant steam jet impinges against blades attached to the steam
turbine shaft causing the shaft to turn, thereby converting the kinetic
energy into useful work.
Impulse Principle
The figure below illustrates the four distinct steps in the conversion of the
thermal energy of steam into mechanical energy:
1. Steam in an impulse turbine passes through stationary nozzles
2. Stationary nozzles convert some of the thermal energy contained in
the steam (indicated by its pressure and temperature) into kinetic
energy (velocity).
3. Stationary nozzles also direct the steam flow onto the blades of the
turbine wheel.
4. As they rotate, the blades and moving wheel convert kinetic energy of
steam into mechanical rotational energy. In turn, the shaft or rotor
turns a generator or an attached power coupling.
Power plant turbines normally consist of multiple stages with a stage being
one set of rotating blades and nozzles. The multistage approach allows
more energy extraction from the steam and conversion to kinetic energy.
Figure: Impulse Turbine Concepts
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Rev 1
Reaction Principle
Steam passes through a row of "fixed blades" which act as nozzles to
expand the steam or decrease pressure in a reaction turbine. This process
increases the steam's velocity. The fixed blades also direct the highvelocity steam into the "moving blades", which are almost identical in shape
to the fixed blades as shown in the figure below:
Figure: Reaction Turbine Concepts
The difference between an impulse turbine and a reaction turbine is that
when the steam flows into the reaction turbine’s moving blades, the moving
blades act as nozzles. The moving nozzles convert more thermal energy of
the steam into kinetic energy than the static nozzles of the impulse turbine.
The kinetic energy imparts a rotational force on the movable nozzles and
turbine shaft as the steam accelerates through the nozzles. A reaction
turbine exhibits a drop in both pressure and velocity across the moving
blades as opposed to a drop in velocity alone in the impulse turbine. The
pressure drop across the moving blades provides available energy or
reaction principle. Changing the direction of the steam flow in the impulse
turbine blades allows additional energy extraction from the steam or
reaction principle.
Impulse Turbine
The impulse turbine consists of two basic elements:

Rev 1
A fixed nozzle to convert the steam energy or thermal energy into the
kinetic energy
13

A rotor consisting of blades mounted on a disk to absorb the kinetic
energy of the steam jet to convert it into rotary motion.
The figure below shows a basic impulse turbine.
Figure: Basic Impulse Turbine
When the high velocity steam strikes the turbine blade, some of the steam's
velocity energy converts into an impulse force acting on the turbine blade.
The blade is mounted on a wheel, and the force will rotate in the direction
of the impulse force.
Newton's first law states that a force is required to change either the speed
or the direction of a body in motion. A greater force acts on the blade if the
blade curves in such a manner as to cause the jet of steam to reverse its
direction. The torque developed in a wheel with reversing blades is nearly
twice as great as the force developed in a wheel with flat blades.
Turbine blading should be designed to convert as much of the kinetic
energy of the steam leaving the nozzle into work as is practical. Turbine
blades from large turbines are often called "buckets" because their size and
concavity resembles a bucket.
There are several nozzles directing the steam against the blades or buckets
to turn the rotor. See the left half of the figure below as reference. As
steam exits the first row of blades or rotor, it still has a high velocity and is
still capable of doing more work. A second row of stationary blades may
direct the steam toward a second row of moving blades, if designed with a
second stage, thus converting more of the steam’s kinetic energy into work.
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Rev 1
Figure: Impulse/Reaction Turbine Comparison
The figure below shows a two-stage impulse turbine, where the shape of the
vanes in the stationary diaphragm redirect steam exiting from the first stage
to the moving blades of the second stage.
Figure: Turbine Moving and Stationary Blades
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Reaction Turbine
A reaction turbine differs from the impulse turbine in that nozzles mounted
on the disk replace the blades of the impulse turbine. In the reaction turbine
steam expands in the moving nozzles shown below
Figure: Basic Reaction Turbine
Steam enters the unit and flows to the nozzles. Heat energy converts to
kinetic energy and produces a reactive force when it expands through the
nozzles from a high pressure to a low pressure. The reactive force will
cause rotation opposite to the direction of the steam jet.
This principle of creating a reaction force is identical to the principal of a
rocket engine. Fixed blades direct steam through moving blades attached to
the turbine shaft in a reaction turbine, as seen in the right half of the
Impulse/Reaction Turbine Comparison figure above. As steam passes
through each set of moving blades, a reaction force occurs that is opposite
in direction to the flow of steam. This reaction force causes the turbine
shaft to turn. One stage is a combination of one set of moving blades and
one set of stationary blades. The moving blades of the reaction turbine act
like nozzles. Between each two rows of moving blades are fixed blades that
function as nozzles. Velocity increases while pressure decreases as steam
passes through them.
The reaction turbine has all the advantages of the impulse turbine, plus
greater efficiency.
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Rev 1
Turbine Characteristics
As the kinetic energy in the steam converts into work moving the blades of
a reaction turbine, there is a drop in the steam’s velocity and pressure. This
is one major difference between the impulse turbine and the reaction
turbine. In the impulse turbine, there is no pressure drop across the blades,
only across the nozzle. The reaction turbine has a pressure drop across each
set of blades.
Impulse Turbine Characteristics
The upper portions of the two figures below show a cross-section with the
nozzle and blade arrangement for a simple impulse and actual impulse
turbine. The lower section of each figure shows the variation in steam
properties along the cross-section during the conversion from potential
energy to kinetic energy, and then to work.
Figure: Steam Property Variation in Simple Impulse Turbine
In a simple impulse turbine, the steam enters the nozzle with a maximum
pressure and a minimum velocity. The steam velocity and volume increase
while the pressure decreases. Steam leaves the nozzle at peak velocity and
enters the moving blade section of the turbine, where its kinetic energy
converts to useful work. There is no expansion of steam in the moving
blades of the turbine; therefore, the steam pressure and volume are constant
across the blade section through the exhaust. However, the velocity of the
steam greatly decreases in passing through the blades during the conversion
of the steam jet kinetic energy (a direct function of velocity) to work.
Turbines of this type have a very high relative speed because the maximum
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efficiency occurs when the velocity of the blades is one-half the velocity of
the steam jet leaving the nozzle.
The figure below shows a cross-section in an actual impulse turbine, with
the steam properties graphed along the cross-section.
Figure: Steam Property Variation In Actual Impulse Turbine
In an impulse turbine, a set of stationary blades directs the steam toward a
second row of moving blades that can extract more work. The figure above
shows a cross-section of such a turbine and the change in steam properties.
Steam leaving the first set of moving blades enters a second row of
stationary blades that redirect the flow of steam. Steam leaves the second
row of fixed blades with no changes in pressure or volume, and enters a
second row of moving blades where the steam velocity decreases as the
steam performs more work.
Reaction Turbine Characteristics
The figure below illustrates a cross-section and the variation in steam
properties as steam passes through two stages of a reaction turbine. As in
the impulse turbine, there are fixed nozzles between the rows of moving
blades. The stationary nozzles, shaped like a blade, are slightly convergent,
permitting an expansion of steam.
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Rev 1
Figure: Steam Property Variation in a Reaction Turbine
The steam jet enters a set of stationary nozzles, where steam velocity and
volume increase as the steam expands before impinging upon the first row
of moving blades. The moving blades are also nozzle-shaped to permit a
further reduction of steam pressure and increase in velocity. From the
velocity curve, it appears that a reduction in velocity takes place in the
moving blades. This is because the moving blades also have their own
velocity at this point and the curve above shows the absolute velocity. The
absolute velocity is the relative difference between the moving blade and
steam velocities.
After the steam leaves the first row of moving blades, the steam enters
another set of nozzle-shaped stationary blades where the steam pressure
decreases further, and the jet velocity increases. This set of stationary
blades directs the steam flow to the second row of moving blades. Turbines
use a large number of stages between inlet and exhaust conditions in order
to limit the pressure drop across any stage. The small pressure drop in the
nozzles results in a low steam velocity per stage. Thus, in general the
velocity of reaction turbine blades is less than the velocity of impulse
blades.
Each successive set of blading is larger. The thermal energy contained in
the steam is being converted to mechanical energy (rotation of the turbine)
as steam flows through the turbine. As a result, the temperature and
pressure of the steam will decrease. The specific volume of the steam
increases as the steam pressure decreases. The later stages of the turbine are
physically larger than earlier stages to ensure that the amount force acting
on the turbine blades remains relatively constant from stage to stage.
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Figure: Actual Turbine Blading
The turbine can extract energy by successive pressure drops, in which case
the turbine is termed pressure-compounded. Alternatively, the turbine can
extract energy by successive velocity decreases, in which case it is termed
velocity-compounded. A pressure-compounded turbine must consist of two
or more stages since pressure decreases occur only through nozzles.
However, a velocity-compounded turbine may consist of only one stage: a
nozzle followed by a set of moving blades, a set of fixed blades and another
set of moving blades. The figure below shows this arrangement, which is
sometimes referred to as a Curtis Wheel.
Figure: Pressure – Velocity in a Curtis Stage
The most important motive force in a reaction turbine is the jet-like thrust
that results when the steam expands through the tail of the teardrop shaped
20
Rev 1
blades. The reaction turbine differs from an impulse turbine in that the
casing has no nozzles between successive sets of blades, but has fixed
(immovable) reaction blades very similar to those on the rotor. They serve
to redirect steam as well as increase its velocity.
Nozzle Diaphragms
Nozzle diaphragms, illustrated in figure A below, are installed to admit
steam to the rotating blades of each stage of a pressure-compounded
impulse turbine.
The diaphragms contain nozzles that admit steam in an arc of a circle
around the blades. Diaphragms that only admit steam to certain quadrants
of the circle are "partial arc admission diaphragms". Diaphragms that have
nozzles extending around the entire circle of blades are "full arc admission
diaphragms".
Because of the pressure drop that exists across each diaphragm, steam
pressure leaks across the diaphragm and along the rotor. A labyrinth
packing ring (similar to the shaft gland packing) located in a groove in the
inner periphery of the diaphragm, shown in figure B below, minimizes
pressure leakage. Any leakage through the inner periphery of the
diaphragm reduces the amount of the steam thermal energy converted to
mechanical energy and, therefore, reduces the work developed by the stage.
Decreasing leakage is another reason to use multiple stages that reduce the
pressure drop across any individual stage. The right side figure below
shows the placement of these rings, which are installed in sections and are
spring-backed to hold them together and in place.
Figure: Turbine Diaphragm and Cross-Section
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21
Knowledge Check
What is the function of fixed blades in a reaction
turbine?
A.
Maintain steam flow direction
B.
Act as nozzles and expand the steam (decrease
pressure)
C.
Increase steam pressure before impacting next movable
blade.
D.
Change direction of steam flow to impact buckets in
next stage.
Knowledge Check
Which of the following is NOT a reason turbines
consist of multiple stages?
22
A.
There is a smaller pressure drop across each stage
B.
Allows more energy to be extracted from the steam
C.
Equalizes axial thrust on the shaft
D.
Accommodates for the expansion of the steam through
the turbine
Rev 1
ELO 1.3 Throttling Characteristics
Throttling is the process of restricting full flow through a restrictor, such as
an orifice or partially opened valve. The restriction causes a drop in fluid
pressure and a corresponding increase in velocity. This change takes place
without work interactions or changes in kinetic energy or potential energy.
There is no change in enthalpy from state one to state two (h1= h2), no work
is done (W = 0), and the process is adiabatic (Q = 0) during a throttling
process. This section will compare what we can observe with the above
theoretical assumptions to increase understanding of the theory of the ideal
throttling process.
In the figure below, we can observe that: Pin > Pout, velin < velout, (where P =
pressure and vel = velocity). Recall h = u + Pv (v = specific volume), so if
pressure decreases then specific volume must increase if enthalpy is to
remain constant (assuming u is constant). Because mass flow is constant,
the change in specific volume causes an increase in velocity.
The throttling process has a constant enthalpy with a large change in
entropy. The downstream fluid flow is somewhat turbulent from the
process.
Figure: Throttling Process by a Valve
Determining Downstream Properties Step-by-Step Table
Step
1.
Rev 1
Action
First, determine the condition upstream of the throttle or leak
(temperature, pressure (psia), quality or superheating). This is
usually given in the problem.
23
Step
Action
2.
Find the corresponding beginning point on the Mollier diagram
or in the steam tables.
3.
Determine the downstream pressure in psia. This is normally
given in the problem is some form.
4.
Draw a horizontal line from the initial condition point (constant
enthalpy) to the intersection of the constant pressure line for the
downstream pressure. The final condition is established by this
point (temperature, quality or superheating) (See diagram below
for explanation), or in the steam tables find the corresponding
enthalpy at the downstream pressure and determine other
properties required.
The diagram below shows step 4 above. Find initial point 1 and draw a
horizontal line until it intersects the downstream pressure which could be a
wet vapor under the dome (2) or superheated above the dome (3).
Figure: Throttling Process on a Mollier Diagram
Throttling Process Demonstration
In performing an analysis of the throttling process, we again assume steady
flow conditions (m1 = m2). We also select boundary locations sufficiently
away from the throttling location for flow to have returned to a stable,
uniform flow condition. With these conditions, we can analyze the process
as follows:
24
Rev 1
The elevation change from boundary 1 to boundary 2 is insignificant.
𝑃𝐸1 = 𝑃𝐸2
Inlet piping and outlet piping diameter are equal and there is no change in
fluid velocity.
𝐾𝐸1 = 𝐾𝐸2
There is no work done on or done by the fluid as it flows through the
throttle.
𝑊𝐼𝑁 = 𝑊𝑂𝑈𝑇 = 0
Assume insulation on the piping, so there is no heat transferred into or out
of the fluid.
𝑄𝐼𝑁 = 𝑄𝑂𝑈𝑇 = 0
This gives us the following results for a throttling process:
𝑃1 𝜈1
𝑃2 𝜈2
+ 𝑢1 =
+ 𝑢2
𝐽
𝐽
ℎ𝑖𝑛 = ℎ𝑜𝑢𝑡
As shown in the figure below, enthalpy remains constant while entropy
increases, the process does no work (J=joules), and no heat is added. The
result is a pressure drop and slight velocity increase.
Rev 1
25
Figure: Property Diagrams of a Throttling Process
Throttling can be beneficial, particularly in controlling flow rate to maintain
desired conditions in a system. However, the nature of the process (that is,
constant enthalpy) must be understood in order to recognize throttling
conditions. Failure to understand the downstream tailpipe temperature
indications of a Power Operated Relief Valve contributed to the events of
the Three Mile Island accident that changed the face of the nuclear industry
in the United States.
Ensure the students are comfortable working with throttling process
problems using the Mollier Diagram and the steam tables. NRC exams test
this topic heavily, as it is one of only two K/As in this chapter which have
related questions (value >2.5).
Example 1
A power-operated relief valve is stuck open at 2,200 psia in the pressurizer.
The valve is discharging to the pressurizer relief tank at 25 psig. What is
the temperature of the fluid downstream of the relief valve?
On the Mollier diagram, go to the 2,200-psia point on the saturation line.
Cross the constant enthalpy line (throttling is a constant enthalpy process) to
26
Rev 1
the 40 psia line (25 psig + 15 psi atmospheric = 40 psia). Follow that line
up to the saturation curve. The constant temperature line that ends at that
point on the curve establishes the temperature of the fluid. The temperature
is approximately 270F. The table below presents these steps in tabular
form.
Step
Action
1.
Determine the condition upstream of the throttle or leak
(temperature, pressure (psia), quality or superheating)
2.
Find the corresponding point on the Mollier diagram. (2,200
psia, saturated vapor)
3.
Determine the downstream pressure in psia. (25 psig = 40 psia)
4.
Go from the initial condition point along a horizontal line
(constant enthalpy) to the intersection with the constant pressure
line for the downstream pressure. This point establishes the final
condition. (temperature, quality or superheating)
Example 2
The RCS is operating at 2,185 psig. What would be the expected tailpipe
temperature of a leaking pressurizer safety valve assuming downstream
pressure is 35 psig? (Also, assume that the steam quality is 100 percent in
the pressurizer)
Solution:
𝑃1 = 2,185𝑝𝑠𝑖𝑔 + 15𝑝𝑠𝑖 = 2,200𝑝𝑠𝑖𝑎
𝑃2 = 35𝑝𝑠𝑖𝑔 + 15𝑝𝑠𝑖 = 50𝑝𝑠𝑖𝑎
From the Mollier diagram, the final condition is a mixture. Therefore the
tailpipe temperature must be at the saturation temperature corresponding to
the pressure.
From steam tables, 𝑇𝑠𝑎𝑡 = 281°𝐹
Knowledge Check
Which one of the following is essentially a constantenthalpy process?
Rev 1
27
A.
Throttling of main steam through main turbine steam
inlet valves
B.
Condensation of turbine exhaust in a main condenser
C.
Expansion of main steam through the stages of an ideal
turbine
D.
Steam flowing through an ideal convergent nozzle
Knowledge Check
A nuclear power plant is maintained at 2,000 psia with
a pressurizer temperature of 636°F. A pressurizer
relief safety valve is leaking to a collection tank which
is being held at 10 psig. Which one of the following is
the approximate temperature of the fluid downstream
of the relief valve?
A.
280°F
B.
240°F
C.
190°F
D.
170°F
TLO 1 Summary
Review each ELO with the class by using good questioning techniques.






Example of an effective method for asking directed questions:
I have a question...I will select someone to respond"
Ask the question
Pause
Select an individual to answer the question
Ensure that everyone heard and understood the response, amplify and
re-state as necessary
ELO 1.1
What is a nozzle? A nozzle is a mechanical device designed to control the
characteristics of a fluid flow.
How do nozzles work? Nozzles change the energy of a fluid from one form
to another frequently the goal is to increase the kinetic energy of the
flowing medium at the expense of its pressure and internal energy.
28
Rev 1
Describe a convergent nozzle. Convergent nozzle is a narrowing down
from a wide diameter to a smaller diameter in the direction of the flow.
Describe a divergent nozzle. Divergent is an expanding from a smaller
diameter to a larger one.
What are other uses of nozzles? A nozzle can serve as a flow restrictor to
limit flow, create a differential pressure for flow measurement, or create
high velocities for use in a turbine.
Explain how an air ejector works. The nozzle in an air ejector lowers
pressure and increases velocity. Supersonic flow creates very low pressures
to maintain the heat sink. Diffuser recovers pressure and slow velocity.
ELO 1.2
What at the two major designs of turbines? Two turbine types: impulse and
reaction
Why do turbines normally have multiple stages? Turbines normally consist
of multiple stages to allow more energy extraction from the steam.
How does a reaction turbine extract more energy from the steam? Reaction
turbine steam passes through a row of "fixed blades" which act as nozzles
and expand the steam (decrease pressure)
Increases steam's velocity and directs it into the "moving blades."
ELO 1.3
Define the throttling process. Throttling is the process of restricting full
flow using a restrictor such as an orifice or partially opened valve.
An isenthalpic process enables the exit state of a saturated or superheated
fluid to be determined on a Mollier diagram or with steam tables.
The principle can be applied to leaks is system boundaries.
Explain the steps in solving throttling problems using the Mollier Diagram.
Step
Action
1.
First, determine the condition upstream of the throttle or leak
(temperature, pressure (psia), quality or superheating)
2.
Find the corresponding point on the Mollier diagram.
Rev 1
29
Step
Action
3.
Determine the downstream pressure in psia.
4.
Draw a horizontal line from the initial condition point (constant
enthalpy), to the constant pressure line for the downstream
pressure.
This point establishes the final condition. (temperature, quality or
superheating)
Objectives
Now that you have completed this lesson, you should be able to:
1. Describe the operation of nozzles to include:
a. Functions of nozzles in flow restrictors
b. Functions of nozzles in air ejectors
2. Explain the design of turbines, including the functions of nozzles,
fixed blading, moving blading, and the reason turbines are multistage.
3. Determine exit conditions for a throttling process.
TLO 2 Compression Processes
Overview
Gas is another working fluid used throughout the plant. Gas responds
differently to temperature, pressure, and volumetric changes than steam, so
it requires additional explanation.
A gas is a state of matter distinguished from the solid and liquid states by
the following:





Relatively low density and viscosity
Relatively great expansion
Contraction with changes in pressure and temperature
Ability to diffuse readily
Spontaneous tendency to distribute uniformly throughout any
container.
A vapor is often confused with a gas. Vapor has evaporated from a liquid
or solid such as water.
Most familiar gases are colorless and odorless and include the following:



30
The oxygen and nitrogen of the atmosphere
The bubbles of carbon dioxide that rise in a glass of soda
The helium gas that is used to fill balloons.
Rev 1
A few gases have characteristic color, such as:


Nitrogen dioxide is red-brown
Iodine vapor has a beautiful violet color
Anything that we can smell can exist in the gaseous state because our sense
of smell reacts only to gases.
Gases have many observable physical properties. They fill whatever space
is available, but applying pressure can compress them into a smaller
volume. Temperature affects them; they can expand and contract, or exert
different pressures, depending on the temperature. It is obvious from the
force of the wind on a stormy day that gases can flow readily from place to
place and that they have mass. However, gases are not very dense; a vessel
filled with air floats on the surface of a pond because the air is less dense
than the water.
Temperature, pressure, and volume must always be specified when gases
are discussed because of their interrelated effect. The quantitative
relationships among the temperature, pressure, and volume of a gas are
expressed in the gas laws, which were first explored in the eighteenth and
nineteenth centuries.
Importance
Compression and pressurization processes are very common in many types
of industrial plants. These processes vary from being the primary function
of a piece of equipment, such as an air compressor to an incidental result of
another process, such as filling a tank with water without first opening the
tank's vent valve. Operators maintain important plant parameters such as
the safety injection accumulators within required legal and design limits
using gas compression and expansion. Understanding the relationships
between temperature, pressure, and volume of gases are important to ensure
operating within required parameters.
Upon completion of this lesson, you will be able to do the following:
1. Describe the ideal gas laws and explain how to solve for an unknown
pressure, temperature, or volume.
2. Describe the effects of pressure and temperature changes on confined
fluids.
Rev 1
31
ELO 2.1 Gas Laws
Introduction
Because of their interrelated effect, temperature, pressure, and volume must
always be specified when gases are discussed. The quantitative
relationships among the temperature, pressure, and volume of a gas are
expressed in the gas laws, which were first explored in the eighteenth and
nineteenth centuries.
The gas laws are useful because at low pressures all real gases behave like a
perfect gas. Monatomic gas behavior is very similar to perfect gas
behavior; the Ideal Gas Law is therefore accurate for predicting the gas
behavior. Accuracy will decrease with diatomic and polyatomic gases.
Still, the Ideal Gas Law is useful to develop the behavior of even these
gases with experimentally derived corrections made to produce the desired
accuracy.
Charles’s Laws
Charles’s law or the law of volumes is an experimental gas law that
describes how gases tend to expand when heated.
The figure below shows a piston and cylinder assembly filled with a gas at
absolute temperature (T1 = 300°K) and volume (V1 as shown). The piston is
free to move against a constant external pressure.
Figure: Charles’s Law for Constant Pressure
Adding heat causes the temperature of the gas to increase. The volume
increases and applies pressure against the piston causing the piston to move
outward as the gas temperature increases. The piston will continue to rise
until the cylinder pressure on the internal piston face equalizes to the
external pressure on the piston, restoring system equilibrium. The initial
and final pressures are the same but the absolute temperature (T2 = 600°K)
32
Rev 1
is higher and volume (V2) is twice as large as (V1) since the absolute
temperature was doubled.
Repeating the process of adding heat to the gas, causing the piston to move
farther upward, and re-measuring the process variables of gas volume and
temperature, will lead to the following conclusion:
"The volume of a gas at constant pressure is directly proportional to
the temperature of the gas at low pressures.
Charles, as the result of experimentation also concluded that the
"pressure of a gas varies directly with temperature when the volume
is held constant".
The mathematical expressions of Charles’s Law are:
𝑉1 𝑇1
𝑃1 𝑇1
=
𝑜𝑟
=
𝑉2 𝑇2
𝑃2 𝑇2
Boyle's Law
Now imagine that the piston and cylinder assembly without the heater. Gas
fills the cylinder to a gas at volume (V1), temperature (T1), and at an
absolute pressure (P1). The cylinder adds no heat to the gas, so the gas
temperature remains constant.
We move the piston physically to a new position by adding or removing
weights, as shown in the figure below. The volume (V2) and absolute
pressure (P2) are measured, and the procedure repeated. Examining the
measured variables, we develop the following conclusion about the gas:
Figure: Boyle's Law
Boyle's Law
"At low-pressures, the volume of a gas at constant temperature is inversely
proportional to the absolute pressure of the gas."
Rev 1
33
This statement is Boyle's Law, written mathematically as:
𝑃1 𝑉1 = 𝑃2 𝑉2 = 𝑃𝑉 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
Combined Gas Law
Charles’s Law and Boyle's Law are valid for ideal gases and real gases in
the pressure range that the real gas behaves like an ideal gas. Therefore,
any real gas at low pressure will obey both these laws, stated as follows:
"For a given mass of any gas, the product of the absolute
pressure and volume occupied by the gas, divided by its
absolute temperature, is a constant."
The figure below shows how Boyle’s and Charles’s Laws relate to
compression and temperature increases of gases.
Figure: Combined Gas Law
This statement is the Combined Gas Law, written mathematically as:
𝑃1 𝑉1 𝑃2 𝑉2 𝑃𝑉
=
=
𝑇1
𝑇2
𝑇
The P-T-V diagram below shows all three relationships from the above
equation.
34
Rev 1
Figure: PTV Diagram for Combined Gas Law
Example
A compressor discharges into an air receiver, and cycles off when the
pressure in the receiver reaches 160 psia. During the compression, the
compressor added heat to the air and its temperature in the receiver is
140°F. Assuming no air loads are in service, at what temperature (°F)
should the compressor restart to maintain the receiver above 150 psia?
Solution:
Assuming an ideal gas:
𝑃1 𝑉1 𝑃2 𝑉2
=
𝑇1
𝑇2
The receiver volume is constant, therefore:
𝑃1 𝑃2
=
𝑇1 𝑇2
𝑇1 (°𝑅) = 460°𝐹 + 140℉ = 600°𝑅
𝑃1 = 160 𝑝𝑠𝑖
𝑃2 = 150 𝑝𝑠𝑖
160 𝑝𝑠𝑖 150 𝑝𝑠𝑖
=
600°𝑅
𝑇2
Rev 1
35
𝑇2 =
600 × 150
160
𝑇2 (°𝑅) = 562.5°𝑅
𝑇2 (°𝐹) = 562.5°𝑅 − 460° = 102.5℉
Ideal Gas Law
By combining the results of Charles’s and Boyle's experiments the
following is obtained:
𝑃𝑣𝑇 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
This constant is the ideal gas constant, designated by R. Pressure, volume,
and temperature determines the state of an amount of gas, according to the
equation:
𝑃𝑣 = 𝑛𝑅𝑇
Where:
P = the absolute pressure (Pa)
V = the volume (m3) of the vessel containing n moles of gas
n = the amount of substance of gas (mole)
R = the gas constant (8.314472 m3·Pa·K−1·mol−1)
T = the temperature in degrees Kelvin (°K)
The ideal gas constant (R) depends on the units used in the formula. The
value given above, 8.314472, is for the SI units of Pascal cubic meters per
mole per degree Kelvin, which is equal to joule per mole per degree Kelvin
(J mol-1 K-1). Another value for R is 0.082057 liter atmosphere per mole per
degree Kelvin (L·atm·mol−1·K−1).
Mole
It is common practice to discuss quantities of substances in terms of a
measurement called a mole. In order to define a mole, we must first define
another term, Avogadro's number. Avogadro's number is the number of
carbon atoms in 12 grams of carbon-12. The experimentally determined
value of Avogadro's number is 6.023 x 1023 atoms. One mole of any
substance is equal to the amount of that substance having Avogadro's
number of atoms.
Normally, atomic mass units (amu) quantify a substance's atomic mass
(atomic weight). One-twelfth (1/12) of the mass of a carbon-12 atom
36
Rev 1
defines one amu, which is equivalent to 1.6604 x 10-24 grams. One mole of
an element is equal to the atomic mass number of that element in grams.
1 𝑚𝑜𝑙𝑒 = 6.023 × 1023 𝑎𝑡𝑜𝑚𝑠
6.023 × 1023 𝑎𝑡𝑜𝑚𝑠 (12
𝑎𝑚𝑢
) = 72.27 × 1023 𝑎𝑚𝑢
𝑎𝑡𝑜𝑚𝐶12
𝑔
= 72.27 × 1023 𝑎𝑚𝑢 (1.6604 × 10−24 𝑎𝑚𝑢) when
𝑃𝑣
𝑇
= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
= 12 𝑔𝑟𝑎𝑚𝑠
Using the element's atomic weight improves the accuracy of the calculation,
but the added accuracy is insignificant and is not usually required.
Simplifying the relationship yields:
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑒𝑠 =
𝑀𝑎𝑠𝑠(𝑔𝑟𝑎𝑚𝑠)
𝑔𝑟𝑎𝑚𝑠
(𝐴𝑡𝑜𝑚𝑖𝑐 𝑀𝑎𝑠𝑠) (
)
𝑚𝑜𝑙𝑒
An ideal gas was defined as one in which PV/T = a constant under all
circumstances. Though no such gas exists, the fact that a real gas behaves
approximately like an ideal gas provides a specific target for theories for the
gaseous state.
Experimenters found the constant, in terms of the number of moles (n) of
gas in a sample, by making use of the fact that the molar volume of a gas at
standard temperature and pressure (STP) is 22.4 liters.
At STP: 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒(𝑇) = (0°𝐶 = 273°𝐾)
𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒(𝑃) = 1 𝑎𝑡𝑚
𝑉𝑜𝑙𝑢𝑚𝑒(𝑉) = (𝑛) (
Thus,
𝑃𝑉
𝑇
22.4 𝑙𝑖𝑡𝑒𝑟𝑠
)
𝑚𝑜𝑙𝑒
= 𝐾, 𝐾 = 𝑎 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
𝑃𝑉
22.4 𝑙𝑖𝑡𝑒𝑟𝑠
1
= (𝓃)(1 𝑎𝑡𝑚) (
)(
) = 𝑛𝑅
𝑇
𝑚𝑜𝑙𝑒
273°𝐾
The figure below shows the classic Ideal Gas Law expression:
Rev 1
37
Figure: Ideal Gas Law
The figure below expresses the mole-volume relationship of an ideal gas at
standard temperature and pressure:
Figure: Mole - Volume Relationship
We cannot refer to gases that do not obey this law as ideal. Water vapor
DOES NOT obey the ideal gas laws.
An ideal gas has properties that are constant throughout its mass and whose
molecular movements are not influenced by chemical reactions or external
forces.
There is no known ideal gas. The ideal gas equation is a good
approximation to real gases at sufficiently high temperatures and low
pressures; that is, PV = RT, where P is the pressure, V is the volume per
mole of gas, T is the temperature, and R is the gas constant.
At low pressures, all real gases behave like a perfect gas. The ideal gas law
is the most accurate for monatomic gases at high temperatures and low
pressures. This follows because the law neglects the size of the gas
molecules and the intermolecular attractions. Neglecting molecular size
becomes less important for larger volumes, i.e., for lower pressures. The
relative importance of intermolecular attractions diminishes with increasing
thermal kinetic energy.
Engineers use the ideal gas law because it is simple to use and approximates
real gas behavior. Most physical conditions of gases used by man fit this
description.
38
Rev 1
Knowledge Check
According to Charles’s Law, at low pressure, the
_____ of a gas at constant _____ is directly
proportional to the temperature of the gas.
A.
density; pressure
B.
volume; pressure
C.
pressure; volume
D.
weight; volume
Knowledge Check
Calculate the value of the missing property.
P1= 100 psia; P2 = ?
V1 = 50 ft3; V2 = 25 ft3
T1 = 60°F; T2 = 70°F
A.
233 psi
B.
210 psi
C.
204 psi
D.
200 psi
ELO 2.2 Compression Process
Introduction
The most common use of gas behavior is during the compression process
using ideal gas approximations. A compression process may occur at
constant temperature (ΔT = constant), constant volume (ΔV = constant), or
adiabatic (no heat transfer). The amount of work that results from it
depends upon the process, as brought out in the study of the first law of
thermodynamics. When using ideal gas assumptions, the compression
process results in work performed on the system, and is essentially the area
under a P-V curve. Maintaining constant temperature or maintaining
constant pressure results in different amounts of work as shown in the
figure below.
Rev 1
39
Figure: Pressure-Volume Diagram
Compressibility
A fluid is any substance that conforms to the shape of its container; a fluid
may be either a liquid or a gas.
A fluid is considered incompressible when the velocity of the fluid is
greater than one-third of the speed of sound for the fluid, or if the fluid is a
liquid. We assume that such a fluid has a constant density. The variation of
density of the fluid with changes in pressure is the primary factor
considered in deciding whether a fluid is incompressible.
Because compressible fluids experience density changes, their property
relationships vary more than incompressible fluids. In addition, it is easy to
determine the state of a liquid if you know its temperature and pressure.
The process becomes more difficult once the substance becomes a gas.
Figure: P-V Diagram for Gas
40
Rev 1
Constant Pressure Process
As shown on the above P-V diagram, the work done in a constant pressure
process is the product of the pressure and the change in volume.
𝑊1−2𝑎 = 𝑃(𝛥𝑉)
Constant Temperature Process
The work done in a constant temperature process is the product of the
temperature and the change in volume.
𝑊1−2𝑏 = 𝑇(𝛥𝑉)
Constant Volume Process
The work done in a constant volume process is the product of the volume
and the change in pressure.
𝑊1−2𝑐 = 𝑉(𝛥𝑃)
The above equation also applies to liquids. The power requirement for
pumps that move incompressible liquids (such as water) can be determined
by replacing the volume (V) with the product of the specific volume and the
mass.
Power Requirements
𝑊1−2𝑐 = 𝑚𝑣(𝛥𝑃)
Taking the time rate of change of both sides determines the power
requirements of the pump.
𝑊̇1−2𝑐 = 𝑚̇𝑣(∆𝑃)
Effects of Pressure Changes on Fluid Properties
The predominant effect of a pressure increase in a compressible fluid, such
as a gas, is an increase in the fluid density. A pressure in an incompressible
fluid will not result in a significant effect on the density. For example,
increasing the pressure of 100°F water from 15 psia to 15,000 psia will only
increase its density by approximately 6 percent. Therefore, in engineering
calculations, we assume that the density of incompressible fluids remains
constant.
Effects of Temperature Changes on Fluid Properties
An increase in temperature will tend to decrease the density of any fluid.
The effect of a temperature change will depend on whether the fluid is
compressible if the fluid is confined in a container of fixed volume.
Rev 1
41
A gas will respond to a temperature change in a manner predicted by the
ideal gas laws. A 5 percent increase in absolute temperature will result in a
5 percent increase in the absolute pressure.
If the fluid is an incompressible liquid in a closed container, a fluid
temperature increase will have a tremendously greater and potentially
catastrophic effect. The fluid tries to expand, but the walls of the container
prevent its expansion as the fluid temperature increases. Because the fluid
is incompressible, this results in a tremendous pressure increase for a
relatively minor temperature change. The change in specific volume for a
given change in temperature is not the same at various beginning
temperatures. Resultant pressure changes will vary. A useful thumb rule
for water is that pressure in a water-solid system will increase about 100 psi
for every 1°F increase in temperature.
Knowledge Check
When can a fluid be considered incompressible?
A.
if it is liquid
B.
if it is steam but not flowing
C.
if it is a saturated vapor
D.
if it is a superheated steam
Knowledge Check
A contained fluid is heated. The resulting change in
pressure will be…
42
A.
greater for an incompressible fluid.
B.
greater for a compressible fluid.
C.
the same for both fluids.
D.
the same for both fluids only if the volume is held
constant.
Rev 1
TLO 2 Summary
Review each ELO with the class by using good questioning techniques.
Example of an effective method for asking directed questions:





I have a question...I will select someone to respond"
Ask the question
Pause
Select an individual to answer the question
Ensure that everyone heard and understood the response, amplify and
re-state as necessary
ELO 2.1
What is Charles’s Law, and what is the mathematical relationship?
The volume of a gas at constant pressure is directly proportional to
the temperature of the gas at low pressures.
𝑉1 𝑇1
𝑃1 𝑇1
=
𝑜𝑟
=
𝑉2 𝑇2
𝑃2 𝑇2
What is Boyle's Law, and what is the mathematical relationship?
At low-pressures, the volume of a gas at constant temperature is
inversely proportional to the absolute pressure of the gas
(𝑃1 )(𝑉1 ) = (𝑃2 )(𝑉2 ) = (𝑃3 )(𝑉3 ) = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
What is the mathematical expression of the combined law?
𝑃1 𝑉1 𝑃2 𝑉2 𝑃𝑉
=
=
𝑇1
𝑇2
𝑇
What pressures and temperatures do we use in solving the gas laws?
Temperature and Pressure MUST BE IN ABSOLUTE.
Explain the ideal gas law.
Ideal gases follow the above laws. A specific gas constant is used to
account for difference in gases atomic structure (R).
𝑃𝑣 = 𝑅𝑇
What is a mole of gas?
One mole of any substance is that amount having Avogadro's Number of
6.023 x 1023 atoms. We use moles to account for large volumes of gas in
the ideal gas equation.
Rev 1
43
ELO 2.2
When can we assume that a fluid is incompressible?
A fluid may be considered incompressible when the velocity of the
fluid is greater than one-third of the speed of sound for the fluid, or
if the fluid is a liquid.
What is the major parameter used to determine incompressibility?
Variation of fluid density with pressure changes is a primary factor
considered in deciding whether a fluid is incompressible. An
increase in the pressure of an incompressible fluid will not have a
significant effect on the fluid density. Increasing the pressure of
100°F water from 15 psia to 15,000 psia will only increase the water
density by approximately 6 percent.
Explain how a compressible fluid responds to temperature changes.
For a fluid in a closed container of fixed volume, the effect of a
temperature change will depend on whether the fluid is
compressible. If the fluid is a compressible gas, it will respond to a
temperature change in a manner predicted by the ideal gas laws.
A 5 percent increase in absolute temperature will result in a 5
percent increase in the absolute pressure.
If the fluid is an incompressible liquid in a closed container, an
increase in the temperature will have a tremendously greater and
potentially catastrophic effect.
Rule of thumb for water: pressure in a water-solid system will
increase about 100 psi for every 1°F increase in temperature.
Objectives
Now that you have completed this lesson, you should be able to:
1. Describe the ideal gas laws and explain how to solve for an unknown
pressure, temperature, or volume.
2. Describe the effects of pressure and temperature changes on confined
fluids.
44
Rev 1
Thermodynamic Processes Summary
This chapter examined various processes that occur in a plant; many of
these processes are invisible to the operator. For instance, we examined
how nozzles located within the plant piping systems perform their design
function of converting fluid energy into the desired fluid properties. We
looked at how nozzles can create increased mass flow rates as in the jet
pumps or create large differential pressures to choke flow if needed. The
design of the nozzle throat determines whether the fluid reaches sonic or
supersonic velocity and how the properties of fluids changed when they
were supersonic. We saw that instrumentation determines flow rates based
on the inherent pressure drop in nozzles.
We then looked at the use of nozzles within the turbine to create the desired
pressure or velocity compounding to maximize the work of the turbine. The
use of the nozzle to create high velocity steam flow to impinge on the
moving part of an impulse turbine was shown to be less efficient than using
nozzle shaped movable blades to create a reaction turbine.
Certain processes are termed throttling processes. We can easily determine
downstream fluid properties in throttling processes, because throttling
processes do no work and are isenthalpic. This means that the enthalpy
entering the process is the same as the enthalpy exiting the process.
Entropy will increase slightly through the process.
We then examined how gases respond differently than steam to certain
process variables. Gases follow laws relating their temperature, pressure,
and volume. Although no gas is ideal the use of the ideal gas law allows
close approximations to how a gas will behave when the variables are
changed.
The module explained compressibility, along with the differences between
compressible and incompressible fluid response to pressure and temperature
changes. If the plant is taken water solid, it is filled with an incompressible
fluid that will expand with any temperature increase creating large and
possibly damaging internal pressures.
Objectives
Now that you have completed this module, you should be able to
demonstrate mastery of this topic by passing a written exam with a grade of
80 percent or higher on the following TLOs:
1. Explain thermodynamic systems and processes.
2. Explain compression processes and the laws associated with them.
Rev 1
45