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THESIS

2
200\

This is to certify that the

thesis entitled

Study of Steam Chest Control Valve Failure in Steam Turbines

presented by

Hon Kit Sam

has been accepted towards fulfillment
of the requirements for

MS Mechanical Engineering

 

degree in

Ag- 1“
MajonBEessor

4/26/01
Date

 

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

 

 

 

LIBRARY
Michlgan State
University

 

 

 

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6/01 cJCIRC/DateDuopss-pts

STUDY OF STEAM CHEST CONTROL VALVES IN STEAM TURBINES
By

Hou Kit Sam

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Department of Mechanical Engineering

2001

ABSTRACT
STUDY OF STEAM CHEST CONTROL VALVE FAILURE IN STEAM TURBINES
By

Hou Kit Sam

Steam turbine control valves are the typical mechanism for regulation of flow into
the main turbine itself. However, there has been a long history concerning the failure of
the control valves. The failure that the valves experience all seems to be at the same area,
which is failure between the valve stem and the top of the valve plug. It also has been
theorized that the valve failure is due to fluid-flow induced Vibration. This study
investigates the valve failure and attempts to recreate the flow through a valve to obtain
data points at various positions along the valve plug head as well as the valve seating.
The main system studied is a quad-valve system, with the main complication occurring
with the middle two valves during their lift action. Current fundamentals of flow theory
around valves was considered and integrated with previous research concerning valve
failure due to fluid-induced vibration. The actual problem concerning the current valves
was then studied and the general causes investigated. Theoretical calculations based on
basic theory of fluid-flow induced vibrations were done to obtain an initial theoretical
View of the induced Vibrations to design an actual experimental setup. Preliminary valve
flow calculations were conducted to assist in the design of the experimental testing setup
and to predict the possible data that is expected from the actual testing. The primary
design concepts for the experimental setup include a single-valve, half-scaled design,

with the use of a vacuum pump to induce the flow.

To my family, friends, and the people responsible for my education.

iii

ACKNOWLEDGEMENTS

This research project would not have been made possible without the assistance of
Elliot Turbo-machinery Co. in Jeannette, Pennsylvania. The people responsible for their
assistance are Naresh Amineni and James Hardin. Their suggestions, questions, and
answers have helped guide the general direction of the project and enabled me to move
on to each step of the project as quickly as possible.

I would also like to give thanks to my faculty mentor, Dr. Abraham Engeda, who
provided me the research project, in seeing the potential of getting the project to a good
start. He has also given me direction in the project and allowed me to work with some
freedom as to how the project is handled, how the research experimental setup is
developed, and in making sure that he and Elliot Turbo-machinery Co. approved the
design.

Next, I would like to acknowledge all other professors and friends that have
helped me during my stay here in the university, providing me with some help in little
bits and pieces, and for being their in helping cope with the stress.

Lastly, I would like to thank my entire family back in Malaysia for providing me
infinite support over my college years in helping me with problems that I may have in
studying in the Masters program as well as everyday life. I would also like to especially
thank Dr. Tom Shih and Dr. Indrek S. Wichman for being part of the final thesis defense

and also their time in the classroom for assisting me during the Masters program.

iv

TABLE OF CONTENTS

INTRODUCTION

CHAPTER 1
CURRENT RESEARCH OF QUAD-VALVE SYSTEM FAILURE
1.Current Research on Control Valves

1.] Acoustic Resonance
1.2 F low-Induced Valve Instability

CHAPTER 2
FUNDAMENTALS AND FLOW THEORY OF CONTROL VALVES
1.Brief Fundamentals of Venturi Control Valves
2.Fluid Forces in Control Valves
2.] Problems with Valve Travel
2. 2 Large Side Loadings and Excessive Torque
2. 3 Vertical Bufleting and Horizontal Vibrations
2.4 Bi-stable Action fi'om Negative Gradients
2.5 Emergence of Unpredictable Vortexes
2. 6 Complications from a Minor Loop Cycle in the Process
System
2. 7 Complications from Cavitation, Noise, Erosion, and
Compressibility

CHAPTER 3
PREVIOUS RESEARCH AND TESTING OF FLUID-INDUCED VIBRATION
1.Description of Fluid Vibrations with Vibrational Model of
Control Valve
2.Previous Research for a Two-Dimensional Test
2.1 The Two-Dimensional Model Test
2.2 The Results and Observations of the Two-Dimensional Test
3.Previous Research for a Three-Dimensional Test
3.] The T hree-Dimensional Model Test
3.2 Results and Observations of the Three-Dimensional Test
3.3 Closer Analysis of Vibration from Pressure Variation of F low
3. 4 Application of the Model Testing to the Actual Valve System

10
12
13
14
17

18

18

20

20
23
23
24
27
28
3O
35
38

CHAPTER 4
SIMPLE THEORETICAL RESEARCH OF SELF-INDUCED VIBRATION
l. Self-Induced Vibration
2.1 Fluid Force Estimation
2. 2 Stability

CHAPTER 5
THE CURRENT RESEARCH ON THE QUAD-VALVE SYSTEM
1.General Problems Found from the History of Valve Failure Study
1.1 Instability Commencement of Valves
1. 2 Bending Loadings
1.3 Valve Spinning
2.Research Problem with Quad-Valve System
2.1 Preliminary Theoretical Calculations of Valve F low
3. Preliminary Design concepts and Calculations to Scaling
3.1 Method of F low Calculations
3.1.1 Initial Flow Calculations
3.1.2 Secondary Flow Calculations
4.Scaling and Design of Experimental Setup
4.1 The Valve and Valve Chest
4.2 The Flow System
4.2.1 The ROOTS RAMTM Whispair 616 DVJ
Dry Vacuum Pump

APPENDIX A

APPENDIX B
APPENDIX C

vi

4O
4O
41
44

47
47
47
48
49
52
53
54
56
58
60
62
62
65

67
75

81
88

Table 1.

Table 2.

Table 3.

Table 4.

Table 5.

Table 6.

Table 7.

Table 8.

Table 9.

LIST OF TABLES

Acoustic Natural Frequency Values Found with Finite
Element Analysis

Properties for the Commencement of Flow Calculations

The results of one-dimensional isentropic compressible-flow
functions for an ideal gas with constant specific heats and
molecular weights.

Initial Conditions

Results for Throat Position Calculations at Pressure Ratio of 3

Table of Results for Venturi Position Calculations at
Pressure Ratio of 3

Performance Table
Ambient and Standard Conditions for Vacuum Pump Operation

Input Conditions for Vacuum Pump Operation for Pressure
ratio of 10

Table 10. Input Conditions for Vacuum Pump Operation for Pressure

ratio of 10

Table 11. Input Conditions for Vacuum Pump Operation for Pressure

ratio of 3

Table 12. Input Conditions for Vacuum Pump Operation for Pressure

ratio of 3

Table 13. Composition Table for aluminum 2024

Table 14. Physical Properties of Aluminum 2024

Table 15. Mechanical Properties of Aluminum 2024

Table 16. Thermal Properties of Almninum 2024

vii

56

57

62

62

67

68

68

69

69

69

88

89

89

9O

LIST OF FIGURES

Figure 1: Venturi Valve
Figure 2: Relation Between Steam Flow and Valve Lift
Figure 3: Balanced Valve Lift Correlation with Plug Force.

Figure 4: Unbalanced Valve Lift Correlation with Plug Force.

Figure 5: Reality Correlation with the Valve Lifi and the Vertical Forces.

Figure 6: Force Curve of Unbalanced Valve Design.
Figure 7: Force Curve of Balanced Valve.
Figure 8: Vibration Model.

Figure 9: Experimental Testing Setup to Observe Two-Dimensional
Flow through a Valve System

Figure 10: Flow through the Valve at a High Pressure Ratio.

Figure 11: Flow through the Valve at a Low Pressure Ratio.

Figure 12: Relationship between b/R and r/R.

Figure 13: Main Testing Apparatus for Three-Dimensional Testing
Figure 14: Positions of Pressure Sensors on Valve and Valve seating.
Figure 15: Flow Pattern of Two-Dimensional Flow.

Figure 16: Flow Pattern of Three-Dimensional Flow.

Figure 17: Time Traces of Valve Surface.

Figure 18: Surface Pressure Fluctuations.

Figure 19: Surface Pressure Fluctuations.

Figure 20: Power Spectra of Surface Pressure Fluctuation and
Acceleration for the Three-Dimensional Model Valve.

viii

11

11

13

15

16

20

24

25

25

27

29

30

31

32

32

33

34

35

Figure 21:

Figure 22:

Figure 23:
Figure 24:
Figure 25:
Figure 26:
Figure 27:
Figure 28:
Figure 29:
Figure 30:
Figure 31:
Figure 32:
Figure 33:
Figure 34:

Figure 35:

Figure 36:

Figure 37:

Figure 38:

Figure 39:

Figure 40:

Vertical and Horizontal Accelerations for Model Valve.

Horizontal Displacement Response against Valve Surface
Pressure Fluctuation

Typical valve Lifi Characteristic Curve.

Theoretical Vibrational Model for Analysis

Relationship of Fluid Force Coefficient in Terms of Frequency
Relationship of Damping Ratio and Assumed Frequency
Relationship of Actual Frequency and Assumed Frequency
Relationship of Vertical Force on a Valve to the Valve Lifi
Two-Dimensional View of Plug Eccentricity

Four-Valve System.

Early Dual-Valve

Early concept of Singular Valve Design

Simple Converging Diverging Theory

Initial Testing Setup

Relationship of Temperature Rise and Blower Speed for
Pressure Ratio of 10

Relationship of Inlet ACF M and Blower Speed for Pressure
Ratio of 10

Relationship of Brake Horsepower and Blower Speed for
Pressure Ratio of 10

Relationship of Temperature Rise and Blower Speed for
Pressure Ratio of 3

Relationship of Inlet ACFM and Blower Speed for Pressure
Ratio of 3

Relationship of Brake Horsepower and Blower Speed for
Pressure Ratio of 3

ix

36

37

38

41

45

46

47

50

53

55

56

57

66

70

70

71

71

72

72

Figure 41:
Figure 42:
Figure 43:
Figure 44:
Figure 45:
Figure 46:
Figure 47:
Figure 48:
Figure 49:
Figure 50:
Figure 51:
Figure 52:
Figure 53:

Figure 54:

Flow Pattern of Valves

Mach Number Profile for 0.4595 inch Lift
Pressure Profile for 0.4595 inch Lift

Velocity Profile for 0.4595 inch Lift

Mach Number Profile for 0.639 inch Lift
Pressure Profile for 0.639 inch Lift

Velocity Profile for 0.639 inch Lift

Main Testing Valve Pressure Chest

Side Plating Dimensions for Pressure Chest Opening
Valve and Seating Pressure Gauge Arrangement
Overall Shaft Design for Valve Lift

Dimensions for Main Valve Plug Head
Dimensions for Valve Stem and Plate Bolt

Dimensions for Main Valve Seating

74

75

76

77

78

79

80

81

82

83

84

85

86

87

psi

d/dt
dz/dtz

pa

'TJW
{I}

W\
pl.
:3

N

H FUD-.3353 gcwem‘oca—

8
.D
A
“U
v

<>Q F§S.Z‘<:H:\1.Ho‘<x

LIST OF SYMBOLS OR ABBREVIATION

pounds per square inch
Pascal

feet per second

meter per second

inch

millimeter

pounds

Newton

Hertz

differentiation

double differentiation

mass

damping coefficients (a is arbitrary denotation)
spring constant (a is arbitrary denotation)
force (a is arbitrary denotation)
diameter

flow of velocity

density

speed of sound

angular vibration frequency
pressure

valve lift

pounds per inch square
meter cubed

feet cube

throat width

cylinder radius

radii of curvature

power spectrum density
x-axis displacements

y-axis displacements
x-axis velocity

y-axis velocity

x-axis acceleration
y-axis acceleration

sum of the added masses and valve masses (a is arbitrary denotation)

sink flow rate or mass flow rate
gravitational constant

stem length

stress

area

tangential velocity

xi

valve diameter
momentum change
joule
kilogram
Kelvin
British thermal unit
english mass unit
rankine
atmospheric reading
gas constant
mach number
mach number at throat
area at throat
stagnation pressure
stagnation temperature
stagnation density
ratio of specific heats (a is arbitrary denotation)
cubic feet per minute
actual cubic feet per minute
standard cubic feet per minute
brake horsepower
revolutions per minute

xii

INTRODUCTION

As the technology for steam turbines progressed, the industry commenced the
construction of larger and more powerful steam turbines. However, along with the size
and capacity increase, more importance was also stressed in the regulation of the flow by
the control valves. Based on the rotational speeds or loading signals, the control valves
regulate the amount of flow through the turbine to control the output. The turbine that is
being investigated possesses a four-valve system. There has been a long history
regarding the reliability of these control valves. Even with four valves, operations at such
high temperatures and pressures and vast pressure differences between the inlet and outlet
of the turbine will subject the valve to enormous dynamic and static hydraulic forces and
subjects the valves to abnormal vibrations. This research project’s objective is to take an
in—depth look and to determine if it is indeed the fluid-flow induced vibrations that cause
failure of the valves. The failure of the control valves in this turbine under study occurs
in two of the four valves, the two center ones to be specific. An initial theoretical study
of fluid-flow induced vibrations was made and a brief history of the most recent study on
similar valve failures was also conducted to provide a direction towards the best method
to tackle this problem. It was then decided that a single valve, half-scale model would be
adequate, designed to minimize cost of construction, and calculated to be adequate in
terms of data collection. The half-scale size is slightly more than enough to position and
fit in the necessary static and dynamic pressure gauges. Once the data is analyzed, a
more in-depth realistic view of the valve flow can be made. It is hoped that this research

will help provide a more definitive look on valve failure.

CHAPTER 1
The Current Research of Quad-Valve System Failure
1. Current Research with Control Valves

The problem that is currently being studied involves a quad-valve system that
controls the steam flow into the turbine. The steam chest operates at about 1600 psi (1 1
Mpa) and with fully lifted valves; the pressure drop is at about 100 psi (0.69 Mpa).

With valve flow operating at a choked flow, which is approximately about 2000
ft/s (609.6 m/s) at a valve lift of about 0.7 in (17.78 m), an increase of steam pressure
causes the number 2 valve to fail due to severe vibrations. From a closer physical
analysis and simple initial failure analysis, it was determined that the valve experiences
an extremely high lateral vibration at that valve lift position. An axial force of about
3200 lbs (14234 N) is estimated to be experienced at this lift. The number 2 valve, which
is one of the problem valves that have been tested, with an infinitely stiff support, has a
high lateral, or bending, resonance of 600Hz, and as the support stiffness reduces, the
resonance are found to be as low as 350Hz.

The Mach number, pressures, and flow velocities of the actual valve have been
mapped out with two lifi positions that experience the instability and vibration most
commonly. The main problem occurs during the valve wide-open lift, which is at 0.639
inches. The other lift, at 0.4595 inches, experiences the same type of vibrations and
instability, although not as intense in magnitude. For comparison purposes, and to
observe the apparent increase in the undesirable effects of instability and vibration, the

profiles for the 0.4595-inch lift is shown first, followed by the 0.639-inch lifts. Patterns

for the Mach number, pressure and velocities change as the lift increases. These profiles
can be found in Appendix A.

Two causes for the unusual vibration have been identified. The first cause, which
is more specific, deals with the acoustic inlet resonance in the steam chest box. The
second cause, involves the flow-induced forces that cause the lateral vibration and
instability. With high-speed flows in the operation of the turbine, both the acoustic
environment and the mechanical resonant characteristics of the valve will be adversely
affected.

1.1 Acoustic Resonance
The method to check acoustic resonance is to use finite element modeling. The
steam flows are what is usually modeled. The natural frequencies of the flow path are
determined using a 3-D model using a standard value for the speed of sound. Additional
analysis was used with variations of the speed of sound value by roughly 10 percent.
Scaling these frequency values can be done for any pressure and temperature because

these natural frequencies are linearly proportional to the speed of sound.

 

 

 

 

 

 

 

 

 

 

 

 

Downstream Outer Channel Inner Channel
Flow Paths 1st Mode 2"d Mode 1st Mode 2"d Mode
2000 ft/s 337.8 558.7 428.9 744.5
Zero 337.8 558.7
Impedance at
End
2200 fi/s 371.6 614.6 471.8 818.9
1800 fi/s 304.0 502.8 386.0 670.0
Using a Finer 337.6 552.5 427.1 744.7
Mesh
Theoretical 333.0 460.0
Hollow
Cylinder of
Same Length

 

 

 

Table 1. Acoustic Natural Frequency Values Found with Finite Element Analysis

From the table above, we see the various natural frequencies at various speeds and
modes in the outer and inner channels. The interior nozzles have a first mode frequency
of 558 Hz when the speed is at 2000 ft/s. However, in order to have a lower frequency at
this mode, the speed of sound was found to be lower for this to occur. With a 350 Hz
mode found in the outer nozzles and not in the inner nozzles, the acoustic response of the
nozzles is not the contributors to the actual valve vibrations. This conclusion can be
further confirmed with the fact that the valves vibrate laterally, while the acoustic modes
is a longitudinal mode, with very little lateral components.

1.2 F low-Induced Valve Instability

This has been most probably the leading cause of vibrations in the lateral
direction. Although a summary of how this affects the valve has been given, a further
account for its contribution to the actual research problem at hand will be mentioned
here.

The flow-induced instability is usually velocity dependent, density dependent and
is highly dependent on the flow geometry. Other factors that can be included that
contribute to the instability are the local acoustic modes and the mechanical resonance.
Increasing pressure operation in the steam chest has been observed to create higher
vibrations. Changes in stem stiffness also contribute to the instability of the valves. With
an offset valve lift, or valve eccentricity, which will be explained later, the flow velocity
on the side with the smaller flow area will increase, and the flow in the larger flow area
will decrease. The lower velocity area will tend to have an increase in local pressure,
resulting in a net force developed. This force will cause a bending moment on the valve

and a bending stress. And once the force bends the valve the other direction, it will close

the flow area on the other side and the development of the force will occur on the other

side and bend the valve the opposite direction. This is the vibrational characteristic of

this lateral bending in the valve. The phase of these forces to the valve inertial, stiffness

and damping forces are the important components to developing the large amplitude

responses. The flow-induced vibrations involving such mechanical responses to the flow

as mentioned above are typical of one of three categories.

1)

2)

3)

Forced responses can occur when the valve structure responds to the flow forces.
The structural motion does not really influence the basic characteristics of the
fluid forces. For this particular problem, the transition from choked flow to
normal flow could generate unsteady non-symmetrical forces, which could
possibly be responsible for the strong lateral vibrations.

Some divergent instability can occur during stiffness-dominated events in
structure and fluid interactions, which causes the structural responses to be small,
until it meets some critical threshold. This critical threshold is when the
structure’s response turns divergent. This divergence can be limited however and
when it does, it may appear with an oscillatory characteristic.

With the presence of an oscillatory instability, this response can increase in
magnitude when the mechanical damping is negated by the interaction of the

valve structure and the fluid flow.

The second and third categories are mechanisms of self-excited vibrations. The

amplitude responses to these mechanisms are usually large and extreme, which can lead

to failure in short periods of time. Both these mechanisms do not require a periodicity in

the flow for the instability to occur and to have the response to occur.

With many factors that can trigger the instability of the valve, it is extremely hard
to determine which are the outstanding factors that contribute to the valve failure.
However, a simple forced response cannot really be identified as the sole cause. Since
many factors are involved in studying these vibrations, scale modeling and testing is the

most reliable method of studying this problem.

CHAPTER 2
Fundamentals and Flow Theory of Control Valves

1. Brief Fundamentals of Venturi Control Valves

Valves are used to regulate the flow of the fluid into a turbine in a very accurate
and precise manner. Secondary functions of valves include control valves that are speed-
responsive to control flow through the turbine, emergency valves to prevent uncontrolled
over-speeding, and auxiliary functions such as steam-seal-regulator pressure control of
gland seal steam. Various types of valves are used for all these functions. This research
concerns with inlet control valves of a venturi type. The venturi type valves are used
because of their low wide-open pressure drop and high flow coefficient to permit the use
of smaller sized valves to pass a given flow. Valve-contact diameter is used to calculate
the valve unbalance against which the steam unbalance pressure will react. The actuators
that control these valves must be able to tolerate and lift the valve against this force. The
valve disk is a hemisphere with a short, conical seat so that when the valve is closed,
there is total line contact and no flow can penetrate. Figure 1 shows the typical venturi

valve design.

 

 

 

 

 

Figure 1: Venturi Valve

The valves are usually located within a pressure chest, and they are positioned in
response to signals from the overall control system so that the flow can be controlled to
produce the amount of power to correspond to the load at the desired frequency or speed.
Therefore, regardless of the size of the turbine, the control valves must be able to
withstand pressures of all magnitudes, and must be able to tolerate all forms of valve lifts,
from just barely opened to wide-open positions. Control valves must also maintain the
thermal efficiency of the steam turbine in operation, and higher pressure drops yield
lower thermal efficiencies. Thus it is important to maintain low pressure drops within a
turbine. Substantial pressure drops can be done without much loss of thermal efficiency
through a multiple control valve system. The programming of the valves is such that
only one valve is lifted in a certain sequence at time, while the other valves are at a lift
that provides a minimum pressure drop. It is also important that the flow through the
valve should be proportional to the lift of the valve because the power output of the steam
turbine is also influenced by the valve flow characteristics. If this proportionality can be
made into a linear relationship, then the turbine output can also be made into a linear
relationship. This is the ideal relationship for the control valves, and design of the
control system should be made so that this proportionality is achieved. For the multi-
valve system, the correct sequence must be configured so that this proportionality is
observed. In reality, this does not occur exactly, but the linear relationship can be closely
replicated, and it can only be done at a valve lifi range of 0 to 20 percent. Turbine power
output will change at a more drastic rate between valve lift ranges of a smaller increment
than a lift range of a larger increment. Larger power increment at a smaller lift change is

known as a steep flow travel curve, and the smaller power increment at a larger lift range

is known as a flat spot. Below is a simple graph that shows 2 turbines that operate in

conjunction, with one turbine operating on the steep flow travel curve, and the other on

   
 

 

 

the flat spot.
S
; R= Overall
a Reg
m
F x is steep portion
(1) y is flat spot
w

Valve Lift

Figure 2: Relation Between Steam Flow and Valve Lifl
(Source: Installation and Service Engineering Training Manual: Version 2.1)

Notice that the turbine operating on the steep flow travel curve will take almost all
of the load change, while the one with the flat top operation will take almost no load at
all. Both cases are not the most satisfactory operating conditions. Depending on the
desired operating conditions, changing the shape of valves and/or seating would change
the relationship of the steam flow. The other method would be to alter the valve lift
timing and sequence of valve operation.

2. Fluid Forces in Control Valves
In order to study the problem and to observe their behavior in the research, a brief

understanding of the fluid forces involved in control valve flow must be established. It

has been traced that fluid flow problems have occurred on the moving parts of the plug of
the valve due to fluid forces. In properly understanding the forces involved, phenomena
during the experimental testing can be identified and observed. There have been 11
different types of fluid reaction that have been observed and identified. These forces are
observed in the moving parts of the valve, in this case the plug of the valve. After this
section, it can be seen that most service limitations of control valves are dependent on
pressure differences. Limiting valve body velocity has been seen as a universal remedy
for valve failure, and the limitation of hydraulic power or mass velocity as another, but
it’s the pressure drop that is the measure of the magnitude of the valve failure problem,
which in turn is the limiting condition for the operation of a turbine.
2.1 Problems with Valve Travel

During the closed position of a plug valve, the action of fluid forces is minimal,
even when there is a high pressure increment across the valve. Pressures on the plug
commence variation with fluid momentum and pressure losses as the valve lift increases.
This results in a varying vertical force along different positions of the plug head, and this
may exceed the force that is observed when the plug is in the closed position. With the
selection of an actuator based on a zero-lift unbalance, the valve would stroke less than
the specified signal span. But, if the full-lift force is of a tensile nature, a full valve lift
might be smaller than expected. Below is a graph that describes the relationship between
the plug force and the valve lift in a balanced valve. As the valve lifts, this force
decreases, even becoming tensile for a bit before the fluid exerts a larger vertical force on

the moving plug.

10

1p ........................................

Compression

 

 

 

Lift Travel

(no-30"?) cos—“U
o

Tension

 

Figure 3: Balanced Valve Lift Correlation with Plug Force.
(Source: Understanding Fluid Forces in Control Valves, May 1971)

For an unbalanced valve, more complications will arise, as described above. This

is summarized in the figure below.

 

   
   

 

 

 

“‘3’“ "’""’““"§ro?traar'r

1!) g \\ Full Signal

“'3

g r

F e

o S ‘x‘

r S x

c l Full Travel \\

e 0 Partial Signal ‘\
Ilc ‘q

0 max

Lift Travel

Figure 4: Unbalanced Valve Lift Correlation with Plug Force.
(Source: Understanding Fluid Forces in Control Valves, May 1971)

ll

Figure 4 shows that maximum compressive force occurs at zero lift. During
unbalanced to zero-lift, full travel either will not occur or it will occur with only a partial
signal span.

Since a portion of the plug force is a direct function of the pressure drop across a
control volume around the plug, it is essential that the force on the plug be known if the
valve is going to work with the intended valve lift, given the required signal span. Much
of the force is related to variations in fluid momentum and thus is proportional to mass-
velocity changes. It has been shown that fluid-momentum forces are directly
proportional to the pressure drop and independent of other service limitations, such as
flow velocity or hydraulic power.

In summary, many have speculated that once the force crosses the zero plug force
line in figure 1, it stands as a potential area where valve instability occurs. However,
there is no solid evidence to prove this, and sometimes can be neglected in an analysis of
valve plug forces.

2. 2 Large Side Loadings and Excessive Torque

With the theory that vertical forces on the valve are a direct proportion to pressure
change also apply to forces that are perpendicular to the valve, which are found applied to
the stern. Even with the established pressure change as the governing criteria, it is still
difficult to choose certain values for it to result in a clean, good operation. Temperature
and materials composition further complicate the selection of values of pressure change.
Side loadings can still be determined as a function of pressure change, and still be just a

function of pressure change, and independent of flow velocity or hydraulic power.

12

As for torque effects, it has been shown that they are also dependent on pressure
drops, but their effects are very uncommon. This is probably due to poor wing guiding of
the plug, which limits the plug to just low pressure uses.

2.3 Vertical Bufleting and Horizontal Vibrations

This is the phenomenon that has contributed to many valve failures over the years.
Figure 3 in the previous section show only a balanced valve lift correlation with vertical
force when only the steady-state component of the vertical force is mapped. The figure

below shows the actual relation in reality.

 

(Dal-10"?) (rec—NU

Travel

 

Figure 5: Reality Correlation with the Valve Lift and the Vertical Forces.
(Source: Understanding Fluid Forces in Control Valves, May 1971)

This graph is a general result of test data with real time-varying vertical forces.
As it is shown, buffeting occurs due to the time-varying component. A flat force
spectrum can be seen in a range of frequency from 0 to 100 Hz. This however, may
develop peak-to-peak force values exceeding 1000 lbs. Buffeting forces are proportional
to pressure drops while the resisting forces are related to the system’s friction and

possible actuator stiffness. Because of this, calculation and prediction of buffeting can be

13

done, and therefore can be avoided by using appropriate pressure drop limits. Depending
on the magnitude of the frequency of buffeting forces, they can extend into the realm of
the ultrasonic, with the forces acting in almost all directions and planes. Moving parts
that resonate in a certain directions give rise to complications. Resonance of the moving
parts at its natural frequency, such as the valve stem and plug, results in noise, parts
heating, and eventual failure. At high frequencies, this problem may not be isolated to
just the pressure change, but a more complicated function of pressure change as well as
valve aerodynamic noise generation.

Vibration, a horizontal form of buffeting, is probably the most common form of
buffeting. The time-varying forces involved in vibration are still a function of pressure
change, but unlike vertical buffeting, their prediction and solutions are often difficult to
investigate, at least in the lower frequency ranges. Certain types of valves vibrate at
lower frequencies, so sometimes their vibration characteristics are somewhat predictable,
with the basis as a function of pressure change. However, other types of valves have the
vibrational characteristics complicated with buffeting forces cause by secondary flow
paths and by stabilizing effects of steady-state lateral forces. During experimental tests,
results from repeated tests provide different data, making a conclusion for a general
relationship describing vibrations a complex task. At higher pressure drops, vibrations
are even harder to predict, and are usually not satisfactory if they are made with some
solutions although some progress is being made.

2. 4 Bi-stable Action fiom Negative Gradients
This means a variety of problems that occur when the valve/actuator system is

unable to maintain a fixed position along its travel range. The cause of this problem has

14

been identified as a negative fluid force gradient. This gradient exists in any valve which
has movement of the plug resulting in a change in fluid force which will lead to the
movement of the plug in the same direction, whether its lifting or closing. For a
configuration in which the actuator is above the valve, a negative gradient will exist on 2
occasions. The first is the “Push-down-to-close valve”, in which the force curve shows
decreasing tension as the valve opens. The other is the “Push-down-to-open valve”
situation, in which the force curve shows increasing tension as the valve opens.

Force curves are derived with a constant pressure change, and then extrapolated
by the proportional relationship between pressure change and force. In order for a
problem to be completely predicted with a solution, the maximum negative gradient must

be calculated. Taking the slope of the constant pressure change force curve does this.

 

 

 

 

max.w
P
l T
u e
g n
s
F i
0 o
I n
c
e
00 max.

Travel

Figure 6: Force Curve of Unbalanced Valve Design.
(Source: Understanding Fluid Forces in Control Valves, May 1971)

This design is bi-stable, with a fixed position only occurring in the fully open or

closed position. A negative force gradient is seen here, which shifts the plug off its

15

assigned position. With a constant actuator force being applied, the plug goes to full
open position, since less tensile force is required to keep it opening. Similarly, when the
valve is closing, The actuator still applies a constant force, but more tensile force is
required to keep it closing, so the valve goes to full closed position.

In reality, when constructing a constant pressure change force curve, the data can
be extrapolated directly. However, with the plug movement affecting the differential, the
gradient must be reconstructed to regard the steady state and transient differentials. This
results in a more severe negative gradient that is found, or installed, on an inherent
negative gradient. Therefore, it is not uncommon to find an installed negative gradient
force curve on a valve/actuator design that has either no inherent negative gradient or a
positive gradient. Valves with a “push-down-to-close valve” design operating with a
stem in tension and valves with a “push—down-to-open valve” design with a stem in

compression will generally have this phenomenon present.

 

    
    

 

C
0 Travel max.

 

(DOHO’TJ (ms—"U

Figure 7: Force Curve of Balanced Valve.
(Source: Understanding Fluid Forces in Control Valves, May 1971)

16

Bi-stable plug action can still be present in this valve design shown in figure 7.
Change in actuator force will stroke the valve to point A, and a further force change in
the same direction will satisfy the force requirements for point B and the valve will jump
over to that position. If the actuator reverses the direction of the force, the plug will
move slowly back to point C, but will then jump over to position D. It’s during these
jumps that there is bi-stabilization and thus the presence of a negative force gradient.

With the existence of these negative gradients from cases described above, the
closed-loop oscillation frequency can vary from a low operating frequency to a maximum
at the natural frequency of the valve/actuator spring mass system. The only solution for
the negative gradient in this case is to provide an actuator with a positive gradient that
exceeds the negative gradient. Some valve designs are substantially well balanced for
steady-state conditions, which involve low plug velocity, but can still possess a negative
gradient during a high-speed operation. In this case, a common solution is plug redesign
or a stiffer actuator. A solution for all valve type designs would be to limit the plug
stroking speed for small actuator signals while still allowing high stroking speeds for
large signals.

2.5 Emergence of Unpredictable Vortexes

Tests from laboratories have described the phenomenon as a product of 2 distinct
flows that occur at the same valve position and pressure drop. These unpredictable
vortexes are found in almost all valve types, but are more prominent in flow-close angle
valves. In a closed loop system the problem shows up as a low frequency cycle. Some
reactions occur during the flow switching but this low frequency cycle is dominated by

flow changes rather than force changes. If these vortexes are found during low plug lifts,

17

the problem can be solved or minimized by valve trimming. However, if higher lifts are
required for the valve system, then the best solution is to apply an anti-vortex web.
2. 6 Complications fiom a Minor Loop Cycle in the Process System

Most of the control valve problems described above are part of the major loop
cycle, which involves the actuator, the valve, process, transmitter and controller. An
important minor loop cycle is formed by process pressure feedback to the summing point
of the valve plug force. Negative gradients cause a positive feedback, or even a negative
feedback where there is a significant time lag in the process. This may lead to
difficulties, as the cycle will occur at the plug/actuator natural frequency if loop gain is
high. This problem can be solve by inserting a higher rate spring or increased damper,
but if the damping is obtained by way of friction, then this solution may cause
deterioration in the steady-state performance.
2. 7 Complications from Cavitation, Noise, Erosion, and Compressibility

Although it has been identified that the pressure change is the significant service
condition to base all functions of force, the question arises as to which pressure change
should be used. Since mass flow rate contributes much to the overall force of a valve
system, it has to be decided whether the total pressure change be used, or the pressure
change that only produces the mass flow rate changes. The decision is made based on the
significance that the 2 types of pressure changes have to the forces. If the mass flow rate
forces are more dominant, then the pressure change that affects the change in mass flow
rate should be used, but only in this case. All other cases it is much more appropriate to
use the total pressure change. If the flow forces reach a maximum when the outlet

pressure is decreased such that choked flow occurs, then it is better to use the total

18

pressure change. This applies to tests that involve buffeting. For large loadings,
excessive torques and horizontal vibrations, the total pressure change is also used. The
same applies for vertical forces on the stem and pressure forces near the valve seating.
At higher lifts, the mass flow rate forces start to dominate, and another variable is used to
assist in the prediction and calculation. This new variable is usually the pressure ratio.
Cavitation also uses the pressure change as the dominant service condition.
Noise, however, has another variable that is used, which is the body outlet velocity.
Noise is a rather complicated problem and prediction and solutions cannot be achieved as
simply as other phenomenon which used pressure change as the dominant variable.
Erosion is also another complex phenomenon, which involves many variables, including
body velocity. However, it is not enough to have simple guidelines constructed for
prediction and solutions, as with the other problems mentioned in previous sections.
There is no simple limit to establish on the fluid flow that will cause erosion of the
material of the valve or seating to be set to a minimum or non-existent amount.

Therefore, a much more complicated study is being ensued to solve this problem.

19

CHAPTER 3
Previous Research and Testing of Fluid-Induced Vibration

1. Description of Fluid Vibrations with Vibrational Model of Control Valve

Looking at the valve system, it is clear that the long valve stem might be
susceptible to vibrations. The primary directions for the vibration are in the longitudinal
direction as well as the horizontal direction, or bending direction. This valve can be
modeled in the 2 directions, the horizontal and longitudinal directions, much like spring-
mass system as shown in the figure below.

__

’ l

o
‘ o

C 'C

 

 

l.
/”’ .. I ‘ ’0. 0..
‘ C
L. ‘
o \ .’ l, ‘o . .
I “\\. "O"’. 4' OI .
\ 'I .
z/ =

Figure 8: Vibration Model.
(SourcezFluid Induced Vibration of Steam Control Valves UDC 534.11.001.5:621.165-3)

The following equations of motion for the models shown in figure 8 are shown

below as equations 1 and 2.

dzx dx
m-dt—Z‘l'CBE'l'kB-szx (1)

20

2
mi—+Cv-c-1—+kvz= 172(2)
Clt2 dt

where m is the mass, CB and Cv are the lateral and longitudinal damping coefficients, kg
and kv are the lateral and longitudinal spring constants, and x and z are in the lateral and
longitudinal displacements respectively. Fx and F2 are the directional forces in the x and
2 directions respectively. Although these models do not reflect the real actions of the
valve, a simple linearization of the problem can be made with this model to estimate and
explain the measurement results with the real valve behavior in the actual turbine.

To describe the variables responsible to calculate the forces in the horizontal and
vertical directions, we see below the forces expressed as a function of these variables.

Note that the variables are of the dimensionless form.

2
Fx,Fz — xD

 

 

, 9

u, UPD

m

(P ”B1111“ “’0 P” h —]

where D is the diameter of the valve opening, U is the flow of the velocity, p is
the density, a is the speed of sound, a) is the angular vibration frequency of the valve, and
P is the pressure. Looking at the dimensionless variables, some can be related to well-
known dimensionless numbers. The first in the brackets is the Mach number, and the
following ones are, in order, the Reynolds number, a dimensionless frequency term,
pressure ratio, and a valve-opening ratio. As in the previous section, the limiting
condition for the prediction and solution for vibrational force is the pressure change,
which is seen here.

For this model, there is also the assumption that there are compelling forces

present, namely damping and restoration forces, that are found to vibrate with the

21

pressure fluctuations whish are proportional to the velocity of the valve vibration. The
amplitude of these vibrations can be expressed by variables and are found in the x and 2

directions. Their relationships are shown below.

xl_ f £B—t CB D(I)in —I)out)f
V m ’Jka , k3

Ia, C. 00:. —P..>f

2"” Z’m’ 4.

Equations that are defined by these 3 variables, in a sense are extremely powerful.

 

 

This is because if the 3 variables are made such that they correspond to those of the
actual turbine when simulating the actual turbine with a model, these 3 variables can be
directly determined. The first 2 variables in the brackets are determined by examining
the valve structure, while the hydraulic force due to the flow around the valve structure
determines the last one, which is also considered a spring constant ratio. The value f is
determined by hydrodynamic parameters shown with the equations above.

Looking at the correlation of the equations above, it can be seen that if the
pressure change in the turbine is very high, the Reynolds number is also very high.
Reynolds numbers can be calculated based on representative dimensions of valve lift,
representative velocity of flow rate, and another representative dimension of valve
diameter. However, since it is impossible that the predicted Reynolds number is the same
as the actual one, the relations above is somewhat tweaked, such that the dependency of
the Reynolds number is small in the flow through the valve. Thus the Reynolds number

will not be the determining factor in the prediction and solution for this research.

22

2. Previous Research for a Two-Dimensional Test

This section describes the method and some tests results regarding an experiment
that was conducted on a previous research, based on a two-dimensional model. It will
describe some simple models and data acquisition methods to obtain some data results.
2.1 The T wo-Dimensional Model Test

In order to determine the flowing pattern within the valve system, a two-
dimensional, transparent model of the valve is used, so as to obtain an initial observation
of the flow. With a two-dimensional model, the valve structure makes the valve
impossible to vibrate in the parallel direction. This makes the natural frequency of the
valve very high, and thus it can be assumed that the valve is a rigid body. Thus influence
of the valve vibration on the fluid can be neglected. The inlet pressure that was used was
about 24 Mpa (3480 lb/in.2) at the valve inlet and about 0.005 Mpa (0.725 ib/in.2) at the
valve outlet. This gave a pressure ratio of about 0.00021 , with a supersonic flow
velocity. With a higher valve lift, the pressure ratio will eventually get larger and the
valve flow will get slower. Through this range of pressure ratio we have to observe the
change of flow patterns. The model constructed was also scaled down to 1/3 of the actual
size.

The main apparatus used in this previous research test was a wind tunnel with the
capability of a blow down. A main reservoir tank with a capacity of 45 m3 (1590 ft3)
with a pressure of 3 Mpa (427 lb/in.2) is used to flow through a control valve into a surge
tank with a capacity of 10 m3 (353 ft3). The model valve is then connected to the outlet
of the surge tank via another control valve. To ensure that turbulence and non-uniform

inflow wasn’t a factor in the data, the passage before the inlet of the model valve was

23

made adequately large so that the velocity was reduced to a point that laminar flow was
still present. This also makes the pressure ratio between the inlet and outlet of the model
valve maintained.

Since looking at the flow was the main priority in this test, the valve was made so
that the aspect ratio between the valve width and depth exceeded a value of 2. Static and
dynamic pressure gages were positioned with 5 around the valve, 2 in the valve wake

flow diffuser area, and 2 at the valve inlet. The overall testing setup is shown below.

 

 

 

 

 

 

Figure 9: Experimental Testing Setup to Observe Two-Dimensional Flow through a
Valve System
(SourcezFluid Induced Vibration of Steam Control Valves UDC 534.11.001.5z621.165-3)
2.2 The Results and Observations of the Two-Dimensional Test

The main objective of the two-dimensional test was to observe the flow through
the valve. At any pressure ratio, the test resulted in a two-dimensional free jet flow,
without a random wake or a turbulent flow vortex, which will be observed once the three-
dimensional flow test is examined. The pressure ratio affects the shape of the flow

through the valve and valve seating. At high pressure ratios, the jet flow through the

valve on one side seems to stick with the valve up to the point near the center of the

24

valve, while the other jet flow on the other side is free flowing and flows downstream.

Both jet streams in this case are right-left asymmetric, and are shown in figure 10.

 

Figure 10: Flow through the Valve at a High Pressure Ratio.
(Source2Fluid Induced Vibration of Steam Control Valves UDC 534.11.001.5z621.165-3)

With a small pressure ratio, the flow on both sides are free-flow jet streams, and
are both right-left symmetrical which join together after flowing past the valve. This

phenomenon is shown in figure 11.

 

Figure 11: Flow through the Valve at a Low Pressure Ratio.
(SourcezFluid Induced Vibration of Steam Control Valves UDC 534.11.001.52621.165-3)

25

This sort of flow can be simulated by having a flow between 2 cylinder columns,
but only if the area of flow observed does not include the effect of right and left flows
joining together in the wake flow. Considering 2 different sized cylinder columns, with a
large pressure ratio, the flow was found to adhere to the cylinder of larger radius of
curvature. A small pressure ratio yields the flow moving away from both cylinders, and
thus a free jet flow is observed.

Looking at both the flows through the model valve and the flow pattern, it was
concluded that the flow behavior at high or low pressure ratios is the result of non-steady
state flow patterns. These flow patterns occur by turns at irregular intervals in the
transient flow area. The pressure corresponding to these flow patterns also change in
sync by turns of irregular intervals on the wall surface of the valve and valve seat. With
the free jet flow produced with a small pressure ratio, the jet stream itself vibrates and
possesses a pressure variation spectrum vibrating at a peak frequency. If the pressure
ratio is large, the jet stream is randomly patterned, with the randomness decreasing as the
frequency of the spectrum increases. In correlation to the test results of the valve
experiment, the non-steady state flow does not occur except at the boundary where the
pattern of flow changes and at small pressure ratios where the flow is a free jet. Great
pressure variations occur as the flow becomes unstable, and to prevent this from
occurring during high pressures, the flow must adhere to the valve or the flow pattern
must change without undergoing the unstable state. From further examination of the
results from the flow through the 2 cylinder columns, the unstable area is a fimction of

the ratio of the throat width b to the radius of curvature of the 2 cylinders R, and the ratio

26

of radii of curvature of the two cylinders r/R. The figure below shows the relationship

between the 2 ratios.

 

 

 

 

b/R,D; :' '
l _.._ L

r/R = 0.25 Pressure Ratio
P1

1'
r 0 0
P2 P2

Figure 12: Relationship between b/R and r/R.
(SourcezFluid Induced Vibration of Steam Control Valves UDC 534.11.001.5z621.165-3)

 

 

 

r/R = 0.25
P1

3. Previous Research for a Three-Dimensional Test

The two-dimensional flow test has resulted in an understanding of a two-
dimensional flow that concerns the free jet flow through the valve and valve seating.
Adding in the third dimension, we now look at the one aspect omitted in the flow during
the two—dimension test. This includes the random wake or a turbulent flow vortex, which

will appear around the vicinity of the valve surface.

27

3.1 Three-Dimensional Model Test

The previous research test has shown us the relationship between the flow
patterns and the static pressures and to observe the pressure variations on the valve
surface as well as the valve seating. However, the flow in a real valve system is not two-
dimensional and is in fact, axially right-left asymmetric three-dimensional.

Unlike the use of the Schlieren method to make the flow pattern visible in the
two-dimensional flow, it is not possible to make the flow here visible at all, so the flow
pattern has to be analytically determined using the results of the previous test. The main
concerns for this analysis are: pressure variation, static pressure, temperature and valve
acceleration in all directions on certain positions of the valve and valve seating. The 3-D
experimental setup is more complicated than the 2-D setup. It basically consists of a
plug-type valve and seating enclosed in a pressure-chest. Flow is directed through the
inlet orifice and out through the seating. The lift is controlled via a simple lever. The

main testing apparatus is shown below.

28

 

 

Adustable
Lever

 

 

  

 

 

 

 

Fa

Valve Plug ll .,

 

 

 

Pressure 3...}:
Sensors
Valve Seatingb ! Pressure
Sensors
Flow Outlet ‘ hi

Figure 13: Main Testing Apparatus for Three-Dimensional Testing
(SourcezFluid Induced Vibration of Steam Control Valves UDC 534.1 1.001 .5:621 . 165-3)

A 1/3 scale model was used, with natural frequencies in bending and longitudinal
directions at about 300 Hz and 2500 Hz respectively. The actual valve frequencies vary
as much as about 100 Hz and 700 Hz in the respective directions, but the testing was
assumed that the scaling would compensate for this variation, and was concluded that the

results can apply to reality. The source of flow was the same as used in the previous test,

29

which was the main capacity tank and surge tank. Semiconductor pressure sensors were

used and attached to positions between the throat and central portions of the valve at 90-
degree intervals around the valve and one sensor in the center of the valve. Two sensors

were attached to the valve seat, in the area of the wake flow and an accelerometer was

also imbedded within the valve plug head. Figure 14 shows this arrangement.

5

 

 

 

 

A\ \\\ "-k'\\\

Figure 14: Positions of Pressure Sensors on Valve and Valve seating.
(SourcezFluid Induced Vibration of Steam Control Valves UDC 534.11.001.5z621.165-3)

The overall configuration, therefore, is shown above with four sensors positioned

on the valve, two on the valve seating, and one accelerometer within the plug head.

3. 2 Results and Observations of the Three-Dimensional Test

As mentioned, the flow pattern of the three dimensional test cannot be made

visual, so its analysis must be correlated to the flow pattern observed in the two-

30

dimensional test. The free jet flow is observed here, as well as the adherence to the valve
surface during high pressure ratios. The vibration of flow at irregular intervals is also
observed, but in the form of rectangular waves. Jet flowing in contact with the valve
surface has a random-varying pressure, with larger variations found in those areas that
when the flow is separated. The flow direction also fluctuates where the flow is
supersonic, with pressure variations occurring at one frequency. Static pressures on the
valve surface where flow is in contact is also found to be lower than pressures found
where the flow is not in contact with the valve surface. Lastly, the ratio of static ‘
temperature found in the valve outlet to the inlet total temperature decreases as the

pressure ratio decreases. This decrease is gradual with contact flow and rapid with non-

contact flow.

Region C Region D

 

 

 

 

h/D, %

Figure 15: Flow Pattern of valve lift and pressure ratio for a Two-Dimensional Flow.
(SourcezFluid Induced Vibration of Steam Control Valves UDC 534.11.001.52621.l65-3)

31

 

 

 

 

 

 

 

 

 

 

 

Figure 16: Flow Pattern of valve lift and pressure ratio for a Three-Dimensional Flow.
(Source:Fluid Induced Vibration of Steam Control Valves UDC 534.11.001.5z621.165—3)

W‘Wv—N Wm. M
M'M‘r MW w
”M "WW W
W W W

M W W
WNW WWW «Wayne-v.2

Region A Region B Region B' Region C

 

 

Figure 17: Time Traces of Valve Surface.
(Source:Fluid Induced Vibration of Steam Control Valves UDC 534.11.001.5:621.165-3)

The pressure variation waveform and the accelerator waveform at each point were

also recorded with the imbedded accelerometer. The variations are large for when there

32

is adhesion of flow to the valve surface, and the jet flow fluctuates. Changes in the flow
pattern results in changes in the pressure waveform.

The magnitude of the pressure variation of the flow pattern (B) is large in the area of the
throat and smaller in the center. Separation of the jet from the valve surface can also be
observed, and is found where pressure pulses are produced at either the same time, or
adjacently in 2 different directions. This phenomenon is also found in flow pattern (B’),
but with the flow separation near the valve center.

This phenomenon is probably due to the random wake or turbulent flow vortex.

"U

   
  

High Lift

(b-ermo-x

Low Lift

 

 

MSG—'"NCHOC—‘Tfll

Pressure Ratio

Figure 18: Surface Pressure Fluctuations.
(Source:Fluid Induced Vibration of Steam Control Valves UDC 534.11.001.52621.165-3)

33

Figure 18 shows the data of amplitude of pressure variations as a relationship of
pressure ratio and valve lift ratio, taken at the area of the valve throat. Figure 19 below
shows the data of amplitude of pressure variations as a relationship of pressure ratio and

valve lift ratio, taken at the area of the valve center.

(b-lcmwrnv-l'o

  

* High Lifts

Low Lifts

 

(ADO—'HQJCHoc—"n

 

Pressure Ratio

Figure 19: Surface Pressure Fluctuations.
(Source:Fluid Induced Vibration of Steam Control Valves UDC 534.11.001.5:621.l65-3)

With a large valve opening, the pressure variation reaches a maximum at a ratio
of 0.7, and with small valve openings, the same occurs at a pressure ratio of 0.2 to 0.3

and about 0.8.

34

3.3 Closer Analysis of Vibration fiom Pressure Variation of F low

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

V f '7' I t "1 ' HZ

h/D = 0.078, Pressure Ratio = 0.61

Figure 20: Power Spectra of Surface Pressure Fluctuation and Acceleration for the Three-
Dirnensional Model Valve. This spectra corresponds to the flow pattern (B)
(Source:Fluid Induced Vibration of Steam Control Valves UDC 534.1 1.001.5z621 .165-3)

35

It is shown that the pressure variation waveform can vary depending on the area
in which the flow is analyzed. However, the vibration spectrum varies randomly without
any outstanding features to the data as shown in figure 20.

As mentioned, the valve natural frequencies were 300 Hz and 2500 Hz in the
lateral and longitudinal directions respectively. There are significant valve accelerations
corresponding to these frequencies, resulting in a resonance type excitation caused by
unsteady hydraulic forces. Accelerations were found to be extremely high in the region
of great pressure ratios with large valve openings, and high in regions with small pressure
ratios with small valve openings. This phenomenon was found in both the lateral and

longitudinal directions.

  

 

 

 

 

A . .

c High LifiS
c

e r >

1 High Lifts /‘

e x

r

a ' f r

l

‘ Low Lifts LOW Lifts
0

n Pressure Ratio

5 Longitudinal Lateral

Figure 21: Vertical and Horizontal Accelerations for Model Valve as a relationship of
pressure ratios for different valve lift ratios.
(Source:Fluid Induced Vibration of Steam Control Valves UDC 534.11.001.5z621.165-3)

36

Y

O. O C’
to, :0”
l 3:"

3

——m«-+DON-:OII‘.
”soBoom—UM_.U
020306030”
0
o

 

 

 

 

Valve Surface
Pressure Fluctuations

Figure 22: Horizontal Displacement Response against Valve Surface Pressure Fluctuation
(Source:Fluid Induced Vibration of Steam Control Valves UDC 534.11.001.5:621.165-3)
The varying working force on the valve surface can be determined by integrating
the pressure variations over the entire surface. Pressure variations occur when fluid flows
or when a pressure wave is transmitted, resulting in a smaller integrated force result.
However, this approximation is based on small pressure changes and no spatial
correlation, so the result is slightly larger. The equation below calculates the Root Mean
Square (RMS) value of the vibration amplitude. This is based on the assumption that the

power spectrum density is flat in the area of the resonance point.

37

17 = WIPE?” (3)

where Wq(p) is the power spectrum density, p = \l(k/m), §= C/2pm, and p, C, and A are
constant. There is a linear relationship between the square root of the power spectrum
density of the fluid force and the RMS value of the vibration displacement, as shown in
figure 22. Even though the plotting is scattered, it can be observed that there is a linear
relationship between the two variables, and therefore equation (3) can be a used for a
good approximation.

3. 4 Application of the Model Testing to the Actual Valve System

Pl/P2

.-- - co-cuunu-n

    
 

.-
“

  

o~oe+mw

(Danton/Janna
OOQSGDD‘O
(DHCUJUJCDH'U

 

 

 

h/D, %

Figure 23: Typical valve Lift Characteristic Curve.

(Source:Fluid Induced Vibration of Steam Control Valves UDC 534.11.001.5z621.165-3)
The above figure describes the typical valve lift characteristic profile for a plug

type valve. With an increase in the valve lift ratio, the pressure change between the valve

inlet and outlet will increase, and the pressure ratio increases. With a ‘/4 valve lift, the

pressure ratio is about 0.8. With a 1/2 lift, the pressure ratio becomes about 0.98. Looking

38

back at figure 16, the region A signifies a small pressure variation, at a small valve lift
ratio. As this ratio gets to about 0.05, the pressure ratio goes to 0.7 and enters region B,
where the pressure variation starts to increase. Region B is also reached when the
opening ratio is 0.15 with a pressure ratio of 0.98. Pressure variations will reach a
maximum at a pressure ratio of 0.8, corresponding to regions B and B’. The pressure
variation will decrease after the pressure ratio goes beyond that.

Based on these results, it can be concluded that the valve vibration is a result of
non-steady flow, and that self-excited flow does not occur. The fluid force due to the
valve vibration acts as a negative damper in the testing. The best method of reducing the
vibration in the valve would be to redesign the valve and seating shapes so that fluid

forces would not have that much of an effect on the valve to induce the vibration.

39

CHAPTER 4
Simple Theoretical Research of Self-Induced Vibration

1. Self-Induced Vibration

Self-induced vibration is the product of aerodynamic instability, and this field is
growing largely into a very concerning aspect of turbine technology. As mentioned,
valve inlet systems are very vital to the entire turbine system itself, with its failure to
function bringing with it the entire malfunction of the turbine. This section will discuss
the fundamentals of theoretical calculations for fluid-force estimation and stability of the
valve. Doing so will provide a better comprehension to the results obtained through
experiments and in comparing them to theoretical results, whether the data is valid and
can be used for checking. It is meant to complement the experimental portion of the
entire research, which is explained in chapter five.
2. Simple Theory of Self-Induced Vibration

This theory is usually complemented with a series of airflow tests that involve

types of valves. During the tests, the self-excited vibrations of the plug were observed
and was concluded that this occurred as a combination of aerodynamic forces on the
valve plug surface and the vibrational characteristics of the plug structure. These tests
were conducted based on the law of similarity for the fluid-flow induced vibrations. It is
rather difficult to relate this, and there were some problems encountered, but the
prediction of instability for the valve can be done with this use of the similarity law.
With the measurement of aerodynamic forces and valve lift in testing, it was possible to

predict the instability of the plug based on an eigenvalue analysis code.

40

2.1 Fluid Force Estimation

The fluid force estimation was based on plug model that assumed that the valve
stem was rigid in the longitudinal direction, and that the lateral direction portion of the
structural characteristic can be estimated with a spring-mass-damper system. This
analysis only concentrates on the lateral vibration, or bending of the valve, and assumes
that the longitudinal direction, or the direction of the stem, is a rigid body. This
assumption can be made, because it is more likely that bending would occur at a much
larger magnitude that longitudinal vibrations. However, in real testing, longitudinal

vibrations must be included. The model for this analysis is shown below.

Seal Rin
/ g

 

 

 

(Rigid Body)

0

f} j ' Valve Plug

Valve Stem

Figure 24: Theoretical Vibrational Model for Analysis
(Source: Study of Self-Excited Vibration of Governing Valves for Large Steam Turbines,
Mitsubishi Heavy Industries, Ltd)

This analysis is based on small vibration amplitudes. The equation of motion for

the model above is shown in a matrix form.
V” “llxllc” ”I’ll” Milli“)
nyKWy nyCWy MyxMWj} F,

41

where,
kxx, kxy, kyx, kyy are from the sum of flows: induced stiffness and stem stiffness
Cxx, ny, ny, Cyy are from the sum of flows: induced damping and stem damping
Mxx, Mxy, Myx, Myy are the sum of the added masses and valve masses
Fx, Fy are the inducing forces
x, y are the valve displacements in the x and y axes
The above equation can be simplified to a simple matrix form, but with the matrix
coefficients taking the form of equations.

Z xx Z xy x _ F;

Zyx Zyy [yj— Fy (5)
where,
zxx = K... + icoc.x - 652M...
2,, = xx, + iway - (PM.y
z... = K... + icony — 62M”.
2,, = Ky, + iacyy - (62Myy

F x and Fy are calculated from the output of the pulse counter targeted for the

unbalanced mass, and the x and y displacements are measured by a displacement sensor.
The unknown coefficients of the four Z values are determined using certain relationships
to equation (2). The Z coefficients were determined using two forms of excitation, a
forward circular excitation and a backward circular excitation.

The forward circular excitation matrix form

42

(Zn ZXY][xF]_[FxF]
— 6
Zyx Zyy yF FyF ( )
The backward circular excitation matrix form
(Zn ny][x8] _[F;B]
" 7
Zyx Zyy yB FyB ( )

The sum of the fluid forces coefficients and structural coefficients can be determined

from the combination of the matrixes above to the following matrix form.

 

 

 

 

 

(Z...) er y; 0 0 TVFg)
ny : O O xF yr FyF
Zyx x3 y8 0 O FxB (8)
\Zyy/ (0 0 x3 y3) (FyB)

 

All of the matrix equations above can easily be solved using simple matrix algebra and
rules. The above equations would provide the results for the coefficients, which include
the mass of the valve, the valve stem stiffness and the damping. The fluid forces are
easily obtained by subtracting the coefficients with compliance without flow from the
coefficients with compliance with flow. Thus, the fluid forces obtained would be a

function of frequency. Figure 25 shows this relationship.

43

‘t

ALL“ A

Resonance

 

 

#—

OOHO'TJ cums—"n
Hbe—-O-H3—l-,(DOO

Frequency (Hz)
Figure 25: Relationship of Fluid Force Coefficient in Terms of Frequency

(Source: Study of Self-Excited Vibration of Governing Valves for Large Steam Turbines,
Mitsubishi Heavy Industries, Ltd)

2. 2 Stability
The stability analysis is conducted in conjunction with the fluid flow coefficients

obtained from the equations above. The equation of motion for stability is show below:
MS, 0 56 + C5, 0 x + K, 0 x
0 M a )7 0 _ C. J" 0 K. y
it?” A7,, [55) 5,, 5,, [x]+ 1?... K,, [x] (9)
= _ _ + _ _ . _ T
M y, M W y C y, C W y y

where,

M [j is the added mass, Cij is the induced damping, Ki} is the flow-induced stiffness,
M S, is the valve mass, C5, is the stem damping, and K s, is the stem stiffness

44

This equation can be made to the eigenvalue matrix form as shown below.

((5 ?)+(: film-:0

Instability occurs when the real part of the complex eigenvalues become positive.
The matrix forms for M, C, and K depend on frequency, and they all add up to result in
the fluid force coefficients and the structural coefficients. To find the frequencies that
determine the M,C, and K coefficients, we assume a frequency and plot them against
calculated damping ratios and calculated frequencies. The coefficients that are required
are the ones that the imaginary parts of the eigenvalues agree. Examples of these 2

graphs are shown below.

r First Mode i
let.“

#7:

’1 ' h i... .
lit-Jud t
.l . 11¢.)

 

 

 

   

m:—-'oamc
o—r-rmzt

 

 

 

 

 

" i ' , Third Mode
)- lnStablltiy
r Second Mode
Assumed Frequency (Hz)

Figure 26: Relationship of Damping Ratio and Assumed Frequency
(Source: Study of Self-Excited Vibration of Governing Valves for Large Steam Turbines,
Mitsubishi Heavy Industries, Ltd)

45.

Frequency of Instability
Third Mode

 

 

wosacna-l'fi
is.

' I».
1\

First Mode
l 1 1 1 1 1 1 1 1 1 1 1 _1 1 1 1

Assumed Frequency ( z)

.1

Figure 27: Relationship of Actual Frequency and Assumed Frequency
(Source: Study of Self-Excited Vibration of Governing Valves for Large Steam Turbines,
Mitsubishi Heavy Industries, Ltd)

Looking at figure 26 and 27, we see three curves representing each of the three
natural modes that occur from the relationship. In this case, by looking at the first mode
curves in both figures, the first mode frequency and damping ratio is 50Hz, and 0.12.
The second mode yields 65 Hz, and 0.04. Therefore, it is concluded that the first mode is
stable, while the second mode isn’t.

From this study, the frequencies, vibration modes and damping values can be
determined from air-flow tests, much like the method examined in Chapter 3. These
results can easily be extended to obtain an estimation of the performance of an actual
machine by just looking at the structural and fluid properties. The predicted frequencies
from the eigenvalue method are also accurate as compared to the experimental results as

well. With these positive results, it is possible to estimate and predict behavior and self-

excited forces on the valve structure without heavy use of experimental tests.

46

CHAPTER 5
The Current Research on the Quad-Valve System

1. General Problems Found from the History of Valve Failure Study

1.1 Instability Commencement of Valves

f c

A

(Do-$051

v-v

 

Lift

 

 

 

Figure 28: Relationship of Vertical Force on a Valve to the Valve Lift.
(Source Elliot Turbo-Machinery Co., 1976)

This figure shows the typical cycle and force experienced on a valve. It has been
concluded in the past that anytime there is a negative slope present in a force-lift graph,
there will be instability. The instability is dependent on the equivalent spring stiffness,
the damping and the value of the negative slope of this relationship. Point A on the graph
represents the force due to a partial loading on the turbine. The loading is then changed
to correspond to point B on the graph. Point A is considered stable because it is during a

positive slope and the servo-system operates in an “open valve” mode so it provides force

47

to sustain the lifting force at point A. Point B, however, is unstable because it is along a
negative slope. This slope corresponds to the change in opening from point A to B, but
requires the servo-system to supply additional force to go from point A to point C. But
after the point C, the force on the valves drops while the servo-system is supplying an
even higher force than C within the response time. This means that depending on the
system damping, the negative force slope, and the servo-force characteristics, the valves
will open in an accelerated rate to point B and continue to open till it reaches the next
valve and tries to open it. During that time, the turbine speed will increase and the
turbine governors will signal the servo-systems to close the valves because the steam
flow is larger than necessary for the turbine loading. If the steam flow does not meet the
turbine loading needs, the turbine will signal the servo-system to open the valves again,
and the cycle repeats itself. It is believed that the description of the above phenomenon is
the start of a valve vibration problem that tends to lead to a more fatigue type problem,
which is the cause of this valve failure.

The turbine speed will increase and the turbine governors will signal the servo-
systems to close the valves because the steam flow is larger than necessary for the turbine
loading. If the steam flow does not meet the turbine loading needs, the turbine will signal
the servo-system to open the valves again, and the cycle repeats itself. It is believed that
this phenomenon is the start of a fatigue type valve failure.

1. 2 Bending Loadings

Other valve forces that tend to lead to the fatigue problem of valve failure come

from bending loadings. From the potential flow theory, if the sink flow rate is uniform,

there will be a force on the sink.

48

mm,
11
go ( )

 

where F is the force on the sink, m is the sink flow rate, U0 is the uniform flow, and go is
the gravitational constant.

If we represent the valve as such with a sink in uniform flow of velocity equal to
the steam velocity in the steam chest, the force F will cause a bending moment, with a

bending stress calculated with the equation below

 

 

0' _ _— — ._
” 7rd3 7: d3 It god3 “2)

_ 32M, _ 32(FL)_32mUL
where m is the mass flow rate, U is the steam velocity at the steam chest, d is the stem
diameter, L is the stem length, and go is the gravitational constant.

1.3 Valve Spinning
As the phenomenon indicates, this occurs when some form of torque is present on
the valve, which will cause spinning of the valve if it is not somehow rigidly positioned.
The only cause of this valve spinning is the fluid and how it flows. The torque is induced
by a change in angular momentum as it passes through the valve. This can occur from
many reasons, but the two most common reasons are as follows:
1) Non-uniform velocity distribution at the steam chest
2) Eccentricity between the valve and its seating
If the potential flow model of a sink is considered again, but in a parallel flow, it
is observed that due to the non-uniformity of the external flow, U, the separating

streamline will be unsymmetrical. This causes a resultant force, and hence, a resultant

torque caused by the force acting perpendicular on a moment arm that starts from the sink

49

to the point of action of the force. This also causes an additional effect, which is the

second of the two reasons mentioned above.

Valve eccentricity is more easily comprehensible at a 2 dimensional view.

 

 

Figure 29: Two-Dimensional View of Plug Eccentricity

The mass flow rate through the valve is given by the equation
dm = pUdA (13)

where U is perpendicular to dA. From this, the total mass flow rate is given by

271' 7t 27:
m: Jdm=Jdm+Jdm (14)

With the assumption that the flow area at this point is minimum with a choked flow, thus

making the density and the velocity constant, we have the mass flow rate as:

7: 2n
n‘z=pU[jdA+ ldA]=pU(Al+Az) (15)
0 It

50

Angular momentum change of the fluid is given by

dM = gram (,6)

ang

where V is the tangential velocity component to the plug surface and D is the valve plug
diameter.

Therefore, the net change in angular momentum can be found with the general equation.

— ,jJ—Vdn'zz :lp—U—DVdA— :p—U—DFdA
2

M10] VdA oil/61A] (17)

This equation can be simplified for some special cases. One special case is if it
was assumed that the tangential velocity component is symmetrical around the valve

plug, the equation becomes

AM =p—U—D

net

Oman—61A,) (,8)

Another special case, which is the assumption that there is no change in angular

momentum, the equation simplifies to
71' -7I
IVdA = deA (19)
0 0

This can be further simplified to Valel = Vav2A2 and since the areas and the

velocities terms are not equal, the boundary layer will thus not be symmetrical around the

51

valve plug surface. Accordingly, a frictional force will cause the torque to the valve
stem. Therefore, with these 2 assumptions, a resultant torque will always be present.
2.Research Problem with Quad-Valve System

From the previous sections describing the previous research on this problem, and
previous subsequent testing, data acquired from past research has shown insufficient data
to really determine the basic mechanism that causes the valve vibration and subsequent
failure. However, simple forced response has been speculated to not be the problem.
With the size and type of the valve system in study, with a high mass flow rate; it would
seem to suggest that there is a high probability that the root cause of the valve vibration is
caused by an instability mechanism. Increases in steam chest pressures and the resulting
mass flow rate are the causes of this instability. It is also thought that the changes in stem
stiffness with the resulting change in valve lateral resonant frequencies are also
contributing factors. With the presence of large dynamic pressures upstream and
downstream, it is still unclear whether these pressures contribute to the strong lateral
response. The best solution for investigating the vibrations in the quad-valve system
would be to use a reduced or full-scale modeling and testing method. The possibility of
unsteady fluid forces generated from the transition from choked to unchoked flow, as the
lift increases, has not been completely omitted from the analysis as the causes of the
valve vibration and failure. Depending on the results of the testing, if the cause of the
vibration is not from instability but from unsteady fluid forces from the pressure field
around the valve, the tests should still be able to record any data that would assist in

documenting the dynamic loadings.

52

2.1 Preliminary Theoretical Calculations of Valve Flow
During operation when inducted with the steam turbine, the 2“d and 3rd valve seem
to break the most often under operation, with the 2M valve being the primary breakage

valve, and at various times. Below is a picture of the four-valve system under study.

a“... ”H

 

 

 

 

 

 

 

Opening 4 2 1 3
Order °"'""'""'""" """""""""""""""""""" " """"
Figure 30: Four-Valve System.

Many experimental designs were brainstormed, most with singular or dual valve
systems. The actual valve design is of a regular plug-type valve. The actual shaft,
however, has been altered to a square shaft with chamfered corners. The shaft has been
redesigned from a pure circular cross section to this chamfered square shaft cross section
to eliminate the presence of change in angular momentum caused by non-uniform
velocity distribution or valve eccentricity, which causes valve spinning, as mentioned in
the previous section. The valve opening sequence is the 3rd valve, then the 2'”, with the

4th valve after that, and the lSt valve to finish the sequence. Flow charts of various valve

53

lifts, were also charted, with problems or observed theoretical instability occurring at lifts
of 0.454 and 0.639 inches. The instability is most notable when the lift is at 0.639 inches.

The experimental rig design was finally confirmed with a singular valve design.
The valve stem was kept circular but a locking mechanism will be used to ensure fixed
positioning of the valve during operation. The valve chest initially had a strong
transparent window on one of the sides of the valve chest for outside observation, but was
eventually dropped for simplicity and the fact that it is impossible to physically observe
the flow. The range of pressure ratio is from 1 to 3 and the flow through the valve at
each pressure increment was calculated at choked flow to find the maximum flow
properties. This theoretically will be the result that can be used for comparison with the
actual test data obtained. With a high flow rate obtained in the calculations with a full-
scale sized valve, a size reduction was made to '/2. At this scale, the size of the valve
wordd just be adequate to accommodate all the static and dynamic pressure gauges
required to obtain the necessary data. Even at V2 scale, the flow rate is still high, and the
use of a compressor or large blower could prove hazardous at such high flow rates.
Therefore, the alternative, which is to use some sort of vacuum device to suck the flow
through the chest, would be less hazardous and perhaps provide a more simplified testing
method.
3. Preliminary Design concepts and Calculations to Scaling

Based upon the actual pressure chest design and previous research done on similar
problems from various turbines, accurate information can be obtained from a single valve
design at a relatively small scale. It was, however, desired that the scale be as large as

possible with possibly a full quad-valve design to observe the total behavior of the actual

54

valve design. After much consideration to the easiest path to observing the valve
behavior, the first reduction to the test design was to a dual valve design at full scale. A

simple concept of this is shown below.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 31: Early Dual-Valve

After further discussions with the people from Elliot Turbo machinery Company,
a singular valve design was adequate for the analysis, even though that perhaps the
analysis of two valve operating together would be vital in the influence of the valves on
one another during operation. This however, was not nearly as important as decreasing
the time and cost to construct the valve when a singular valve design would still be

adequate in analyzing the valve behavior, since the 2nd valve was the primary breakdown

valve.

55

 

 

 

 

 

Figure 32: Early concept of Singular Valve Design

Several calculations had to be made to theoretically observe the flow rate through
the design and then the search for the appropriate vacuum pump that can provide such a
flow can be researched and found.
3.1 Method of F low Calculations

This is done with several important initial conditions, using some equations that

relate to thermodynamics of high-speed fluid flow.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Conditions Units
Ratio of specific heats of the fluid (k) Dimensionless
Specific heat at the inlet static J/kg-K (Btu/(slug-°R)
temperature (C?)
Gas constant for the fluid (R) ' Pa-m3/kg-K (ft-lbf/slug-°R)
Venturi Area (A.) m2 (fiz)
Static inlet temperatures (T) K (°R)
Stagnation inlet temperatures (To) K (°R)
Static inlet pressures (P) bar or Pa (lbf/ftz)
Stagnation inlet pressures (Po) bar or Pa (lbf/ftz)
Mass flow rate (252) kg/s (slug/s)
Flow rate at the inlet (v) m3/s (cfrn)

 

Table 2. Properties for the Commencement of Flow Calculations
The calculation for density will be important for the determination of the mass flow

rates. The formula that will be important here is of the form:

56

P

(”347

(20)

where P is the pressure (static or stagnation), R is the Gas constant, and T is the
temperature (static or stagnation). The idea of this initial calculation is to treat the flow as

though it is going through a simple converging diverging nozzle.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

T T
P P
Inlet _.._.. ~—* Outlet
V V
M M
Figure 33: Simple Converging Diverging Theory
M M" A/A* P/Po p/po T/To

0 0 00 1.00000 1 .00000 1 .00000
0.10 0.10943 5.8218 0.99303 0.99502 0.99800
0.20 0.21822 2.9635 0.97250 0.98027 0.99206
0.30 0.32572 2.0351 0.93947 0.95638 0.98232
0.40 0.43133 1.5901 0.89562 0.92428 0.96899
0.50 0.53452 1.3398 0.84302 0.88517 0.94238
0.60 0.63480 1.1882 0.78400 0.84045 0.93284
0.70 0.73179 1.09437 0.72092 0.79158 0.91075
0.80 0.82514 1.03823 0.65602 0.74000 0.88652
0.90 0.91460 1.00886 0.59126 0.68704 0.86058
1.00 1.00000 1.00000 0.52828 0.63394 0.83333
1.10 1.08124 1.00793 0.46835 0.58169 0.80515
1.20 1.1583 1.03044 0.41238 0.53114 0.77640
1.30 1.2311 1.06631 0.36092 0.48291 0.74738
1.40 1.2999 1.1149 0.31424 0.43742 0.71839
1.50 1.3646 1.1762 0.27240 0.39498 0.68965
1.60 1.4254 1.2502 0.23527 0.35573 0.66138
1.70 1.4825 1.3376 0.20259 0.31969 0.63372
1.80 1.5360 1.4390 0.17404 0.28682 0.60680
1.90 1.5861 1.5552 1.4924 0.25699 0.58072
2.00 1.6330 1.6875 0.12780 0.23005 0.55556

 

 

 

 

 

 

 

 

Table 3. The results of one-dimensional isentropic compressible-flow functions for an
ideal gas with constant specific heats and molecular weights.

57

With the use of the table above, results can be easily found at the throat. This
table records the results of one-dimensional isentropic compressible-flow functions for an
ideal gas with constant specific heats and molecular weights.

However, the manual process can be done with three specific filnctions, each one

relating to pressures, densities and temperatures.

P k—l —k/(k—1)

—= 1+—M2

P. l 2 l ‘2”
-1/(k-l)

Po 2
-1

1%”?sz (23)

0

where P is the pressure, T is the temperature, M is the Mach number, and k is the
ratio of specific heats. The velocity of the flow is used to calculate the resultant flow rates

and mass flow rates. The equation used is:

v = \lkRT (24)

3.1.1 Initial Flow Calculations

These calculations are based on a 1/2 scale modeling of the actual valve system.
The first method of calculation assumes that the Mach number reaches one at the throat,
or that the flow becomes choked. The highest flow rate that would be experienced during
the experiment is when the pressure is at a 3 to 1 ratio. This model also assumes that the
flow rate maintains a Mach number of 1 through the throat and into the venturi area. The

ideal gas is air, and the process is considered isentropic. There is also the introduction of

58

a taft cut-off percentage of venturi flow area, which determines the minimum flow that
maintains the pressure ratio, which is explained later. The initial conditions to commence

these calculations are tabulated below.

 

 

 

 

 

 

 

 

 

 

 

 

Conditions Units
Ratio of specific heats of the fluid (k) 1.4
Gas constant for the fluid (R) 287 (1714.4)
Pa-m3/kg-K (ft-lbf/slug-°R)
Venturi area (A.) 0.001188 (0.012788) m2 (fiz)
Static inlet temperatures (T) 300 (540) K (°R)
Stagnation inlet temperatures (To) 300 (540) K (°R)
Static inlet pressures (P) 1 or 100000 Pa (2116.8) bar or Pa (lbf/ftf)
Stagnation inlet pressures (Po) 1 or 100000 Pa (2116.8) bar or Pa (lbf/ftr)
Mass flow rate (151) 0 kg/s (slug/s)
Flow rate at the inlet (v) 0 m3/s (cfm)

 

Table 4. Initial Conditions
Using equation (20), we can determine both the static and stagnation densities. Since the
inlet flow is negligible, the static and stagnation temperatures, pressures and the densities
are all the same. Thus the density calculated is 1.16144 (0.002287) kg/m3 or slugs/ft3.
Using table 3 or the equations (21) through (23), the temperatures, pressures and densities
at the throat at choked conditions can be found. The temperature, pressure and density
are found to be 250 (450) K (°R), 0.5354 bar or 53542 (1118.263) Pa (lbf/ftz) and 0.748
(0.00145) kg/m3 or slugs/R3. The resulting velocity through the throat using equation
(24) is 316.88 (1039.63046) m/s (ft/s).

The more important results stem from the calculations in the venturi area, which
is the main area of interest. As mentioned, the greatest flow occurs at a pressure ratio 3
to 1. With a vacuum pump, a pressure ratio of 3 to 1 would occur at a venturi pressure of
0.333333 bars if the inlet pressure were at 1 bar. Thus the pressure and density are just
1/3 of their values at the inlet. This makes them 0.3333 bar or 33333 (705.6) Pa (lbf/ftz)

and 0.392971 (0.000762171) kg/m3 or slugs/ft3.

59

 

The choked venturi mass flow rate is calculated using the equation:

ti? = pVA (2 5)
thus, obtaining a 0.28125 (0.019264) kg/s (slugs/s) mass flow rate, with the density and
velocity results taken from the throat or choked position. The volumetric flow rate is
simply the mass flow rate divided by the density, giving a 0.37633 (13.29) m3/s (ft3/s)
flow rate. The volumetric flow rate at the venturi area, which will determine the flow
that is required to simulate the operating conditions of the actual valve chest, is found to
be 0.7157 (25.27471) m3/s (ft3/s), or 42.942 (1516.5) m3/min (cfin) by dividing the
choked mass flow rate with the density found at the venturi area. This flow rate is the
desired flow rate in which to maintain a 3 to 1 pressure ratio at a wide-open valve lift of
0.639 inches.’ To find the minimum flow required to maintain this pressure ratio, the
earlier mentioned taft cut-off percentage of venturi valve flow area is applied to the
calculation. At a 0.016231 (0.639) m (inch) lift, the cutout pOSition where instability was
observed, the original valve (at full scale) had a flow area of 0.002793 (4.329) m2 (inz),
which is 58.77% of the full-open venturi area. This percentage is the taft cut-off
percentage of venturi valve flow area. Applying this to the 42.942 (1516.5) m3/min (cfm)
flow rate, the minimum flow rate to maintain the 3 to 1 ratio is found to be 25.237
(891.2367) m3/min (cfm).
3.1.2 Secondary Flow Calculations
These calculations are basically similar to the to the ones for the initial calculations, but it
is somewhat more accurate. The equations used are identical and the starting initial
conditions are the same as in table 4. However, the calculations from the throat area to

the venturi are not as simple as the factoring of the pressure ratio of 3 to 1 as in the

60

previous calculations. With the same inlet conditions as shown in table 4, and with the
use of equation (20), the static and stagnation densities are the same as before at the inlet
conditions. Using table 3 or the equations (21) through (24), the temperatures, pressures
and densities at the throat at choked conditions are 250 (450) K (°R), 0.52828 bar or
52828 (1103.336) Pa (lbf/ftz) and 0.736283 (0.0014286) kg/m3 or slugs/ft3. The
resulting velocity is 316.938 (1039.823) m/s (ft/s).

The venturi area is calculated in a similar fashion as fiom the inlet to throat
position, than just the simple factoring of the pressure ratio, which was done in the
previous calculations. With the known pressure ratio of 3 to 1, we use the table 3 or the
equations (21) through (24) again to find the temperatures, pressures, and densities,
which are 219.8655 (395.76) K (°R), 0.33333 bar or 33333 (705.6) Pa (lbf/ftz) and
0.534453 (0.001037) kg/m3 or slugs/ft3. Using equation (24) the velocity through and out
the venturi area is 401.252 (1316.4436) m/s (fl/s). The mass flow rate with equation (25)
is 0.25477 (0.01746) kg/s (slugs/s). This gives us a volumetric flow rate of 0.47669
(16.834) m3/s (ft3/s) or 28.6014 (1010) m3/min (cfm).

From the initial calculations, the flow rate calculated was 42.942 (1516.5) m3/min
(cfm), with a minimum flow rate of 25.237 (891.2367) m3/min (cfm) to maintain the
pressure ratio at 0.016231 (0.639) m (inch) lift. A more accurate calculation for the flow
was 28.6014 (1010) m3/min (cfm). The initial results were used for the selection of the
flow system, as it would be trivial to use the higher flow rate to enable calculations and

predictions on a possible worst-case scenario.

61

 

 

 

Throat Total Static Total Static Densi Velocity Mass Flow
position Temp. Temp. Press. Press. Kg/m m/s (ft/s) Flow Rate
K (R) K (R) bar bar (slugs/f?) Rate m3/s
(lbf/ftz) (lbf/ftz) kg/s (ft’ls)
(slugs/s)
Initial 300 250 1 0.5354 0.748 316.88 - -
(540) (450) (2116.8) (1118.3) (0.00145) (1039.63)
Secondary 300 250 1 0.52828 0.7363 316.94 - -
(540) (450) (21 16.8) (1 103.34) (0.001429) (1039.82)

 

 

 

 

 

 

 

 

 

 

 

Table 5. Results for Throat Position Calculations at Pressure Ratio of 3

 

 

 

 

 

 

 

 

 

 

 

 

Venturi Total Static Total Static Densi Velocity Mass Flow
position Temp. Temp. Press. Press. Kg/m m/s (ft/s) Flow Rate
K (R) K (R) bar bar (slugs/11’) Rate 111%
(lbf/ftz) (lbf/fi’) kg/s (ft3/s)

Ms/s)
Initial 300 250 1 0.3333 0.748 602.44 0.28125 0.7157
(540) (450) (21 16.8) (705.6) (0.00145) (1976.5) (0.01926) (25.275)
Secondary 300 219.866 1 0.3333 0.534453 401.252 0.25477 0.47669
(540) (395.76) (21 16.8) (705.6) (0.001037) (1316.4436) (0.01746) (16.834)

 

 

Table 6. Table of Results for Venturi Position Calculations at Pressure Ratio of 3
4. Scaling and Design of Experimental Setup

From the results above, the flow rates are exceptionally high, even with the half-
scaling. It was, however, previously stated that the half-scale size was the bare minimum
in terms of valve size to be able to fit the desired number of pressure gauges, both
dynamic and static.
4.1 The Valve and Valve Chest
The final valve and valve chest design was made to be a single valve design, much
similar to the concept drawing from figure 32. The single valve will replicate a simple
plug-type valve used in the actual turbine machine. However, with the advent of pressure
gauges on the valve and seating, room must be made for the wiring and simple access to
them. The seating would not have much problem positioning the gauges and the wiring
can easily be done to not interfere with the operation of the experimental setup. The

valve, however, does prove some challenges in positioning the gauges as well as the

62

wiring. The basic setup would have 3-4 rows of pressure gauges on the valve and 4-5
rows on the seating. Each row would have dynamic pressure gauges at the north-south-
east-west positions, with 2 static pressure gauges at 45 degrees between 2 dynamic
gauges at opposite ends. The configurations as well as the actual model valve
dimensions are shown in Appendix B. The emphasis was on the dynamic pressures,
since they are responsible for the stresses and vibrational forces experienced when the
valve is under operation. Another consideration was that the pressure gauges on the
valve plug and seating must be placed such that they are as close as possible to the
surface as possible. At high flow rates, the slightest deformation on a surface could alter
pressures at that area, altering the results in vibration amplitudes and stresses. The plug
head itself can separate into 3 different pieces, the plug head, a mounting plate between
the plug head and the stem, and the stem piece. The plug head and the valve stem will be
made hollow to make way for the internal wiring of the pressure gauges. Four screws are
used to attach all three pieces together. With Aluminum 2024 as the working material, it
must be noted that preliminary calculations must be made for forces and stresses on the
model valve to ensure that failure does not occur during the operation. From the
information of Aluminum 2024 found in Appendix C, the yield stress of aluminum is
58000 psi. From chapter 5, section 1.2, which describes the potential theory of bending
loadings, the equation for force on the sink is
m UO

8 0

 

F = (8)

where F is the force on the sink, m is the sink flow rate, U0 is the uniform flow, and go is

the gravitational constant.

63

If we represent the valve as such a sink in uniform flow of velocity equal to the
steam velocity in the steam chest, the force F will cause a bending moment, with a

bending stress calculated with the equation below

 

 

_ 32M, 32(FL) _ 32 mUL
- (9)

0" 7 7:413 —7 73— 7g0d3
where m is the mass flow rate, U is the steam velocity at the steam chest, d is the stem
diameter, L is the stem length, and go is the gravitational constant. Using the initial
calculation values for the theoretical flow through the testing setup, the total force on the
sink is about 20.01 lbf. The resulting axial stress is 51090 psi. This number is less than
the aluminum yield stress, so the valve will hold up during operation.

Valve lift control is made from using an internally threaded shaft. The main valve
stem will be externally threaded and will go through the shaft. A simple lever mechanism
is attached to the top of the stem once through the shaft. The valve lift is set by screwing
the stem to the proper position and then immobilized with 2 simple lock nuts, one on
each end of the shaft. This entire mechanism is attached to the valve pressure chest. The
pressure chest is made large enough such that the flow and the initial conditions of
pressure, temperature, density, and flow velocity does not change as the flow reaches
through the passageway created by the valve. The dimensions to the current development
of the pressure chest are shown in Appendix B. To simulate as close as possible the flow

into the pressure chest, the inlet orifice is exactly 1/2 scale to the actual orifice size. The

exit orifice is the same size as the valve seating component.

64

4.2 The Flow System

With the scale of the experimental setup limited to the pressure gauge configuration, the
next step was to select a method of producing the flow through the setup. The higher
flow from the initial theoretical calculation was selected to plan the setup, to assure that
any discrepancy in calculations would be accounted for in the real experiment. With a
compressor already present in the university, it was considered a very likely possibility
that it could be used for the experiment, as it can easily reproduce the pressure and flow
requirements. However, due to the extreme pressure ratios that the experiment was to
experience, the compressor was ruled out, mainly because of safety and hazardous
reasons. Unless the pressure chest was built in a more professional manner to tolerate
certain standards of safety, and then officially tested to observe that it withstood these
standards, which could be extremely time-consuming, an alternative had to be found to
produce the flow. The idea of the utilization of a vacuum pump seemed the most
promising method of producing the flow without too much concern, as the pressure ratios
could be attained without much danger and the flow could easily be produced. However,
vacuum pumps that operate at such a low vacuum level and simultaneously produce a
flow of at least 1500 acfin were extremely rare. To find a pump that was also affordable
by university standards made the search even more complicated. The search for the ideal
vacuum pump went underway, regardless of the rarity of an affordable pump that met the
desired requirements. During this time, the experimental setup was still planned with the

use of a vacuum pump as the system to produce the flow.

65

 

Inlet plenum — Atm inlet

 

 

 

Test valve

 

 

. Atm dischar e
Atm Inlet —%-- Outlet plenum —6— 9

Possible
Vacuum pump
reg valve or blower

 

 

 

Figure 34: Initial Testing Setup

This was the initial testing plan, without the certainty of a variable speed motor to
run the vacuum pump to attain adjustable flow rates and pressure ratios, which makes use
of plenums and some regulatory valves and by-pass valves. The basic requirements for
the vacuum pump was to be able to attain a high flow of 1500 acfrn at a low pressure
ratio of 3, of getting a low flow of about 335 acfrn at a low pressure ratio of 10, and to be
able to regulate the test valve discharge pressure and flow at a high pressure ratio.
Varying the pump/blower speed can do this regulation, as well as throttling the
pump/blower inlet, or using a by-pass valve. Each possible regulatory method has some
issues to them, such as whether the variation of pump/blower speed is adequate to
produce a slow flow and whether the slow flow required can be reached to attain the
desired pressure ratio. If throttling the inlet was the method to regulate the discharge, is it
safe for the machine and can such a low flow be attained with just throttling? Using a by-

pass valve requires the checking of any problems if the pumping was done with no load.

66

Detroit Air Compressor (DAC), a company that supplies vacuum pumps, blowers
and compressors, had found the ideal pump that very much met all the above
requirements and answered much of the questions above regarding the regulation of flow.
The unit is a positive displacement blower, made by ROOTS. The blower is a ROOTS
RAMTM Whispair 616 DVJ Dry Vacutun Pump.

4.2.1 The ROOTS RAMTM Whispair 616 DVJ Dry Vacuum Pump

This Whispair dry vacuum pump is a heavy-duty unit with an exclusive discharge
jet plenum design that allows cool, atmospheric air to flow into the casing. This unique
design permits continuous operation at vacuum levels to blank-off with a single stage
unit, without water injection. Standard dry vacuum pumps are limited to approximately
16" Hg vacuum because operation at higher vacuum levels can cause extreme discharge
temperatures resulting in casing and impeller distortion. The Roots Whispair vacuum
pump's cooling design eliminates the problems caused by high temperatures at vacuum
levels beyond 16" Hg. Whispair vacuum pumps reduce noise and power loss by utilizing
an exclusive wrap-around plenum and pro-prietary Whispair jet to control pressure
equalization, feeding backflow in the direction of impeller movement, aiding rotation.

The general statistics of the vacuum pump are shown in the table below.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Frame Speed Maximum 12” Hg 16” Hg 20” Hg 24” Hg 27”Hg
Size RPM Free Air Vac. Vac. CFM Vac. CFM Vac. CFM Vac. CFM
CFM CFM at at BHP at BHP at BHP at BHP
BHP

6161 1750 2367 1015 36 901 47 748 59 448 71 * 80
2124 1310 44 1196 58 1043 72 743 86 "' 97

2437 1556 51 1443 67 1290 83 990 99 244 111

3000 2001 63 1887 83 1734 102 1434 122 688 137

 

 

Table 7. Performance Table

This pump, with a 100 HP motor, however, cannot produce the desired flow of

1500 acfm. However, looking back at section 2.1.1, the minimum flow required to

67

 

maintain the pressure of ratio 3 was 25.237 (891.2367) m3/min (acfm). With a 100 HP
motor at a pressure ratio of 3, the vacuum pump can produce a maximum flow of about
1300 acfm. It was also calculated that with this 100 HP motor, the flow produced at a
pressure ratio of about 10 would be 54 acfm. It was decided that this pump with a 100
HP motor would suffice for the experiment since at both ends of the operating range of
the vacuum pump the flows produced at the required pressure ratios was satisfactory, or
at least close enough the to desired values. A powerful motor would reach the desired
flow rates and speeds required, but it would require more funds, and the trade-off for
spending more funds to obtain just a little more power to meet the desired values was not
satisfactory. The performance curves and the performance summary for the vacuum

pump operating at the 2 ends of the pressure ratio range of 3 and 10 are shown below.

 

 

 

 

 

 

 

 

Gas Air Elevation 0 feet
Relative Humidity 36 % Pressure 14.7 PSIA
Molecular Weight 28.7 Temperature 68 °F

k-Value 1.4 Relative Humidity 36 %
Specific Gravity 0.991
Ambient Pressure 68 °F

 

 

 

 

Table 8. Ambient and Standard Conditions for Vacuum Pump Operation

 

 

 

 

 

 

 

 

 

Actual Volume 400 ACFM
Standard Volume 54 SCFM
System Inlet Pressure 26 inches Hg vacuum
Inlet Pressure Loss 0 PSI
System Discharge Pressure 14.7 PSIA
Discharge Pressure Loss 0 PSI
Inlet Temperature 68 °F

 

 

Table 9. Input Conditions for Vacuum Pump Operation for Pressure ratio of 10

68

 

 

 

 

 

 

 

 

 

 

 

Speed 2165 RPM Jet Volume Flow 899 ACFM
Power at blower 94.9 BHP Gear tip speed 3404 FPM
shaft
Blower differential 12.71 PSI V-belt Estimated 60560 hours
pressure B10 Brg Life
Temperature Rise 236 °F Coupling Est. B10 571958 hours
Brg Life
Discharge 304 °F Est Free Field Noise 96.4 dBa
Temperature at 1 meter
Discharge volume 1353 ACFM CFR 0.789
Jet Pressure 14.4 PSIA Shaft Diameter 2 inches
Jet Temperature 68 °F Minimum Sheave 8.5 inches
Diameter
Jet Weight Flow 64.7 lb/min Inlet/Discharge 8F/10F/8F (JET)
Connection

 

 

 

Table 10. Input Conditions for Vacuum Pump Operation for Pressure ratio of 10

 

 

 

 

 

 

 

 

Actual Volume 1284 ACFM
Standard Volume 430 SCFM
System Inlet Pressure 20 inches Hg vacuum
Inlet Pressure Loss 0 PSI
System Discharge Pressure 14.7 PSIA
Discharge Pressure Loss 0 PSI
Inlet Temperature 68 °F

 

 

Table 11. Input Conditions for Vacuum Pump Operation for Pressure ratio of 3

 

 

 

 

 

 

 

 

 

 

 

 

 

Speed 2165 RPM Coupling Est. B10 1096189 hours
BrgLife
Power at blower 76.9 BHP Est Free Field Noise 89.6 dBa
shaft at 1 meter
Blower differential 9.78 PSI CFR 0.789
pressure
Temperature Rise 35 °F Shaft Diameter 2 inches
Discharge 103 °F Minimum Sheave 8.5 inches
Temperature Diameter
Discharge volume 458 ACF M Inlet/Discharge 8F/6F
Connection
Water Injection 6 GPM
Gear tip speed 3404 F PM
V-belt Estimated 116067 hours
B10 Brg Life

 

Table 12. Input Conditions for Vacuum Pump Operation for Pressure ratio of 3

69

 

 

 

 

 

260
255
250
245
240
235
230
225
220

1 500 2000 2500 3000

Blower Speed (RPM)

l Temperature Rise vs Blower Speed
1

 

 

 

ET RisEl

 

Temp. Rlee (F)

 

 

 

 

 

L_. - _.

Figure 35: Relationship of Temperature Rise and Blower Speed for Pressure Ratio of 10

 

Inlet ACFM vs Blower Speed

1000 .

 

800 -
600 4
400 -

 

 

[—0— ACFM]

 

 

Inlet ACFM

 

200 +

 

 

 

 

 

 

1500 2000 2500 3000
Blower Speed (RPM)

 

 

 

 

Figure 36: Relationship of Inlet ACFM and Blower Speed for Pressure Ratio of 10

70

 

BHP vs Blower Speed

140
120
1 00
80
60
40
20

 

 

BHP

 

 

 

 

1500 2000 2500 3000
Blower Speed (RPM)

 

 

 

 

 

Figure 37: Relationship of Brake Horsepower and Blower Speed for Pressure Ratio of 10

 

Temperature Rise vs Blower Speed

 

 

11:11 Rise ‘ .

 

 

Temp. Rise (F)

 

0 500 1000 1500 2000 2500 3000
Blower Speed (RPM)

 

 

 

Figure 38: Relationship of Temperature Rise and Blower Speed for Pressure Ratio of 3

71

 

1 Inlet ACFM vs Blower Speed

 

Inlet ACFM
on
8

 

400

 

0 500 1000 1500 2000 2500 3000
Blower Speed (RPM)

 

 

L___

 

Figure 39: Relationship of Inlet ACF M and Blower Speed for Pressure Ratio of 3

BHP vs Blower Speed

f +3.45)

BHP

 

 

0 500 1000 1500 2000 2500 3000
Blower Speed (RPM)

 

 

 

 

Figure 40: Relationship of Brake Horsepower and Blower Speed for Pressure Ratio of 3
The entire vacuum pump package includes the ROOTS RAMTM Whispair 616

DVJ Dry Vacuum Pump mounted on a Stoddard D93 10X8 combination inlet and

discharge silencer. The vacuum pump is belt-driven, enclosed by an OSHA belt guard,

with a 100 Horsepower 1800-RPM TEFC 3/60/230 460-volt motor. Looking at the initial

72

setup, varying the flow could be done by either varying the pump/blower speed, throttling
the pump/blower inlet, or using a by-pass valve. However, there were some concerns for
each method for regulating the flow. Using the bypass valve would draw in a tremendous
amount of flow and may increase the noise during operation. The simplest method of
varying the flow speed would be to vary the motor speed, which can be done using a
variable-speed motor. However, the purchase of a variable-speed motor increases the
price of the overall vacuum pump. Throttling the inlet would work without too much
concern for the operation of the pump because of the jet discharge. Since the motor can
only run at one speed, and hence provide a fixed flow rate through the overall system,
throttling the inlet would decrease the flow through the test valve. However, the rest of
the flow to fulfill the fixed flow rate can be drawn through the jet silencer. A reticulation
valve could also work, but it might overheat as the lift of the valve increases. Even at

' low flows at high pressure ratios, the motor could provide a 54 SCF M, but that is at the
maximum power from the motor. A bypass valve to draw in more air into the inlet would
be beneficial, as the motor would not have to run at maximum capacity, and hence
prevent a possible overheat. It would have to be drawn from upstream of the flow-
measuring orifice, so the bypass flow would not be counted in the flow measurement.
The capabilities of the vacuum pump to produce the flow at the opposite ends of the

pressure range are mapped on this figure to observe the accuracy of the model valve to

73

the actual valve.

 

 

Percent Lift Vs Pressure Ratio

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

“ Region B

'3 Unstable with low frequency

. with pressure fluctuations between

'1 throat & plug center

'. II. Region 8'
P2 . ‘. Unstable with low frequency with

Reglon A .
/ ..... Stable .4; A! pressure fluctuations at plug center
P l I I ’1’ \\ J
. x ’ ‘ I
d l; +ran
.. - I. ' +Eq“3‘°
Elm; \ +0104012
“,1? ' Region C \ +C104012R1
b Unstable with high frequency 1 I
>219“ Elliot Valve R/r = 0.429
1 Test Data R/r = 0.468
0 1.
o
(h/D)*100

Figure 41 : Flow Pattern of Valves
(Source: Elliot Turbo-Machinery Co., 2001)

-74

Appendix A
Profiles for the 0.4595 and 0.639 Inch Lifts

Profiles for 0.4595 Inch Lift

0.4595 inch lift (3.1 in2)
1655 psia in, 1445 psia out. steam properties

 

Figure 42: Mach Number Profile for 0.4595 inch Lift
(Source: Elliot Turbo-Machinery Co., 2001)

75

 

 

0.8

0.6

0.4

0.2

0.0

 

 

0.4595 inch lift (3.1 in2)
1655 psia in, 1445 psia out, steam properties

 

Figure 43: Pressure Profile for 0.4595 inch Lift
(Source: Elliot Turbo-Machinery Co., 2001)

76

 

 

P-Psia
1700
1600
1 500

1400

1300
i 1200

l 100
1000
900
800
700
600
500
400

 

 

0.4595 inch lift (3.1 in2)
I655 psia in, 1445 psia out, steam properties

 

[I

 

Figure 44: Velocity Profile for 0.4595 inch Lift
(Source: Elliot Turbo-Machinery Co., 2001)

77

 

 

 

 

Speed
2583

2325
2067
1808
1550
1291
1033

775

517

258

 

 

Profiles for 0.639 Inch Lift

 

0.639 inch lift (4.3 in2) Mach
1655 psia in, 225,000 Ibm/hr, steam properties 0.55

0.50
0.45
0.40
0.35
0.30

invader-2T:-

0.25
0.20
0.15
0.10
0.05
0.00

 

 

 

 

Figure 45: Mach Number Profile for 0.639 inch Lift
(Source: Elliot Turbo-Machinery Co., 2001)

78

0.639 inch lift (4.3 in2)
1655 psia in, 225,0001bm/hr, steam properties

 

Figure 46: Pressure Profile for 0.639 inch Lift
(Source: Elliot Turbo-Machinery Co., 2001)

79

 

 

P-Psia
1700

1650

p 1600

1550

. 1500
_ 1450
.1 1400

- 1350

1 300

 

 

0.639 inch lift (4.3 in2)

1655 psia in. 225,000 lbm/hr, steam properties

 

 

 

 

Figure 47: Velocity Profile for 0.639 inch Lift
(Source: Elliot Turbo-Machinery Co., 2001)

80

 

 

 

Speed
5 1054

949
843
738
632
527
422
316
21 I
105

 

 

Appendix B
Pressure Chest and Valve Design Dimensions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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81

Figure 48: Main Testing Valve Pressure Chest

395 How” <m_<a 0:8"

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 49: Side Plating Dimensions for Pressure Chest Opening

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Figure 50: Valve and Seating Pressure Gauge Arrangement

83

 

 

 

 

 

———‘ \

 

 

 

 

 

 

 

 

 

 

 

 

Valve Stem \ Lever
‘ Threading
E/
/ Internal threaded shafi
/
Locknut V
\\
Bolt-on plate to Pressure Chest

 

 

 

 

 

 

 

 

\

Valve plug

r /
rt]

 

 

 

 

 

Overall Shaft Design

for Valve Lifi Control
No Drawn to Scale

Figure 51: Overall Shaft Design for Valve Lift

84

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 52: Dimensions for Main Valve Plug Head

85

 

 

 

 

 

3mm: <E<o Sam

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 53: Dimensions for Valve Stem and Plate Bolt On

86

4.28"

 

 

JL

 

/

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

\r/(l

1.5315"

3.22"

 

 

 

 

 

 

.—1_
L
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\ rt ‘r
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' l
l
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L .
2.115"
‘ 2.28"

Main Valve Design and Seating

Not drawn to scale

Figure 54: Dimensions for Main Valve Seating

87

 

Appendix C
Aluminum 2024-T851
Subcategory: Aluminum Alloy; Nonferrous Metal; 2000 Series Aluminum Alloy

Key Words: Aluminum 2024-T851; AA2024-T851; UNS A92024;

Composition:

 

 

 

 

 

 

 

 

 

 

 

 

COMPONENT WT. %
AL 93.5

CR MAX 0.1
CU 3.8 - 4.9
COMPONENT WT. %
FE MAX 0.5
MG 1.2 - 1.8
MN 0.3 - 0.9
COMPONENT WT. %

SI MAX 0.5
T1 MAX 0.15
ZN MAX 0.25

 

 

 

 

Table 13. Composition Table for aluminum 2024

Material Notes: Weldability = C; Stress Corrosion Cracking Resistance = B; General
Corrosion Resistance = D (A = best; E = worst). Good machinability and surface finish
capabilities. A high strength material of adequate workability. Has largely superceded

2017 for structural applications.

Uses: Aircraft fittings, gears and shafis, bolts, clock parts, computer parts, couplings, fuse
parts, hydraulic valve bodies, missile parts, munitions, nuts, pistons, rectifier parts, worm

gears, fastening devices, veterinary and orthopedic equipment, structures.

Most data provided by Alcoa.

88

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

PHYSICAL VALUES COMMENTS US / Other
PROPERTIES Units
Density, g/cc 2.77 2.77 ggcc
Hardness, Brinell 128 500 kg load/ 10 mm ball 128
Hardness, Knoop 161 Estimated from Brinell 161
Hardness, 49 Estimated from Brinell 49
Rockwell A
Hardness, 79 Estimated from Brinell 79
Rockwell B
Hardness, Vickers 146 Estimated from Brinell 146
Table 14. Physical Properties of Aluminum 2024
MECHANICAL VALUES COMMENTS US / Other
PROPERTIES Units
Tensile Strength, 455 Minimum value 65,975 psi
Ultimate, MPa
Tensile Strength, 400 Minimum Value 58,000 psi
Yield, MPa
Elongation %; 5 5 %
break
Modulus of 72.4 Estimated from other heat 10,498 ksi
Elasticity, GPa treatments.
Poissons Ratio 0.33 Estimated from other heat 0.33
treatments.
Fatigue Strength, 117 500,000,000 cycles; 16,965 psi
MPa completely reversed; R. R.
Moore Machine and
specimen.
Machinability, % 70 0-100 Scale (A=90; B=70; 70
C=50; D=30; E=10)
Shear Modulus, 27 Estimated from similar Al 3,915 ksi
GPa alloys.
Shear Strength, 296
MPa 42,920 psi

 

 

 

 

 

Table 15. Mechanical Properties of Aluminum 2024

89

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

THERMAL VALUES - COMMENTS US / Other
PROPERTIES Units
CTE, linear 20°C, 23.2 average over 20-100°C 13 uin/in-°F
pm/m-°C
CTE, linear 24.7 Average over the range 20— 14 uin/in-°F
250°C, um/m-°C 300°C
Heat Capacity, 0.875 921
J/g-°C BTU/1b-°F
Thermal 151 1 048 BTU-
Conductivity, iri/hr-fi2-°F
W/m-K
Melting Point, °C 502 Solidus 936 °F
Solidus, °C 502 936 °F
ELECTRICAL VALUES COMMENTS US / Other
PROPERTIES Units
Electrical 0.0000045 0.0000045
Resistivity, Ohm- Ohm-cm
cm

 

 

 

 

Table 16. Thermal Properties of Aluminum 2024

90

 

BIBLIOGRAPHY

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92