International Journal of Latest Technology in Engineering, Management & Applied Science (IJLTEMAS)
Volume VI, Issue VIII, August 2017 | ISSN 2278-2540
www.ijltemas.in Page 102
Random Vibration and Stress Analysis of Fluidization
Reactor System
Swetal Patel
1
, Reena R. Trivedi
2
, Bhadresh Jariwala
3
1, 2
Mechanical Department, Institute of Technology, Nirma University, S.G Highway, Ahmedabad, Gujarat, India.
3
CAD HOUSE 101, Prasam Apt. (H3 Hospital Bldg.) Nr. Ashok Pan House, City Light Rd, Surat, Gujarat 39500, India
Abstract—This dissertation work focuses on performing
vibration analysis to find dynamic stress and defection of the
fluidization reactor. Reactor consists of many vertical and
horizontal stacks, ladder, platforms etc. It is constitutes complex
dynamic system. While design reactor of petrochemical
refineries. It is very important to consider vibration
characteristics into account. Fluidization systems running at high
temperature and pressure close to the natural frequency of the
system results in excessive deformation and large stress which
leads to catastrophic failure of the system. With a view to this, an
effort has been made in carrying out a feasibility study of
dynamic behavior like dynamic stresses and displacement of the
structure to determine with well-established theoretical method
and performing the FEA (Finite Element Analysis. FEA
performing when the reactor is operating condition and non-
operating condition and conclusion is drawn based on the
validation both theoretical and FEA results of dynamic analysis
of the reactor.
Keywords— Reactor, ASME, Analytical Modal Analysis, FEA,
Random Vibration analysis.
I.
INTRODUCTION
luidized bed reactors are a relatively new tool in the
chemical engineering field. The first fluidized bed gas
generator was developed by Fritz Winkler in Germany in the
1920s.One of the first United States fluidized bed reactors
used in the petroleum industry was the Catalytic Cracking
Unit, created in Baton Rouge, LA in 1942 by the Standard
Oil Company of New Jersey. This FBR and the many to
follow were developed for the oil and petrochemical
industries. Here catalysts were used to reduce petroleum to
simpler compounds through a process known as cracking.
The invention of this technology made it possible to
significantly increase the production of various fuels in the
United States.
Today fluidized bed reactors are still used to produce
gasoline and other fuels, along with many other chemicals.
Many industrially produced polymers are made using FBR
technology, such as rubber, vinyl, chloride, polyethylene,
styrenes, and polypropylene. Various utilities also use FBR's
for coal gasification, nuclear power plants, and water and
waste treatment settings. Used in these applications, fluidized
bed reactors allow for a cleaner, more efficient process than
previous standard reactor technologies.
A fluidized bed reactor (FBR) is a type of reactor device
that can be used to carry out a variety of multiphase chemical
reactions. In this type of reactor, a fluid (gas or liquid) is
passed through a solid granular material (usually
a catalyst possibly shaped as tiny spheres) at high
enough velocities to suspend the solid and cause it to behave
as though it were a fluid. This process, known as fluidization,
imparts many important advantages to the FBR. As a result,
the fluidized bed reactor is now used in many industrial
applications.
Structural Integrity of important component like reactor is
necessary for operational safety, reliability and economic
plant operation. These structures are prone to excessive
vibration resulting in flutter and fatigue failure. Performance
of many structures such as Reactor, pressure vessel, vertical
tower is severely affected by undesired vibration. It is
required that structures must safely work during its service
life. It is very much important to characterize the dynamic
behavior of the space structures to ensure its survivability
against excessive vibrations. In the study of dynamic behavior
of structure, usually modal parameters like Natural Frequency
Mode shapes and damping to be extracted.
The mechanical design of pressure vessels is done in
accordance with the guideline provided in the ASME Pressure
Vessel Code, Section VIII Div. 1, and Div. 2. Pressure vessels
are made in all shapes and sizes, from a few cm in diameter to
5698 diameter and 40426 mm height including skirt support.
The pressure may be more than 29.1 bar. Reactor vessel have
more applications ranging from chemical industries, oil and
gas plant, ammonia plant, heat exchanger, petroleum
refineries & fertilizer industry etc. They are subjected to
mechanical as well as thermal operating condition, therefore
cylinder shows some limitations. In order to reduce weight /
volume, thickness or to increase life of vessel, its durability
and burst pressure researcher used multi-layer vessel.
In this dissertation work focus on vibration and dynamic
analysis of skirt supported vertical reactor vessel for specific
load cases. The dynamic displacements and material stresses
must not exceed the specified maxima. The main problem
while designing a reactor is loading conditions to control the
F
International Journal of Latest Technology in Engineering, Management & Applied Science (IJLTEMAS)
Volume VI, Issue VIII, August 2017 | ISSN 2278-2540
www.ijltemas.in Page 103
vibration of vessel under operating condition and selection of
proper members to ensure design requirement. For which an
additional requirement of designing safe, while they are
designing the reactor for all the cases the displacement and
stresses should be less than allowable limit of the reactor as
per specification S-G000-5351-001.
Vibration and stress analysis of the overall fluidization
system on the structural support shall be performed. Reactor
to be supported in order to control vibrations, supporting
structure/ foundation details shall be defined after stress
analysis;
1. In the first stage of the work, understanding for all the
codes used by the industry to design of pressure
vessel. After that getting the allowable limit of
stresses of the specification of the project.
2. Make solid model for the project geometry in
SIMENSE NX 8.5 and check all bodies and edges to
completely swappable and splitting all bodies
symmetrical of model.
3. Checking all the process nozzles are passing in PV
ELITE software to considering all load and forces
applied at certain location.
4. Performing modal analysis, when reactor is not
working condition as a fixed-free condition in order
to finding the frequency values obtained in the
preliminary analysis of FEA model.
5. When reactor is operating condition, performed the
static structural analysis for future analysis of modal
analysis to obtain the excited natural frequency.
Those all frequency extract for the random vibration
fr determine the dynamic response of the structure.
6. Check the theoretical approach of modal and random
vibration analysis results are validating with
analytical analysis result of the FEA model.
All literature related to free transverse and random
vibration of simple structures i.e. Beams are reviewed. Then
various techniques of modal analysis i.e. Analytical,
operational and experimental are reviewed.
The American Society of Mechanical Engineers [ASME]
Section VIII, Division 1 & 2 [1], According to The standard
gives the procedure to carry out the combined stress analysis
of pressure vessel. The pressure vessels are designed as per
ASME section viii division 1 & 2.Most of all type of pressure
vessel design based on the ASME section VIII division I.
Moss, D. R., Pressure Vessel Design Manual [2], This book is
the manual for the pressure vessel design. It covers all the
aspect of the design procedure of the pressure vessel Freese,
C. E. [3], this paper has primarily concerned with the
vibration of vertical tall tower, vessel and column. It described
the accurate method to estimate the fundamental frequency
and period of vibration of the tall and uniform vessel. Eugen
Megyesy & Paul /buthod [7], Pressure vessel design
handbook, this is book of design and construction of pressure
vessel and guideline of stress analysis of different component
of vessel.it gives also to formula of natural frequency of
vessel under wind loading of vertical tall stack tower for
different dynamic loading condition. Jaap Wijker [17], Author
presents the book on the Random Vibrations in Spacecraft
Structures Design Theory and Applications. This book covers
the most of all fundamentals of the random vibration of the
structure. Anil K Chopra [11], Author present book on
Dynamics of Structures (Theory and Application to
Earthquake Engineering) which gives information regarding
fundamental of vibration and also information regarding
earthquake engineering and response of the structure during
earthquake and describe the fundamental of vibration of static
structural problem.
While designing the Pressure Vessels, Reactor, Vertical
tower, wind and seismic conditions shall be checked by the
designer as they can have the major roll in failing the vessel.
These structures are prone to excessive vibration resulting in
utter and fatigue failure. Performance of many vertical vessel
structures is severely affected by undesired vibration. It is
very much important to characterize the dynamic behavior of
the structures to ensure its survivability against excessive
vibrations. So, the main motivation behind this project is to
provide some guidelines to the designer, to use the codes
without wasting much time by compiling these codes at one
place, which are applicable to vessels only.
II. MODAL ANALYSIS
Modal analysis has become the most important technology
in improving and optimizing dynamic characteristics of
engineering structures in the past few years. It is not only used
for in aeronautical and mechanical engineering, but modal
analysis has also research another applications for civil and
building structures, space structures, and transportation.
A. Finite Element Model:
The solid model of the reactor is used for life assessment.
The geometric modeling of the reactor is carried out in NX
ver. 8.5 software. All the necessary partitions & splits are
made in NX software. Partition and splits are made based on
the meshing requirement, load application and restraints entire
document should be in Times New Roman or Times font.
Type 3 fonts must not be used. Other font types may be used
if needed for special purposes.
The analysis software used is Ansys Version 16.2. The
model generated in the NX is transferred to Ansys Design
Modeller, as a Para solid, for Analysis and further process.
Material Properties are defined in Ansys Engineering Data.
The Meshing, application of the load and boundary conditions
are done in Ansys Mechanical. Ansys APDL is used for
solving the model and the results are view in Ansys
Mechanical.
B. Modeling Data:
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Volume VI, Issue VIII, August 2017 | ISSN 2278-2540
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By considering the below-mentioned dimensions a 3D
model of reactor is made for assessment:
TABLE I
Modeling Data
Shell Inner Diameter
= 2819.5 mm
Shell thickness
= 60 mm
Hemispherical Head Crown thickness
= 48 mm
Crown thickness (Bottom)
= 56 mm
Skirt thickness
= 30 mm
Insulation thickness
= 40 mm
Corrosion allowance
= 3 mm
Fig. 1 Solid model of reactor
Reactor as shown in fig 1 is used in chemical process plant.
Reactor containing catalyst, conducting highly exothermic
process like hydrocarbon, naphthalene, oxidation of ethylene
and hydrogenation reaction.
C. Meshing Properties:
Solid185 Quad elements are used for meshing the structure.
SOLID185 is a first order 3-D 8-node solid element that
exhibits linear displacement behavior. The element is defined
by 8 nodes having three degrees of freedom per node:
translations in the nodal x, y, and z directions.
As per ANSYS design manual for good mesh quality there
some criteria for the fine mesh elements for meshing. The
detail of meshing for analysis with 3 elements across section
is as given below:
Total number of elements in the part: 254192
Total number of nodes in the part: 327576
Aspect ratio: 0.9997
Skewness (< 0.95): 0.2685
Orthogonal quality (>0.1): 0.8345
Fig. 2 Meshing detail of FEA model
For evaluating the natural frequency and the mode shapes
due to mechanical loads, the Nodes on bottom surface of
support Skirt are fixed in all direction.
D. FEA Results:
Modal Analysis is performed using workbench ANSYS
16.2 software package. After that, we got the natural
frequency and each natural frequency have own mode shapes.
Figure 3: Mode shapes 1 & 2 of Natural frequency
Figure 4: Mode shapes 3 & 4 of Natural frequency
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Volume VI, Issue VIII, August 2017 | ISSN 2278-2540
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Figure.5: Mode shapes 5 & 6 of natural frequency
TABLE II
Natural Frequency
MODE
NATURAL FREQUENCY (Hz)
1
2.1142
2
2.1445
3
7.3813
4
7.5907
5
11.097
6
14.901
Figure.6: Graph of mode shape vs. frequency
E. Theoretical Approach:
E. Megyesy, natural frequency formula [5]:
As, a result of wind, another dynamic loading, vertical
vessel develop vibration. The period of the vibration should
be limited, since large natural periods can lead to fatigue
failure. The allowable period has been computed from the
maximum permissible deflection.
Formula’s for period of vibration:
Period of vibration: T (sec)
T
Natural frequency: f
n
(Hz)
D
=
Outside diameter, ft.
H
=
Length of vessel including skirt, ft.
g
=
32.2 ft. per sec square, acceleration.
t
=
Thickness of skirt at the base, in
V
=
Total shear, lb.
W
=
Weight of tower, lb.
w
=
Weight of tower per foot of height, lb.
f
n
=
Natural frequency , Hz.
The period of vibration:
T
T = 0.476604635 sec
Natural frequency:
=
= 2.098175 Hz.
Similarly we get all natural frequency for all mode shape.
TABLE III
Validation Results
Natural frequency (Hz)
MODE
ANALYTICAL
RESULT
THEORETICAL
RESULT
1
2.1142
2.0981
2
2.1445
2.1284
3
7.3813
7.3650
4
7.5907
7.5844
5
11.097
11.062
6
14.901
14.356
III. STATIC ANALYSIS
The stress analysis of the shell and nozzle is required under
design condition & differential pressure. This analyses and
evaluates the mechanical stresses due to the discontinuities
and that due Internal Pressure and another loading condition.
A. Loading Condition:
The design data required for the analysis is as given below.
Design code:
: ASME Sec. VIII Div. II Ed.2015
Design Pressure
: 2.91 MPa
Design Temperature
: 170 °C
Operating Pressure
: 2.28 / 2.35 MPa
Operating Temperature
: 40 / 125 °C
Corrosion Allowance
: 3 mm
Vertical Loading
: 10200 KN (-Y Direction)
Shear Loading
:520 KN (+X Direction)
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Volume VI, Issue VIII, August 2017 | ISSN 2278-2540
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Figure.7: Loading and boundary condition
B. Mechanical results:
Mechanical results are obtained as per the load cases define
the von misses stress plot & displacement plot for load cases.
Maximum displacement observed is as listed in the table
below.
Figure 8: Static Structural Analysis Results
Load Case
Total Deformation
Equivalent (Von misses) stress
LC 1
11.077 mm
291.17 MPa
Here the equivalent stress is above the allowable stresses so
we linearized stresses where maximum stress is observed. The
stress evaluation for each of the SCL and at the end nodal
points of SCL’s is done as per Code ASME Section VIII,
Div2, Ed. 2015, and Part 5. The Linearized Stress results
calculate membrane, bending, peak, and total stress along a
straight line path in the Mechanical application.
Figure 9: SCL FEA Analysis Results
Allowable stress Limits are considered as per Part5, ASME
Section VIII, Div 2. It is tabulated in table for all materials.
TABLE IV
Allowable Stresses
Stress category
Stress Limit
SA 516 GR
70
@170°C
(N/mm
2
)
SA 105
@ 170°C
(N/mm
2
General Primary
Stress
Pm= Sm
152.4
132.4
Local Primary
Stress
PL=1.5Sm
228.6
213.6
Primary +
Secondary Stress
PL+Pb+Q=3Sm
457
427.2
The Stress intensities at SCL's and nodal end point of SCL's
are categorized as primary and primary plus Secondary
stresses as per Code and the stress intensities are checked with
allowable limits. A computer program is made and membrane
and bending component is found along each defined path.
TABLE V
Primary Membrane Equivalent stress
SCL
Location with
material
Stress
Category
Equivalent
stress MPa
Allowable
Stress MPa
SCL 1
Shell
( SA 516 Gr 70)
PL=1.5Sm
110.5
228.6
SCL 2
Shell
( SA 516 Gr 70)
PL=Sm
75.461
152.4
SCL 3
Nozzle 24_
(SA 105)
PL=1.5Sm
36.609
213.6
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Table show that Summary of primary membrane equivalent
stress for Mechanical Loading@ 170 °C (LC1).
TABLE VI
Primary + Secondary Equivalent
Stress
SCL
Location with
material
Stress
Category
Equivalent
stress MPa
Allowable
Stress MPa
SCL 1
Shell
( SA 516 Gr 70)
PL+Pb+Q=
3Sm
111.8
457.6
SCL 2
Shell
( SA 516 Gr 70)
PL=1.5Sm
113.41
228.6
SCL 3
Nozzle 24_
(SA 105)
PL+Pb+Q=
3Sm
99.405
427.2
Table show that Summary of primary + secondary equivalent
stress for Mechanical loading@ 170 °C (LC1)
Here all case of Equivalent stresses is below the allowable
stresses so design is safe for stress analysis.
This mode shapes are imposed in random vibration dynamic
for determining the dynamic response of the structure. Refer
below mode shapes for FEA plots.
Figure 10: Mode shape 1 & 2 of Excited Frequency
Figure 11: Mode shape 3 & 4 of Excited Frequency
Figure 12: Mode shape 5 & 6 of Excited Frequency
IV. RANDOM VIBRATION ANALYSIS
Random vibration analysis is used to define the structure
response under random loading. ANSYS uses the power
spectral density (PSD) spectrum as random vibration analysis
of the load input. Power spectral density is a kind of
probability statistics method, and is the root mean square
value of random variables, including a measure of the random
vibration energy and frequency information. Power spectrum
that can be displacement, velocity, acceleration or force power
spectral density and other forms.
Random vibration is extracting all mode shapes for
determining the dynamic response of the structure. Without
modal analysis we cannot determine the any type of dynamic
response of the structure. In random vibration analysis the
random excitation force give in the form of power spectral
density. Then solver solving the above load case and
determines the dynamic stresses and deformation and
response of the structure.
Random vibration is getting all load case and boundary
condition taking from the previous analysis and excites the all
mode shape getting base excitation forces for evaluation
maximum deformation and stresses.
A. Random Excitation Force:
In random vibration analysis, the input excitation force
applied in +X direction in form of PSD G acceleration. Power
Spectral Density (PSD) is the frequency response of a random
or periodic signal. It tells us where the average power is
distributed as a function of frequency. The input forces like as
PSD G ACCELERATION :( as per frequency range)
TABLE VII
PSD G Acceleration
Frequency
G
2
/ Hz
5
0.0387
10
0.0417
15
0.0463
20
0.0463
25
0.0387
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The Hz value in [G2/Hz] refers to a bandwidth rather than
to the frequency in Hz along the X-axis. The RMS value of a
signal is equal to the standard deviation, assuming a zero
mean. The standard deviation is usually represented by sigma.
Figure 13: PSD Curve
PSD response analysis: Taking the PSD G acceleration as
input base excitation spectrum as the input condition, then
basing on the results of the modal analysis we can analyses
the random vibration response and getting the maximum
stress under the action of the random load spectrum. For
maximum dynamic stresses and deflection, it may be used the
scale factor 3 sigma and probability 99.73%for determine
Random vibration response of the structure. Getting the
direction deformation in X direction and equivalents stress in
X & Y direction.
Figure 14: Directional deformation in x direction
Figure 15: Equivalent stresses in X direction
Here Equivalent stresses are below the allowable stress
value so design safe in random loading condition. And
Directional deformation is also below the allowable limit
according to E. Megasy approach. So design safe.
B. Dynamic Response of reactor:
To compute the RMS values from these breakpoints we
need to compute the area under the curve defined by the
breakpoints. From dynamic stress evaluation we get the
maximum deformation and stresses as per dynamic loading
condition. We can show that the maximum deformation
occurred at the top nozzle place on top head of the reactor.so,
we find the displacement response PSD of those nodes at
different frequency as per dynamic loading condition
Mechanical results are obtained as per the load cases define
the von misses stress plot
Displacement response:
All boundary and loading conditions are taken from the
random vibration analysis. From FEA analysis of the random
vibration we show that the maximum deformation occurred at
top of the vessel so we select that node for determine the
displacement and acceleration response of the reactor.
In displacement response, give results of the displacement of
that node for different excited frequency and plot graph of the
all displacement as per frequency. Its show in fig.
Figure 16: Response curve of the displacement response
Figure 17: FEA results of displacement response
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Acceleration response:
Acceleration response to compute the RMS values from
these breakpoints we need to compute the area under the
curve defined by the breakpoints. Similarly all psd
acceleration excited for different frequency to plotting the
graph of acceleration response curve.
Figure 18: Response curve of acceleration response
Figure 17: FEA results of acceleration response
V. VALIDATION OF FEA RESULTS
A. Theoretical approach of Total Deformation:
Eugene Megasy Theory [5],
The deflection due to wind load may be calculated by using
the formula for uniformly loaded cantilever beam.
Maximum deflection:
Wind pressure
=
Maximum deflection:
=
= 0.438531 inch = 11.13871 mm
As per Megasy approach,
The maximum allowable limit of deformation of Tower
should be designed to deflect no more than 6 inches per 100
feet of height.
So, our FEA model height (including skirt height) is 132.67
ft. for determine the maximum deformation.
Maximum allowable deflection: 4.523812 in = 114.9051 mm
Theoretical deformation value of the vessel is less than the
maximum allowable deflection so design is safe in working
condition.
B. Validation of deformation of the vessel:
Comparing the theoretical and analytical value of the total
deformation for validate the results.
TABLE VIII
Validation Results of deformation
Load case
Theoretical approach
Analytical approach
LC1
11.138 mm
11.077 mm
C. Theoretical approach for Acceleration response of the
reactor:
A random spectrum is defined as a set of frequency and
amplitude breakpoints, like these:
To compute the RMS values from these breakpoints we need
to compute the area under the curve defined by the
breakpoints. At first glance this appears simple because the
area can be split up into a group of squares and triangles,
which are easy to compute. But note that the triangles are the
result of straight lines on log-log graph paper, and not on
linear graph paper. We can still take advantage of the
triangles; however we need to use a special formula for
computing the area of triangles on log-log graph paper.
The definition of a straight line on log-log graphs between
two breakpoints (f1, a1) and (f2, a2) is a power relationship,
where the slope is the exponent, and the offset is the
multiplicative factor.
Area =offset * f
slope
The slope and offset that define this straight line, are
computed as follows.
Slope =
Offset =
Given this slope and offset we can integrate from
to
to
compute the area under the line.
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Area =
*
(if slope ≠ -1)
When slope=1 we have a special case where this formula
doesn’t hold. For this case we note that (a = offset / f) which
integrates to a natural log function.
Area =
(if slope = 1)
(Hint: some programs, including Microsoft Excel define the
log () function as a base-10 logarithm, and define the ln ()
function as the natural (base-e) logarithm. Be sure to use the
correct function in your calculation. As a test, for a natural
logarithm, log (2.71828182845905) = 1.0.)
Area =
(if slope = -1)
So, for each pair of breakpoints we can use equations (4) or
(5) to compute the area under the curve. The total area under
the curve will then be the sum of the individual area
calculations between each pair of breakpoints, and this sum is
the mean-square acceleration. We take the square-root of the
result to get the RMS acceleration level.
Using our example breakpoints, the sum is computed as
follows:
From frequency 5 to 10 Hz:
Determine the slope and offset:
Slope =
Slope =
Slope = 0.107714
Offset =
Offset =
Offset =
Here slope value is positive so determine area under curve by
using equation
Area =
Area =
Area (A
1
) =
Similarly calculate area under the all frequency range from
given table.
TABLE IX
Acceleration
Response
Frequency
(Hz)
Amplitude
( G2/Hz)
Slope
Offset
Acceleration
area
5
0.0387
*
*
*
10
0.0417
0.1077
0.03254
0.2017
15
0.0463
0.2580
0.02301
0.2205
20
0.0463
0
0.0463
0.2315
25
0.0387
-0.8035
0.5140
0.2112
Total
0.8650
Root mean square value
0.93009
Acceleration (Grms)=
0.93018
D. Theoretical approach for Displacement response of the
reactor:
According to Random vibration by Barry controls[10],
Displacement could be analyzed in the same manner as
acceleration, except that rather than using units of g2/Hz, the
units would be in2/Hz. The RMS displacement would be the
square root of the area under the curve of in2/Hz. However,
since accelerometers are the most frequently used method of
measuring random vibration, alternate methods are used to
determine displacement. For a band limited white spectrum,
the RMS displacement can be shown to be given by:
Xrms = Grms *
For most cases, f 2 is significantly higher than f l so above
Equation 4 can be rewrite in different form:
Xrms =
We can show that, In FEA analysis of random vibration the
maximum deformation occurred at the nodes of the top nozzle
of the vessel those placed on the top of the head so we can
determine the displacement response of that node.
Grms = input acceleration = .930092 G
g = acceleration constant = 9810 mm/s
2
f1 = lower frequency, = 5 Hz
f2 = upper frequency = 25 Hz
Displacement response:
Xrms =
= 9.539244 mm
Validation of the Dynamic Responses Results of the
Structure:
Comparing the FEA response results and theoretically
response results, from below table we can show that both
results are nearly equal. The displacement of that node result
has nearly to the allowable limit of the theoretical approach.
So design of reactor has not more conflict with dynamic
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loading condition.
TABLE X
Validation Results of Response
Dynamic response
Theoretical approach
Analytical approach
Displacement response
9.53922 mm
9.9264 mm
Acceleration response
9120.73 mm/s
2
9982.57 mm/s
2
IV. CONCLUSIONS
This dissertation aimed for performing Random vibration
and Stress analysis of vertical skirt supported fluidization
reactor. The finite element methodology is used to predict the
dynamic responses of the fluidization reactor.
When Reactor is non-operating condition, the parametric
study of the natural frequency and mode shapes of the reactor
results obtained analytically using E. Megasy method and
validating results is found to be in close confirmation with
FEA results.
The Static structural analysis to determine the Total
Deformation and Equivalent stresses under operating
condition. Discontinuity stress analysis at cone to shell and
nozzle junction is carried out using ASME Sec VIII Div. 2
Part 5, stresses at junction is maximum compared to other
parts in model and stresses are less than allowable stress 228.6
MPa, hence design is safe.
The Modal analysis and Random vibration analysis is
performed to evaluate the Dynamic stresses and Deformation
of the reactor under operating dynamic conditions using FEA
(Finite Element Analysis). And also determine the
Displacement Response and Acceleration Responses of the
structure under random excitation force in operating condition
using FEA. The results obtained from analytical process are
successfully validated with Finite element analysis and good
agreement found between FEA and analytical results are
within allowable hence design is safe.
ACKNOWLEDGMENT
I take this opportunity to express deep sense of gratitude
and sincere thanks for the invaluable assistance that I have
received during report at the worthy hands my honorable and
taught guides Mr. Bhadresh Jariwala (Head of Design
Department, Cad House). They are the constant source of
encouragement and momentum that any intricacy becomes
simple. I gained a lot of invaluable guidance and prompt
suggestions from them during my thesis work. I remain
indebted of them forever and I take pride to work under them.
I would like to thank internal guide Dr. Reena R. Trivedi who
helps me to understand the subject, stimulating suggestions,
encouragement. I am sincerely thankful for this valuable
guidance and help to enhance my thesis writing.
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