UPTEC F10 006
Examensarbete 30 hp Februari 2010
Design and dimensioning of pressure vessel for a marine substation
Lars Eriksson
Teknisk- naturvetenskaplig fakultet UTH-enheten
Besöksadress:
Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress:
Box 536 751 21 Uppsala Telefon:
018 – 471 30 03 Telefax:
018 – 471 30 00 Hemsida:
http://www.teknat.uu.se/student
Abstract
Design and dimensioning of pressure vessel for a marine substation
Lars Eriksson
This thesis presents the mechanical design and dimensioning of a pressure vessel, which is to be used as housing for a marine substation in a wave power park. A concept for generation of electricity from ocean waves is being developed at the Division of electricity at Uppsala University. The concept is based on the use of a permanent magnet linear generator, placed on the seabed, connected via a line to a buoy at the surface. The generated electricity from a group of generators is
transmitted in sea cables to a marine substation where conversion and transformation takes place before the electricity is transmitted to shore. To reduce the risk of water leakage, the gas pressure inside the marine substation is larger than the surrounding water pressure. The substation can be pressurized before submersion, which requires the housing to be designed as a pressure vessel. The pressure vessel has been
dimensioned with formula based methods according to EN 13445, the European standard for unfired pressure vessels. The construction has been based on modifying a standard pressure tank. The housing has been designed for installation and sealing of a large number of electrical connectors. The connectors have been placed in a way that allows for future cable coupling with remotely operated vehicles and simplifies maintenance of the substation. Another design consideration has been to facilitate submersion by reducing the buoyancy of the substation.
ISSN: 1401-5757, UPTEC F10 006 Examinator: Tomas Nyberg Ämnesgranskare: Mats Leijon Handledare: Magnus Rahm
Svensk sammanfattning
Detta examensarbete omfattar mekanisk konstruktion av ett tryckkärl till ett marint ställverk som ska användas för vågkraft. Vid avdelningen för elektricitetslära vid Uppsala Universitet utvecklas ett koncept för generering av elektricitet från
havsvågors rörelser. Konceptet bygger på en linjärgenerator placerad på havsbottnen som via en lina drivs av en boj vid ytan. Linjärgeneratorn är direktdriven vilket innebär en enkel mekanisk konstruktion men också att elektriciteten som genereras har varierande frekvens och amplitud. För att elektriciteten ska kunna användas i elnätet behöver den konverteras till växelström med konstant frekvens. För att inte få stora resistiva förluster i transmissionskabeln som går in till land, behöver
elektriciteten också transformeras till högre spänning. Konvertering och
transformering av elektriciteten från en grupp av linjärgeneratorer sker i ett ställverk placerat på havsbottnen i närheten av generatorerna.
Lysekilsprojektet går ut på att testa detta vågkraftskoncept under realistiska förhållanden i havet utanför Lysekil. För närvarande är tre linjärgeneratorer
installerade och inkopplade till ett ställverk på 25 meters djup. Parken ska utökas till totalt tio linjärgeneratorer och två ställverk de närmaste åren. Detta examensarbete berör det andra ställverket i Lysekilsprojektet.
Kraftelektroniken och transformatorerna i ställverket behöver skyddas från
havsvattnet och för att minska riskerna med eventuellt vattenläckage är lufttrycket i ställverket högre än det omgivande vattentrycket. Detta kan åstadkommas genom att konstruera ställverkets inneslutning som ett tryckkärl som innan sjösättning kan trycksättas med högre tryck än vattentrycket vid arbetsdjupet. Inneslutningen måste då tåla ett inre tryck på ca. 3 bar vilket innebär att regelverken för konstruktion, kontroll och certifiering av tryckkärl måste följas.
De olika tryckkärlskomponenterna har dimensionerats med formelbaserade metoder från SS-EN 13445 – Tryckkärl, ej eldberörda, som är en del av den europeiska
tryckkärlsstandarden. Metoderna för dimensionering har implementerats i Matlab och konstruktionen samt ritningsframställningen har utförts i SolidWorks. Vissa
simuleringar med finita elementmetoden har också utförts med SolidWorks Simulation, för att undersöka hållfastheten vid lastfall som inte täcks in av de formelbaserade metoderna.
Utformningen av kärlet har utförts med avseende på att sjösättning och återhämtning för underhåll ska vara så enkel som möjligt. Ställverket har ett tjugotal
genomförningar för kablar kopplade till undervattenskontakter. Konstruktionen har förberetts för att kontaktering i framtiden ska kunna utföras med en
undervattensrobot. Konstruktionen har baserats på en vertikalt stående trycktank med kupade gavlar som har en volym på 5 m³. Att tillverka inneslutningen genom att modifiera en färdig trycktank är ett kostnadseffektivt alternativ till att specialbeställa ett tryckkärl. Kärlet har förstärkts med förstyvningsringar för att tåla större yttre tryck.
Den nedre gaveln har avlägsnats och bytts ut mot ett lock som fästs i en skruvfläns.
Kärlet har utrustats med kabelgenomföringar i form av stutsar som är förberedda för kabelförskruvningar, samt lyftöglor dimensionerade för att lyfta ställverket och dess fundament vid sjösättning. Möjligheten att använda en platt nedre gavel har också undersökts, vilket har fördelen att kärlet blir mer kompakt som i sin tur medför att fundamentet kan göras lättare.
Om liknande framtida ställverk skulle placeras på större djup, och trycksättas innan sjösättning, skulle inneslutningen behöva tåla större inre tryck, och möjligheterna att dimensionera för detta har undersökts. Möjligheten att trycksätta kärlet under
sjösättningen diskuteras också, vilket skulle innebära att kärlet behöver tåla betydligt mindre inre tryck och inte behöver tryckkärlcertifieras. Tre konstruktionsalternativ presenteras, som skiljer sig åt med avseende på tryckkärlets infästning till
fundamentet samt den nedre gavelns konstruktion. De slutliga
konstruktionsritningarna har sedan färdigställts baserade på ett av dessa konstruktionsalternativ.
Nomenclature and abbreviations
d [mm] Diameter
r [mm] Radius
e [mm] Required thickness
P [MPa] Calculation pressure
f [N/mm2] Nominal design stress
σ [N/mm2] Normal stress
ReH [N/mm2] Upper yield strength Rm [N/mm2] Tensile strength
S - Safety factor
z - Joint coefficient
ε [%] Strain
E [MPa] Modulus of elasticity
ν - Poisson’s ratio
m [kg] Mass
V [dm3] Volume
ρ [kg/dm3] Density
AC Alternating Current
DBA Design By Analysis
DBF Design By Formulae
DC Direct Current
FEM Finite Element Method
LVMS Low Voltage Marine Substation
MABE Maschinen und Behälterbau GmbH
NDT Non-Destructive Testing
PED Pressure Equipment Directive
ROV Remotely Operated Vehicle
WEC Wave Energy Converter
Unit conversion for pressure:
1 MPa = 1 N/mm2 = 10 bar
2
Table of contents
1 Introduction... 4
1.1 Background ... 4
1.2 The Lysekil project ... 6
1.2.1 ROV cable coupling... 6
1.2.2 Installation and retrieval of marine substation... 7
1.3 Aim of thesis ... 7
2 Theory ... 7
2.1 Pressure vessel regulations ... 7
2.2 Control and inspection regulations ... 8
2.3 Design of components... 11
2.3.1 Cylindrical shells, internal pressure ... 12
2.3.2 Cylindrical shells, external pressure ... 12
2.3.3 Dished ends, internal pressure ... 14
2.3.4 Dished ends, external pressure... 14
2.3.5 Flat ends ... 15
2.3.6 Flanges ... 15
2.3.7 Openings ... 16
2.3.8 Lifting eyes ... 17
3 Method ... 17
4 Conditions for the design ... 17
4.1 Manufacture of the vessel ... 18
4.2 Protection against corrosion... 18
4.2.1 General corrosion... 18
4.2.2 Galvanic corrosion ... 19
4.3 Mounting of components ... 19
4.4 Connection and sealing of cables... 20
4.4.1 ROV adaptation ... 20
4.4.2 Cable sealing ... 20
4.4.3 Placement of openings ... 21
4.5 Buoyancy of the substation ... 21
4.5.1 Using a flat lower end ... 21
5 Results... 22
5.1.1 Material ... 22
5.2 DBF calculation results... 22
5.2.1 Shell without stiffeners ... 22
5.2.2 Shell with stiffeners ... 23
5.2.3 Flat end... 24
5.2.4 Flanges ... 24
5.2.5 Nozzles... 25
5.2.6 Lifting eyes ... 27
5.2.7 Dimensioning for larger pressure... 28
5.3 FEM analysis results ... 28
5.3.1 FEM analysis of reinforcement for footings on the dished end... 28
5.3.2 FEM analysis of the bolted flat end ... 29
5.4 Buoyancy of the substation ... 31
6 Discussion ... 32
6.1 Summary of calculation results... 32
6.2 Design alternatives... 33
6.2.1 Placement of nozzles... 33
3
6.2.2 Lower end and foundation ... 33
6.3 Future development ... 34
7 Conclusions... 35
8 References... 36
Acknowledgements... 37 Assembly drawings of the vessel………...Appendix 1 Drawing of the flat end………..Appendix 2
4
1 Introduction
1.1 Background
A concept for generation of electricity from ocean waves is being developed at the division of electricity at Uppsala University. The concept is based on linear generators being driven by floating buoys that acts as point absorbers. A linear generator consists of a translator mounted with permanent magnets that moves vertically inside a stator.
The stator contains a three-phase coil winding and is placed in a water-tight housing, standing on the seabed. A point absorber is a buoy of small size compared to the average wave-length [1]. The buoy is connected to the translator of the linear
generator with a line. The waves set the buoy and translator in motion and voltage is induced in the stator winding. A point absorber connected to a linear generator is called a Wave Energy Converter, WEC, as seen in Figure 1.1.
Figure 1.1 Conceptual drawing of a wave energy converter, © Division of Electricity, UU
A general challenge for wave power technology is survivability. During storms, the average power level in waves can reach 50 times the overall power level [2]. The mechanical design of WECs must consider extreme weather conditions. In the wave power concept developed in Uppsala, most of the sensitive equipment is placed on the seabed and is in that way protected from the direct impact of waves.
Another advantage of this system is the mechanical simplicity. Many previous wave power concepts use standard generators [3]. This means that the slow motion of the waves must be mechanically converted to a fast rotating motion. In the concept
5 from Uppsala University, the generator is designed for the wave motion. The
mechanical energy conversion is minimized and instead the electric output is modified with power electronics. Standard electronic components can be used, that can be expected to need very little maintenance compared to a mechanical energy conversion system.
The electricity generated from a WEC will have a varying frequency, amplitude and phase order, dependent on the ocean waves [2]. This means that the electricity must be converted with power electronics before it can be used in the grid.
Transmitting the electricity from each WEC directly to shore in individual cables would lead to large losses because of the relatively high current and low voltage output from the linear generators. By transforming the electricity to higher voltage near the WECs, losses can be reduced. Conversion of the generated electricity to constant frequency AC and subsequent transformation to higher voltage, can take place in a Low Voltage Marine Substation, LVMS, placed on the seabed in the close vicinity of the WECs. A visualization of this concept can be seen in Figure 1.2.
Several WECs can be connected to one LVMS where the generated electricity from each linear generator is rectified. The combined DC is then inverted to 50 Hz AC before transformation to higher voltage. The output from the LVMS will be through a single three-phase AC cable.
Figure 1.2 Visualization of a wave power plant, © Seabased Industry AB
The electrical components in the marine substation must be protected from water. An effective method of avoiding water leakage is to have the gas pressure inside the marine substation slightly higher than the surrounding water pressure. This way any imperfection of the seals on the housing will result in gas leaking out while water is still prevented from leaking in. Leakage can be detected by monitoring the gas pressure or moisture content in the vessel. If the vessel is to be pressurized before installation on the seabed, the internal gas pressure will be several times higher than the atmospheric pressure and the vessel must be designed to withstand this high internal pressure. In case the vessel should for some reason loose the internal
6 overpressure before or during submersion, the design should also be able to withstand the external water pressure at the seabed.
Another alternative is to pressurize the vessel during the submersion. That way the maximum pressure difference between the in- and outside of the vessel can be limited to a much lower value than the water-pressure at the operational depth.
1.2 The Lysekil project
A project for testing and evaluating the wave power concept is currently taking place outside of Lysekil on the West coast of Sweden. The first wave energy converter was installed in 2006 and was connected to a measuring station on shore. Two more WECs and a Low Voltage Marine Substation, see Figure 1.3, are now installed. The plan is to install another seven WECs and one more LVMS. When everything is installed, the first LVMS and the seven new WECs will be connected to the new LVMS. The generated electricity from all ten WECs will be transmitted to shore through a single AC cable.
Figure 1.3 Pressure vessel for the first LVMS, the dished lower end with underwater connectors in front, © Division of Electricity, UU
1.2.1 ROV cable coupling
One large expense of the research project is the diving for the installation of
equipment under water. Diving also requires good weather which limits the time when it is possible to work. A solution to these problems is to use a remotely operated vehicle, ROV, for the work under water. This means that the equipment of the wave power plant, including the marine substations must be adapted to ROV operation. One task that ROVs could be used for is cable coupling. This requires that the connectors
7 on the substation are positioned so that they can be reached by the ROV. It might also be necessary to have an installation that allows the ROV to dock with the marine substation [4].
1.2.2 Installation and retrieval of marine substation
The marine substation and its concrete foundation will be lowered down to the seabed from a ship. For this it is necessary to consider how the lifting will take place. The first LVMS was designed with the lifting points on the foundation. The new LVMS will be designed with lifting eyes which will make the lifting procedure easier.
The submersion and elevation of LVMS at sea could be simplified if the
substation with the foundation has small positive buoyancy. That means the structure floats, but can be submerged by adding a relatively small amount of extra weight.
1.3 Aim of thesis
The aim of this thesis is to design the pressure vessel for the second low voltage marine substation in the Lysekil project. It will be placed on a depth of 25 m and have an internal pressure of 3 bar. If the vessel is to be pressurized before submersion, the regulations for pressure vessels must be followed when designing the housing.
The marine substation will have electrical inputs from seven wave energy converters. The size must be large enough to contain transformers and power
electronics for processing the electricity from the connected wave energy converters.
It will also have an AC input from the first LVMS, an AC output and a number of sensor equipment outputs. The connectors must be mounted in a way that is adapted for coupling with remotely operated vehicles. The marine substation should be designed to make the lifting and installation on the seabed as simple as possible.
2 Theory
2.1 Pressure vessel regulations
The European standard concerning unfired pressure vessels, EN 13445, is a part of the Pressure Equipment Directive (PED) prepared by the European Committee for
Standardization. In 2002, PED was given the status of national standard in Sweden, replacing the previous Tryckkärlsnormen. The Swedish version SS-EN 13445 is published by Swedish Standards Institute (SIS). The following parts have been used in this thesis:
• Part 1: General
• Part 2: Materials
• Part 3: Design
• Part 4: Fabrication
• Part 5: Inspection and testing
Limitations of EN 13445
The design rules in EN 13445 are primarily intended for non-cyclic loads, which means that the number of pressure cycles are lower than 500. For cyclic loads, methods for fatigue evaluation are given. EN 13445 applies to unfired pressure
vessels with maximum allowable pressure greater than 0.5 bar but can also be used for
8 lower pressures. It applies for maximum allowable temperatures where creep effects do not need to be considered. A number of applications are excluded from EN 13445, such as transportable pressure equipment, equipment for nuclear use, riveted vessels, pipelines etc.
2.2 Control and inspection regulations
The PED gives manufacturers the freedom to choose between many ways of
designing, manufacturing and inspecting pressure vessels, as long as they satisfy the requirements of the directive1. A notified body is an organization responsible for inspection, testing and certification of pressure vessels. It is allowed that the
manufacturer can carry out some inspection activities, though one of the criteria for that is a quality assurance system, approved and monitored by the notified body. A system of 13 modules determines which of the control activities can be carried out by whom, see Figure 2.2. The factors that determine which combination of modules to be used are: the hazard category of the pressure vessel, whether the manufactures have an approved quality assurance system and finally whether unit or serial production is carried out.
Hazard category of the vessel
The hazard categories I-IV are dependent on the fluid in the vessel, volume and maximum pressure [6]. Fluids are divided in two groups. Group 1 comprises
dangerous fluids that are explosive, flammable, toxic or oxidizing. Group 2 comprises any other fluids. A vessel designed for gases of group 2 is categorized by the diagram in Figure 2.1. The Figure shows that a vessel with volume over 1000 l and maximum pressure between 0.5 and 4 bar is of category III.
Figure 2.1 Hazard categories of vessels for gases of group 2 (non-dangerous fluids) [6]
1 Inspecta, The Directive for Pressure Equipment,
<http://www.inspecta.se/downloads/produktblad/158_Pressure_Equipment_Directive.pdf>
(2009-04-02)
9 Relevant modules of the PED
If design and manufacture are carried out as unit production, without an approved quality assurance system, and the pressure vessel is of category III, modules B1 (EC design examination) and F (product examination) are to be used [6]. However, it is also allowed to use a module from a higher hazard category but the category remains the same2. The equivalent for category IV is module G (EC unit verification). See Figure 2.2.
Figure 2.2 The control modules of the PED1
2The pressure equipment web-site of the European Commission,
<http://ec.europa.eu/enterprise/pressure_equipment/index_en.html> (2004-04-13)
10 The relevant modules (B1, F and G) states, among other things, that:
• The manufacturer must apply to a notified body for unit verification or an EC design examination. The application must include technical documentation to enable an assessment of the conformity of the pressure equipment with the PED.
• The notified body must examine the technical documentation with respect to the design and the manufacturing procedures, assess the materials, approve the procedures for the permanent joining of parts and carry out the final inspection and proof test.
• The notified body must affix its identification number and the manufacturer must affix the CE marking to the pressure equipment.
• EC design examination certificates or certificate of conformity with the PED issued by the notified body must be kept by the manufacturer for ten years and must be made available on request.
Testing groups and extent of non-destructive testing
The testing of pressure vessels is dependent on which testing group the vessel is designed for [5]. There are four groups and groups 1-3 are each divided into two sub groups. The testing group determines the allowed materials, maximum thickness, allowed welding process, service temperature range, joint coefficient and extent of non-destructive testing (NDT) of welded joints. Group 1 has the least limitations but requires the most extensive testing, while group 4 has the most limitations but requires the least testing. In group 4 generally no NDT is required, with very few exceptions.
When designing the pressure vessel, the testing group must be considered. If the material, maximum thickness, welding process and temperature range meets the requirements, it can be possible to place the vessel in a higher testing group, and less NDT is required. If that is the case, the joint coefficient to use must be adjusted to the testing group. The joint coefficient is 1 for group 1 and 2, 0.85 for group 3 and 0.7 for group 4. Lower joint coefficient means that the required thickness of shells will be larger for a given pressure.
Final assessment and proof test
A pressure vessel designed and manufactured according to EN 13445 has to be subjected to final assessment consisting of:
• Visual and dimensional inspection
• Examination of the documentation
• Proof test
• Examination after proof test
• Inspection of safety accessories
The proof test is normally a hydrostatic pressure test, since pneumatic testing is potentially much more dangerous. The proof test takes place after all fabrication and inspection have been performed, however operations that influence the inspection possibilities such as painting, lining, galvanizing etc. shall be carried out after the proof test examination. The test pressure shall be the greatest of:
t a s
t f
P f
P =1.25 [MPa] (1)
11 and
s
t P
P =1.43 [MPa] (2)
where Pt is the test pressure measured at the highest point of the vessel in test
position, Ps is the maximum allowable pressure, fa is the nominal design stress at test temperature and ft is the nominal design stress at maximum allowable temperature.
After the final assessment, the vessel shall be marked with direct stamping or a permanently attached nameplate.
2.3 Design of components
EN 13445-3 gives rules to be used for design of pressure bearing components, such as shells of various shapes, flat walls, flanges etc. For these components the Design by Formulae (DBF) method is generally followed. DBF means that formulas are given to find stresses which have to be limited to safe values. General prescriptions for Design by Analysis (DBA) are also given to evaluate designs not covered by DBF methods.
The following sections describe the DBF methods and basic equations for different pressure components given in EN 13445-3.
Conditions for the calculations
For non-austenitic steels (carbon steel is non-austenitic while stainless steel often is austenitic) the maximum allowed nominal design stress is as follows. For operation loads:
=
4 .
; 2 5 .
min R1p0.2/t Rm/20
f [N/mm2]. (3)
For test loads:
05 . 1
/ 2 .
0 t
p test
f = R [N/mm2]. (4)
For test conditions f is replaced by ftest in all equations in the following sections. The minimum 0.2%-proof strength Rp0.2 above can be replaced by the upper yield strength ReH if the former is not available in the material standard. The nominal stress shall be multiplied by 0.9 for testing group 4.
Explanation of thickness definitions:
e – required thickness en – nominal thickness
emin – thinnest possible manufacturing thickness ea – calculation thickness
c – corrosion addition
δe – absolute value of negative tolerance of nominal thickness δm – margin for thinning during manufacturing
eex – extra thickness up to nominal thickness
Relationships between thickness definitions are showed in Figure 2.3.
12
Figure 2.3 Thickness definitions for shells [4]
2.3.1 Cylindrical shells, internal pressure
The required thickness of a cylindrical shell subjected to internal pressure is given by
P z f
d
e P e
+
⋅
= ⋅
2 [mm], (5)
where de is the external diameter, P is the calculation pressure and z is the joint coefficient. For a given thickness the maximum internal pressure is given by
m a
d e z P = 2f ⋅ ⋅
max [MPa], (6)
where ea is the calculation thickness and dm is the mean diameter.
2.3.2 Cylindrical shells, external pressure
EN 13445-3 gives methods for verifying that the dimensions of a cylindrical shell are adequate to withstand a given external pressure. Both unsupported shells and shells reinforced with stiffeners are covered.
For unsupported shells the pressure where the mean ring stress reaches the yield strength is
m a
y r
P =σ ⋅e
[MPa], (7)
and the theoretical elastic instability pressure is
m a
m r
e
P = E⋅ ⋅ε [MPa], (8)
where σ is the normal stress, ea is the calculation thickness, rm is the mean diameter, E is the modulus of elasticity and ε is the mean value of circumferential elastic
stretching at collapse. The collapse pressure Pr is given by the experimentally
13 determined curve [7] in Figure 2.4, which shows Pr/Py as a function of Pm/Py. The condition
S
P< Pr [MPa] (9)
must be satisfied for the shell to withstand the external pressure P, where S is a safety factor.
Figure 2.4 Pr/Py plotted against Pm/Py. Curve 1 is for cylinders and cones, curve 2 is for spheres and dished end [4]
Shells can be reinforced by stiffeners which are rings welded to the shell on the outside or inside. Stiffeners are categorized as light or heavy. A light stiffener is e.g. a flat ring and a heavy stiffener can be a flange. For light stiffeners calculations must be made considering interstiffener collapse, elastic instability and maximum stress in the stiffener. The calculation of interstiffener collapse is for large diameters exactly the same as the calculation of unsupported shells above, but using the distance between the stiffeners as the unsupported length. The calculation of elastic instability is made to ensure that the external pressure is lower than the elastic instability pressure which is the sum of the pressure from the stiffener and a certain length of the shell.
Calculations are also made to ensure that the maximum stress in the stiffener is lower than the nominal elasticity limit of the material.
For heavy stiffeners equivalent calculations are made but only for the stiffener itself, independent of the support from the shell. This means that more material is needed but the calculations are simpler.
14 2.3.3 Dished ends, internal pressure
A torishperical end is a type of dished end which consists of a central part with internal radius r1 and a torodial knuckle with internal radius r2, see Figure 2.5. A korbbogen end is a torishperical end where r1/de=0.8 and r2/de=0.154.
Figure 2.5 Geometry of a torishperical end
For a given geometry the maximum internal pressure shall be the lowest of:
a a
ds r e
e z P f
5 . 0 2
1+
⋅
= ⋅ [MPa], (10)
) 2 . 0 75 . 0
( 1 i
a
dy r d
e P f
+
= ⋅
β [MPa], (11)
and
825 . 0 2 5 . 1
1 0.2 75
.
111 0
= +
i i
a b
db d
r d
r f e
P [MPa], (12)
where
5 . 1
/ 2 .
0 t
p b
f = R [N/mm2], (13)
ea is the calculation thickness and di is the internal diameter. The factor β can be determined by iterative calculations and is dependent on ea/r2 and r2/di.
2.3.4 Dished ends, external pressure
The dimensions of torisherical ends subjected to external pressure is verified the same way as unsupported cylindrical shells with the differences that
e a
y r
P = 2σ⋅e
[MPa] (14)
and
15
2
21 2
. 1
e a
m r
e
P = E⋅ [MPa], (15)
where ea is the calculation thickness and re is the external diameter.
2.3.5 Flat ends
The required thickness of a circular welded flat end is calculated by
f d P A
ewelded = ⋅ i [mm], (16)
where di is the internal diameter of the shell and A is a form factor dependent of geometry, stress limits, pressure and fatigue situation of the connection between the flat end and the shell. If the vessel is subject to non-cyclic loads the required thickness will be considerably smaller than for cyclic loads [7].
The required thickness of a bolted flat end with a full face gasket is calculated by
f C P
ebolted =0.41 [mm], (17)
where C is the bolt circle diameter. The required thickness of the flange area is given by
bolted
flange e
e =0.8 [mm]. (18)
2.3.6 Flanges
A number of different flange designs are covered in EN 13445-3. Narrow face flanges have the gasket inside of the bolt circle and have no contact between the sides of the flange outside the bolts. Full face flanges have contact of the sides over the entire flange surface.
If a flange has a compressible gasket, both sides of the flange are separated from each other by the gasket. The compression of the gasket, which determines its sealing ability, is dependent on the force from the bolts [8]. If a flange has an o-ring sealing the sides of the flange have metal-to-metal contact and the compression of the gasket is not dependent on the bolt force. An o-ring sealing is placed in a groove in one of the flange sides. The surface finish in the groove is critical for the sealing ability of the o-ring.
A distinction is made between flanges where the inner diameter of the flange is the same as the inner diameter of the shell, which is called smooth bore and flanges where the diameters differ, called stepped bore. The connection between the flange and the shell can be in form of a machined taper hub, otherwise fillet welds are normally used. Different types of flanges are shown in Figure 2.6.
The required thickness of a full face flange with metal-to-metal contact is
(
h)
R
d n C f e M
⋅
= − π
6 [mm], (19)
16 where MR is the balancing radial torque in the flange at the bolt circle, dependent of the dimensions of the flange and the internal pressure, C is the bolt circle diameter, n is the number of bolts and dh is the diameter of the bolt holes
Figure 2.6 Cross-sections of three different types of flanges
2.3.7 Openings
Openings in shells often require that the area around the opening is reinforced to compensate for the reduction of the pressure bearing section. The reinforcement can consist of a nozzle, a ring in the opening, a plate on the shell or increased thickness of the shell around the opening. One method of reinforcement is to use nozzles. A set-on nozzle is a piece of pipe placed on the hole and welded to one side of the shell. A set- in nozzle is placed in a hole and welded to both sides of the shell. The method used in EN 13445-3 is called the pressure-area method. It is based on verifying that the reactive force from the material in the reinforcement is equal or grater than the load from the pressure. The reactive force from the material is the sum of the product of the average membrane stress in each component and its stress loaded cross-sectional area. The load from the pressure is the sum of the product of the pressure and the pressure loaded cross-sectional areas.
The general equation for the reinforcement of an opening is
( )( ) ( ) ( )
(
Ap Ap Apϕ)
P
P f
Af P f
Af P f
Af Af
b s
ob b op
p s
w s
⋅ + +
≥
⋅
− +
⋅
− +
⋅
− +
5 . 0
5 . 0 5
. 0 5
.
0 (20)
where fob=min(fs;fb) and fop=min(fs;fp).
The terms in the equation above are defined as following:
Af refer to stress loaded cross-sectional areas effective as reinforcement Ap refer to pressure loaded areas
The following subscripts apply to the terms above:
b – a nozzle
p – a reinforcement plate s – the shell
φ - additional pressure loaded area for an oblique nozzle connection
17 Some of these symbols are explained in Figure 2.7.
Figure 2.7 Cross-section of a set-on nozzle showing pressure- and reinforcement-areas [4]
2.3.8 Lifting eyes
The method for calculation of shells subject to local line loads can be directly applied to lifting eyes without reinforcing plates. Lifting eyes with reinforcing plates can be calculated as a superposition of local line loads. The force acting on the lifting eye is calculated and compared to the maximum allowed forces on the shell in longitudinal and circumferential direction.
3 Method
Most of the pressure vessel components have been dimensioned using DBF methods given in SS-EN 13445-3. MATLAB have been used for the calculations. Individual MATLAB programs have been written for each of the sections of SS-EN 13445 that have been used. In comparison with manual calculations this gives the possibility to alter the input values in a much easier way. Iterative calculations can also be made very easily.
For design and creation of drawings the 3D CAD software SolidWorks have been used. 3D models have been created with dimensions from the DBF calculations and from drawings of the pressure tank which the design is based upon, discussed further in Section 4.1. FEM analysis on the 3D models has been performed using
SolidWorks Simulation.
4 Conditions for the design
Some design features used on the first LVMS are very basic and also applies to the second LVMS. The pressure vessel must have an opening large enough to install the components inside. To minimize the potential damage if water leakage should occur, all openings should be as close to the bottom end as possible. The most obvious way
18 to achieve this is to design the pressure vessel as a vertical cylinder where the bottom end is removable. The openings for cables can be placed either on the removable lid or on the lower part of the cylindrical shell. The ends of the cylinder can be dished or flat; tough a flat end would have to be considerably thicker and heavier to withstand the pressure. The pressure vessel will be attached to a concrete foundation. It must be big enough to stand stable on the sea floor considering the buoyancy of the vessel.
4.1 Manufacture of the vessel
The design of the pressure vessel will be based on a pressure tank manufactured by Maschinen und Behälterbau GmbH (MABE) in Germany and retailed by Esska teknik in Sweden. The reason for this is economical; to buy a mass-produced vessel and then modify it will be cheaper than to manufacture a single customized vessel. The
standard pressure tanks from MABE are available as both horizontal and vertical models in sizes from 50 to 10000 liters. The tanks have dished end of korbbogen type.
The vertical 5000 liter model is available with diameter 1400 and 1600 mm. The need for space in the marine substation has been evaluated and the 5000 liter model with diameter 1600 mm has been selected as the most suitable. All MABE tanks are available as models designed for a maximum pressure of 11 or 16 bar. The less expensive 11 bar model will be used as both will have a wall thickness more than sufficient for the marine substation.
The MABE tank has four footings on the bottom end. These could be used to attach the tank to the foundation. Some reinforcement might be needed as the footings are not dimensioned for the drag force they will be subjected to when the substation is lifted. Another alternative is to mount the foundation with longer beams attached to the side of the cylindrical shell. The tank also has lifting eyes but they are
dimensioned for lifting only the empty tank and will probably be too weak for lifting the substation with its foundation.
The MABE tanks are fitted with connection sockets for use with compressed air and a manhole. These features will not be needed on the marine substation. The bottom dished end will also have to be separated from the rest of the shell. The choice will be to either order a tank without these features or to order a standard tank and then modify the unneeded features while the other necessary modifications are made.
The latter alternative will involve some unnecessary work but which alternative is the most inexpensive is not obvious since a specially ordered tank will result in a higher price.
4.2 Protection against corrosion
Being submerged in seawater, the substation will be exposed to a very corrosive environment. Protection from uniform corrosion and galvanic corrosion must be considered.
4.2.1 General corrosion
General corrosion means that a metal surface reacts with water and forms iron oxide, also known as rust. The reaction occurs uniformly over the entire surface and results over time in decreased thickness of the material. General corrosion can be avoided by coating the surface e.g. by painting or choosing a corrosion-resistant material. The material choice must however also consider the conditions for galvanic corrosion.
19 4.2.2 Galvanic corrosion
Galvanic corrosion occurs when two electrochemically dissimilar metals are in contact and surrounded by an electrolyte. The difference in electric potential will result in a current flow trough the electrolyte. The metal with the higher potential will act as the anode and corrode faster, while the metal with lower potential will act as the cathode and corrode slower. The rate of galvanic corrosion on the anode can be much higher than the general corrosion rate.
Electric potentials can be compared with an anodic index; lower index means that the metal is nobler. Some examples of anodic index for different metals are seen in table 4.1.
Table 4.1 Anodic index for various metals3
Metal Anodic index [Volt]
Gold 0
Brass 0.40-0.45
Stainless steel 0.50-0.60 Plain carbon steel 0.85
Zinc 1.25
Magnesium 1.75
The rate of corrosion is also dependent of the areas of the metals. Small anodic area and large cathodic area means the corrosion rate on the anode will be higher. For this reason, small details such as bolts and nuts should never be of a less noble metal than the rest of the structure [9].
One way of avoiding galvanic corrosion is to use metals with similar potential.
For a salt water environment the difference in anodic index should be less than 0.15 V
3. The pressure vessel steel used for the substation is a plain carbon steel and can therefore not be allowed to have contact with i.e. stainless steel or brass, while simultaneously having contact with water. Other ways to avoid galvanic corrosion is to either isolate the metals from each other or isolate the metal from the electrolyte.
So-called cathodic protection means that sacrificial anodes of metal with high electric potential, e.g. zinc, are used [9]. The sacrificial anodes are in contact with the electrolyte and attached in a conducting way to the structure. The anodes will then corrode while the rest of the metal in the structure will be protected.
The protection against galvanic corrosion applies to the design of the substation in a number of ways. One example is the choice of material in the cable glands
(discussed further in section 4.4.2), which are available in brass, stainless steel or plastic. The two metals both have lower electric potential than the steel in the shell.
This means that the corrosion rate of the shell would be increased. It would be
difficult to isolate the cable glands from the shell or from the water so the best choice with aspect to corrosion is to use plastic cable glands. The vessel will also be painted with several layers of anti-corrosive paint and sacrificial anodes of zinc will be attached to the outside of the shell.
4.3 Mounting of components
The electrical components can be mounted either on the inside of the shell or on a frame placed inside the vessel. In the first LVMS, the components are mounted on flat
3 Engineers Edge, Galvanic Corrosion,
<http://www.engineersedge.com/corrosion/galvanic_corrosion.htm> (2009-06-05)
20 steel plates welded to the inside of the cylindrical shell. This concept will be used and further developed in the new LVMS. The components with high losses should be in direct contact with the shell to get sufficient cooling. The internal structure must be designed so that these components will have a large contact area with the inside of the cylindrical shell. Other components with less need for cooling can be mounted on an external structure that is inserted into the vessel.
4.4 Connection and sealing of cables
4.4.1 ROV adaptation
The LVMS must be adapted to the use of ROVs for cable coupling. This means that the type of connectors to be used as well as their placement must be considered. On the first LVMS the connectors are placed on the lower dished end, normal to the shell.
This means that they all have an individual angle which makes it difficult for a ROV to reach them. Mounting the connectors directly on shell of the pressure vessel is then not a good alternative. Having the connectors placed horizontally with the same angle is a less problematic set-up for cable coupling with an ROV [4].
It has been decided that the connectors will be mounted on one or several plates, placed on the foundation or on the vessel shell. The sealing and the connector for each cable will then be separated. This solution is flexible since the ROV adaptations only have to consider the connector plates and not the pressure vessel itself.
4.4.2 Cable sealing
The sealing of the WEC input cables and the sensor equipment cables will consist of cable glands screwed into the nozzles, see Figure 4.1. Cable glands rated IP68, which means waterproof up to a pressure of 15 bar, are available in different materials and for different diameters of cables4. Available cable glands with an outer connection thread M40 and a sealing range for cables of diameters 20-32 mm would be suitable for the cables mentioned above. The nozzles will also be filled with a sealing
compound to give extra protection against leakage. For the AC input from the first LVMS and the AC output, thicker cables might be necessary. How the sealing around these thicker cables will be designed has not been decided, but a maximum inner diameter of 70 mm for the nozzles has been specified.
This means that two sizes of nozzles must be designed. At least 20 nozzles with inner diameter 40 mm will be needed for the WEC and sensor cables, and two nozzles with inner diameter 70 mm for the AC in- and outputs.
4 Pflitsch blueglobe cable gland, <http://www.pflitsch.de/en/produkte/blueglobe/pa.htm>
21
Figure 4.1 Disassembled cable gland4
4.4.3 Placement of openings
The cable openings can be placed either on the bottom end or on the lower part of the cylindrical shell. The main advantage of openings on the lower end is that the level of potential leakage is as low as possible since the openings will be below the flange.
The disadvantage is that the closing and opening of the lid will be more complicated since the cables go through it. Placing the openings on the cylindrical shell means that all components and sealing around cables can be mounted independently of the lid and shorter cables can be used. The disadvantage is that the higher level of potential leakage means that the space available for mounting components safely will be smaller.
4.5 Buoyancy of the substation
The pressure vessel has a volume of around 5 m3 and the weight of the vessel
including the internal components will be much less than 5 tonnes, so the vessel will have positive buoyancy, it will float. The weight of the concrete foundation must give negative buoyancy enough to make the substation stand steadily on the sea floor. The needed mass of the concrete foundation to give zero buoyancy can be calculated by
−1
⋅
= −
concrete water
vessel water vessel
concrete
V m m
ρ ρ ρ
[kg]. (21)
It would be suitable to give the foundation a weight that gives the entire substation a positive buoyancy of a few hundred kilos. Adding this relatively small weight will submerge the substation. This makes it possible to submerge and elevate the LVMS without the need for a ship with a large crane.
4.5.1 Using a flat lower end
If the cable openings are placed on the cylindrical shell, the space inside the lower dished end will be unused. An alternative design could then be to use a flat lower end.
A flat end would have to be much thicker than a dished end to withstand the pressure, but for the relatively low design pressure, it could be a viable solution. The advantage would be a smaller volume and larger weight of the vessel, which means less
buoyancy and that the overall weight of the vessel with its foundation could be lower.
If a flat end is used there is no need for footings underneath it and the vessel could be bolted directly to the foundation outside of the flange.
22
5 Results
This section presents calculation results for different pressure vessel components to be used in the design of the LVMS. An overview of the components can be seen in Figure 5.1. All calculations have been made according to DBF methods in SS-EN 13445. Some FEM analysis results for components not covered by DBF methods are also presented.
Figure 5.1 Overview of pressure vessel components for two possible design alternatives
5.1.1 Material
All components are calculated to be constructed of pressure vessel steel P265GH with the following specifications:
Material number 1.0425 according to European standard EN 10028-2 Reh = 265 N/mm2
Rm = 410 N/mm2 E = 212 GPa ν = 0.3
The material will not be subjected to high temperatures that significantly affect the strength during operation.
5.2 DBF calculation results
5.2.1 Shell without stiffeners
Calculations have been made to find the maximum internal and external pressure for the given geometry. The maximum internal pressure must be higher than 0.3 MPa for operating conditions and higher than 0.45 MPa for test conditions. The maximum external pressure must be higher than 0.3 MPa.
23 The data for the geometry is taken from a drawing supplied by MABE. A
corrosion allowance of 1 mm and a thinning allowance of 0.4 mm have been considered for the shell calculations. The joint factor z = 0.7 have been used which give the most conservative results and allows the vessel to be placed in testing group 4 for the inspection.
Stress limit for operating conditions is according to Eq. 3: f = 0.9×Rm/2.4 = 153.8 N/mm2
Stress limit for test conditions is according to Eq. 4: ftest = Reh/1.05 = 252.4 N/mm2 Geometry of the cylindrical shell
• External diameter de = 1600 mm
• Nominal thickness en = 7.1 mm
• Calculation thickness ea = 5.7 mm for operating conditions and ea = 6.7 mm for test conditions
Geometry of the torishperical ends
• External diameter de = 1600 mm
• Internal large radius r1 = 1280 mm
• Internal knuckle radius r2 = 246.4 mm
• Nominal thickness en = 6.8 mm
• Calculation thickness ea = 5.4 mm for operating conditions and ea = 6.4 mm for test conditions
The calculated maximum allowable internal and external pressures for the
unsupported shell are shown in Table 5.1. The results show that the cylindrical shell must be reinforced to withstand the required external pressure.
Table 5.1 Calculation results, maximum allowable pressures for the unsupported shell Internal
pressure [MPa], operating
conditions
Internal
pressure [MPa], test conditions
External
pressure [MPa], operating conditions
External
pressure [MPa], test conditions Cylindrical
shell
0.77 2.12 0.11 0.15
Dished end 0.89 1.77 0.48 0.66
5.2.2 Shell with stiffeners
Suitable stiffeners have been designed by testing different geometries. The maximum allowable pressures must be larger than 0.3 MPa and the stress in the rings must be lower than the yield strength 265 N/mm2.
The chosen design uses two rings on the outside of the shell. The unsupported length is the distance from the flange at the bottom end, which can be considered a heavy stiffener, and the dished end at the top. The lower 2/5 of the dished end height of 430 mm is considered unsupported.
24 Geometry of the stiffeners
• Axial height 10 mm
• Radial width 55 mm
• Unsupported length between stiffeners 658.3 mm
• External diameter of shell de = 1600 mm
• Calculation thickness of shell ea = 5.7 mm
The calculation results in Table 5.2 show that this geometry reinforces the shell enough for the external pressure.
Table 5.2 Calculation results, maximum allowable external pressures for reinforced shell, and stresses in the rings
External pressure to avoid collapse between rings [MPa]
External pressure to avoid elastic instability [MPa]
Stress in rings[N/mm2]
Operating Test Operating Test Operating Test
0.36 0.50 1.59 2.16 235 167
5.2.3 Flat end
Calculations have been made to find the required thickness of a bolted flat end to be used instead of the lower dished end of the pressure vessel.
Section 10 in SS-EN 13445-3 covers bolted flat ends with narrow- and full face gaskets but not o-ring gaskets. Required thickness of flat end bolted to a full face flange with a soft gasket covering the entire surface can be calculated with Eq. 17. A bolt circle diameter C = 1680, gives a required thickness of e bolted = 28.9 mm. The required thickness of the flange part will then be 0.8 × e bolted = 23.1 mm and this lower thickness must be limited to a region outside of a circle with diameter 1176 mm.
5.2.4 Flanges
Calculations have been made for full face flanges both with o-ring sealing and with soft gasket covering the entire surface. In both cases the flange is bolted with 32 M24 8.8 bolts. The flanges have stepped bore, no tapered hub and are welded to the outside of the shell. The o-ring diameter is 10 mm.
Figure 5.2 Geometry of a flange with o-ring groove
25 Geometry of flanges
• Outer flange diameter 1760 mm
• Inner flange diameter 1600 mm
• Bolt hole diameter dh = 26 mm
• O-ring groove mean diameter 1630 mm
• Depth of o-ring groove 8.4 mm
• Width of o-ring groove 13.5 mm
For the soft gasket flange the required thickness is to a large extent dependent of the gasket factor m and minimum seating pressure y. The lower values of the gasket factors in Table 5.3 is for soft rubber with hardness below 75° IRH (International Rubber Hardness Degrees), and the higher values is for rubber above 75° IRH, values are taken from table H.1 in SS-EN 13445-3.
Table 5.3 Calculation results, required thickness of flanges Chosen bolt circle
diameter C [mm]
Minimum thickness [mm] Chosen thickness, e [mm]
m=0.5,y=0 m=1,y=1.4 Gasket covering
entire surface
1680
19.2 28.8
30
O-ring sealing 1694 17.0 20
5.2.5 Nozzles
Calculations have been made to find sufficient dimensions to give enough
reinforcement for the nozzles placed on either the dished end or the cylindrical shell.
The quota Pressure area / Reinforcement area (R/P) have been calculated according to the Pressure area method described in Section 2.3.7, both for single and multiple nozzles. For single nozzles the maximum internal pressure has also been calculated.
For nozzles placed on the cylindrical shell calculations must be made for both the transverse and longitudinal cross-section, while all directions are symmetrical for a spherical shell.
The calculations also consider how the reinforcement area is affected by the distance between the nozzles and the distance to discontinuities in the shell. For the dished end, the distance to a discontinuity is the distance to a circle 0.8 × the external diameter. For the cylindrical shell the distance to a discontinuity is the distance to the flange and the calculations assume the shortest allowed distance to the flange, which is 20 mm for the given geometry. For the calculation of multiple large nozzles, the closest surrounding nozzles are assumed to be large, which is a conservative assumption since the small nozzles give more reinforcement.
The distances between the nozzles and the distances to the discontinuities on the dished end have been calculated assuming that the nozzles are placed in four rows as in Figure 5.3.
26
Figure 5.3 Placement of nozzles on the dished end
On the cylindrical shell the nozzles are placed between the bolt holes in the flange.
This means that there is room for 32 nozzles around the perimeter of the shell and the distance between the nozzles will be 157 mm.
All nozzles are of set-on type, welded only to the outside of the shell. The length of the nozzles is the maximum length that contributes to the reinforcement for the given diameters. Making the nozzles longer will not give more strength but longer nozzles could be preferable if they are to be filled with sealing compound.
Geometry for small nozzles
• Outer diameter 50 mm
• Inner diameter 40 mm
• External length 15 mm Geometry for large nozzles
• Outer diameter 80 mm
• Inner diameter 70 mm
• External length 25 mm
The calculation results in Table 5.4 and Table 5.5 shows that this geometry gives enough reinforcement.
Table 5.4 Calculation results, reinforcement from nozzles on dished end R/P single
nozzle
Pmax[MPa] R/P multiple nozzels
Small 4.5 1.3 4.4
Large 4.2 1.3 4.0
Table 5.5 Calculation results, reinforcement from nozzles on cylindrical shell R/P single nozzle
transverse
Pmax [MPa], transverse
R/P single nozzle longitudinal
Pmax [MPa], longitudinal
R/P multiple nozzles
Small 7.7 2.3 3.6 1.1 7.4
Large 7.0 2.1 2.8 0.8 6.2
27 5.2.6 Lifting eyes
Lifting eyes have been designed to lift the entire marine substation vertically and to lift the vessel without the foundation horizontally. The critical aspect of the
dimensioning of lifting eyes is to limit the local loads on the shell. The problem is the strength of the shell, not the strength of the lifting eyes themselves. Reinforcement plates placed between the shell and the lifting eyes can be used to distribute the force and torque over a larger area of the shell.
The four lifting eyes on top of the vessel are dimensioned for lifting a total mass of 10 tonnes vertically. One of the lifting eyes on the side combined with one of the lifting eyes on top are dimensioned for lifting 4 tonnes horizontally.
Figure 5.4 Angles of forces on lifting eyes, w1-w3 are angles to the direction of the weight, β1- β3 are angles to the normal of the shell, distances in mm
Figure 5.4 shows assumed angles when lifting the substation in vertical and horizontal direction. Increasing angles will increase the actual forces but will also increase the allowed forces.
Figure 5.5 Dimensions of lifting eyes [4]
28 Geometry of lifting eyes
• Thickness of reinforcement plate e2 = 10 mm
• Length of reinforcement plate b3 = 320 mm
• Width of reinforcement plate b2 = 80 mm
• Length of lifting eye b1 = b3/1.5 = 213.3 mm
• Distance from load to reinforcement plate a2 = 50 mm
• Eccentricity of load a1 = 40 mm
The geometry is explained in Figure 5.5 and the calculation results presented in Table 5.6 show that these dimensions are adequate.
Table 5.6 Calculation results, force per lifting eye
Maximum allowed force FR,max [kN]
Actual force FR [kN]
Lifting eyes on top, vertical lift 29.1 26.0 Lifting eye on top, horizontal lift 46.9 22.0 Lifting eye on side, horizontal lift 26.7 23.7
5.2.7 Dimensioning for larger pressure
In the future it might be necessary to place marine substations at greater depths than 25 m. If this pressure vessel concept is to be used for the housing, the internal pressure would have to be larger. For this reason the possibility to dimension this vessel for a pressure of 6 bar have been briefly investigated.
The cylindrical shell and dished ends would withstand 6 bar internal pressure without modification. The nozzles could be made slightly thicker, which would not present any problems. If the vessel is to hold up an equivalent external pressure, the cylindrical shell can be designed with more and stronger stiffeners. The dimensions of the dished end would cause some problems since it will only withstand an external pressure of 4.8 bar. Some kind of reinforcement would be needed, however EN 13445 contains no DBF methods for reinforcement of dished ends.
The required thickness of both the flanges and the flat end is proportional to the square-root of the pressure and this gives a required thickness of around 22 mm for the flange and 41 mm for the flat end. The flange would have to be bolted with 42 – 44 bolts if type M24 8.8 is used.
5.3 FEM analysis results
5.3.1 FEM analysis of reinforcement for footings on the dished end The footings on the lower dished of the MABE tank are intended for supporting the vessel when standing upright. If the foundation is mounted to the footings they will be subjected to a drag force when the substation is lifted and this means that the shell might have to be reinforced. According to EN 13445, reinforcement of footings should be made with plates, similar to the way lifting eyes are reinforced. It is also stated that footings should be placed on the large radius region of the dished end, but the footings on the MABE tank are placed partly on the knuckle region. This means that the footing would have to be moved if the DBF method for reinforcement is used.
29 FEM analysis of an alternative reinforce method have been performed. The shell is reinforced by welding supports to the in- and outside, as shown in Figure 5.7. To reduce the number of elements, only one quarter of the lower part of the vessel has been simulated. Because the vessel has four footings, symmetry constraints can be used.
Figure 5.6 Stress plot of dished end with 25 mm flange. Internal pressure 3 bar and a force of 15 kN applied downwards on the footing. The plot shows high stress on the knuckle region above the footing.
Figure 5.7 Stress plot of the same conditions as in Figure 5.6 but with reinforcements on both sides of the shell. The stress above the footing is reduced to approximately the same level as in the surrounding shell.
5.3.2 FEM analysis of the bolted flat end
A bolted flat end in combination with o-ring sealing is not covered by the DBF methods in EN 13445. FEM analysis of the flat end has been performed to compare the stress levels between the o-ring option and the full face gasket option. Based on the calculations in section 5.2.3 and 5.2.4, a flat end and flange both of thickness 30
30 mm would be sufficient for an internal pressure of 3 bar, so this scenario has been investigated with FEM analysis.
To reduce the number of elements in the simulation, only a section of 1/32 of the vessel has been modeled, since the flange has 32 bolts which make it possible to use symmetry constraints. Also only short portion of the cylindrical shell is modeled, since the high stress on the shell will emerge close to the flange.
Figure 5.8 Stress plots showing a section of a flat end with an o-ring groove bolted to a flange on a cylindrical shell. The internal pressure is 3 bar. The flat end is in direct contact with the flange outside of the o-ring groove which results in high stress in the shell above the flange. The lower plot has exaggerated deformation.
Figure 5.8 shows a flat end with a o-ring groove bolted to a flange on the cylindrical shell. An internal pressure of 3 bar on the flat end and shell is applied. A bolt load from a M20 bolt is simulated in the hole. The o-ring itself is not simulated, but this will not influence the results very much, since it would not contribute with any significant force in the rest of the structure. When the flat end is subjected to internal pressure it deforms. Since the flange is in direct contact with the flat end, torque is transferred to the flange and it bends upwards. This means that the thin shell is also deformed and results in unacceptable high stress in the shell.
