paraphrasing
jhh19970724
file.pdf
MACE43001/MACE 61057: Structural Integrity Lecturers: Dr. KB Katnam & Prof. Q. Li
Page 1 of 8
COURSEWORK: Structural Integrity IMPORTANT INFORMATION Course Unit: Structural Integrity Course Unit Code: MACE43001 / MACE61057 Course Co-ordinator: Dr. KB Katnam Course Lecturers: Dr. KB Katnam & Prof. Q. Li Submission date: The deadline for submission is 18:00, 24 Mar 2020 (Week 9) Submission type: Blackboard submission Late submissions: Penalties will apply for late coursework submissions (10% reduction
per day up to one week; 0 marks for more than one week) Assessment: 20% weightage in the final unit score Coursework feedback: During lecture hours in Week 11
ACADEMIC MALPRACTICE
Academic Malpractice can result from a deliberate act of cheating and may be committed
unintentionally. Academic malpractice can take many different forms. Plagiarism is only one
example. The University defines plagiarism as, presenting the ideas, work or words of other people
without proper, clear and unambiguous acknowledgement. There are University guidelines on
avoiding plagiarism and other forms of academic malpractice such as; collusion or the fabrication
or falsification of data that are explained in, The University of Manchester Guidance To Students
on Plagiarism and Other Forms of Academic Malpractice, from the Teaching and Learning Support
Office;
http://www.tlso.manchester.ac.uk/map/teachinglearningassessment/assessment/sectiond-
theprocessofassessment/academicmalpracticeincludingplagiarism/
Academic malpractice is taken seriously by the University and further information on plagiarism can
be found in the ‘School of MACE, Undergraduate/Postgraduate Course Handbook’ which you
received during Welcome Week.
To help you avoid plagiarism, the University Library has a number of resources on the Library
Website: http://subjects.library.manchester.ac.uk/referencing
MACE43001/MACE 61057: Structural Integrity Lecturers: Dr. KB Katnam & Prof. Q. Li
Page 2 of 8
DESIGN OF PENSTOCK PIPE FOR A HYDROELECTRIC PUMPED STORAGE STATION
SYNOPSIS
The task posed in this case study is to choose between two candidate steels for the construction of pressure pipes within a hydroelectric pumped storage power station. Having selected the steel, you are required to specify the wall thickness of the pipe given the internal pipe diameter, load history, design life and non-destructive inspection limitations. Each student will have a different set of parameters to work with. You are required to write a report, which should include the design decision you have made with full justification and also your recommendations on inspection intervals. PUMPED STORAGE POWER STATION
What is pumped storage?
Hydro-electric power stations use water falling from a high-level source to produce electricity. The water drives turbines which, in turn, drive the generators that produce the electricity. A pumped storage power station differs from a normal hydro-electric station because it has two reservoirs and uses the same water again and again. After driving the turbines the water is pumped from the lower reservoir back to the upper reservoir ready to be used again when needed. In some pumped storage schemes, the turbines and pumps are separate machines but at others the turbine-generators will work in reverse, as motor-pumps, to return the water to the top reservoir, powered by electricity from the national grid.
Why is pumped storage need?
Electricity cannot be stored in large quantities but the electricity supply companies must have a large, quickly available reserve of power to meet sudden increases in demand on the national grid and to safeguard the nation's electricity supplies in the event of major failure of generating/transmission plant. In the UK this 'immediate reserve' is normally provided by operating coal and oil-fired power stations at below their full economic capacity so that their output can be increased quickly to meet additional demand when required. They are supported by gas turbine stations operating for short periods while output from bigger steam stations is increased. Pumped storage schemes, in effect, use water to store electrical energy. Electricity is used to pump water to the high reservoir. This is done mainly at night when demand for electricity is low and electricity for pumping is, therefore, cheaper, being provided by the most efficient, base-load power stations. Hydro-electric pumped storage stations can be brought into operation much more quickly and reliably than other types of stations. For instance, the pumped storage station at Dinorwig in North Wales (see Figures 1 & 2) can be brought on-line to reach an output of 1320 MW in 10 seconds. Pumped storage stations help to meet peak demands in the winter when the grid system is called upon to produce the greatest amount of electricity. It also helps to meet sudden surges in demand that occur throughout the year (such as those created at the end of popular television programmes as millions of people switch on electric kettles to make cups of tea or coffee). In the future, pumped storage schemes may play a valuable role in smoothing out the unpredictable electricity generation of on- and off-shore wind turbines.
MACE43001/MACE 61057: Structural Integrity Lecturers: Dr. KB Katnam & Prof. Q. Li
Page 3 of 8
Figure 1: A pumped-storage power station at Dinorwig in North Wales (Courtesy: Google Maps)
Figure 2: A schematic of the pumped-storage hydro-electric station at Dinorwig in North Wales*
Marchlyn Mawr
MACE43001/MACE 61057: Structural Integrity Lecturers: Dr. KB Katnam & Prof. Q. Li
Page 4 of 8
DESIGN PROBLEM
This concerns the design of the steel pipes that deliver water from the reservoir to the turbines. Specifically, we are interest in the intermediate penstocks (see Figure 3) as these pipes are not supported by surrounding rock and concrete, and consequently they have to be able to withstand the full loading of the water pressure throughout the design life of the system.
Figure 3: Illustration of intermediate penstocks*
The penstocks must last for 50 years. It is envisaged that the inside wall will be stripped and repainted every 5 years, and also will be repaired if cracks > 15 mm in size are found. The range of sizes under consideration is 2.0 to 2.6 m internal diameter. You will be given a specific diameter for your case study. As critical load-bearing components, the penstocks will be subjected to non- destructive ultrasonic testing and inspection after fabrication and during service. The range of detectable crack sizes under consideration is 2.0 to 6.0 mm depth. NOTE: You will be given a specific crack size for your case study (the individual parameters are given on Blackboard). The penstocks are loaded hydraulically. The largest possible transient pressure is due to a 'water hammer' effect which could occur under an unlikely coincidence of certain machine trip conditions, which will be referred to as the 'fault condition'. This fault condition will, hopefully, never occur, but we must design the penstock so that it will survive this fault condition if it did occur at any time in the 50 year operation of the power station. The range of pressure transients under consideration is 700 to 775 m head of water. NOTE: You will be given a specific head height for your case study (the individual parameters are given on Blackboard).
MACE43001/MACE 61057: Structural Integrity Lecturers: Dr. KB Katnam & Prof. Q. Li
Page 5 of 8
Changes in water pressure occur during operation of the system. When the station changes from pumping to generating, or vice versa - a 'mode change', the main inlet valve is closed, the pressure in the penstock falls to zero, and valve is re-opened to allow water to flow in the opposite direction. The intermediate penstock is therefore subjected to a pressure change. This is expected to occur 7500 times each year. The range of pressure changes under consideration is 0 to 500, 525, 550 or 575 m head of water. NOTE: You will be given a specific pressure change for your case study (the individual parameters are given on Blackboard). In addition, there will be residual stresses in the pipe that arise from the localised heating and cooling during welding. A post weld heat treatment will be carried out to reduce these stresses, but you should assume that a local stress of 70 MPa remains around the welds. The hoop stress due to the water pressure must not exceed 60% of the yield stress of the material under any loading conditions at any time in the life of the power station. Examples of cracked penstocks in service or from proof test loading are shown in Figures 4 & 5.
Figure 4: A longitudinal brittle failure of a penstock at a hydro-electric plant in Idaho*
Figure 5: Proof test failure of a turbine spiral casing originally destined for Ffestiniog, North Wales*
MACE43001/MACE 61057: Structural Integrity Lecturers: Dr. KB Katnam & Prof. Q. Li
Page 6 of 8
CANDIDATE MATERIALS
For the design of penstocks, two alternative materials are proposed:
(a) Steel A, a medium strength, low-alloy, quenched and tempered steel QT445; (b) Steel B, a carbon-manganese pressure vessel steel conforms to BS1501-223 Grade 490L.
The chemical compositions, material properties and prices of these steels are given in Table 1.
Composition Steel A QT445
Steel B BS1501 490LT50
C 0.15-0.21 <0.20
Si <0.90 0.10-0.50
S <0.04 <0.03
P <0.04 <0.03
Mn 0.80-1.10 0.90-1.60
Cr 0.50-0.80 <0.25
Mo 0.25-0.60 <0.10
Ni - <0.30
Zr 0.05-0.15 -
Cu - <0.30
B 0.0005-0.000 -
Nb - 0.01-0.06
Yield strength, 𝜎𝑌 (in MPa) 700 350
Ultimate tensile strength, 𝜎𝑢 (in MPa) 800 500
Fracture toughness, 𝐾𝐼𝑐 (in MPa√𝑚) 100 130
Elongation (in %) 18 20
Price of rolled plate (in £ per 1000 kg) 965 525
Density (in kg/m3) 9750 9750
Table 1: Material specifications*
COURSEWORK TASKS
Using your individual parameters* and considering all the design requirements:
(a) Decide which steel to use for the intermediate penstock and specify the wall thickness;
(b) Recommend an inspection interval and give guidance on the crack size that requires the penstock to be repaired for propagating cracks;
(c) Document your work in a written report. The report must include the technical justifications for your decision and key calculations, and must be ≤ 10 pages. Note: use 2 cm page margins (for left, right, top and bottom) for page layout and font Arial with size 11.
*NOTE: If your individual parameters are not included in the list uploaded on Blackboard, please contact the unit coordinator (Dr. Katnam, [email protected]) immediately.
MACE43001/MACE 61057: Structural Integrity Lecturers: Dr. KB Katnam & Prof. Q. Li
Page 7 of 8
Additional Information and Hints
1. A suggested series of steps:
(a) Overload assessment:
You can start by determining the wall thickness for the penstock based on limiting the hoop stress under the worst loading condition to the maximum allowable design stress. Obviously, the wall must withstand the largest load applied, whether static or transient. In order to provide a 'factor of safety', the design requirements from the client are that the largest principal stress in the material should not exceed 60% of the yield strength. The penstocks are fabricated like pressure vessels by longitudinally and circumferentially welding shaped steel plates.
(b) Fracture assessment:
(i) Consider the effects of cracks on the integrity of the structure using FAD.
(ii) How sensitive is the assessment to the accuracy of the NDT methods?
(iii) How sensitive is the assessment to your assumption of the shape of the defect?
(iv) How sensitive is the assessment to the assumption of a 70 MPa residual stress?
(c) Lifetime assessment:
Estimate the fatigue lifetime of the penstocks and compare your values with the number of cycles expected over a sensible inspection period.
(d) Revise assessment:
If necessary, revise your chosen wall thickness to achieve the design life, but remember the cost of the penstock increases as the wall thickness increases.
2. Defect geometry:
(a) The simplest case is to consider the growth of a long surface edge crack lying parallel to the axis of the pipe, under the action of the hoop stress that is generated when the penstock is filled with water. The calibration function for a similar geometry is given as an edge crack in a finite width plate in tension.
(b) A more realistic geometry would be a shallow, surface breaking semi-elliptical crack lying parallel to the axis of the pipe.
3. If the geometry calibration function Y varies with crack size, the critical crack size ac is the solution of the
non-linear algebraic equation, 𝐾𝐼𝑐 = 𝑌𝜎√𝜋𝑎𝑐. You can use a graphical or an iterative method to find 𝑎𝑐.
4. Be aware that the cracks will be in the welds and the heat affected zones, and yet the toughness data is given for parent plate materials.
5. You may assume that the Paris equation, 𝑑𝑎 𝑑𝑁⁄ = 𝐶(∆𝐾𝐼 ) 𝑚, applies to both steels with the constant
values 𝐶 = 1 × 10−11 (where a is measured in metres and 𝐾𝐼 is in MPa√𝑚) and 𝑚 = 3. Integration of this equation is best done numerically. But you can do it by assuming the geometry factor Y as approximately constant (e.g. calculate the average value from the Y values for the initial crack length and the critical crack length).
6. Assuming a thin walled vessel with ( 𝑟
𝑡 ) > 10, the hoop stress in a pipe of mean radius 𝑟, wall thickness 𝑡,
under internal pressure 𝑝 is, 𝜎ℎ = 𝑝𝑟 𝑡⁄ ; where 𝑝 = 𝜌𝑔ℎ (with water density 𝜌 = 1000 𝑘𝑔/𝑚 3, 𝑔 =
9.81 𝑚/𝑠2 and head of water ℎ in metres).
* References are intentionally not included
MACE43001/MACE 61057: Structural Integrity Lecturers: Dr. KB Katnam & Prof. Q. Li
Page 8 of 8
MARKING SCHEME:
50+ 60+ 65+ 70+ 75+ 80+
1. Applying FAD for initial cracks for material A & B
2. Selecting and justifying material type for design
3. Estimating fatigue crack growth life for the material selected
4. Revising wall thickness after fatigue life estimate
5. Justifying crack shape and its role on Kr and Lr
6. Including tensile residual stresses for Kr
7. Applying FAD for a repairable crack for the material selected
8. Revising fatigue crack growth life for the material selected
9. Justifying the design for a 50 year service life
10. Justifying the maintenance and repair plan
11. Excellent report quality and critical thinking
