Background information
Pumped storage is mechanism that can be used in the storage of electrical energy in form of water stored in the reservoir. The water moves from the reservoir to the powerhouse through the penstock at a very high pressure. In pumped hydroelectric power, there is some water which is stored in the reservoir, this water will then be released through the penstock to the powerhouse at a very high speed. In the powerhouse, the high-speed water is directed to the water turbines which will then rotate and in turn rotates the generators which are coupled with the turbines. This then will result in the generation of electrical power. 3wTherefore for the design of the penstock, tensile strength must be considered to ensure that the pipe does not collapse while water is traveling at a higher speed. The below is a prototype of how the penstock is connected to the pumped energy storage system.
Fig 1: Showing how the penstock is connected to the pumped energy storage system. (Webinars, 2012).
Pumped storage is employed since it is used in the storage of water during the rainy seasons and then used the stored water during the dry season when there is no sufficient water for the supply of the required electric power.
Objectives of the proposal
The main aim of this proposal is to develop a very strong penstock which will be able to withstand the high pressure of water from the reservoir to the powerhouse resulting to the production of more electrical energy due to the higher pressure of water subjected to the water turbines.
The significance of the proposal
This proposal suggests a design of a penstock which will highly help to increase the amount of electrical power generated and it will also help to reduce the cost of maintenance of the electrical power plant.
Project Summary
Hydropower, a renewable and mature energy source utilizes water from higher to lower altitude to generate power. Hydro Power is one of the proven, predictable and cost effective sources of renewable energy. Hydropower system (Fig 2) comprises of hydro source, diversion/storage system, water conductor system (channel/tunnel/penstock), power house building, generating and control equipment. Penstock is a conduit or tunnel connecting a reservoir/forebay to hydro turbine housed in powerhouse building for power generation. It withstands the hydraulic pressure of water under static as well as dynamic condition. It contains the e closing devices (gates /valves) at the starting (just after reservoir/forebay) and at the tail end just before turbine to control the flow in the penstock. The penstock material may be mild steel, glass reinforced plastic (GRP), reinforced cement concrete (RCC), wood stave, cast iron and high density polyethylene (HDPE) etc. However, in the most of the cases, mild steel has been used for penstock since long due to wider applicability and availability. The penstock cost contributes an appreciable percentage towards the total civil works cost of the hydroelectric project. By optimizing the penstock diameter, maximum energy generation can be obtained at minimum cost. The above mentioned materials employed in the design will for sure provide that strength which will help to sustain the higher pressure. After the design the assessment of the penstock will be done to ensure that the penstock operates as required.
Fig 2: Showing Penstock and Hydropower system schematic layout. (Pardalos, 2008)
For the design of the penstock the following specifications are given, this design is done to ensure a tensile strength for a period of 50 years.
|
Crack length (mm) |
Pipe diameter (m) |
Static head (m) |
Water hammer (m) |
|
4 |
2.4 |
534 |
704 |
For this design of the penstock, there is two case study which one of them was used in the design (Papers, 2011). The case study (a) was selected for the design. Option (a) has the following parameters.
Steel A (a medium strength, low-alloy, quenched and tempered steel QT 445). And the chemical composition and specification of the steel A is given in the table below,
|
Composition |
Steel A |
|
C |
0.15-0.21 |
|
Si |
<0.90 |
|
S |
<0.04 |
|
P |
<0.04 |
|
Mn |
0.80-1.10 |
|
Cr |
0.50-0.80 |
|
Mo |
0.25—0.60 |
|
Ni |
– |
|
Zr |
0.05-0.15 |
|
Cu |
– |
|
B |
0.0005-0.0000 |
|
Nb |
– |
|
Yield strength |
700 |
|
Ultimate tensile strength |
800 |
|
Fracture toughness |
100 |
|
Elongation ( in %) |
18 |
|
Price of the rolled plate ( in £ per 1000 kg) |
965 |
|
Density (in Kg/m3) |
9750 |
The wall thickness of the penstock can be determined by using the design specification of the internal diameter of 2.4 meters. So if the thickness is taken 0.25m. Then the external diameter will be 2.9m.
Presume new pipe to be steel penstock, 704 m long, the design flow is taken as 25 m3/s and a gross head of 534 m.
Calculate and diameter and wall thickness.
Select diameter as, D =2.4 m
Flow velocity V = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Flow velocity V =
Flow velocity V = 5.525 m/s
If the Surface roughness of a medium strength, low-alloy, quenched and tempered steel QT 445 is taken as f = 0.3
So K/D = 0.3/300 = 1x 10-3
From Moody chart f = 0.005
From Darcy’s equation,
h f = ½ x 5.525 x 2400 x 0.0046 / 9.81x 25= 12.23 m
in our case gross head = 534 m
H f = ×100
Hf = 2.29%
Therefore with the above specifications, water which flows at a velocity of 5.525 m/s. This velocity can safely increase by 2.29% without the breakage of the penstock (Nelson, 2014). Therefore the maximum velocity is
× 5.525 = 5.6515m/s.
Fracture assessment:
The fracture assessment can be analysed using the following equation,
Kic= ?α . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Where Kic is Fracture toughness, α is applied engineering stress, ac is the crack size and ? is the geometrical factor.
Crack length is taken to be more than 15 mm hence 20mm was employed. Stress is 70 MPa. Therefore the value of geometric factor can be determined from the equation 2 above (McMurry, 2015).
Therefore during the design, the steel of the options A should have the ? of 5.698 ×10-6 according to the design specifications (McMurry, 2015).
FAD
Once the mechanical and fracture toughness properties of the penstock are determined experimentally, the next point involves the structural integrity assessment of penstock pipe having crack-like defects under different loading conditions (Pardalos, 2008)
Therefore, the integrity of the material is proportional to the crack of the penstock. NDT
None Destructive Testing methods may be employed to assess the accuracy of the fracture assessment of the penstock design material (Brown, 2015).
This method of assessment is basically done through the use of either the naked eyes or the use of the camera to fully assess the perfection of the design and check keenly on the crack and see if it is okay and will work best for the penstock. This can be illustrated in the figure below;
Fig 2: Showing the use of inspection as a method of NDT (Bhatt, 2012)
In some cases, radiations like x-rays are employed to aid the correct testing of the cracks in the penstock (Petlyuk, 2012). This can be illustrated by the following diagram.
Fig3: Showing x-rays employed in the NDT method (Pardalos, 2008)
Most of the NDT methods are very accurate since they can access very minute cracks which are in form of micrometres. Therefore there are very accurate, they are almost 95% accurate in assessing the crack fractures in the penstock.
The shape of the crack will as well determine the sensitivity of the determining the crack in the penstock (Bilmate, 2013). The cracks which are very straight are very difficult to determine while those cracks which are bent or somehow curve can be easily assessed. And in some cases, they can be assessed through NDT (observation through naked eyes) depending on the size of the fracture (Bajpai, 2016). And in most cases, other NDT like x-rays can be employed to fully assess it.
For the fatigue lifetime estimated to be for a period of 5 years, it will have a cycle of 1.205 cycles.
The thickness of the penstock for the design is taken as 0.25 m, but this design specification of the thickness can be increased to aid in the strength of the penstock. The increase of the thickness of the penstock will not only increase the strength but also increase the lifetime of the penstock. If this thickness of 0.25 m is may be increased to 0.5 m then the cost of the material is increased twice (Bany, 2012). The fatigue lifetime will also be increased hence the cycles will be increased for the same period of time.
The hoop stress which is created by the water flowing through the penstock affecting the edge crack of the penstock. The calibration function for the geometry of the edge crack of the known width plate of the tension caused by the flowing water (Williams, 2013). The surface of the penstock would break easily when it is semi-elliptical. The semi-elliptical lying parallel penstock crack to the axis of the penstock is more prone to cracking than a perfect circle (Richard, 2013). This is due to the pressure exerted on the walls of the pipe is more for the semi-elliptical as compared to that of a perfect circle (Ramesh, 2011). The figure below shows the steel employed in the construction of the penstock.
Fig 4: Showing the steel used in constructing the penstock (kawilt, 2010)
When water from the reservoir moves at a very high velocity down to the power house, there are a lot of pressure which will be created on the walls of the penstock. These pressure are due to the cylindrical hoop stress which is given by the following formula.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Therefore the strong and durable penstock will basically allow the movement of the liquid at a very high speed and pressure without any breakage for a longer period of time.
Fig 4: Showing the cylinder illustrating the loop stress acting on the walls of the penstock. (Pardalos, 2008)
This project is a little bit heavy since it requires some structural analysis and calculations to ensure that the high pressure moving water does not result in the bursting of the penstock rather withstand the pressure. The acquisition of the required materials will as well make this project to take relatively longer time for it to be completed. Roughly the whole project will take roughly about eight months. The figure 4 below illustrated the Gantt chart
Fig 5: Showing the Gantt Chart for the completion of the project
The estimated cost of all the components required for the implementation of the liquid level controller is as shown in the table below:
|
Component |
Cost(USD ) |
|
Penstock materials and constructions |
20,000 |
Conclusion
In summary, the project proposal suggests a design of a penstock which will actually help in the generation of a lot of electrical energy since the proposed penstock will be able to carry moving water at a very high speed and higher pressure. Water moving at a higher pressure will result in the generation of more electrical energy since the turbines will be rotated at a very high speed, and this is supported by Faraday´s law
Bajpai, P., 2016. hydro generation plant. 2nd ed. Chicago: Springer.
Bany, J., 2012. electrical energy storage technology. 3rd ed. New Delhi: Indian press.
Bhatt, S., 2012. Land and People usage in the generation of electrical energy through water. 2nd ed. New Delhi: Gyan Publishing House.
Climate, H., 2013. Technologies used in the storage of electrical energy. 2nd ed. Washington: CRC.
Brown, W. H., 2015. Introduction to General technology in the generation of electrical energy. 2nd ed. New Delhi: Cengage Learning.
kawilt, K., 2010. Guidelines for Safe Storage and Handling of Reactive Materials with a high tensile strength. 4th ed. Hull: John Wiley & Sons.
McMurry, J. E., 2015. How pressure high-pressure head can be achieved. 4th ed. Amsterdam: Cengage Learning.
Nelson, V., 2014. Introduction to Renewable Energy. 4th ed. Chicago: Springer.
pakistan, M. o. f. g. o., 2013. Project Preparation/Feasibility for the energy storage technologies. 1st ed. Quetta: IPDF.
Papers, A. T., 2011. American Society of Mechanical Engineer. 2nd ed. Florida: ASME.
Pardalos, P. M., 2008. The higher pressure head results in a higher energy generated. 2nd ed. Chicago: Oxford press.
Petlyuk, B., 2012. The amount of discharge in a reservoir affects the energy produced. 2nd ed. London: Cambridge University Press.
Ramesh, A., 2011. Construction of a good powerhouse. 3rd ed. London: Springer.
Richard, W., 2013. Performance and Testing of Thermal Interface material used in making the water turbines. 1st ed. hull: Microelectronics Journal.
Thomas, T., 2013. The principle of energy generation. Hull: CRC.
Webinars, D., 2012. Why a Feasibility Study is Important in starting hydropower. 1st ed. Chicago: CRC.
Williams, P., 2013. Transformation of energy from potential to kinetic energy. s.l.: France Loisir
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