M. Said Jiddan Walta
Contents
Introduction
Hello, my name is M. Said Jiddan Walta, commonly referred to as Jiddan. This page will be a platform for me to describe the results of my conscious learning and development during my short time in the Numerical Method class.
NPM: 2106718256
Major: Mechanical Engineering
E-mail: m.said11@ui.ac.id
Session Review
23 May 2023 Class
As an introductory class, our lecturer Dr. Ahmad Indra Siswantara introduced himself and his focus of study on the concept of consciousness, and invites us to participate in the discussion on the importance of applying consciousness in our daily lives as well as the recurrence of difficult concepts in the problems that we face that remind us to practice consciousness about the limitations of human understanding. Outside class time, a follow-up discussion was conducted in the class group for practicing consciousness by inviting discussion on the most realistic solution of a typical limit problem. We were invited to explore the notion of infinity and the limitations of computing involving values that are typically referred to as 'undefined'. Lastly, our project for the remainder of the semester was introduced.\
30 May 2023 Class
In todays class of Numerical Method, Pak DAI asked us to discuss the Hydrogen Tank Design and Optimization project within the class with every class member to gain better knowledge on developing our overall results. Throughout the class, the discussion was moderated by Patrick Samperuru as a replacement for the class coordinator, M. Jiddan Walta, who was at the time absent due to exchange matters. In this discussion, we started by making an outline on the project objective function which was to create a functional hydrogen tank design that is optimized following the constraint parameters of pressure at 8 bars, a capacity of 1 liter, and a maximum budget of 500,000 IDR. According to Benarido Amri, the ideal material for a high pressure cylinder has a very high tensile strength, a low density, and does not react with hydrogen or allow hydrogen to diffuse into it. Most pressure cylinders to date have used austenitic stainless steel. Patrick Samperuru then continued the discussion on the material by stating several potential materials that can be used based on the types of the hydrogen tanks, being type I of all metal, type II of metal with carbon fiber wrap, type III composite with metal lining, type IV composite with non-metal lining stating that type I and II is the most probable for the design. Next, M. Azkhariandra Aryaputra stated the importance of several design considerations such as storage tank design, safety measures, leakage mitigation, and material compatibility. Following the discussion of materials, Ariq Dhifan and Fadhlan Dindra added several materials that they want to use.
Next, we conversed the 3 main points needed in our optimization. This include the design variable, objective function, constraint which can be different for every class member. Patrick Samperuru started by explain that his objective function is to accommodate the use of hydrogen tanks in the field that is more complex and dynamic meaning it would need a constraint of a high strength and wear fatigue so that is can used for long term, which is achieved by choosing an all metal tank. For Vegantra Siaga, he wanted a pressure constraint because hydrogen storage systems often have pressure limits to ensure safe operation, where pressure constraints can be defined as upper and lower bounds on the hydrogen storage pressure that prevent the storage system from operating outside the desired pressure range. According to Faris Pasya, space and weight constraints can be used as well depending on the application, there may be limitations on the available space or weight of the pressurized hydrogen system. These constraints can influence the choice of tank size, material selection, and system layout. Next, M. Annawfal Rizky stated that he wants the constraint to be the compatibility with hydrogen, The tank material should be compatible with hydrogen gas to prevent any chemical reactions, embrittlement, or degradation that could affect the tank's performance or safety. Material selection is crucial to ensure compatibility and avoid hydrogen diffusion or leakage. For M. Ikhsan Rahadian, we chose safety due to the high pressure of hydrogen, and its highly flammable, the safety of the tank is very important. choosing the right material such as aluminum alloy 6061 can increase the strength and safety, and also choose the right design.
Numerical Method - Case Study of Pressurized Hydrogen Storage
Substance Study
For the Numerical Method class, we were tasked with a project on the design and optimization of a Pressurized Hydrogen Storage, with the constraint parameters being the gas pressurized at 8 bars and the required storage volume being 1 liters. Hydrogen as a gas is useful for many industrial purposes as well as an energy source for certain vehicles and industrial appliances, and is often stored by the hundreds of liters in large tanks.
Hydrogen in its frequently encountered diatomic form of H2 gas is the lightest gas in the universe and is generally unreactive, but is readily combustible in its gaseous form. As an ultra-light gas, hydrogen occupies a substantial volume under standard conditions of pressure, i.e. atmospheric pressure. In order to store and transport hydrogen efficiently, this volume must be significantly reduced. The general methods for improving hydrogen transport and storage efficiency is through high-pressure storage in the gaseous form, very low temperature storage in the liquid form, or hydride-based storage in the solid form, though the most common being the first two. Having the highest yield of hydrogen in a fixed container volume requires pressurization up to 700 bars or more, which requires large amounts of energy and strong container design. Liquid hydrogen is cryogenic in nature, and therefore needs to be stored in extremely low temperatures to keep it in its liquid state, or at least to keep a majority of it from evaporating. For the case that we are assigned, the required storage amount is small and the pressure is also constrained, therefore the focus is not the efficiency of hydrogen yield being stored but instead the cost and material effectiveness of the container.
For the purpose of this project, it is important to begin designing the product with understanding the substance that it is meant to store, in this case hydrogen pressurized at 8 bars.
In its gaseous form at 8 bars of pressure and local indoor temperature in Indonesia being around 30 degrees Celsius, hydrogen gas has a density of 0.627 kilograms per cubic meter, which results in 1 liter or 0.001 cubic meters of the gas weighing 0.627 grams or less than 0.001 kg. This means that storing the gas at these conditions will only require a container material and design that can withstand wall pressure of 8 bars, while ideally having lower density such that the total weight of the container far exceeds the weight of the gas being stored.
Material Choice
Our goal in this case is to select a suitable material for the storage tank, with our priorities being focused on fulfilling the load requirements presented by the hydrogen in a safe manner, low weight, and cost-effectiveness. Safety is of great importance when designing hydrogen storage. The material used must possess high strength, resistance to fracture, and be capable of withstanding high pressures. Metals like steel and aluminum alloys are commonly employed due to their mechanical properties. However, special attention must be given to hydrogen embrittlement, a phenomenon that can cause material degradation and reduce safety. Thus, selecting materials with high resistance to hydrogen embrittlement, such as specific grades of steel, becomes crucial. Hydrogen has the smallest molecule size, which means it can permeate through certain materials over time. Permeation can lead to hydrogen loss, compromising the efficiency of the storage system and potentially raising safety concerns. Hence, selecting materials with low hydrogen permeability is important. Metals like steel and aluminum have relatively low permeability, especially when coated with appropriate barriers to minimize permeation. Composites, on the other hand, can have higher permeability, although this can be mitigated by employing diffusion barriers or modifying the polymer matrix.
On the topic of optimization of weight, composite materials, such as carbon fiber reinforced polymers (CFRP), offer an advantageous balance between strength and weight. CFRP has been commonly used for hydrogen storage tanks in certain regions, having the walls consist of a lightweight polymer matrix reinforced with carbon fibers, providing exceptional strength-to-weight ratios. These materials enable the construction of lightweight tanks. The cost of materials plays a significant role in the overall economics of hydrogen storage systems. Metals like steel are relatively affordable and widely available, making them cost-effective choices for bulk storage applications. However, advanced alloys with improved resistance to hydrogen embrittlement can be more expensive. In contrast, composite materials like CFRP have higher upfront costs due to their manufacturing processes.
With these factors in mind, the most likely choice is selecting a lighter grade of steel with mechanical properties that can supplement the requirements, with additional modifications and treatments to the material to further lower its hydrogen permeability.
Numerical Method - Design of Pressurized Hydrogen Storage
Geometrical Constraint
One of the main components of designing the pressurized hydrogen storage is the measurements and geometry of the storage. Through our discussions in class and individual case studies, students in our class collectively agreed that the ideal shape of the storage is a cylindrical shape akin to those generally utilized by the industry. The parameters of the cylindrical shape however still needs to be found out using the methods that we have learned over the entire course of Numerical Method class.
The goals of the optimization process of this hydrogen storage as mentioned above in the case study section is to create a pressurized hydrogen storage that fulfills the requirements while remaining cost-effective. One of the main contributors to cost of production is the amount of material being used, which in the case of a cylindrical container, equal to the surface area of the product. The lower the total surface area of the product, the lower the total effective material that is required to craft it. For our case, the surface area needs to be minimized while maintaining a constraint of volume being equal to 1 liter or 1000 cubic centimeters. The radius and height of a cylinder that fulfills both qualities can be obtained using a simple optimization function that can be numerically computed using suitable code made in Python or MATLAB. For the purpose of this project, I utilized Python to create a code that manually computes the radius and height of a cylinder of 1000 centimeter cubic volume. There are other libraries such as SciPy that has compiled code for optimization into a singular function, but for the purpose of learning the following code is done manually.
The first section of the code is to obtain a general range of radius values where the surface area is minimum, shown below:
from math import pi
import pprint
'''
r = radius
circle_area = pi * r**2
circle_circumference = 2 * pi * r
h = height
cylinder_volume = pi * r**2 * h
cylinder_surface = 2 * (pi * r**2) + (2 * pi * r * h)
constraint for cylinder_volume be a constant of 1 liter (cubic centimeter)
cylinder_volume = 1000
h in terms of r
h = 1000/(pi * r**2)
substitute in
cylinder_surface = 2 * (pi * r**2) + (2 * pi * r * 1000/(pi * r**2))
'''
mylist = [] # create a list of (surface area, radius)
for r in range(1, 21): # assume a maximum of 20cm radius
cylinder_surface = 2 * (pi * r**2) + (2 * pi * r * 1000/(pi * r**2))
mylist.append((cylinder_surface, r))
# test
pprint.pprint(mylist)The code above displays iterations from radius of 1 cm to 20 cm and their corresponding surface area values. By inspection, we can see that the minimum surface area occurs in the region between radius of 5 and 6 cm. For precision, we continue the code with a looping function to obtain the precise point where the minimum surface area occurs, and continue with computing the height for verification.
# once we find the range where area is minimum
# we can increment in smaller steps for precision
r = 5
surface_list = []
while True:
cylinder_surface = 2 * (pi * r**2) + (2 * pi * r * 1000/(pi * r**2))
surface_list.append((cylinder_surface, r))
r += 0.01
if r > 6:
break
print('minimum surface area and radius: ', min(surface_list))
min_surface = min(surface_list)[0]
sf = "Minimum surface of a 1000ml tank = {:0.2f} square centimeters"
print(sf.format(min_surface))
radius = min(surface_list)[1]
print("Radius of 1000ml tank = {:0.2f} centimeters".format(radius))
height = 1000/(pi * radius**2)
print("Height of 1000ml tank = {:0.2f} centimeters".format(height))
sf = "Ratio of height to radius of a minimized surface can = {:0.2f}"
print(sf.format(height/radius))
The result obtained by the code is shown on the right, where the suggested geometry for a cylindrical tank for 1 liter volume should maintain a 2:1 height to radius ratio with the radius being 5.42 cm, and the height at 10.84 cm consequently.
Strength Constraint
