# Fadhlan Dindra

## Contents

**Biodata**

PAGI TEKNIKK!! My name is Fadhlan Kiska Anargya Dindra and my friends casually call me **Dindra**. Currently studying Mechanical Engineering at the University of Indonesia. Fast learner, well-organized, and responsible person. Always look forward to doing something new. Have an interest in sports, arts, and automotive.

**Name**: Fadhlan Kiska Anargya Dindra

**Date of Birth**: September 7th, 2003

**NPM**: 2106658414

**Major**: Mechanical Engineering

**E-mail**: fadhlan.kiska@ui.ac.id

I made this blog for the purposes of Numerical Method KKI that i took this semester. Special appreciation to Mr. DAI for creating this website to open new opportunities for us in learning through digital media. I will use this blog as my personal space to create my creativity in learning Numerical Method lectures.

**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.

**Pressurized Hydrogen Storage Case Study**

**Pressurized hydrogen storage** is a method of storing hydrogen gas by compressing it to high pressures inside storage vessels or tanks. Pressurized hydrogen storage plays a vital role in enabling the utilization of hydrogen as a clean energy carrier. By effectively storing hydrogen gas at high pressures, it becomes more viable for various applications, contributing to the advancement of hydrogen-based technologies and the transition to a sustainable energy future. Our goals in this class are to finalized the design and optimization for Pressurized Hydrogen Storage but with the specification of gas being pressurized at 8 bars and volume is 1 liter.

A hydrogen tank, also known as a hydrogen storage tank, is a container designed to store hydrogen gas for various applications. Hydrogen tanks are an essential component of hydrogen fuel cell vehicles, industrial processes, and energy storage systems. They provide a means to store hydrogen safely and efficiently until it is needed for use.

Hydrogen tanks are designed with safety features such as pressure relief valves, burst discs, and leak detection systems to ensure safe operation and prevent overpressure or leaks. The tank design, material selection, and construction adhere to specific standards and regulations to ensure the integrity and safety of the hydrogen storage system.

It's important to note that the choice of hydrogen tank depends on various factors, including the specific application requirements, storage capacity, weight considerations, safety considerations, and system efficiency. Different technologies and tank designs offer trade-offs in terms of cost, storage capacity, weight, and safety, and the selection should be made based on the specific needs of the application.

### Material Selection

To design a hydrogen tank with a gas pressure of 8 bars and a volume of 1 liter within a maximum cost of 500,000 IDR, several factors need to be considered, such as material selection, manufacturing process, and safety requirements.

4130 steel, also known as chromoly steel or alloy steel, is a low-alloy steel that contains chromium and molybdenum. It is commonly used in various applications, including aerospace, automotive, and structural components. For the material properties, 4130 steel offers a good balance of strength, toughness, and cost-effectiveness. It has a tensile strength of around 560-700 MPa (81,000-101,000 psi) and a yield strength of approximately 460-590 MPa (67,000-85,000 psi), depending on the heat treatment and condition. The addition of chromium and molybdenum improves the steel's hardenability, strength, and corrosion resistance compared to standard carbon steels.

4130 steel is generally compatible with hydrogen gas but may require appropriate surface treatment or coating to mitigate potential issues such as hydrogen embrittlement. Proper precautions should be taken during the manufacturing and handling processes to minimize hydrogen absorption and ensure long-term integrity. 4130 steel can be easily formed and welded, making it suitable for tank fabrication. Common manufacturing processes for 4130 steel tanks include seamless tube fabrication, welding (such as TIG or MIG welding), and heat treatment as needed.

### Geometrical Constraint

In this case, i choose a **Cylindrical Shape** as the geometry of the tank because cylindrical tanks can maximize the use of available volume and allowing for efficient storage of hydrogen. Moreover, the cylindrical shape provides a larger internal volume compared to other shapes with the same external dimensions. For the structural, cylindrical tanks distribute stress uniformly along the walls, resulting in a structurally efficient design. The cylindrical shape inherently provides good resistance against internal pressure, making it suitable for high-pressure hydrogen storage.

### Surface Area Optimization

By minimizing the surface area of the cylindrical geometry, we can optimized the budget-cost without compromising safety factors and reducing existing specifications. To know the minimum radius and minimum height, we can do some iteration in python (or another coding software). The iteration in the provided code is achieved using nested loops. The outer loop iterates over different radius values, while the inner loop iterates over different height values. This combination of nested loops allows for systematically considering various combinations of radius and height for the cylindrical structure.

The process of systematically exploring all possible combinations of values using nested loops is commonly referred to as "nested iteration" or "nested looping". In this specific case, it helps to iterate through all the possible radius and height values within the specified range to find the cylindrical structure with the minimum surface area that meets the minimum capacity requirement.

```
import math
def calculate_surface_area(radius, height):
# Calculate the surface area of a cylinder
base_area = math.pi * radius**2
lateral_area = 2 * math.pi * radius * height
total_area = 2 * base_area + lateral_area
return total_area
def find_minimum_surface_area(min_capacity):
min_surface_area = float('inf')
best_radius = 0
best_height = 0
for radius in range(1, 101): # Consider radii from 1 to 100
for height in range(1, 101): # Consider heights from 1 to 100
volume = math.pi * radius**2 * height
if volume >= min_capacity:
surface_area = calculate_surface_area(radius, height)
if surface_area < min_surface_area:
min_surface_area = surface_area
best_radius = radius
best_height = height
return best_radius, best_height
# Specify the minimum capacity in liters
min_capacity_liters = 1
# Convert the minimum capacity to cubic centimeters (1 liter = 1000 cubic centimeters)
min_capacity = min_capacity_liters * 1000
# Find the cylindrical structure with the minimum surface area
radius, height = find_minimum_surface_area(min_capacity)
# Print the results
print("Minimum Surface Area Cylindrical Structure:")
print(f"Radius: {radius} cm")
print(f"Height: {height} cm")
print(f"Surface Area: {calculate_surface_area(radius, height)} cm^2")
print(f"Volume: {math.pi * radius**2 * height} cm^3")
```

After that, we can run the code and the result as follows:

```
Minimum Surface Area Cylindrical Structure:
Radius: 5 cm
Height: 13 cm
Surface Area: 565.4866776461628 cm^2
Volume: 1021.0176124166828 cm^3
```

Hoop stress, also known as circumferential stress or tangential stress, is a type of stress that occurs in a cylindrical or spherical object, such as a pipe or a pressure vessel. It is caused by the internal pressure acting on the walls of the object and tends to stretch or expand the object circumferentially. For knowing its hoop stress, we can calculate using iteration in python by input the **8 bars** pressure to its iteration.

```
r = 5e-2 # The radius value
p = 800000 # Gas being pressurized at 8 bars
t = 2.5e-3 # minimum thickness
while t < 10e-3:
hoop = (r * p)/(t)
print('for thickness', t, 'hoop stress =', hoop, "Pa")
t += 0.1e-3
if hoop > 435e9: # Yield strength for AISI 4130
break
```

Result:

```
for thickness 0.0025 hoop stress = 16000000.0 Pa
for thickness 0.0026 hoop stress = 15384615.384615386 Pa
for thickness 0.0026999999999999997 hoop stress = 14814814.814814817 Pa
for thickness 0.0027999999999999995 hoop stress = 14285714.285714287 Pa
for thickness 0.0028999999999999994 hoop stress = 13793103.448275866 Pa
for thickness 0.002999999999999999 hoop stress = 13333333.333333338 Pa
for thickness 0.003099999999999999 hoop stress = 12903225.806451617 Pa
for thickness 0.003199999999999999 hoop stress = 12500000.000000004 Pa
for thickness 0.0032999999999999987 hoop stress = 12121212.121212127 Pa
for thickness 0.0033999999999999985 hoop stress = 11764705.882352946 Pa
for thickness 0.0034999999999999983 hoop stress = 11428571.428571435 Pa
for thickness 0.003599999999999998 hoop stress = 11111111.111111118 Pa
for thickness 0.003699999999999998 hoop stress = 10810810.810810817 Pa
for thickness 0.003799999999999998 hoop stress = 10526315.78947369 Pa
for thickness 0.0038999999999999977 hoop stress = 10256410.256410263 Pa
for thickness 0.0039999999999999975 hoop stress = 10000000.000000006 Pa
for thickness 0.004099999999999998 hoop stress = 9756097.560975615 Pa
for thickness 0.004199999999999998 hoop stress = 9523809.523809528 Pa
for thickness 0.004299999999999998 hoop stress = 9302325.581395352 Pa
for thickness 0.0043999999999999985 hoop stress = 9090909.090909094 Pa
for thickness 0.004499999999999999 hoop stress = 8888888.888888892 Pa
for thickness 0.004599999999999999 hoop stress = 8695652.173913045 Pa
for thickness 0.004699999999999999 hoop stress = 8510638.297872342 Pa
for thickness 0.0048 hoop stress = 8333333.333333334 Pa
for thickness 0.0049 hoop stress = 8163265.306122449 Pa
for thickness 0.005 hoop stress = 8000000.0 Pa
for thickness 0.0051 hoop stress = 7843137.2549019605 Pa
for thickness 0.005200000000000001 hoop stress = 7692307.692307691 Pa
for thickness 0.005300000000000001 hoop stress = 7547169.811320754 Pa
for thickness 0.005400000000000001 hoop stress = 7407407.407407406 Pa
for thickness 0.005500000000000001 hoop stress = 7272727.272727271 Pa
for thickness 0.005600000000000002 hoop stress = 7142857.142857141 Pa
for thickness 0.005700000000000002 hoop stress = 7017543.859649121 Pa
for thickness 0.005800000000000002 hoop stress = 6896551.724137928 Pa
for thickness 0.0059000000000000025 hoop stress = 6779661.01694915 Pa
for thickness 0.006000000000000003 hoop stress = 6666666.666666663 Pa
for thickness 0.006100000000000003 hoop stress = 6557377.049180325 Pa
for thickness 0.006200000000000003 hoop stress = 6451612.903225803 Pa
for thickness 0.0063000000000000035 hoop stress = 6349206.349206346 Pa
for thickness 0.006400000000000004 hoop stress = 6249999.999999996 Pa
for thickness 0.006500000000000004 hoop stress = 6153846.15384615 Pa
for thickness 0.006600000000000004 hoop stress = 6060606.060606057 Pa
for thickness 0.0067000000000000046 hoop stress = 5970149.253731339 Pa
for thickness 0.006800000000000005 hoop stress = 5882352.941176467 Pa
for thickness 0.006900000000000005 hoop stress = 5797101.449275358 Pa
for thickness 0.007000000000000005 hoop stress = 5714285.71428571 Pa
for thickness 0.007100000000000006 hoop stress = 5633802.816901404 Pa
for thickness 0.007200000000000006 hoop stress = 5555555.555555551 Pa
for thickness 0.007300000000000006 hoop stress = 5479452.0547945155 Pa
for thickness 0.007400000000000006 hoop stress = 5405405.4054054 Pa
for thickness 0.007500000000000007 hoop stress = 5333333.333333328 Pa
for thickness 0.007600000000000007 hoop stress = 5263157.894736838 Pa
for thickness 0.007700000000000007 hoop stress = 5194805.19480519 Pa
for thickness 0.0078000000000000074 hoop stress = 5128205.128205123 Pa
for thickness 0.007900000000000008 hoop stress = 5063291.139240501 Pa
for thickness 0.008000000000000007 hoop stress = 4999999.999999995 Pa
for thickness 0.008100000000000007 hoop stress = 4938271.604938268 Pa
for thickness 0.008200000000000006 hoop stress = 4878048.780487801 Pa
for thickness 0.008300000000000005 hoop stress = 4819277.108433732 Pa
for thickness 0.008400000000000005 hoop stress = 4761904.761904759 Pa
for thickness 0.008500000000000004 hoop stress = 4705882.352941174 Pa
for thickness 0.008600000000000003 hoop stress = 4651162.790697672 Pa
for thickness 0.008700000000000003 hoop stress = 4597701.149425286 Pa
for thickness 0.008800000000000002 hoop stress = 4545454.545454544 Pa
for thickness 0.008900000000000002 hoop stress = 4494382.022471909 Pa
for thickness 0.009000000000000001 hoop stress = 4444444.444444444 Pa
for thickness 0.0091 hoop stress = 4395604.395604395 Pa
for thickness 0.0092 hoop stress = 4347826.0869565215 Pa
for thickness 0.0093 hoop stress = 4301075.268817205 Pa
for thickness 0.009399999999999999 hoop stress = 4255319.148936171 Pa
for thickness 0.009499999999999998 hoop stress = 4210526.315789474 Pa
for thickness 0.009599999999999997 hoop stress = 4166666.666666668 Pa
for thickness 0.009699999999999997 hoop stress = 4123711.3402061868 Pa
for thickness 0.009799999999999996 hoop stress = 4081632.653061226 Pa
for thickness 0.009899999999999996 hoop stress = 4040404.040404042 Pa
for thickness 0.009999999999999995 hoop stress = 4000000.000000002 Pa
```

From the result of the thickness above, we can take the mean from 2 mm to 9.9 mm which is around 6 mm of the thickness. Therefore, we already got the suitable specifications for the tank.

**Radius: 5 cm**

**Height: 13 cm**

**Thickness: 6 mm**

### Cost Budgeting

To calculate the price of a cylindrical tank, we need to consider the cost of the material and the manufacturing process.

**Specification**:

Radius (R) = 5 cm

Height (H) = 13 cm

Surface Area (A) = 565.4866776461628 cm^2

Volume (V) = 1021.0176124166828 cm^3

Thickness (T) = 6 mm = 0.6 cm

Material: 4130 steel

The material cost is typically based on the weight of the material required. Since we have the surface area and thickness, we can calculate the weight of the material using the formula:

Weight = Surface Area * Thickness * Density

The density of 4130 steel is approximately 7.85 g/cm^3.

Weight = 565.4866776461628 cm^2 * 0.6 cm * 7.85 g/cm^3 Weight = 2649.097 g = 2.649097 kg (approx.)

The cost of the material can vary, but for estimation purposes, let's assume a cost of 29.668 IDR per kg of 4130 steel (This price is the rough approximation based on the internet).

Material Cost = Weight * Cost per kg Material Cost = 2.649097 kg * 29.668 IDR Material Cost = 78.590 IDR (approx.)

Then, we can approximate the manufacturing process cost is around 50.000 IDR

Total Cost = Material Cost + Manufacturing Cost Total Cost = 78.590 IDR + 50.000 IDR Total Cost = 128.590 IDR (approx.)

Therefore, the estimated price of the cylindrical tank with the given specifications (Radius: 5 cm, Height: 13 cm, Surface Area: 565.4866776461628 cm^2, Volume: 1021.0176124166828 cm^3, Thickness: 6 mm, Material: 4130 steel) would be approximately **128.590 IDR**. But please note that the price of the tank may vary due to the price difference or the certain specification of the steel. Also, there are some tools that are not included in the calculation like the port, pressure sensor, dome protector, polymer linen with high-density specification, and so on. But overall, this design has not passed even far from the specified budget limit.

### Conclusion

The cylindrical shape is the most suitable geometry for hydrogen tank since cylindrical shape can efficiently utilized volume, uniform stress distribution, ease of fabrication, and integration flexibility. Tank has a volume of **1021.02 cm³**, which exceeds the minimum required capacity of 1 liter (1000 cm³). Therefore, it meets the minimum capacity requirement.

For the material, 4130 steel is a commonly used material in pressure vessel applications due to its high strength, good weldability, and resistance to deformation under pressure. It is a suitable material choice for the hydrogen tank. In conclusion, based on data and calculation above, the hydrogen storage tank with a radius of 5 cm, height of 13 cm, and made of 4130 steel appears to be suitable. The tank meets the minimum capacity requirement of 1 liter, and the choice of a cylindrical shape, along with the selected material, is appropriate for the pressurized hydrogen storage application.

**My Conscious Efforts in Numerical Method Learning and its Application in Hydrogen Storage Design Optimization**

My presentation video can be accessed on: https://www.youtube.com/watch?v=tuaOrQ4YyXo

**I am My Consciousness** is a very good phrase to implement in everyday life. After waking up in the morning, we consciously rushed to campus to learn something. While on campus, we must consciously pay attention to the lecturer. When doing assignments, quizzes, or homework, we also have to be conscious and serious when doing it. Without realizing it, we actually always implement **I am My Consciousness** on our daily basis.

In terms of Numerical Method lectures, we can correlate them with the consciousness theory. For example, We consciously recognize that the expression (X^2 - 1) /(X-1) becomes undefined when X is equal to 1. But, when we're conscious enough to solve it, there will be an exact result by canceling the number first before directly calculating it. Therefore, consciousness is relevant in understanding the significance of division by zero and recognizing the undefined result in this particular case.

Nothing is achieved without obstacles and struggles. Our knowledge limitation and the time bound must be the one. However, when we are conscious and widely open our eyes, nowadays, access to academic journals or other sources is very easy to obtain. We can put much effort on reading journals and learning new things outside the class to gaining out knowledge. When we start struggling, just remember and conscious that there is The Creator who will always make things easier for us.

MESIN!!!
**BERSYUKUR BERSYUKUR BERSYUKUR!!!**