# Ghaisani Khoirunnisa

## Introduction

Greetings, everyone! my name is Ghaisani Khoirunnisa, feel free to call me Gisa. NPM 2106637025. During college I lived in a boarding house located in the Kukusan area, Beji, Depok.

## Lecture Resume on 26/05/2023

At the first meeting of the "Metode Numerik" course, I gained an understanding about the principles and practical implementation of the Numerical Method in solving mathematical problems using numerical approaches. Complex problems that are difficult to answer analytically using formulas are solved using a mathematical technique known as the Numerical Method. This approach is particularly helpful when dealing with problems without closed form solutions or when using computationally intensive analytical approaches.

The course emphasized the significance of consciousness in recognizing and addressing problems with the goal of finding solutions. Consciousness refers to an individual's cognitive ability to understand the existence of a problem, and to be actively involved in finding solutions or solving the problem.

In one of our class examples, we explored the expression (x^2-1)/(x-1), where substituting x=1 directly resulted in an indeterminate form of 0/0, lacking a consistent or logically defined solution. We then employed alternative methods such as limit calculations or value approximation, which yielded a result of 2. However, it is important to understand that this value is not absolute. Numerical methods are employed to conduct calculations and utilize approaches that generate the closest possible accurate value. It is crucial to acknowledge that these values are not definitive, as absolute truth can only be attributed to God Almighty.

## Design & Optimization of Pressurized Hydrogen Storage

To design the hydrogen cylinder, I utilized various resources, including existing tools like ChatGPT. I relied on ChatGPT to gather the necessary information for my design process. Here are the summarized outcomes and findings obtained through interactions and information searches with ChatGPT.

Design and optimize a pressurized hydrogen storage system with the following specifications :

• Storage capacity : 1 liter
• Pressure : 8 bars
• Fee limit : IDR 500,000

First, we need to consider the design and material for the storage vessel. A common choice for hydrogen storage is a high-pressure cylinder made of a composite material, such as carbon fiber. These cylinders are light, durable and able to withstand high pressure. Considering the cost constraint, we will explore options that fit within the specified budget. To achieve this, we can consider the following approaches:

Cylinder Selection : Research and compare different options for hydrogen storage cylinders available in the market. Look for cylinders specifically designed for high-pressure applications and check if they meet the requirements of 1-liter capacity and 8-bar pressure. Consider factors such as material, weight, and cost. Choose a cylinder that offers the best balance between performance and affordability.

Material Optimization : Optimize the material selection for the cylinder while keeping the cost in mind. Look for materials that provide the necessary strength and safety while being cost-effective. Carbon fiber composite cylinders are commonly used for hydrogen storage due to their lightweight nature and high strength. Evaluate different materials and choose the one that fits within the budget.

Supplier Comparison : Reach out to multiple suppliers and request quotations for the selected cylinder. Compare the prices provided by different suppliers and negotiate for the best possible deal. Consider factors like warranty, delivery time, and after-sales support. Choose a reputable supplier that offers a competitive price and meets the requirements.

Safety Considerations : Ensure that the selected cylinder meets safety standards for pressurized hydrogen storage. Check if the cylinder has necessary safety features such as pressure relief valves, burst discs, and proper certifications. Safety should never be compromised, so prioritize cylinders that meet stringent safety requirements.

Cost Optimization : Explore cost optimization techniques such as bulk purchasing or negotiating for a lower price. Consider buying multiple cylinders to leverage volume discounts if applicable. Seek partnerships or collaborations with other stakeholders to share the cost of the system. By optimizing the procurement process, it may be possible to reduce the overall cost within the given budget.

System Integration : Evaluate the overall system requirements and consider any additional components needed for the pressurized hydrogen storage system, such as valves, regulators, and pressure gauges. Research and select cost-effective components that meet the system specifications. Ensure that the cost of these additional components is included in the overall budget.

System Efficiency : Consider system efficiency to optimize the hydrogen storage capacity. Explore options such as advanced compression techniques or thermal management systems that can maximize the amount of hydrogen stored within the 1-liter capacity. This will help to optimize the system's performance and make the most of the available storage space.

## Final Report of Design & Optimization Hydrogen Storage

There are several aspects that need to be considered in designing and optimize a pressurized hydrogen storage system.

• Choose an efficient storage cylinder: When selecting a storage cylinder for a motor engine, it is important to consider its weight and dimensions. A cylinder that is too heavy or too large may not be suitable or difficult to install on the motor engine. Therefore, make sure to choose a cylinder with the appropriate size and weight for efficient use.
• Consider the cylinder material: Selecting the right cylinder material is crucial. Choose a cylinder made of lightweight, corrosion-resistant, and strong material. A lightweight cylinder facilitates handling and usage, while corrosion resistance protects the cylinder from damage due to harsh environmental exposure. Cylinder strength is also important to withstand the required pressure.
• Pay attention to the working pressure: Ensure that the selected storage cylinder can withstand the required pressure for the motor engine. Typically, the cylinder should be capable of withstanding a pressure of 8 bars or more. Make sure the cylinder has adequate safety measures, such as sufficient strength and a sturdy design, to prevent leaks or dangerous damages.
• Safety factors: Safety is a crucial aspect of using storage cylinders. Ensure that the cylinder is equipped with an excess pressure release valve that will release pressure in case of dangerous pressure buildup. Additionally, ensure the presence of other safety systems that comply with applicable safety standards to prevent potential accidents or hazards.
• Cost efficiency: When choosing a storage cylinder, also consider cost efficiency. Set a suitable maximum cost limit, such as Rp. 500,000,-, and consider the cost of the storage cylinder itself, valves, pressure regulators, and other necessary components. Strive to select components that are cost-efficient without compromising quality and safety.
• Testing and verification: Before using the storage cylinder in a motor engine, it is essential to conduct testing and verification. Ensure that the cylinder has been designed and manufactured according to applicable safety standards. Perform testing to ensure the cylinder's safety, reliability, and good performance. If needed, consult with experts or competent laboratories for more thorough testing.
• Comply with regulations and standards: Lastly, make sure to comply with all applicable regulations and safety standards regarding the use of hydrogen in motor engines. These regulations and standards are established to protect users, the environment, and prevent potential accidents or serious damages.

### Material Selection of the Pressurized Hydrogen Tanks

As for the material itself, after several searches, I found that 304 stainless steel is a suitable and adaptable material with high corrosion resistance, high strength. It is used for a wide variety of home and commercial applications, it is one of the best known and most frequently used alloys in the stainless steel family. Typical applications include tanks and containers for a wide variety of liquids and solids. Most of it is made of iron, with large amounts of nickel (8%), and chromium (18%). These alloying components provide stainless steel with its ability to resist corrosion, which makes it perfect for a variety of uses, including hydrogen storage.

### Calculation with JavaScript

#### Specification of the Cylindrical Hydrogen Storage Tank

To determine the specifications of the hydrogen cylinder tank, I use JavaScript coding. Let's start by focusing on finding the cylinder dimensions. Here is the code :

// Calculate the volume of the cylinder in cm³
return Math.PI * Math.pow(radius, 2) * height;
}
// Calculate the surface area of the cylinder in cm²
const baseArea = 2 * Math.PI * Math.pow(radius, 2);
const lateralArea = 2 * Math.PI * radius * height;
return baseArea + lateralArea;
}
let bestHeight = 0;
let bestDifference = Number.MAX_VALUE;
let bestSurfaceArea = 0;
// Iterate through the range of radius and height values in cm
for (let height = minHeight; height <= maxHeight; height++) {
// Calculate the volume of the cylinder in cm³
// Calculate the difference between the cylinder volume and the target volume
const difference = Math.abs(volume - targetVolume);
// Check if the current difference is smaller than the best difference found so far
if (difference < bestDifference) {
// Update the best values
bestHeight = height;
bestDifference = difference;
}
}
}
// Output the best results with units in cm
console.log("Optimization Results:");
console.log("Best Height: " + bestHeight + " cm");
console.log("Best Difference: " + bestDifference + " cm³");
console.log("Best Surface Area: " + bestSurfaceArea + " cm²");
}
// Example usage:
const targetVolume = 1000; // 1 liter
const minRadius = 1; // in cm
const maxRadius = 10; // in cm
const minHeight = 1; // in cm
const maxHeight = 20; // in cm

From the code above, the outputs I get are :

node /tmp/bBzmwGMPYP.js
Optimization Results:
Best Height: 20 cm
Best Difference: 5.309649148733797 cm³
Best Surface Area: 603.1857894892403 cm²

Next is finding the thickness of the tank with material properties that I use is 304 stainless steel.

function calculateVolume(surfaceArea, thickness) {
// Calculate the volume
const volume = surfaceArea * thickness;
return volume;
}

function calculateDifference(volume, targetVolume) {
// Calculate the difference
const difference = Math.abs(volume - targetVolume);
return difference;
}
// Given values
const radius = 4; // in cm
const height = 20; // in cm
const surfaceArea = 603.1857894892403; // in cm²
const targetVolume = 1000; // in cm³ (1 liter)
let optimizedThickness = minThickness;
let minDifference = Number.MAX_VALUE;
// Iterate through the thickness range to find the optimized thickness
for (let thickness = minThickness; thickness <= maxThickness; thickness += stepSize) {
// Calculate the volume for the current thickness
const volume = calculateVolume(surfaceArea, thickness);
// Calculate the difference between the volume and target volume
const difference = calculateDifference(volume, targetVolume);
// Update the optimized thickness and minimum difference if a smaller difference is found
if (difference < minDifference) {
minDifference = difference;
optimizedThickness = thickness;
}
}
console.log("Optimized Thickness: " + optimizedThickness.toFixed(2) + " mm");

The output is :

node /tmp/tpnPVffDqn.js
Optimized Thickness: 0.99 mm

The tube's dimensions can be determined from the coding in the manner described below:

• Best Height: 20 cm
• Best Difference: 5.309649148733797 cm³
• Best Surface Area: 603.1857894892403 cm²
• Optimized Thickness: 0.99 mm

### Cost of the Pressurized Hydrogen Tanks

To determine the cost, first I used JavaScript code to determine the weight as the material is priced 800\$/ metric Ton or 0.8\$/kg.

function calculateWeight(volume, density) {
// Calculate the weight
const weight = volume * density;
return weight;
}
// Given values
const radius = 4; // in cm
const height = 20; // in cm
const surfaceArea = 603.1857894892403; // in cm²
const optimizedThickness = 0.99; // in mm (assumed optimized thickness)
// Calculate the volume of the cylinder
const volume = surfaceArea * optimizedThickness * 0.01 * 0.001; // Convert cm² * mm to m³
// 304 stainless steel density
const ssDensity = 7000; // kg/m³
// Calculate the weight of the hydrogen storage tank
let weight = calculateWeight(volume, ssDensity);
console.log("Weight of the Hydrogen Storage Tank: " + weight.toFixed(2) + " kg");

So, the weight of the Hydrogen Storage Tank is :

node /tmp/tpnPVffDqn.js
Weight of the Hydrogen Storage Tank: 41.80 kg

Then the price is \$ 33.44 or IDR 496,267.99, below IDR 500,000 which meets the requirements of a pressurized hydrogen storage system