Farhan Adryansyach

Resume Kuliah Metode Numerik (26/05/2023)

Pada minggu pertama yang diisi oleh Bapak Dr. Ir. Ahmad Indra Siswantara atau biasa disapa Pak Dai, sebagai pendahuluan Metode numerik adalah pengunaan algoritma komputasi untuk menyelesaikan masalah dalam bentuk perhitungan atau analisis yang menggunakan angka dan data numerik.

Menurut Pak Dai, sebagai individu, jika melewati suatu permasalahan harus memiliki conciusness atau kesadaran agar dapat berpikir secara optimal untuk mendapatkan hasil yang terbaik dalam melewati suatu persoalaan.

Begitu juga dengan ilmu matematika, ilmu matematika sebenernya bukan suatu ilmu yang eksak atau memberikan hasil yang absolut pada setiap jawaban atau hasil perhitungannya

kita bisa mendapatkan solusinya, namun semua solusi tidak bisa dibuktikan secara exact apakah solusi tersebut benar atau tidak.

Manusia bisa melalukan pendekatan untuk. pendekatan tersebut dilakukan secara itiriner dimana hasil yang didapatkan semakin mendekati nilai yang paling sempurna seiring dengan jumlah pengulangan yang sesuai.

Ada teknologi yang dinamakan Chat GPT yang dapat kita gunakan secara maksimal untuk mendapatkan dan mencari data konkrit dari sebuah materi yang ingin kita cari tau.

dalam berkuliah, Pak Dai menyarankan jangan hanya datang ke kampus untuk sekadar absen, tanpa pelajaran dari mata kuliah yang kita ambil, maka kita harus jugaa memiliki semangatb untuk mencerna pelajaran dari setiap mata kuliah yang kita ambil.

Design & Optimization of Pressurized Hydrogen Storage

Objective

Design and Optimization Specification

Capacity : 1 L Pressure Level : 8 bar Limitation

Cost should not exceed Rp. 500 K

According to the suggestion from Mr. Dai, that I try to use the GPT chat as a tool in working on and designing according to the specifications of the task given. Here is a explanation of the elements and procedures involved in the design pressurized hydrogen storage system

Designing and optimizing pressurized hydrogen storage systems requires careful consideration of various factors such as safety, efficiency, and cost. Here are some steps to guide you through the process:

Determine storage requirements: Define the specific requirements for your hydrogen storage system, including the desired storage capacity, operating pressure, and duration of storage.

Select storage vessel type: There are several types of storage vessels suitable for pressurized hydrogen storage, such as steel cylinders, composite cylinders, or cryogenic tanks. Evaluate the advantages and limitations of each type based on factors like cost, weight, safety, and storage capacity.

Optimize the design: Work with a mechanical engineer or use computer-aided design (CAD) software to optimize the vessel's design. Consider factors such as weight, dimensions, and manufacturing constraints to ensure cost-effective production.

Determine the material and thickness: Choose a cost-effective material for the storage vessel, such as carbon steel or aluminum alloy. Consult with material suppliers to find an option that balances cost and strength. Determine the required thickness based on the selected material to withstand the desired pressure level of 8 bar.

Cost analysis: Throughout the design process, keep track of the costs associated with materials, manufacturing, safety features, and other components. Continuously evaluate and optimize design choices to stay within the budget limit of Rp. 500 K.

Assess safety considerations: Hydrogen is a highly flammable gas, so safety is of utmost importance. Ensure that the chosen storage vessel and associated equipment comply with safety standards and regulations. Consider features like pressure relief devices, burst discs, and leak detection systems to mitigate risks.

Optimize storage pressure: Determine the optimal operating pressure for your storage system by considering factors such as material compatibility, storage density, and energy efficiency. Higher pressures generally increase the storage density but may require more robust and expensive storage vessels.

Evaluate materials and construction: Consider the materials used in the construction of the storage vessel, valves, and piping systems. Seek materials that have good hydrogen compatibility, high strength, and resistance to embrittlement. Ensure that the vessel is designed to handle the desired pressure and has appropriate reinforcements and safety features.

Consider thermal management: Hydrogen storage systems may require thermal management to prevent temperature-related issues. Evaluate options for insulation, cooling, or heating to maintain the desired temperature range and minimize energy losses.

Optimize storage system layout: Design an efficient layout for the storage system, considering factors such as space availability, accessibility, and ease of maintenance. Ensure proper ventilation and spacing to allow for hydrogen dispersion in case of a leak.

Integrate with other components: Consider how the pressurized hydrogen storage system will integrate with other components of the hydrogen infrastructure, such as production, compression, and dispensing systems. Ensure compatibility and efficiency throughout the entire system.

Perform system analysis and modeling: Utilize computer modeling and simulation tools to analyze the performance of the storage system. This can help optimize parameters like pressure, volume, materials, and thermal management to maximize storage capacity, safety, and efficiency.

Test and validation: Conduct rigorous testing and validation of the designed storage system to ensure it meets the desired performance and safety requirements. Perform leak tests, pressure tests, and other relevant assessments to verify the system's integrity.

Remember that designing and optimizing pressurized hydrogen storage systems can be complex, and it is advisable to consult with experts in the field, adhere to relevant regulations and standards, and follow best practices to ensure a safe and efficient design.

Final Report of Design and Optimization of Pressurized Hydrogen Storage

a result of design optimization of a pressurized hydrogen storage. The method we use is to first measure how large the optimal tube size is to accommodate 1 liter of hydrogen at a pressure of 8 bar. with a cost of less than IDR 500,000.00. The calculation begins with finding the optimal

dimensions of the tube. def objective_function(x):

  radius = x[0]
  height = x[1]
  surface_area = calculate_cylinder_surface_area(radius, height)
  cost = calculate_cylinder_cost(surface_area)
  return cost

def calculate_cylinder_surface_area(radius, height):

  lateral_area = 2 * math.pi * radius * height
  base_area = math.pi * radius**2
  total_area = lateral_area + 2 * base_area
  return total_area

def calculate_cylinder_cost(surface_area):

  # Menghitung biaya berdasarkan luas permukaan tabung
  # Anda dapat menyesuaikan fungsi ini dengan estimasi biaya bahan dan produksi yang relevan
  return surface_area * cost_per_unit_area

1. Mendefinisikan batasan untuk radius dan tinggi tabung

def constraint(x):

  radius = x[0]
  height = x[1]
  volume = math.pi * radius**2 * height
  return volume - 1  # Volume harus sama dengan 1L (1000 cm^3)

1. Mendefinisikan fungsi untuk mencetak solusi terbaik

def print_solution(x):

  radius = x[0]
  height = x[1]
  surface_area = calculate_cylinder_surface_area(radius, height)
  cost = calculate_cylinder_cost(surface_area)
  print("Optimization Result:")
  print("Radius:", radius)
  print("Height:", height)
  print("Surface Area:", surface_area)
  print("Cost:", cost)

1. Menentukan batasan dan inisialisasi nilai awal

x0 = [1, 1] # Nilai awal radius dan tinggi tabung volume_constraint = {'type': 'eq', 'fun': constraint} # Batasan volume harus sama dengan 1L (1000 cm^3) bounds = [(0, None), (0, None)] # Batasan non-negatif untuk radius dan tinggi

1. Melakukan optimisasi menggunakan metode SLSQPresult = minimize(objective_function, x0, method='SLSQP', bounds=bounds,

constraints=volume_constraint)

1. Ekstrak variabel hasil yang dioptimalkan

 radius_optimasi, tinggi_optimasi = hasil.x

1. Hitung luas permukaan yang dioptimalkan

 luas_permukaan_optimal = hitungLuasPermukaan([radius_optimasi, tinggi_optimasi])

1. Tampilkan hasil

 print('Jari-jari teroptimasi:', radius_optimasi, 'cm')
 print('Tinggi teroptimasi:', tinggi_optimasi, 'cm')
 print('Luas Permukaan teroptimasi:', luas_permukaan_optimasi, 'cm^2')

Output Hitungan

Jari-jari teroptimasi: 5.5111852 cm

  Tinggi teroptimasi: 9.9124114 cm
  Luas Permukaan teroptimasi: 534.08519 cm^2

Setelah itu, kita akan mulai mencari ketebalan material optimal untuk dapat mengatasi stress yang diberikan saat penggunaannya. dalam perhitungan ini, digunakan lah rumus hoop stress. lalu, dalam pemilihan material saya menggunakan Stainless steel ASTM 316 dengan tingkat kekuatan yield strength adalah 206 Mpa dan Tensile Strength adalah 517 Mpa. dengan ini, perhitungan yang dilakukan adalah.

     # Definisikan fungsi untuk menghitung tegangan cincin (hoop stress)

def calculate_hoop_stress(thickness, inner_diameter, outer_diameter, pressure):

  inner_radius = inner_diameter / 2
  outer_radius = outer_diameter / 2
  hoop_stress = (pressure * (outer_radius**2 - inner_radius**2)) / (thickness * (outer_radius - inner_radius))
  return hoop_stress
  # Definisikan parameter dan batasan
  target_stress = 206000000  # Target tegangan cincin yang ingin dicapai
  min_thickness = 0.004 # Batasan tebal minimum
  max_thickness = 0.015 # Batasan tebal maksimum

1. Inisialisasi tebal awal

thickness = 0.004

1. Proses iterasi untuk mengoptimalkan tebal plate

while True:

  # Hitung tegangan cincin berdasarkan tebal saat ini
  hoop_stress = calculate_hoop_stress(thickness, inner_diameter, outer_diameter, pressure)
  # Periksa apakah tegangan cincin sudah mencapai target
  if hoop_stress >= target_stress:
      break  # Keluar dari iterasi jika tegangan cincin sudah mencapai target
  # Sesuaikan tebal plate berdasarkan perbandingan tegangan cincin dengan target
  thickness += 0.1
  # Periksa batasan tebal minimum dan tebal maksimum
  if thickness < min_thickness:
      thickness = min_thickness
  elif thickness > max_thickness:
      thickness = max_thickness

1. Cetak tebal plate yang dihasilkan

print("Optimized Plate Thickness:", thickness, 'm') Output hitungan dari ketebalan plate

  Optimized Plate Thickness: 0.01 m

after getting the optimal thickness of the plate material, then we want to know how much the price must be paid to manufacture the pressurized Hydrogen Storage. the thing to do is, we will look for the market price of the material, then we will adjust it to the amount we will use. by doing calculations in excel, it was found that the plate value to be used to design the tube is approximately 5,124 kg. then, the price that must be spent in manufacturing is approximately Rp. 349355.8011 so that a result is obtained that is close to correct or optimal regarding a pressurized hydrogen storage that can accommodate 1 liter of hydrogen with an internal pressure of 8bar. Also, this design tube is still worth less than Rp. 500,000.00 which is the budget limit for manufacturing so that optimal spending is also obtained. it is hoped that the designed design and optimization can work as it should.