Kelas Metode Numerik 2022

DESIGN AND OPTIMIZATION OF PRESSURIZED HYDROGEN STORAGE

When designing the optimization of pressurized hydrogen storage with a volume of 1 liter, pressure of 8 bar, and a production cost not exceeding Rp500,000.00, there are several considerations to take into account. Here are some important factors to consider:

1. Container Material and Construction

Choose materials that are safe and resistant to high pressure and corrosion, such as aluminum, stainless steel, or carbon fiber-reinforced composites.

Ensure that the container construction can safely withstand the desired hydrogen pressure.

2. Safety

Certification and compliance with applicable safety standards such as ISO 15869 or SAE J2579.

Consider adequate safety features, such as pressure relief valves, pressure sensors, and fire suppression systems.

3. Space Efficiency

Design the container to maximize the use of space within the 1-liter volume.

Utilize optimal packaging techniques to maximize the amount of hydrogen that can be stored within the available space.

4. Storage Efficiency

Consider the most efficient method of hydrogen storage, such as physical storage as compressed gas or storage in the form of a fuel cell if hydrogen fuel cells are being :considered.

5. Production Cost

Take into account the cost of materials, production, and testing associated with the storage design.

Optimize the design to achieve a production cost that does not exceed the budgetary constraints.

6. Reliability

Ensure that the container design can maintain a stable pressure over the desired period without leaks or potential damage.

7. Regulations

Ensure that the design complies with applicable regulations and standards in the hydrogen storage industry.

DESIGN CALCULATION

Specification of a Cylindrical Hydrogen Tank

Capacity  : 1 liter
Pressure  : 8 bar
Material  : ASTM A36 sheet metal
Cost      : Rp500.000,00

Code to Optimize The Design of Cylindrical Hydrogen Tank

To optimize the design, i write a code in Python to find the optimium thickness, radius, and the height of the tank with cost and volume as a constant variables. Here is the code that i used:

   from scipy.optimize import minimize
   def objective_function(x):
   thickness, radius, height = x[0], x[1], x[2]
   # Calculate the weight of the tank (assuming density of ASTM A36 sheet metal)
   density_astm_a36 = 7850  # kg/m^3 (density of ASTM A36 sheet metal)
   volume = 3.14159 * radius * radius * height / 1000  # Convert to liters
   weight = density_astm_a36 * volume
   # Calculate the cost of the tank (based on material price per kg)
   material_price = 500000 / weight  # Rp/kg (maximum allowed cost divided by weight)
   cost = weight * material_price
   # Define the objective function as a combination of weight and cost
   # You can adjust the coefficients based on your preference for weight vs. cost
   objective_value = weight + 0.001 * cost
   return objective_value
   def constraint(x):
   thickness, radius, height = x[0], x[1], x[2]
   # Volume constraint: tank volume should be 1 liter
   volume = 3.14159 * radius * radius * height / 1000  # Convert to liters
   # Pressure constraint: tank should handle 8 bar pressure with a safety factor of 2
   allowable_stress = 250e6  # Pa (allowable stress for ASTM A36 sheet metal)
   inside_radius = radius - thickness  # Inner radius of the tank
   pressure = 8e5  # Pa (8 bar pressure)
   stress = pressure * inside_radius / thickness  # Stress in the tank wall
   safety_factor = 2.0  # Safety factor
   stress_allowable = allowable_stress / safety_factor
   return [
       volume - 1,  # Volume constraint (1 liter)
       stress - stress_allowable,  # Pressure constraint
       thickness - 5,  # Minimum thickness constraint (5 mm)
       10 - thickness  # Maximum thickness constraint (10 mm)
   ]
   # Initial guess for thickness, radius, and height (in mm)
   x0 = [10.0, 50.0, 100.0]
   # Define bounds for thickness, radius, and height (in mm)
   bounds = [
   (5, 10),  # Bounds for thickness (assumed range from 5 to 10 mm)
   (1, 50),   # Bounds for radius (assumed range from 1 to 50 mm)
   (100, 1000)    # Bounds for height (assumed range from 100 to 1000 mm)
   ]
   # Define the optimization problem
   problem = {
   'type': 'SLSQP',
   'fun': objective_function,
   'x0': x0,
   'bounds': bounds,
   'constraints': [{'type': 'ineq', 'fun': lambda x: constraint(x)}]
   }
   # Solve the optimization problem
   result = minimize(problem['fun'], x0=problem['x0'], bounds=problem['bounds'], constraints=problem['constraints'], method=problem['type'])
   # Extract the optimal solution
   optimal_thickness, optimal_radius, optimal_height = result.x
   # Calculate the weight of the tank (assuming density of ASTM A36 sheet metal)
   density_astm_a36 = 7850  # kg/m^3 (density of ASTM A36 sheet metal)
   volume = 3.14159 * optimal_radius * optimal_radius * optimal_height / 1000  # Convert to liters
   weight = density_astm_a36 * volume
   # Calculate the cost of the tank (based on material price per kg)
   material_price = 500000 / weight  # Rp/kg (maximum allowed cost divided by weight)
   cost = weight * material_price
   # Print the optimal solution with units
   print(f"Optimal Thickness: {optimal_thickness:.2f} mm")
   print(f"Optimal Radius: {optimal_radius:.2f} mm")
   print(f"Optimal Height: {optimal_height:.2f} mm")
   print(f"Cost: {cost:.2f} Rp")

The result of the code is:

  Optimal Thickness: 5.00 mm
  Optimal Radius: 24.28 mm     
  Optimal Height: 100.00 mm    
  Cost: 500000.00 Rp

3D MODELLING

After finding out the optimum design using the code above, i try to create the 3D Design using Autodesk Inventor: