Tank Sizing

Introduction

Hydrogen, to be used as fuel on an aircraft, first needs to be stored so it can be consumed during the flight. This is typically done either at high pressure around 6 or 7 hundred bar in its gaseous state or at a low temperature near -250°C in the liquid state.

Before we start

You will need approximately 120 - 150 minutes to finish all the tutorial steps.

What are we building?

This tutorial focuses on liquefied hydrogen. The benefits of storing hydrogen in the liquid state are that for a given mass of hydrogen stored, despite having a fluid pressure near atmospheric pressure, the size of the liquid hydrogen tank can be roughly 800 times smaller than at ambient conditions. But how do we realistically implement this technology?

You will learn how to:

• Size the storage tanks under thermodynamic and mechanical constraints.
• Analyze the effect of filling rates on temperature and leakage.
• Pressurization and boil-off during storage with heat ingress.
• Maintaining temperature and reducing leakage while extracting fuel during flight.

Initial Setup

1. Log into Modelon Impact and create a new workspace named HydrogenStorage. This will generate a new workspace with only the Modelica Standard Library 4.0.0. 
2. We need to add Modelon 4.3 and Vapor Cycle Library 2.11. Open the Apps menu from the top toolbar and click on Workspace Configuration. A new tab will open.

3. Click on Edit, then find and drag Modelon 4.3 and VaporCycle 2.11 from the Available Libraries list on the right into the area labeled “Drop libraries here to include them as dependencies”. Click Done and return to the previous tab. You will need to refresh the page for the new libraries to appear on the Libraries list if a prompt doesn’t already suggest so. 

Sizing Experiment

In this section, we will be using tank sizing models from the Vapor Cycle Library. They use cryogenic tank sizing methods suggested by Colozza [1] and by Huete and Pilidis [2]. Geometric parameters are determined by considering the key design factors of mechanical strength, structural design, heat transfer, insulation, dormancy and, boil-off. A revised dormancy estimation methodology by Sielemann et al [3] is used.

The tank sizing is coupled with aircraft sizing so that suitable design constraints are imposed. Therefore, the tank diameter must fit within the fuselage cross section and the overall mass of the tank including the hydrogen fuel is within limits imposed by the maximum take-off weight.

For this example, the storage tank for a two-aisle aircraft with the seating arrangement 2-3-2 (2 seats, an aisle, 3 seats, an aisle, then 2 seats) will be sized for a polyurethane foam insulated tank and a multi-layered insulation (MLI) vacuum insulated tank. This initial design constraint on diameter and weight would be done using the Aircraft Dynamics Library, but we’ll continue with those given by Sielemann et all [3].

The design parameters are shown in the below Table, and we’ll use this to find the appropriate length and wall layer thicknesses.

Tank sizing design parameters for Foam and MLI vacuum storage tanks intended for 2-3-2 seating aircraft

	Foam	Vacuum
Vapor volume fraction at filling [%]	13	13
Available hydrogen fuel [kg]	13620	10220
Outer diameter [m]	4.67	4.67
Filling pressure [kPa]	165.5	165.5
Maximum operating pressure [kPa]	404	210
Insulation material	Foam	MLI
Insulation thickness [mm]	Unknown	127
Dormancy [h]	24	Unknown
Safety factor [-]	2.2	2.2
Mass of accessories per unit tank volume [kg/m3]	3	5
Ambient temperature [K]	288.15	288.15

• The available hydrogen fuel in the Vacuum tank is less because the mass of the tank and the required accessories for a vacuum tank are more per volume than the foam-insulated tank.
• The foam insulation layer thickness is unknown but will be determined based on the 24-hour dormancy requirement.
• The MLI has a minimum practical thickness of 127 mm, so that will be a constraint and the dormancy will be determined.
• The Available hydrogen fuel determined from the aircraft sizing loop shows a higher capacity for the Foam than the Vacuum. This is due to the density of the vacuum’s MLI material, the minimum required thickness in addition to the higher mass of tank accessories per unit volume.

Size the Foam Insulated Tank (Foam232)

1. Create a new model: Workspace.SizingFoam232.
2. Instantiate:
   VaporCycle.Experiments.CryogenicH2.TankSizing.Tanks.DormantFoam and Redeclare Material2 as PolyurethaneFoam.

3. Set the following parameters under the ‘Tank design’ group:

   • Set the safety factor, sf = 2.2

   • Set the maximum operating pressure, p_max = 404 kPa (or 404e3 Pa)

   • Set the percent volume reserved for vapor as a decimal, V_i = 0.13

   • Set the internal tank pressure after filling, p_filling = 165.5 kPa (or 165.5e3 Pa)

4. Next, define the tank sizing problem (group = ‘Tank size and shape’)

   • By coupling the tank sizing with the aircraft sizing we have constraints for the mass and outer radius.

   • So set sizeAndShape = “Prescribe storage size via mass, shape via outer radius”

   • Set the mass of hydrogen fuel that would be available, massHydAvail_prscr = 13620 kg.

   • Set the outer radius, r_outer_par = 4.67 / (2) m.

5. Then define how the insulation will be sized (group – ‘Tank insulation’)

   • The thickness of insulation is unknown so insulationSizing = “Prescribe dormancy duration”.

   • Set the dormancy requirement as 24 hours, dtime_dormancy_par = 24*3600 s.

6. Instantiate Modelica.Thermal.HeatTransfer.Sources.FixedTemperature to represent the ambient temperature and connect it to the dormantFoam. Set the ambient temperature to T = 288.15 K.

7. Simulate the model with Dynamic analysis and view results. We’ve defined the overall radius and mass; then set design parameters for the mechanical strength and dormancy to solve for the storage tank’s length, volume, and thicknesses of the wall layers. For the foam tank, the outer protection layer is fixed to 0.8 mm, but the inner vessel layer is computed based on the maximum pressure and mechanical strength while the insulation layer is computed from the required dormancy. In the result tab filter, search for the following variables:

   • V_inner = 235.197 m³ (Storage tank volume)
   • L_overall = 17.1382 m (Overall tank length)
   • L = 12.4682 m (Length of the cylindrical section of the tank)
   • layer1.thickness = 0.00410957 m (Innermost vessel layer thickness)
   • layer2.thickness = 0.125753 m (Middle insulation layer thickness)
   • layer3.thickness = 0.0008 m (Outermost protection layer thickness)

Size the Multi-Layered Insulated Vacuum Tank (MLI232)

1. Create a new model: Workspace.SizingMLI232

2. Instantiate VaporCycle.Experiments.CryogenicH2.TankSizing.Tanks.DormantVacuum and set the following parameters under the ‘Tank design’ group:

   • Set the safety factor, sf = 2.2
   • Set the maximum operating pressure, p_max = 210 kPa (or 210e3 Pa)
   • Set the percent volume reserved for vapor, V_i = 0.13
   • Set the internal tank pressure after filling, p_filling = 165.5 kPa (or 165.5e3 Pa)

3. Next, define the tank sizing problem (group – ‘Tank size and shape’)

   • By coupling the tank sizing with the aircraft sizing we have constraints for the mass and outer radius.
   • So set sizeAndShape = “Prescribe storage size via mass, shape via outer radius”
   • Set the mass of hydrogen fuel that would be available, massHydAvail_prscr = 10220 kg. The MLI tank has more weight per volume than the foam so the mass of hydrogen it is capable of containing is less.
   • Set the outer radius, r_outer_par = 4.67 / (2) m. Like the Foam232 tank, the MLI232 tank is constrained with the same fuselage cross-section.

4. Then define how the insulation will be sized (group – ‘Tank insulation’)

   • For the Vacuum tank the MLI has a practical minimum insulation thickness so use insulationSizing = “Directly prescribe insulation layer thickness”.
   • Set the prescribed thickness for the insulation layer, thickness_par = 0.127 m.

5. Instantiate Modelica.Thermal.HeatTransfer.Sources.FixedTemperature and connect it to the dormantFoam. Set the ambient temperature to T = 288.15 K.

6. Simulate the model with Dynamic analysis and view results: Again, we’ve defined the overall radius and mass then set design parameters for the mechanical strength to solve for the storage tank’s length, volume, and thicknesses of the wall layers. Since the insulation thickness was prescribed, look for the calculated dormancy. In the result tab filter, search for the following variables:

   • V_inner = 176.484 m³
   • L_overall = 13.593 m
   • L = 8.92296 m
   • layer1.thickness = 0.00211187 m
   • layer2.thickness = 0.127 m
   • layer3.thickness = 0.0266221 m
   • dtime_dormancy = 1798450 s

As expected for the same aircraft design constraints, the foam tank is capable of supporting a larger volume. The minimum required thickness for MLI vacuum insulated tanks and the extra mass from the bi-grid stiffened panels outer shell to avoid buckling used up the available mass limit. However, the MLI tank has a longer dormancy time, so it can store the low-pressure hydrogen longer without the need for venting or excess structural stress.