A.5.2.1.3 Preliminary Design

A.5.2.1 Propellant Tanks 1

A.5.2.1.3 Preliminary Design

Preliminary design for the propellant tanks and pressurant tanks is carried out by sizing the tanks to contain the required amount of propellant and designing the tanks to withstand maximum in-flight internal pressure. We use a safety factor of 1.25 to account for transient spikes in pressure and to cover other failure modes. We also add 5% additional volume to the propellant tanks to account for internal structure and dead space. We specify a minimum tank wall thickness of 0.75mm in the preliminary design algorithms for manufacturability and practicality.

A.5.2.1.3.1 Tanks

The propellant tanks for liquid fuel/oxidizers are designed as cylindrical tanks with hemispherical ends for the purposes of structural efficiency and ease of manufacture. The hemispherical end configuration is stronger and lighter than using elliptical ends, but takes up more space.1 Due to the small size of the launch vehicle, the space savings from using an elliptical-end tank are negligible, so we incorporate the hemispherical end configuration instead. Should a spherical tank be small enough to fit into the stage, we choose a spherical tank instead of a cylindrical tank for structural efficiency. For cylindrical tanks, a maximum length to diameter (L/D) ratio of 6.0 is chosen in preliminary design as a tradeoff between drag and structural efficiency/dynamic stability. This value is later refined to 3.0 in final design based on scaling from existing launch vehicle designs; provided more time to analyze the interaction between size and drag/controllability, a more optimal aspect ratio range could have been determined via simulation runs. However, since the final designs do not reach anywhere near the maximum L/D ratio, we regard this exercise as not crucial to our current design and do not pursue it any further.

Propellant tanks for solid propellants (and the solid components of hybrid rockets) are designed as an open-ended cylinder with an elliptical cap. The same maximum L/D ratio is applied as with the liquid propellant tank design. Spherical tanks are not appropriate for solid rocket fuel, so the tanks were kept cylindrical.

The pressurant tank is designed as a spherical tank, as it is rated to a much higher internal pressure (12 MPa) compared to the propellant tanks (typically ~ 2.0 MPa for liquid propellant tanks and ~ 6.0 MPa for solid propellant tanks). The spherical tank configuration provides the highest structural efficiency for a pressure vessel1 and is the ideal layout for a small, high-pressure tank.

A.5.2.1.3.2 Inter-tank Couplers

The inter-tank couplers connect the pressurant tank to the oxidizer tank, and the oxidizer tank to the fuel tank. They are designed as cylindrical skin sections with longitudinal and hoop stiffeners, and are designed to carry axial and shear load at maximum flight g-loading.

Author: Chii Jyh Hiu

A.5.2.1 Propellant Tanks 1

A.5.2.1.4 Stress Analysis

A.5.2.1.4.1 Tanks

For the purpose of our analysis, we assume that the tanks carry only axial and bending loads, and that the inter-tank couplers and inter-stage skirts carry only axial and shear loads. Tanks are analyzed as thin-walled structures. We consider these assumptions to be a conservative and reasonable approximation of the actual loads seen in the vehicle.

The oxidizer tank is manufactured from Aluminum 7075 spun in two halves, with a full-thickness circumferential weld at the butt. This provides the optimal weld conditions for strength, as the hoop stress in a cylindrical pressure vessel is twice the axial stress (Eqs.(A.5.2.1.4.1) and (A.5.2.1.4.2)). Assuming a weld strength factor of 0.851 for a spot-examined joint, this ensures that the tank wall thickness is designed entirely by the hoop stress due to pressure, as the reserve factor for axial loading will consequently always be greater than for hoop loading.

As mentioned above, the propellant tank is designed to the hoop stress seen due to pressure loading due to internal pressure and hydrostatic pressure at maximum flight g-loading.

where sox_hoop is the hoop stress in the oxidizer tank (Pa), sox_axial is the axial stress in the oxidizer tank (Pa), Pox is the internal pressure in the oxidizer tank (Pa), gmax is the maximum in-flight acceleration (m/s2), h is the height of the fluid level (m), ttank_ox is the thickness of the tank wall (m) and Dox.is the diameter of the oxidizer tank (m).

We then subject the model to further failure mode analyses, buckling and bending, and either add structure or increase the wall thickness as needed to meet our strength requirements.

Tank buckling strength is calculated by using Baker’s buckling criteria3 (Eqs. A.5.2.1.4.3) for unpressurized tanks, and using experimental data from Bruhn Figure C8.114 for pressurized cylinders to determine the proportional increase in strength due to pressurization.

where Pcr is the critical buckling stress of the structure (Pa), ks is the buckling coefficient, E is the Young’s Modulus of the material (Pa), u is the Poisson’s Ratio of the material, t is the thickness of the inter-tank coupler (m), L is the length of the inter-tank coupler (m), D is diameter of the tank (m), DPcr is the non-dimensionalized increase in critical buckling strength (see Section A.5.2.1.6.2) and Pcr_press is the critical buckling stress of a pressurized tank, (Pa).

Tank bending strength is assessed using test data from Bruhn Figure C8.13a4 for unpressurized cylinders and deriving the increase in tank bending allowable due to pressurization from Bruhn Figure C8.144 for pressurized vessels.

Similar to the oxidizer tank, the pressurant tank is manufactured from spun Aluminum 7075 in two hemispheres and joined together with a full thickness weld. Due to the higher criticality of the tank, the weld of the pressurant is to be fully radiographically tested after manufacture. Fortunately, as the pressurant feed tank is smaller than the oxidizer tank, this is easily achieved.

The pressurant tank is designed to withstand a wall stress calculated from Eq. (A.5.2.1.4.4).

where spress is the stress in the pressurant tank (Pa), Ppress is the internal pressure in the pressurant tank (Pa), gmax is the maximum in-flight acceleration in (m/s2), h is the height of the fluid level (m), ttank_press is the thickness of the tank wall (m), and Dpress.is the diameter of the pressurant tank (m).

The LITVC tank is found in the second stage of the rocket, and is designed as a spherical tank to similar principles as the pressurant tank. We place the tank near the nozzle throat. If the need arises, the LITVC tank could be redesigned as a toroidal tank, but this will require additional work not covered in this report.

The LITVC tank is designed to withstand a wall stress calculated from Eq. (A.5.2.1.4.5).

where sLITVC is the stress in the LITVC tank (Pa), PLITVC is the internal pressure in the LITVC tank (Pa), gmax is the maximum in-flight acceleration (m/s2), h is the height of the fluid level (m), ttank_LITVC is the thickness of the tank wall (m) and DLITVC is the diameter of the LITVC tank (m).

A.5.2.1.4.2 Inter-tank Couplers

The inter-tank couplers are designed to carry axial and shear load at maximum flight g-loading.

Fig. A.5.2.1.4.2.1: Inter-tank coupler showing internal supports, 1kg payload

(Chii Jyh Hiu)

The inter-tank couplers are manufactured from rolled Aluminum sheet welded at the seams, with equally spaced I-section hoops and z-section stringers riveted to the inside walls.

We design the inter-tank couplers to withstand axial loads by satisfying the Baker buckling criteria3:

where Pcr is the critical buckling stress of the structure (Pa), ks is the buckling coefficient, E is the Young’s Modulus of the material (Pa), u is the Poisson’s Ratio of the material, t is the thickness of the inter-tank coupler (m) and L is the length of the inter-tank coupler (m).

I-section hoops are added in evenly spaced increments until the inter-tank coupler meets or exceeds the buckling criteria.

We also design the inter-tank couplers to withstand shear loads using the following relations for shear stress:

Fig. A.5.2.1.4.2.2: Inter-tank coupler stringer schematic for analysis

(Jesii Doyle)

where tskin is the skin thickness in m, θ is the angle between stringers (rad), yr is the vertical distance from shear center to stringer r (m), Ar is the area of stringer r (m2), r is the stringer number, Ixx is the area moment of inertia (m4), qr is the shear flow through stringer r (N/m), σr is the shear stress through stringer r (Pa), Sy is the shear force at shear center (N).

Author: Chii Jyh Hiu

A.5.2.1 Propellant Tanks 1

A.5.2.1.5 Effects of Propellant Type on Tank Requirements

In preliminary design, we considered 4 major propellant types: Cryogenic (Liquid Oxygen oxidizer + Liquid Hydrogen fuel), Storable (Hydrogen Peroxide oxidizer + Kerosene), Hybrid (Hydrogen Peroxide oxidizer + HTPB fuel) and Solid (HTPBAPAN) propellant.

For the most part, the design requirements of the different propellant types is similar to the blanket analysis covered in Section A.5.2.1.3 to A.5.2.1.4, but there are several nuances worth mentioning here for anyone who wishes to replicate our preliminary design work.

The first challenge is that the MATLAB code for preliminary design tanks.m has to be versatile enough to consider different propellant inputs and to perform different algorithms for different cases as needed.

Cryogenic propellant presented a unique challenge, as the propellant tanks need thermal insulation for the liquid oxygen and liquid hydrogen. We opt to use similar foam insulation to that used on the Space Shuttle Main Tank5, with a 25.4 mm thick layer of foam insulation on the fuel and oxidizer tanks, which adds a small amount of weight to the tanks. The low density of hydrogen also necessitated very large tanks, which increases both the length and diameter of the fuel tank. This is the prompt for us to implement the maximum L/D ratio of 3.0 discussed in Section A.5.3.2.1.3.1. As the diameter and length of the tank increases, its structural efficiency worsens, and we end up with larger inert mass fractions. In addition, it is found that despite the low thermal conductivity of the insulating foam6, it is insufficient to keep the propellant cooled for the rise time of a balloon launch, and thus limits us to ground launches (aircraft launches were likewise limited by the large diameter and weight of the tanks).

Solid propellant tanks (Hybrid fuel and solid rockets) also require a separate branch in the code, specifically that the tanks have to be cylindrical in shape. As the solid propellant tank is also the combustion chamber, it develops high chamber pressures and also high internal temperature. The solid propellant itself serves as a form of thermal insulation for the tank casing during burn, but additional thermal insulation material may be required on the inner surface of the tank to prevent the aluminum from melting. We assume that this extra weight is accounted for in the otherwise nonexistent engine mass budgeted for the solid/hybrid motor, but further work will have to be done in the area of thermal protection for more detailed design of the solid/hybrid motor. In addition, the solid rocket motor used in the second stage requires a separate tank for LITVC, which is accounted for in the MATLAB code.

References

1 Huzel, D.K., Huang D.H. Design of Liquid Propellant Rocket Engines, NASA SP-125, pp 329-352

2 Megyesevy, E.F., Pressure Vessel Handbook, 10th Edition, Pressure Vessel Publishing, pg 172

3 Baker, E.H., Kovalevsky, L., Rish, F.L., Structural Analysis of Shells, Robert E. Krieger Publishing Company, Huntington, NY, 1981, pgs. 229-240

4 Bruhn, E.F., Analysis and Design of Flight Vehicle Structures, Jacobs Publishing, 1973, Chapter C8 pgs. 347-353

5 National Aeronautics and Space Administration, “External Tank Thermal Protection System”, FS-2005-04-10-MSFC, Pub 8-40392, April 2005

6 Hart, G H, “Grounding The Space Shuttle, NASA’s Foam Insulation Problem”, www.insulation.org/articles/article.cfm?id=IO51204

Author: Chii Jyh Hiu