Figure 2: The B2-BWB
Pressurized vessels – Shape analysis
If the lay-out of a pressure vessel would be a big room, build up from straight panels, the vessel would be subjected to immense bending stresses which results in a high weight penalty. To avoid bending stresses, the structure needs to have the ability to carry the pressurization loads by in-plane stresses. Thin-walled curved shells show these properties. To minimize the weight, iso-tensoid membrane structures provide the lightest solutions.
There are two perpendicular directions in which the curvature of a double curved section is specified, illustrated in Figure 3.
The stress ratio in the two curvature directions for a pressurized vessel is:
From this equation, it is evident that a sphere is the ideal iso-tensoid pressure vessel for isotropic materials, the curvature is in both directions the same and so is the stress.
Figure 3: A doubly curved panel element with curvatures Rp and Rm.
For cylinders, the stress ratio is two. A cylinder provides however more usable cabin space and the use of composite materials is inevitable to create an iso-tensoid cylindrical membrane structure where the fibers are aligned in such a way that each fiber is equally loaded.
The challenge is to establish a similar solution for non-symmetrical pressure fuselages, while still providing usable cabin space. The multi-bubble provides this opportunity and is presented in the following section.
The multi-bubble is composed of three different membrane elements:1) the cylinder which is a constituent of the multi-cylinder, 2) the sections that close the multi-bubble, called the multi-sphere and 3) the toroidal shells that are connected into a multi-torus.
Figure 4: The multi-bubble
The multi-bubble can be constructed into a iso-tensoid membrane structure. The cylinders and toroidal shells are slid into each other and dimensioned such that they only need to be balanced out by a single wall at the intersections where the radii meet. The multi-torus and the multi-sphere need an additional reinforcement ring for equilibrium at each intersection. With use of the fiber reinforced materials, the multi-bubble can be constructed as an iso-tensoid membrane structure, where the fibers are sized and oriented according to the magnitude in the principal directions, which are the stresses in the hoop/axial and circumferential directions. With that, the mass of the iso-tensoid multi-bubble can be calculated with the following equation:
Multi-bubble – Pressure Cabin
For passenger transport, an open structure needs to be created (for passenger acceptance and evacuation) and windows and doors need to be incorporated. The cut-outs for doors and windows are placed in the outer bubble and in the multi-sphere. The structural design of these cut-outs will be future research. To create an open structure, walls need to be transformed into pillars. A promising concept is shown in figure 5.
Figure 5: 3D illustration of multi-bubble analysis-example
The walls are reduced to pillars, and are connected to axial stiffeners/beams that (partly) protect the aerodynamic shell against buckling. The floor floats in the cabin and is attached to the pillars. Pillars are however detrimental to the structural efficiency and from an engineering point of view, it is important to reduce the pillar-pitch as much as possible. Relatively, the mass of the pressure vessel increases considerably with the reduction of walls into pillars. Current research on the interior configuration has shown that the multi-bubble is very efficient when the BWB is primarily used for passenger transportation. The pressurized volume of the BWB multi-bubble is with careful consideration of the geometrical
parameters, 2/3rd of the pressurized volume of that of a conventional aircraft for the same number of passengers.
Used space for payload
1 Cabin floor space 1
In absolute sense, the open multi-bubble still results into an overall weight saving compared to an equivalent cylindrical pressure vessel because the weight of the membrane of the multi-bubble is less and there is also an additional weight saving because less air is transported at cruise altitude. Another advantage of the beams that support the pillars is that they provide opportunities to increase the structural integrity of the aircraft, which is not the case for a thin membrane structure because the pillars and the beams will have multiple stress carrying functions.
There are 3 different options to integrate the multi-bubble with the aerodynamic shell and they can be categorized as follows:
Figure 6: Multi-bubble integration
Option a: The bulkhead carries all pressurization loads
For this option, the multi-bubble is designed as an isotensoid pressure vessel and there is only one position where the multi-bubble is rigidly connected with the aerodynamic shell. All other joints have simply supported as boundary conditions in order to uncouple the stresses and deformation of the multi-bubble with the aerodynamic shell.
Option b: The aerodynamic shell carries the axial loads of the multi- cylinder
When the multi-cylinder is subjected to circumferential stresses exclusively, the fibers only need to be lined-up in circumferential direction. This makes the integration of the aerodynamic shell with a membrane that is flexible in axial direction very easy. The multi-torus and the multi-sphere are rigidly connected with the aerodynamic shell and the multi-cylinder simply adapts to all deformations of the aerodynamic shell.
Option c: The pressure cabin carries all pressurization loads but does not deform in axial direction
A very interesting option is to have a pressure cabin that fully resists the pressurization loads and still preserve structural integrity by integrating the pressure cabin rigidly with the aerodynamic shell. This can be done by selecting an angle ply that contracts in such a way that the axial displacements of the multi-bubble in the flexible membrane are eliminated due to the circumferential displacements of the multi-bubble. (Poisson effect)
Multi-bubble – configuration
Creating a family with BWBs is more closely related to the aerodynamics compared with conventional aircraft. You cannot simply stretch the pressure cabin anymore. Therefore, it is likely that we distinguish the following 3 configurations:
More information on the interior configuration can be found under the student section.
Multi-bubble – Materials
The primary requirements that determine the material selection for the pressure cabin are high specific strength, durability (creep, fatigue, thermal resistivity, moisture absorption, chemical resistivity and UV-sensitivity) and fire retardant properties. Considering the extensive requirements on the structure, the most suitable state of the art material is a membrane of carbon fibers (T800), embedded in a PEI-matrix. This material is already proven technology and is currently used in aircraft structures.