### Question:

The assignment is about the design of a high pressure fluid swivel stack for the extraction of gas from a marginal field using a moored tanker. e.g.: Fluid swivel – De Pretto Industrie The general arrangement of the swivel is shown in the schematic diagram below.

The design will focus on the largest swivel in the stack, with a mean toroidal diameter (through the centre-line of the product passageway) of 2500mm, carrying gas at 210bar. Stub-ends with flanges for one input one output product pipe need to be welded onto the ring at the intrados and extrados, respectively, as shown in Figure 1. The pipe diameter is to be 305mm. The torus is made from two ring forgings, bolted together, but, for the purposes of this design, the cross-section can be considered to be solid, having proportions as indicated roughly in Figure 1. (Note that Figure 1 is for guidance only and that it is up to you to decide on the dimensions that you choose, giving an account of how you did so).

Figure 1: Left: Overall swivel stack arrangement. Right: Schematic section through largest ring forging assembly.

### Part 1: Analytical solutions and rough design

Using the analytical solution for the stress in a thin-walled torus, calculate the wall thickness required to contain the test pressure of 350 bar. You should use the von Mises yield criterion with a factor of safety of 0.8 (i.e. not allowing the stress to exceed 80% of yield) along with the mechanical properties of a duplex stainless steel, giving references for your sources and saying why you selected the particular alloy. Modify the thin-walled analytical solution to consider a thick-walled torus, stating any assumptions that you have made and comment on the adequacy of the thin-walled solution.

Using the 3D analytical solution decided above, determine the worst possible orientation (3D plane) and position of a defect on the outer and inner surfaces of the torus.

Again using an analytical solution, determine the required wall thickness of the product input and output stub ends, if made from the same alloy as the torus. Consider the pipes to be of a single wall thickness, bent into a radius of curvature of your choosing, the bend being considered as a torus for the purposes of stress analysis.

### Part 2: Numerical solutions and detail design

Using the wall thickness you determined in part 2, redistribute the cross-section to match the required cross-section as shown in Figure 1. Use FEA to map the von Mises stress and sculpt the section to ensure that the von Mises stress remains below 80% of yield everywhere.

### Part 3: Discussion

Add the stub ends to your FE model and constrain it at the flanges. The welds will be through-thickness and can be considered to be of the same material as the pipe and torus. Using FEA, determine the worst possible orientation (3D plane) and position of a weld defect on the outer and inner surfaces of the torus.

Discuss all of your results, commenting on the relative importance of FEA and analytical solutions in design, validation and manufacture of complex structures.

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