Optimal geometric configuration of a cross bore in high pressure vessels.

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Nziu, P. K.
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The purpose of this study was to develop analytical and numerical solutions to be used in the design of thick walled high pressure vessels for optimal location of a cross bore. In addition, the effects of internally applied combined thermo-mechanical loading on Stress Concentration Factor (SCF) on these vessels, was also evaluated. An analytical solution, to predict principal stresses on radial circular cross bore, was developed. The developed analytical solution was verified using finite element analysis methods. An optimisation process, using finite element analysis, was further done to determine the optimal combination of the major cross bore geometry that affect stress concentration. The cross bore geometries that were studied included the size, shape, location, obliquity and thickness ratio. The geometrically optimised cross bore was then subjected to combined thermo-mechanical loading to determine the resulting stress concentration effects. A total of 169 finite element part models were created and analysed. Seven thick walled cylinders having either circular or elliptical shaped cross bore positioned at radial, offset or and inclined were investigated. The analytical solution developed correctly predicted all the radial stresses at the intersection of the cross bore and main bore. However, out of 35 studied models, this analytical solution predicted the magnitude of hoop stresses in 9 models and that of axial stresses in 15 models correctly. The lowest SCF given by the radial circular cross bore was 2.84. Whereas, the SCF due to offsetting of the same cross bore size reduced to 2.31. Radial elliptical shaped cross bore gave the overall lowest SCF at 1.73. In contrast, offsetting of the same elliptical shaped cross bore resulted in tremendous increase in SCF magnitude exceeding 1.971. Additionally, the magnitudes of SCF were observed to increase whenever the circular offset cross bores were inclined along the RZ axis of the cylinder. The hoop stress due to internally applied combined thermo-mechanical loading increased gradually with increase in temperature until it reached a maximum value after which it began to fall sharply. In contrast, the corresponding SCF reduced gradually with increase in temperature until it reached a uniform steady state. After which, any further increase in temperature had insignificant change in stress concentration factor. The optimal SCF magnitude due to combined thermo-mechanical loading was 1.43. This SCF magnitude was slightly lower than that due to the pressure load acting alone.
D. Tech. (Department of Mechanical Engineering, Faculty of Engineering and Technology), Vaal University of Technology.
thick walled cylinder, high pressure vessels, cross bore.