Three-dimensional (3D) stability of 2D vortical flow of a liquid metal in a cavity of square cross section is examined. Vortices are produced as a result of free convection and internal heating in the cavity in the presence of a magnetic field. Low-magnetic-Reynolds-number equations are used for the base flow and stability formulation. Finite element methodology is used to discretize the problem. Efficient calculation of the dominant eigenvalues is afforded by the Arnoldi method, while neutral stability diagrams are constructed using continuation techniques. The number of vortices exhibited by the base flow switches from one to two as the internal heating crosses a threshold value. The dominant instability mechanism is the Görtler instability in the case of a single vortex and elliptical instability in the case of two vortices. In elliptic instability, axial vorticity is symmetric, it is characterized by two lobed structures aligned with one of the two principal directions of strain and the dominant eigenmode assumes the form of a traveling wave. The magnetic field opposes buoyancy, alters the direction of maximal strain by accentuating wall shear layers in comparison with the vortex pair in the core and leads to smaller frequencies at criticality.
Pipeline construction projects built in the United States to the recent requirements for operation at 80% SMYS are subjected to high stress pre-service hydrostatic tests. At very high stress levels, pipe diameter expansion, as measured by an ILI caliper tool, should not be a surprising result. In some cases, however, excessive pipe expansion has occurred and been reported by PHMSA in an industry advisory bulletin regarding potentially low yield strength results for X-70 and X-80 grade pipes. In response to this advisory notice, a detailed review was made of pipe expansion conditions for the 270 mile Southeast Supply Header (SESH) pipeline which was built in 2008. This review included a statistical analysis of the pipe yield strength and dimensional characteristics prior to installation, a review of hydrostatic test levels during the pre-service field hydrotest, and the corresponding diameter results measured by the multi-channel in-line inspection caliper tool. The results demonstrate that the pipe yield strength property distribution was well within good X-70 and X-80 process capability. The purpose of this paper is to demonstrate that explanations other than low yield strength pipe may be responsible for pipe expansion.
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