In the two-phase flow scenario you describe, the loads are in the direction of flow because the forces are momentum loads applied to the ends of the pipe at each change in direction of flow, as with a fire hose spraying water at a wall.
Flow-induced vibration is a different phenomenon caused by localized variations in the flow/pressure profile which can cause lateral forces.
I find this easiest to visualize in the case of vortex shedding from wind flowing around a pipe or vessel. This is a flow-induced vibration, although outside instead of inside the pipe. When you see traffic lights moving in the wind, it's primarily perpendicular to the wind direction, either up and down for horizontal light standards, or laterally for vertical ones; i.e. not in the direction of the wind flow, but perpendicular to it. Now try to apply this mental picture to a reducer, tee or orifice plate. Same principle, but more difficult to visualize.
These flow induced loads are usually small, but because we don't always restrain our pipe laterally (to the extent we do vertically), even small loads applied in the right excitation frequency range can cause a system to move around unexpectedly.
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J.