Piping systems having flow discontinuities like bends, tees, reducers and valves can experience acoustic induced vibration (AIV) or flow induced vibration (FIV) due to internal pressure fluctuations (acoustic or turbulent flow sources of excitation). The excitation may range from 20 Hz to 5000 Hz depending on the pipe geometry and flow characteristics. At such frequencies, excessive vibration can cause fatigue-induced failure of the piping system if not designed properly. In some extreme cases, failure may occur in a matter of days or even hours. This paper proposes a practical frequency domain based finite element analysis (FEA) approach/design-tool to calculate the fatigue damage of piping systems due to FIV or AIV.

For a FIV analysis, the two key steps that can be identified in this approach are: (1) the development of a transfer function, and (2) the generation of a pressure fluctuation spectrum over the frequency range of interest. The transfer function defines the relationship between the stress range (∆σ) and a unit pressure fluctuation (∆p) that is used to calculate the fatigue damage. It is assumed that the stress range reaches a maximum when the internal acoustic pressure spatial distribution completely coincides with the natural mode shape of the pipe system. Harmonic analysis is performed to obtain the maximum stress range at each natural frequency of the piping system. From the transfer function and pressure fluctuation spectrum, a stress range spectrum can be calculated. Assuming a Gaussian fluctuating pressure distribution, a Rayleigh distribution is expected for the stress range. The fatigue damage can be calculated using a closed-form solution with an associated S-N curve. A typical tee-joint in a pipe spool will be examined to illustrate the procedure. The proposed procedure can be modified for an AIV analysis specifically, which is not presented here.

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