# Analysis of the Causes of Excessive Noise and Vibrations of Live Steam Pipelines
## 6 Numerical Analysis of Vibrations of the Live Steam Pipelines  
A numerical modal analysis was performed using the finite element method [9] in order to identify the frequency and mode shape in the frequency range above 900 Hz. This range is significant because of the potential excessive noise. FEM calculations were performed  
Figure 14: Results of measurements of sound intensity for the frequency range 929 Hz \(\div\) 1059 Hz at the level of 36 m at a distance of 11.48 m from the sound source. Figure 13: Results of measurements of sound intensity for the frequency range 929 \(\div\) 1059 Hz at the level of 17 m at a distance of 8.1 m from the sound source. on [10] geometrical models of straight pipeline spans for pipes with the following dimensions: \(\mathcal{O}\)508 mm \(\times\) 55 mm, \(\mathcal{O}\)406.4 m \(\times\) 50 mm, and \(\mathcal{O}\)355.6 mm \(\times\) 40 mm, as well as on models of pipeline spans near the spherical Y-pipes. Due to the fact that these are thick-walled elements, their discrete models were created with division into solid elements [4], which are shown in Figure 15.  
The modal analysis includes both the thermal loads and mechanical loads in the form of a temperature and pressure field generated by the flowing live steam. Calculations were performed using the commercial code of ANSYS Workbench 13.0 for two operating states of the power unit. The first was the nominal power state, whereas the second was related to the operating parameters of the unit on the date of measurement. The parameters of the live steam for individual cases of analysis are presented in Table 2.  
Figure 16 shows examples of the modal analysis results of FEM calculations for [1] a span of the live steam pipeline in power unit A for the natural vibrations frequency range of 900-1001 Hz in the pipeline's nominal operating state. \begin{table}
\begin{tabular}{c c c c} \hline  & **Values of Live** & **Nominal Operating** & **Operating State on** \\  & **Steam Parameters** & **State** & **2013-06-07** \\ \hline \multirow{2}{*}{A Unit} & Temperature [\({}^{\circ}\)C] & 575 & 555.6 \\ \cline{2-4}  & Pressure [MPa] & 19.6 & 18.7 \\ \hline \multirow{2}{*}{B Unit} & Temperature [\({}^{\circ}\)C] & 575 & \\ \cline{2-4}  & Pressure [MPa] & 19.6 & \\ \hline \end{tabular}
\end{table} 
Table 2: Values of live steam parameters included in the numerical analysis. Figure 15: Discrete model of a span of the live steam pipeline: (**a**) piping span with dimensions of \(\mathcal{O}\)406.4 \(\times\) 50; (**b**) spherical Y-pipe with piping spans. FEM numerical calculations were performed for a live steam pipeline near the top Y-pipe and for straight spans of pipes used in units A and B [2; 11; 12]. Due to the influence of operating parameters, i.e., temperature in particular [3; 8; 13; 14; 15; 16; 17; 18; 19], calculations were performed for the nominal operating state and for the current operating state on the date of measurements. Table 3 presents a comparison of vibration frequencies for corresponding mode shapes. The comparison in Table 3 between results for unit A and unit B shows that the frequency of vibrations during operation on the date of measurements is approximately 3 \(\div\) 7 Hz higher than the values during nominal state of the unit. The corresponding mode shapes for unit B occur at substantially higher frequencies, i.e., 26 \(\div\) 49 Hz higher in comparison with those for the vibrations for unit A. An analysis of the vibration frequencies in straight pipe segments (Table 4) for corresponding mode shapes shows that the vibration frequencies of the \(\mathcal{O}\)406.4 \(\times\) 50 mm pipe are lower than the vibration frequencies of the \(\mathcal{O}\)355.6 \(\times\) 40 mm pipe by 28, 26, 21, 14, and 6 Hz for subsequent mode shapes. In this frequency range, the \(\mathcal{O}\)508 \(\times\) 55 pipe has only one circular mode shape and one flexural mode shape.