# Numerical and Experimental Analysis of Pressure Pulsation Attenuator Based on Helmholtz Resonator
## 4 Fluent-Based Pressure Pulsation Dynamic Characteristics Simulation Analysis
The results of the steady-state analysis are shown in Figure 8. The results show that the pressure inside the capacitance chamber remains the same, and the pressure at the inlet is higher than the pressure at the outlet. Figure 8b shows the velocity cloud and velocity streamline inside the HTPA. The velocity is small after the capacitance cavity is filled with oil. It analyzes the velocity traces of the HTPA, which is influenced by the main oil path and generates eddy currents due to the change of cross-sectional area at the inlet of the capacitor cavity that causes flow disturbance. \begin{table}
\begin{tabular}{c c} \hline \hline
**Design Variables** & **Parameters** \\ \hline Length of neckline \(L\) & 41 mm \\ The Radius of Chamber \(R\) & 33 mm \\ Height of Chamber \(h\) & 53 mm \\ The internal diameter of neckline \(d\) & 16 mm \\ The internal diameter of mainline \(D\) & 16 mm \\ Length of Pipeline A \(L_{A}\) & 350 mm \\ Length of Pipeline B \(L_{B}\) & 350 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Structural parameters. Figure 7: (**a**) Model of Helmholtz type pressure pulsation Attenuator. 1 Pipeline A; 2 Flange; 3 HTPA; 4 Pipeline B; 5 Three-way connection. (**b**) Mesh generation in fluid computational domain. Continue transient analysis on the results of the steady-state analysis. To more accurately reflect the attenuation effect by installing HTPA, monitoring point A is located 175 mm from the inlet of the HTPA, and monitoring point B is located 175 mm from the outlet of the HTPA. Figure 9a shows the pressure contours at different times, and the pressure variation trends are consistent with the results of the steady-state analysis. Figure 9b shows the velocity streamline at 0.027 s, which is approximately the same as the results of steady-state analysis, and the velocity inside the capacitor chamber and at the neckline is significantly smaller than that of the main pipeline. The liquid column in the neckline is forced to vibrate and absorb the energy of pressure pulsation, thus reducing the flow velocity in the neckline. Figure 10 shows the comparison results of the pressure pulsation at the same monitoring point with and without the HTPA installed. When the HTPA is not installed, the peak pressure pulsation value is: \(\Delta\)P = 0.432 MPa. After the installation of the HTPA, the peak pressure pulsation value is: \(\Delta\)P\({}^{\prime}\) = 0.225 MPa. The pulsation attenuation rate \(\delta\) is 47%. The inlet boundary condition is still set to mass flow inlet. The average mass flow rate is 0.53416 kg/s. The pulsation frequency is set in the step of 25 Hz and in the step of 5 Hz near the peak frequency. The rest of the settings are unchanged. The insertion loss of HTPA at each frequency is simulated in fluent and the curve is plotted. According to Equation (24), Tables 1 and 2, the attenuation characteristic curves of HTPA are plotted. As can be seen in Figure 11, the attenuation characteristic curves of fluent simulation and numerical simulation basically match in the frequency range of 0-250 Hz. In the frequency range of 250-500 Hz, the results of the two are in the same trend. In the frequency range of 350-500 Hz, the insertion loss is above 10 dB, which has good pressure pulsation attenuation. At the peak frequency, there is a certain difference between the numerical simulation and Fluent simulation. The difference between the frequencies \(f\) and  
Figure 8: Pressure and velocity of HTPA under steady-state analysis. (**a**) Pressure contour. (**b**) Velocity contour and velocity streamline. \(P\) = 21 MPa. \(f\) is 8 Hz, and the peak difference is about 38%. This may be due to the neglect of the viscous effect of the medium and the assignment error, etc. Overall, the general trend of the two results coincides. Figure 10: Comparison of pressure pulsation transient analysis results. \(P\) = 21 MPa. Figure 9: Transient analysis of pressure and velocity of HTPA. (**a**) Pressure contour: 0.025 s, 0.026 s and 0.027 s. (**b**) Velocity streamline: 0.027 s. \(P\) = 21 MPa.