# Numerical and Experimental Analysis of Pressure Pulsation Attenuator Based on Helmholtz Resonator
## 5 Experiment and Analysis  
To validate the theoretical model of the HTPA as well as the attenuation effect, the pump outlet pressure pulsation attenuation experiment is performed. The experimental platform is shown in Figure 12, which consists of HTPA, a hydraulic system, two pressure sensors, and a data acquisition system. The hydraulic system includes a motor, nine-piston pump, oil tank, filter, throttle valve, relief valve, etc.  
Set the motor speed to 1500 rpm and the line flow rate to 6 L/min. Change the load pressure of the hydraulic system to 12 MPa, 16 MPa, and 21 MPa, respectively, by adjusting the throttle valve. Compare and analyze the pressure pulsation of monitoring point B with and without the attenuator installed, as shown in Figures 13-15.  
Figure 14: _Cont._  
Figure 13: Pressure pulsation signal under 12 MPa load. (**a**) Time domain signal diagram; (**b**) Frequency domain signal diagram.  
Figure 14: Pressure pulsation signal under 16 MPa load. (**a**) Time domain signal diagram; (**b**) Frequency domain signal diagram.  
Figure 15: Pressure pulsation signal under 21 MPa load. (**a**) Time domain signal diagram; (**b**) Frequency domain signal diagram.  
According to the frequency domain signal plot in Figures 13-15, Table 4 can be obtained. When the load pressure increases from 12 MPa to 21 MPa, the value of the insertion loss at 225 Hz changes less. For the pressure pulsation at 450 Hz, the insertion loss values are all above 15 dB. The insertion loss reaches 19.37 dB at 16 MPa. The installation of HTPA can effectively eliminate the pressure pulsation around 450 Hz and can also play a certain attenuation effect on the pressure pulsation at 225 Hz.  
As can be seen from Figure 16, the pulsation attenuator has a stable attenuation effect on pressure pulsations of 225 Hz, almost independent of the load pressure. However, the value of the insertion loss is small, which is less different from the results of the numerical simulation and simulation. The attenuation of the 450 Hz pressure pulsation is less affected by the load pressure and remains between 15 and 20 dB but differs significantly from the numerical simulation. This is due to energy losses and heat transfer that are not considered in the mathematical model, for example, the energy loss due to the expansion at the neck outlet. Secondly, in the finite element simulation, only the pulsation attenuator and the piping directly connected to it were considered and not modelled in relation to the whole hydraulic system. There are manufacturing and installation errors in the pulsation attenuator, resulting in a deviation in resonance frequency from the theoretically calculated value and a reduction in the actual attenuation effect (IL).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**225 Hz Pressure Pulsation Amplitude**} \\ \hline \multirow{2}{*}{**Load Pressure/MPa**} & **Without HTPA** & **With HTPA** & **Insertion Loss/dB** \\  & **Installed/MPa** & **Installed/MPa** & **Installed/MPa** \\ \hline
12 & 0.0558 & 0.0441 & 2.05 \\
16 & 0.0807 & 0.0641 & 1.99 \\
21 & 0.0905 & 0.0729 & 1.87 \\ \hline \multicolumn{4}{c}{**450 Hz pressure pulsation amplitude**} \\ \hline
12 & 0.0428 & 0.0058 & 17.35 \\
16 & 0.0816 & 0.0088 & 19.37 \\
21 & 0.0855 & 0.0138 & 15.84 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Insertion loss for each frequency at different load pressures.  
Figure 16: Insertion loss at different load pressures corresponding to each frequency. The load pressure \(P\) are 12, 16 and 21 MPa, respectively.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Load Pressure/MPa**} & **Without HTPA** & **With HTPA** & **Pulsation** \\  & **Installed/MPa** & **Installed/MPa** & **Attenuation Rate** \\ \hline
12 & 0.31 & 0.21 & 32\% \\
16 & 0.39 & 0.24 & 38\% \\
21 & 0.49 & 0.29 & 40\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of peak-to-peak pressure pulsation under different load pressures.