## 3 Results
### Simultaneous Grazing and Bias Flows  
Grazing flows and bias flows coexist for perforated liner walls in gas turbine combustors. Therefore, the PVPM model must also be validated for those conditions in order to represent perforated liners in gas turbine engines. [PERSON] [22] experimentally investigated the effect of a simultaneous bias/grazing flow on the acoustic properties of perforated orifice liners. Figure 12 shows the test rig in the experiment by [PERSON] [22]. A tube with a diameter of 35 mm was installed on the side walls of a grazing flow duct. A perforated orifice liner was installed between the two perpendicular ducts. An inlet was linked to the impedance tube through which the bias flow could be introduced in two ways: inflow and outflow. The inflow was introduced into the grazing flow duct, while the outflow was drawn out of the grazing flow duct. Only inflow cases are considered in this work because outflow cases are not realistic in gas turbine combustors. Geometric features of those three orifice liners from this experiment are listed in Table 3. A sine wave signal of 500 Hz was employed in all cases. Transient pressure data were collected and processed by the two-microphone transfer function method [32]. A numerical simulation of the experiment was obtained following the method described in Section 2. Figure 11: Numerical and experimental comparison of normalized specific acoustic impedance as a function of the grazing flow Mach number for (**a**) liner JG1, (**b**) liner JG2, (**c**) liner JG3 and (**d**) liner JG4 [23]. A comparison of the normalized specific acoustic impedance of liners JGB1, JGB2 and JGB3 from the experiments by [PERSON] et al. [22] under various simultaneous bias/grazing flow conditions is provided in Figures 13-15. First of all, all three figures show that acoustic resistance caused by the pure grazing flow rises with the grazing flow speeds, and the presence of the bias flow tends to reduce the impact of the grazing flow. Variations in acoustic resistance with the grazing flow speed are more obvious when the bias flow is very weak. For instance, when \(\mathrm{M_{b}}=0.01\), the acoustic resistance of liner JGB1 increases by three times from approximately 0.6 at \(\mathrm{M_{g}}=0\) to 1.9 at \(\mathrm{M_{g}}=0.174\). However, when \(\mathrm{M_{b}}=0.1\), the resistance only changes from 5.6 at \(\mathrm{M_{g}}=0\) to 4.5 at \(\mathrm{M_{g}}=0.174\). The change in acoustic resistance with the grazing flow speed is much less in the presence of a strong bias flow. The CFD results are also in satisfactory agreement with the experimental results under high-speed bias flow conditions. In these conditions, acoustic resistance and reactance are predominantly determined by the bias flow. The experimental results indicate that the presence of a grazing flow tends to reduce the acoustic resistance in the case of a simultaneous bias/grazing flow, and this was referred to as the \"negative grazing flow effect\" in [PERSON]'s work [22]. However, the physical justification for this is not certain and is not included in the modified PVPM model. A comparison of the acoustic reactance is presented in Figures 13-15. In general, the effects of the simultaneous bias/grazing flow on the acoustic impedance of perforated liners are encouragingly reproduced by the PVPM model, despite a slight difference between the experiment and numerical results existing in those reactance curves. Figure 12: Test rig setup in experiment for the investigation of simultaneous bias/grazing flow effect, [PERSON] et al. [22]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Liner** & **Hole Diameter** & **Liner Thickness** & **Number of** & **Porosity** \\
**No.** & **(mm)** & **(mm)** & **(mHz)** & **(mHz)** \\ \hline JGB1 & 7 & 0.5 & 1 & 4\% \\ JGB2 & 7 & 2 & 1 & 4\% \\ JGB3 & 3 & 2 & 4 & 2.94\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Geometric specifications of the orifice liners, [PERSON] et al. [22].