## 4 Results and Discussion
As displayed in Figure 4, corresponding velocity contours of the computed flow fields are presented to describe the four working states of the fluidic oscillation tool. Figure 5 compares the numerical data of the mean pressure drop and oscillation frequency with the experimental data. The data of the numerical and experimental mean pressure drop and oscillation frequency are almost identical, where only a slight difference is noticed, and the difference does not exceed 15%, showing considerable agreement between the results. The data obtained by the CFD simulations are slightly larger than those of the experimental tests. This is probably due to the fact that the leakage and frictional force were ignored in the numerical simulations. Figure 6 shows the comparison of variation of pressure drop \(P\) with time \(T\), between LFT and ZFT. It indicates that the pressure pulse amplitude increases when increasing the supply flow rate. When the supply flow rate is at a given constant value, the pressure drop of the ZFT will be lower than that of the LFT. The absence of the throttling plate effectively minimizes the pressure drop of an FAOT, and at the same time, the pressure pulse amplitude \(A_{P}\) of the ZFT does not absolutely decline, but even increases compared with the LFT. Figure 4: The measured pressure at three different positions ((i) the inlet of the fluidic oscillator; (ii) one of the side passages and (iii) the front chamber of the cylinder) of a fluidic axial oscillation tool with the absence of a throttling plate when \(Q_{V}=16\) L/s: relation with the measuring time \(T\) and the computed flow field (Velocity contours). Figure 7 provides the variation of measured displacement \(D\) with time \(T\) for different supply volume flow rates \(Q_{V}\). The oscillation motion of an FAOT is quantified by the measured displacement \(D\) which is nearly proportional to the pressure measured at (i). As illustrated in Figure 7, when \(Q_{V}\) = 10 L/s, the measured displacement for ZFT is hovering in a narrow range around a certain value of about 3.2 mm, while the displacement of LFT exhibits relatively obvious fluctuations. The reason for this is that the ZFT the pressure at (i) is not strong enough to prevail over the pre-tightening force of the disc springs (Numbering 5 in Figure 1), thus the oscillation motion of the mandrel is not distinguished. Besides, in another case when \(Q_{V}\) = 12 L/s, the measured displacement for ZFT levels off to a steady value (about 3.2 mm), which is maintained in the bottom of the curve. Hence, it can be inferred that the initial value of the displacement transducer is about 3.2 mm. In addition, similar variation trends of displacements are obtained in the cases when \(Q_{V}\) = 14 L/sand \(Q_{V}\) = 16 L/s. In these cases, there exists two pulses of displacement in a cycle, which coincides with the variable pressure drop displayed in  
Figure 5: Comparison between experimental tests and CFD (Computational Fluid Dynamics) of mean pressure drop \(P_{meta}\) and stroke frequency \(f\). Figure 6: Variation of pressure drop \(P\) with time \(T\) for different supply volume flow rates \(Q_{V}\). Figure 6. Therefore, the frequency of pulses is double the oscillation frequency of the fluidic oscillator. In order to sufficiently generate benign oscillations and to minimize the impact on the Measurements While Drilling (MWD) and Logging While Drilling (LWD) tools, the pulse frequency is encouraged to be limited to 10 per second [1]. According to the study of [PERSON] et al. [22], increasing the diameter of the piston rod will significantly reduce the backward stroke end velocity of the piston, thus decreasing the amplitude of the smaller pulse, as displayed in Figure 6. Moreover, when the liquid force caused by the decreased pressure pulse is lower than the pre-tightening force of the disc springs, the pulse frequency of the displacement will be consistent with the oscillation frequency of the fluidic oscillator, which is about 5\(\sim\)10 Hz.