## 3 Results
### Numerical Simulation Verification by Experiments for 4-5 Tested DN 250 UFMs  
For four and five tested UFMs, only the numerical results were further presented and analyzed, owing to the lack of an adequate number of the same-type tested UFMs (Daniel 3400) in NJMS and the severe work schedule disturbance resulting from highly time-consuming experiments in this study, especially mounting and remounting the tested UFMs. Even so, the numerical methods used for the less-tested UFMs were verified in the previous section.  
Similar to the case of three tested UFMs, the \(E\)-\(Q\) curves for four tested UFMs were also concentrated into two distinctly separate striped regions and exhibited a negative power-law shape, but the \(E\)-\(Q\) curves of UFM3 and UFM4 were closer to that for a single UFM in the lower striped region, whereas those of UFM1 and UFM2 were distributed in the upper striped region, as depicted in Figure 5. Compared with the UFMs' maximum permissible error of 1.0%, the average deviation between the lower and the upper striped region are roughly 0.15%, as \(Q\) > 1000 m\({}^{3}\)/h, and then could be acceptable. This also suggests that it is practical to simultaneously verify four tested UFMs in a tandem arrangement. Furthermore, the increase in \(n\) from three to four may be a trigger for the transposition between \(E\)-\(Q\) curves of downstream UFMs (UFM3, UFM4, or UFM5) and those of upstream UFMs (UFM1 or UFM2), and a similar behavior was found for five tested UFMs. The flow through from UFM2 to UFM3 led to the appearance of the two power-law striped regions of \(E\)-\(Q\) curves for four tested UFMs, namely, a pronounced shift in the \(E\)-\(Q\) curves, whereas that from UFM4 to UFM5 does so for five tested UFMs. These results imply that \(n\) probably decreases the similarity of flow fields at different testing locations, especially the velocity profiles on the same-type paths, which may be partly attributed to the flow distortion at the transducer recesses due to the relatively clear negative velocity and difference in U-Profiles along paths. Thus, it is reasonable to presume that SVUFMST would perform more poorly with more tested UFMs.  
It is noted that once an \(E\) difference is obtained beyond 1/3 of the maximum permissible error, \(E_{\text{max}}\), of the tested UFM (Daniel 3400), SVUFMST cannot be conducted according to the verification regulation of UFMs (JFG1030-2007). For five tested UFMs, there were still two power-law striped regions into which the \(E\)-\(Q\) curves of UFM1-UFM4 and UFM5 are concentrated, respectively. Unlike the grouping of the former \(E\)-\(Q\) curves, only the \(E\)-\(Q\) curve of UFM5 concentrated into the lower striped region, which was, as in our study, the only negative striped region; the other four \(E\)-\(Q\) curves were uniformly distributed, but the UFM located more upstream was associated with the larger relative error E, as mentioned above. The striking average difference of \(E\) between the upper striped region and the lower striped region is higher than 1% on the same level as \(E_{\text{max}}\), as shown in Figure 6b. Table 4 lists the important parameters for the best-fit power-law expressions, in which the sudden decrease in the intercept \(k\) of the \(E\)-\(Q\) curve at UFM5 is equal to 1.713, whereas \(k\) of the other \(E\)-\(Q\) curves (\(n=5\)) is zero. This suggests that as the gas flows through five tested UFMs, the flow distortion was significantly strengthened, and the decrease in the internal flow uniformity significantly destroyed the consistency of the UFMs' measurement conditions. Therefore, the invalidation of the SVUFMST for \(n=5\) is numerically proved.