The pressure head evolutions by the SF-VE, the CB-UF-VE and the MIAB-UF-VE in Figures 8 and 9, the corresponding retarded strain and velocity evolutions in Figures 10(a), 11(a), 12(a), 13(a), 14(a) and 15(a), the elastic strain evolutions in Figures 10(b), 11(b), 12(b), 13(b), 14(b) and 15(b) at T2 and T3 are similar to that at T1 for Case 2, respectively. As can be seen in Figures 3(b) and 8(b), the main difference between the transients at T2 and T1 is that the predicted pressure transient near the maximum at T2 behaves like the transient flow inside an elastic pipeline, although the viscoelastic model also gives the corresponding retarded strain, but the experimental one at T2 behaves like the retarded strain transient in the viscoelastic pipeline. Both the predicted pressure transient characteristics and the experimental one near the maximum pressure at T3 are more like the transient flow in an elastic pipeline. Also, the difference among T1, T2 and T3 is determined mainly by the relative magnitudes of both the corresponding elastic strain and retarded strain. The maximum retarded strain and the maximum elastic strain by the three viscoelastic models at T1, T2 and T3 are shown in Table 2, at T1 are 35, 36 and 34% by the SF-VE, the CB-UF-VE and the MIAB-UF-VE, respectively, at T2 by the three viscoelastic models are all 32%, and at T3 by the three viscoelastic models are all 26%. The maximum total strains at T2 produced by the SF-VE, the CB-UF-VE and the MIAB-UF-VE are 7.11E-4, 7.28E-4 and 7.1E-4, respectively, in Figure 16. The maximum total strains at T3 produced by the SF-VE, the CB-UF-VE and the MIAB-UF-VE are 6.47E-4, 6.54E-4 and 6.47E-4, respectively, in Figure 17. The comparisons of the maximum total strains at T1, T2 and T3 show that the farther away from the downstream valve, the smaller the maximum total strains, which is consistent with the maximum pressure at the corresponding positions.

Table 2

Viscoelastic models . | T1 . | T2 . | T3 . | |||
---|---|---|---|---|---|---|

. | . | . | . | . | . | |

SF-VE | 2.00E-04 | 5.77E-04 | 1.72E-04 | 5.40E-04 | 1.33E-04 | 5.18E-04 |

CB-UF-VE | 2.06E-04 | 5.79E-04 | 1.76E-04 | 5.54E-04 | 1.34E-04 | 5.23E-04 |

MIAB-UF-VE | 2.00E-04 | 5.79E-04 | 1.72E-04 | 5.39E-04 | 1.33E-04 | 5.17E-04 |

Viscoelastic models . | T1 . | T2 . | T3 . | |||
---|---|---|---|---|---|---|

. | . | . | . | . | . | |

SF-VE | 2.00E-04 | 5.77E-04 | 1.72E-04 | 5.40E-04 | 1.33E-04 | 5.18E-04 |

CB-UF-VE | 2.06E-04 | 5.79E-04 | 1.76E-04 | 5.54E-04 | 1.34E-04 | 5.23E-04 |

MIAB-UF-VE | 2.00E-04 | 5.79E-04 | 1.72E-04 | 5.39E-04 | 1.33E-04 | 5.17E-04 |

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

Figure 14

Figure 15

Figure 16

Figure 17

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