Page 249 - 《振动工程学报》2026年第5期

第 5 期 麦耘翔，等：外流与段塞内流联合作用下弹性管流致振动特性研究 1453

∆f in (−0.008,0.042,−1.021)
1.0 ∆f in (−0.065,0.068,−0.024) =4.3% 1.0 l/L=0.96 ∆f ex (1.612,0.087,−0.316) =62.1%
l/L=0.96 ∆f ex (2.251,0.151,−0.109)
0.9 0.9 l/L=0.86 ∆f in (−0.185,0.021,−0.532) =38.1%
∆f in (−0.237,0.060,−0.035) ∆f ex (1.448,0.077,0.285)
=10.9%
0.8 l/L=0.86 ∆f ex (2.046,−0.079,0.969) 0.8 ∆f in (0.308,0.044,1.180) =40.8%
∆f in (0.017,0.073,−0.234) l/L=0.76 ∆f ex (0.522,0.008,2.942)
0.7 l/L=0.76 ∆f ex (2.142,0.098,0.286) =11.4% 0.7 ∆f in (0.140,0.035,−0.184)
=12.9% l/L=0.66
∆f in (0.143,0.069,−0.048) ∆f ex (1.819,0.043,−0.006)
0.6 l/L=0.66 =12.3% 0.6
∆f ex (1.301,0.040,0.376) ∆f in (−0.350,0.015,−0.676) =73.8% l/L=0.56
l / L 0.5 l/L=0.56 ∆f in (−0.340,0.062,−0.215) =18.7% l / L 0.5 ∆f ex (1.029,0.002,0.089)
∆f in (0.181,−0.042,1.649)
∆f ex (2.010,0.019,−0.830)
0.4 l/L=0.46 ∆f in (0.295,0.068,0.101) 0.4 ∆f ex (2.580,−0.035,0.278) =64.0% l/L=0.46
∆f ex (2.063,−0.018,−0.493) =15.0% l/L=0.36 ∆f in (0.022,0.057,−0.372) =19.1%
0.3 l/L=0.36 ∆f in (0.106,0.064,−0.110) =14.8% 0.3 l/L=0.26 ∆f ex (1.801,−0.077,0.804)
∆f ex (1.003,−0.029,−0.499) ∆f in (−0.076,0.021,−0.325)
l/L=0.26 ∆f in (−0.290,0.077,−0.098) =14.5%
0.2 =13.9% 0.2 l/L=0.16 ∆f ex (2.239,−0.111,−0.567)
l/L=0.16 ∆f ex (2.227,−0.111,−0.402) ∆f in (2.088,−0.113,0.193)
∆f in (−0.035,0.066,0.140) l/L=0.06 =62.2%
0.1 l/L=0.06 ∆f ex (1.613,−0.098,−0.452) =9.5% 0.1 ∆f ex (0.094,0.059,1.301)
∆f in (0.333,0.050,0.060) ∆f in (0.103,−0.081,1.288) =89.9%
0 ∆f ex (1.732,−0.087,−0.033) =19.7% ∆f in _total −2.0 0 ∆f ex (1.522,−0.045,0.253) −0.5
0 2 4 ∆f ex _total =12.9% −1.0 −1.5 0 2 ∆f in _total =46.5% 0
∆f ex _total
6
8 10 0 −0.5 4 6 8 d CF / D
d IL / D d CF / D d IL / D 10 0.5
(a) ε g=0.1时，内/外流体力瞬时力比与对应相云图 (b) εg=0.3时，内/外流体力瞬时力比与对应相云图
(a) ε g =0.1, the instantaneous forces ratio and contour of phases (b) ε g=0.3, the instantaneous forces ratio and contour of phases
related to internal flow and external current related to internal flow and external current
2 2
方差 时均值 方差 时均值
1 1
0 0
0.06 0.26 0.46 0.66 0.86 0.06 0.26 0.46 0.66 0.86
l / L l / L
(c) εg=0.1时，内/外流体力比值时均值与方差 (d) ε g=0.3时，内/外流体力比值时均值与方差
(c) ε g=0.1, the time-average values and variances of the (d) ε g =0.3, the time-average values and variances of the
hydrodynamic forces related to internal flow and hydrodynamic forces related to internal flow and
external current external current

图 7 沿管轴向内流与外流作用力瞬时比值、相云图、时均值及方差
Fig. 7 Instantaneous ratio, contour of phases, time-average values and variances of the hydrodynamic forces related to internal flow
and external current along the pipe axis

∆f in (−0.152,0.016,−0.097)
∆f in (0.281,0.043,0.331) l/L=0.96 =7.6%
=35.5% 1.0 ∆f ex (1.956,0.117,−1.319) l/L=0.86
1.0 l/L=0.96 ∆f ex (0.668,0.054,1.030) ∆f in (−0.189,0.033,−0.005)
∆f in (0.367,0.068,0.267) l/L=0.86 =8.7%
0.9 ∆f ex (1.239,0.063,0.401) =35.2% l/L=0.86 0.9 ∆f ex (2.045,0.117,−0.836)
∆f in (−0.009,0.015,−0.004)
∆f in (−0.304,0.027,−0.466) 0.8 =0.8% l/L=0.76 l/L=0.66
0.8 ∆f ex (1.907,0.066,0.552) =28.0% l/L=0.76 ∆f ex (2.246,0.099,−0.707)
∆f in (0.022,0.011,0.024)
0.7 ∆f in (−0.046,0.018,−0.032) =3.3% l/L=0.66 0.7 ∆f ex (1.779,0.051,−0.006) =1.9% l/L=0.66
∆f ex (1.494,0.048,0.955)
0.6 ∆f in (0.306,0.029,0.743) =33.3% l/L=0.56 0.6 ∆f in (−0.056,0.034,−0.148) =8.3% l/L=0.56 l/L=0.46
∆f ex (0.827,−0.020,2.273) ∆f ex (1.604,−0.004,−1.111)
l / L 0.5 ∆f ex (−0.314,0.023,−2.678) =34.9% l/L=0.46 l / L 0.5 ∆f ex (1.714,−0.027,−0.946) =6.2% l/L=0.46
∆f in (−0.054,0.044,0.100)
∆f in (0.238,0.051,−0.909)
0.4 ∆f in (−0.163,0.037,0.034) =15.4% l/L=0.36 0.4 ∆f in (−0.017,0.008,0.026) =1.8% l/L=0.36 l/L=0.26
∆f ex (1.070,−0.031,−0.285) ∆f ex (1.678,−0.051,0.598)
∆f in (0.016,0.002,0.170) ∆f in (0.011,0.004,−0.108)
0.3 ∆f ex (2.259,−0.108,0.877) =7.0% l/L=0.26 0.3 ∆f ex (1.421,−0.082,0.924) =6.4% l/L=0.26
l/L=0.16 ∆f in (−0.006,0.009,0.211)
0.2 l/L=0.16 ∆f in (0.256,0.038,−0.449) =40.4% 0.2 =8.9% l/L=0.06
∆f ex (1.981,−0.106,1.289)
l/L=0.06 ∆f ex (0.209,−0.004,−1.266) l/L=0.06 ∆f in (0.061,0.052,−0.121)
0.1 ∆f in (0.431,0.038,−1.024) =56.9% 0.1 ∆f ex (1.507,−0.068,1.072) =7.9%
∆f ex (0.639,−0.042,−1.846)
0 ∆f in _total −0.5 0 ∆f in _total =5.9% −0.2
0 2 4 ∆f ex _total =28.8% 0 0 2 4 ∆f ex _total 0.2 0
6
8 10 1.0 0.5 6 8 10 1.0 0.4
d IL / D d CF / D d IL / D d CF / D
(a) ε g=0.5时，内/外流体力瞬时力比与对应相云图 (b) εg=0.7时，内/外流体力瞬时力比与对应相云图
(a) ε g =0.5, the instantaneous forces ratio and contour of phases (b) ε g=0.7, the instantaneous forces ratio and contour of phases
related to internal flow and external current related to internal flow and external current
0.4 方差 时均值 0.4 方差 时均值
0.2 0.2
0 0
0.06 0.26 0.46 0.66 0.86 0.06 0.26 0.46 0.66 0.86
l / L l / L
(c) εg=0.5时，内/外流体力比值时均值与方差 (d) ε g=0.7时，内/外流体力比值时均值与方差
(c) ε g=0.5, the time-average values and variances of the (d) ε g =0.7, the time-average values and variances of the
hydrodynamic forces related to internal flow and hydrodynamic forces related to internal flow and
external current external current

图 8 沿管轴向内流与外流作用力瞬时比值、相云图、时均值、方差及选定截面涡量图
Fig. 8 Instantaneous ratio, contour of phases, time-average values and variances of the hydrodynamic forces related to internal flow
and external current along the pipe axis and vorticity magnitude contours of the selected section