Analysis on influencing factors of flow coefficient for the large-diameter butterfly valve
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摘要:
为了准确地描述大口径蝶阀流量特性，采用数值模拟分析了压比、开度、口径和阀前静压对流量系数的影响。结果表明：开度一定时，随着压比减小，流量系数先增加后保持不变，存在临界压比。大口径蝶阀固有流量特性为近似等百分比，当压比一定时，流量系数随开度增大先快速下降，后变得缓慢。口径和阀前静压对流量系数的影响小，可以忽略不计。在此基础上，对压比、开度和口径3个因素进行了影响显著性分析，敏感性主次顺序为开度>压比>口径，压比与开度交互作用的影响显著，其中开度小于等于55°、压比大于等于0.62时，流量系数变化最为显著，蝶阀调节灵敏性好。最后获得了流量系数，通过试验验证表明流量系数值正确，最大相对误差仅为5.07%。
Abstract:The flow characteristics of large diameter butterfly valves are one of the foundations for fast and steady control of air-in total pressure, air-in total temperature, and air-out static pressure in aero-engine altitude simulating test. The numerical simulation was adopted to accurately describe its flow characteristics. The influences of pressure ratio, opening angle, valve diameter, and valve upstream static pressure on flow coefficients of large diameter butterfly valves were researched. The results showed that the flow coefficients firstly increased then remained constant with decrease of pressure ratio. And it had a critical pressure ratio. The inherent flow characteristics of large diameter butterfly valves had approximately equal percentage. The flow coefficients decreased sharply at the beginning, then slowly along with the opening angle. The influences of valve diameter and valve upstream static pressure were smaller and can be ignored. On this basis, the influence significance of pressure ratio, opening angle, and valve diameter may be obtained. The primary and secondary order was opening angle>pressure ratio>valve diameter. The response surface analysis showed that there were significant interaction influences on the flow coefficients between pressure ratio and opening angle. And the flow coefficients varied dramatically when the opening angle was equal or lesser than 55° and pressure ratio was above or equal 0.62, indicating the adjustment sensitivity of the large diameter butterfly valves was good. Finally, the table on flow coefficient of large diameter butterfly valve was obtained on the basis of pressure ratio and opening angle. Using the test results, the maximum relative errors of the simulated values and the corresponding test values were 5.07%.
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图 1 大口径蝶阀三维结构示意图
Figure 1. Three-dimensional structure of the large-diameter butterfly valve
图 3 DN3000开度30°蝶阀的网格划分
Figure 3. Grids of the opening angle 30° DN3000 butterfly valve
图 5 有效/相对流通面积相对偏差与蝶阀开度的变化曲线
Figure 5. Curve of relative deviation of effective/relative flow cross-section area versus butterfly valve opening angle
图 7 流束收缩系数随着压比的变化曲线
Figure 7. Curves of flow filaments contraction coefficient versus pressure ratio
图 8 流量系数随着蝶阀开度的变化曲线
Figure 8. Curves of flow coefficient versus butterfly valve opening angle
图 9 相对流量与相对流通面积之间的关系
Figure 9. Curves of relative flow rate versus relative flow cross-section area
图 10 流量系数随着蝶阀口径的变化曲线
Figure 10. Curves of flow coefficient versus different diameter butterfly valve
图 11 流量系数随着阀前静压的变化曲线
Figure 11. Curves of flow coefficient versus upstream static pressure of valve
图 12 大口径蝶阀流量系数与影响因素的响应面
Figure 12. Response surface on the flow coefficients of large-diameter butterfly valve and influencing factors
表 1 不同开度下网格划分节点数和单元数
Table 1. Number of nodes and units for grid division on the condition of different opening angle
开度/（°） 单元数 节点数 15 5500600 1049723 30 5470119 1039303 45 5505927 1044587 60 5499828 1042493 75 5531984 1048412 
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表 2 不同口径蝶阀下网格划分节点数和单元数
Table 2. Number of nodes and units for grid division on the condition of different diameter butterfly valve
口径/mm 单元数 节点数 1000 4321801 818369 1400 4843862 917397 1800 5289001 1002933 2000 5423421 1029280 3000 5477877 1039607
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表 3 模型常数
Table 3. Model constancies
参数 数值 参数 数值 $ {\beta _1} $ 0.075 $ {\beta _2} $ 0.0828 $ {\beta ^*} $ 0.09 $ {\sigma _{{{k}}2}} $ 1.0 $ {\sigma _{{{k}}1}} $ 0.85 $ {\sigma _{\omega 2}} $ 0.856 $ {\sigma _{\omega 1}} $ 0.5 $ \alpha_2 $ 0.4404 $ {\alpha _1} $ 0.21 $\kappa $ 0.41
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表 4 不同口径蝶阀阀瓣厚度
Table 4. Valve cap thickness of different diameter butterfly valve
序号 口径/m 阀瓣厚度/mm 1 1.0 13.3 2 1.4 18.7 3 1.8 24.0 4 2.0 26.7 5 3.0 40.0
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表 5 模拟分析方案
Table 5. Schemes of simulation analysis
影响因素 序号 固定条件 因素变量 压比 1 DN3000
阀前静压为200 kPa0.10 2 0.30 3 0.40 4 0.46 5 0.48 6 0.50 7 0.51 8 0.52 9 0.60 10 0.61 11 0.62 12 0.70 13 0.80 14 0.90 开度/（°） 1 DN3000
阀前静压为200 kPa10 2 12 3 15 4 18 5 20 6 30 7 35 8 40 9 45 10 50 11 55 12 60 13 65 14 70 15 75 16 80 17 90 口径/mm 1 阀前静压为200 kPa
压比为0.61000 2 1400 3 1800 4 2000 5 3000 阀前
静压/kPa1 DN3000
压比为0.6100 /60 2 125 /75 3 150 /90 4 175 /105 5 200 /120
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表 6 空气的物性参数
Table 6. Physical parameters of air
压力/
kPa比定压热容/
（kJ/（kg·K））导热系数/
（W/（m·K））动力黏度/
10–5 （Pa·s）100 1.0057 0.0259 1.84824 125 1.0059 0.0259 1.84842 150 1.0061 0.0259 1.84861 175 1.0063 0.0259 1.84879 200 1.0082 0.0259 1.85045
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表 7 模拟方法的验证结果
Table 7. Verification test results of simulation method
序号 阀后
压力/kPa阀前
压力/kPa阀门
开度/（°）阀前
温度/K阀门出口流量/（kg/s） 相对
误差/%试验值 模拟值 1 15.8047 52.824 5.88 292.87 16.024 16.641 3.71 2 19.1495 70.164 7.45 300.88 27.149 27.709 2.02 3 19.1824 70.614 9.41 307.99 40.094 40.772 1.66 4 20.0849 75.272 11.89 319.06 57.079 57.701 1.08 5 19.4341 59.679 13.53 310.09 52.077 50.791 2.53 6 19.5386 60.338 14.49 312.56 55.819 56.832 1.78 7 16.9961 59.582 14.58 309.08 56.665 55.712 1.71 8 20.0006 74.457 14.71 319.72 70.680 71.876 1.66 9 20.3668 30.617 32.99 328.73 68.016 65.929 3.17 10 20.4750 30.994 33.41 324.93 70.658 68.612 2.98 11 22.1403 34.178 34.40 363.97 75.889 74.810 1.44
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表 8 不同开度下临界压比
Table 8. Critical pressure ratio at different opening angle
序号 开度（Vp）范围 临界压比 1 Vp≤20° 0.30 2 20°<Vp≤40° 0.40 3 40°<Vp≤50° 0.46 4 50°<Vp≤55° 0.48 5 55°<Vp≤65° 0.51 6 65°<Vp≤75° 0.52 7 75°<Vp≤90° 0.62
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表 9 开度20°时不同口径蝶阀的流量系数
Table 9. Flow coefficients of different diameter butterfly valve under opening angle 20°
口径/m 流量/（kg/s） 流量系数 有效流通
面积/m2相对流通
面积1.0 35.7460 0.844 0.044 0.056 1.4 70.3410 0.848 0.086 0.056 1.8 116.8624 0.852 0.142 0.056 2.0 144.3803 0.853 0.175 0.056 3.0 325.2062 0.853 0.394 0.056
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表 10 开度20°时不同阀前静压的流量系数
Table 10. Flow coefficients of valve upstream static pressure under opening angle 20°
进出口
压力/kPa流量/
（kg/s）流量系数 有效流通
面积/m2相对流通
面积100/60 171.2260 0.852 0.426 0.056 125/75 211.6410 0.852 0.426 0.056 150/90 251.9124 0.853 0.426 0.056 175/105 292.1993 0.853 0.426 0.056 200/120 325.2062 0.853 0.426 0.056
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表 11 因素水平编码
Table 11. Coding table of factor level
水平 因素 压比pr 开度Vp/（°） 口径d/m −1 0.3 15 1.0 0 0.6 45 2.0 1 0.9 90 3.0
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表 12 分析方案与模拟结果
Table 12. Analysis schemes and simulation results
序号 影响因素 流量系数 pr Vp /（°） d/m 1 0.3 15 2.0 1.233 2 0.9 15 2.0 0.696 3 0.3 90 2.0 0.434 4 0.9 90 2.0 0.358 5 0.3 45 1.0 0.558 6 0.9 45 1.0 0.334 7 0.3 45 3.0 0.557 8 0.6 45 3.0 0.541 9 0.6 15 1.0 1.151 10 0.6 90 1.0 0.433 11 0.6 15 3.0 1.167 12 0.6 90 3.0 0.433 13 0.6 45 2.0 0.540 14 0.6 45 2.0 0.539 15 0.6 45 2.0 0.539 16 0.6 45 2.0 0.539 17 0.6 45 2.0 0.539
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表 13 流量系数的方差分析（R2=
0.9929 ）Table 13. Variance analyses of flow coefficient （R2=
0.9929 ）变异来源 平方和 F值 P值 $ {p_{\text{r}}} $ 0.036 84.68 < 0.0001 **$ {V_{\text{p}}} $ 0.29 680.47 < 0.0001 **d 4.478×10–7 1.049×10–3 0.9751 $ {p_{\text{r}}}{V_{\text{p}}} $ 0.011 26.80 0.0013 **$ {p_{\text{r}}}d $ 1.714×10–5 0.040 0.8469 $ {V_{\text{p}}}d $ 8.361×10–6 0.020 0.8927 $ p_{_{\text{r}}}^2 $ 0.017 39.65 0.0004 **$ V_{_{\text{p}}}^2 $ 0.11 264.31 < 0.0001 **d2 4.725×10–5 0.11 0.7491 模型 0.046 108.58 <0.000 1** 注：P<0.01为非常显著，用**表示。
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表 14 大口径蝶阀流量系数表
Table 14. Flow coefficients of large-diameter butterfly valve
pr Vp/（°） 10 12 15 18 20 30 35 40 45 50 55 60 65 70 75 80 90 0.10 2.019 1.611 1.235 1.009 0.909 0.661 0.608 0.576 0.557 0.547 0.542 0.539 0.537 0.529 0.513 0.496 0.432 0.30 2.016 1.609 1.232 1.007 0.908 0.661 0.608 0.576 0.557 0.547 0.542 0.539 0.537 0.528 0.512 0.495 0.433 0.35 2.011 1.603 1.230 1.006 0.906 0.660 0.608 0.576 0.558 0.547 0.542 0.539 0.537 0.528 0.512 0.495 0.433 0.40 2.004 1.598 1.226 1.003 0.903 0.659 0.607 0.576 0.557 0.547 0.542 0.539 0.537 0.528 0.513 0.496 0.433 0.46 1.992 1.590 1.219 0.998 0.898 0.655 0.605 0.574 0.556 0.546 0.541 0.539 0.537 0.529 0.513 0.496 0.433 0.48 1.987 1.586 1.216 0.995 0.895 0.652 0.603 0.573 0.555 0.545 0.541 0.539 0.537 0.529 0.513 0.496 0.432 0.50 1.980 1.582 1.214 0.994 0.893 0.650 0.601 0.575 0.555 0.545 0.540 0.539 0.536 0.528 0.512 0.496 0.433 0.51 1.976 1.579 1.210 0.992 0.891 0.648 0.599 0.571 0.554 0.544 0.540 0.538 0.536 0.528 0.512 0.496 0.433 0.52 1.974 1.576 1.207 0.991 0.888 0.645 0.598 0.570 0.553 0.544 0.539 0.537 0.536 0.527 0.512 0.496 0.433 0.60 1.904 1.507 1.167 0.956 0.853 0.622 0.578 0.556 0.541 0.538 0.535 0.532 0.530 0.523 0.509 0.496 0.433 0.61 1.891 1.506 1.154 0.952 0.849 0.620 0.575 0.553 0.538 0.532 0.530 0.531 0.530 0.523 0.509 0.495 0.433 0.62 1.884 1.505 1.146 0.944 0.841 0.616 0.573 0.551 0.535 0.530 0.528 0.530 0.528 0.522 0.508 0.495 0.432 0.65 1.847 1.477 1.118 0.924 0.825 0.604 0.561 0.543 0.527 0.523 0.523 0.527 0.525 0.520 0.506 0.492 0.432 0.70 1.753 1.386 1.076 0.883 0.797 0.576 0.537 0.523 0.511 0.506 0.494 0.491 0.488 0.485 0.476 0.469 0.418 0.80 1.564 1.219 0.934 0.767 0.683 0.504 0.469 0.461 0.454 0.452 0.447 0.444 0.441 0.432 0.421 0.413 0.383 0.90 1.187 0.919 0.702 0.577 0.509 0.378 0.354 0.351 0.346 0.344 0.342 0.338 0.334 0.326 0.324 0.319 0.305 1.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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表 15 流量系数的验证试验方案和结果
Table 15. Verification test schemes and results of flow coefficients
序号 阀门
开度/（°）压比 流量系数 相对
误差/%试验值 模拟值 1 10 0.35 1.909 2.011 5.072 2 30 0.65 0.585 0.604 3.146 3 35 0.65 0.547 0.561 2.496
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