Analysis and calculation of void fraction of gas-liquid two-phase flow in vertical riser under fluctuating vibration

doi:10.11949/0438-1157.20230300

Abstract

Abstract:

Accurate prediction of void fraction of gas-liquid two-phase flow under undulating vibration is of great significance to the safe and stable operation of floating nuclear power plants. The void fraction characteristics of gas-liquid two-phase flow in vertical riser under different vibration and flow conditions were studied experimentally. The results show that the fluctuation vibration has a significant effect on the void fraction in bubbly flow, however it has a weak effect on slug flow, churn flow and annular flow. Generally speaking, the undulating vibration leads to an increase in the void fraction of the bubbly flow and a decrease in the void fraction of the other three flow patterns. The void fraction calculation model in static pipeline is evaluated. It is found that the existing void fraction calculation model is suitable for the calculation of void fraction under fluctuating vibration, but the prediction error of void fraction under bubbly flow and slug flow is relatively large. Considering the influence of vibration, the Froude number of liquid phase is introduced, and the calculation formula of void fraction considering flow pattern is established, which significantly improves the prediction accuracy of void fraction under fluctuating vibration.

Key words: gas-liquid two-phase flow, fluctuating vibration, riser, void fraction, computational model

摘要：

起伏振动下气液两相流含气率的准确预测对漂浮核电站的安全稳定运行有重要意义。实验研究了不同振动和流动工况下垂直上升管气液两相流的含气率特性。结果表明，起伏振动对泡状流下的含气率影响比较明显，对弹状流、搅混流和环状流的影响较弱。整体来看，起伏振动导致泡状流的含气率增加，其他三种流型下的含气率减小。对静止管道内常用的含气率计算模型进行评价，发现现有含气率计算模型比较适用于起伏振动下含气率的计算，但对泡状流和弹状流下含气率的预测误差较大。考虑振动的影响，引入了液相Froude数，建立了考虑流型的含气率计算关系式，显著提高了起伏振动下含气率的预测准确度。

关键词: 气液两相流, 起伏振动, 上升管, 含气率, 计算模型

CLC Number:

TL 334

Qichao LIU, Yunlong ZHOU, Cong CHEN. Analysis and calculation of void fraction of gas-liquid two-phase flow in vertical riser under fluctuating vibration[J]. CIESC Journal, 2023, 74(6): 2391-2403.

刘起超, 周云龙, 陈聪. 起伏振动垂直上升管气液两相流截面含气率分析与计算[J]. 化工学报, 2023, 74(6): 2391-2403.

Figures/Tables 16

Fig.1 Experimental system

Table 1 Experimental instrument and uncertainty

测量参数	仪器	量程	精度	相对不确定度/%
水流量	电磁流量计（DN15）	0~4 m³/h	0.5%	1.17~10.52
水流量	电磁流量计（DN50）	0~10 m³/h	0.5%	1.17~10.52
气流量	质量流量计（DN15）	0~10 m³/h(标准工况)	0.5%	0.57~15.71
气流量	质量流量计（DN20）	0~30 m³/h(标准工况)	0.5%	0.57~15.71
加速度	加速度传感器	±1 g	0.5%	0.07~16.02
含液量	量尺	3 m	1 mm	0.06~3.2

Fig.2 Change rate of void fraction under different oscillation conditions

Fig.3 Effective oscillation conditions in A-f plots

Table 2 k-β models

模型	公式
Armand^[23]	$α = 0.833 β$
Massena^[24]	$α = 0.833 + 0.167 x β$
Nishino^[25]	$α = 1 - 1 - x x × ρ G ρ L β 0.5$
Greskovich^[26]	$α = 1 + 0.671 (s i n θ) 0.263 F r m 0.5 - 1 β$
Chisholm^[27]	$α = 1 β + 1 - β 0.5 β$
Czop^[28]	$α = 1.097 β - 0.285$
Hajal^[29]	$α = β - α r a l n β / α r a$ ， $α r a = x ρ G 1 + 0.12 1 - x x ρ G + 1 - x ρ L + 1.18 1 - x g σ ρ L - ρ G 0.25 G ρ L 0.5 - 1$

Table 2 k-β models

模型	公式
Armand^[23]	$α = 0.833 β$
Massena^[24]	$α = 0.833 + 0.167 x β$
Nishino^[25]	$α = 1 - 1 - x x × ρ G ρ L β 0.5$
Greskovich^[26]	$α = 1 + 0.671 (s i n θ) 0.263 F r m 0.5 - 1 β$
Chisholm^[27]	$α = 1 β + 1 - β 0.5 β$
Czop^[28]	$α = 1.097 β - 0.285$
Hajal^[29]	$α = β - α r a l n β / α r a$ ， $α r a = x ρ G 1 + 0.12 1 - x x ρ G + 1 - x ρ L + 1.18 1 - x g σ ρ L - ρ G 0.25 G ρ L 0.5 - 1$

Table 3 Slip ratio models

模型	滑移参数
Lockhart^[30]	B₁=0.28，B₂=0.64，B₃=0.36，B₄=0.07
Fauske^[31]	B₁=1，B₂=1，B₃=0.5，B₄=0
Thom^[32]	B₁=1，B₂=1，B₃=0.89，B₄=0.18
Zivi^[33]	B₁=1，B₂=1，B₃=0.67，B₄=0
Turner^[34]	B₁=1，B₂=0.72，B₃=0.4，B₄=0.08
Baroczy^[35]	B₁=1，B₂=0.74，B₃=0.65，B₄=0.13
Smith^[1]	$B 1 = 0.4 + 0.6 ρ L ρ G + 0.4 1 - x x / 1 + 0.4 1 - x x$ ， B₂=1，B₃=1，B₄=0
Chisholm^[36]	$B 1 = 1 - x 1 - ρ L ρ G$ ，B₂=1，B₃=1，B₄=0
Spedding^[37]	B₁=2.22，B₂=0.65，B₃=0.65，B₄=0
Chen^[38]	B₁=0.18，B₂=0.6，B₃=0.33，B₄=0.07
Hamersma^[39]	B₁=0.26，B₂=0.67，B₃=0.33，B₄=0
Petalaz^[40]	$B 1 = 0.735 μ L 2 J G 2 / σ 2 0.074$ ，B₂=-0.2，B₃=-0.126，B₄=0

Table 3 Slip ratio models

模型	滑移参数
Lockhart^[30]	B₁=0.28，B₂=0.64，B₃=0.36，B₄=0.07
Fauske^[31]	B₁=1，B₂=1，B₃=0.5，B₄=0
Thom^[32]	B₁=1，B₂=1，B₃=0.89，B₄=0.18
Zivi^[33]	B₁=1，B₂=1，B₃=0.67，B₄=0
Turner^[34]	B₁=1，B₂=0.72，B₃=0.4，B₄=0.08
Baroczy^[35]	B₁=1，B₂=0.74，B₃=0.65，B₄=0.13
Smith^[1]	$B 1 = 0.4 + 0.6 ρ L ρ G + 0.4 1 - x x / 1 + 0.4 1 - x x$ ， B₂=1，B₃=1，B₄=0
Chisholm^[36]	$B 1 = 1 - x 1 - ρ L ρ G$ ，B₂=1，B₃=1，B₄=0
Spedding^[37]	B₁=2.22，B₂=0.65，B₃=0.65，B₄=0
Chen^[38]	B₁=0.18，B₂=0.6，B₃=0.33，B₄=0.07
Hamersma^[39]	B₁=0.26，B₂=0.67，B₃=0.33，B₄=0
Petalaz^[40]	$B 1 = 0.735 μ L 2 J G 2 / σ 2 0.074$ ，B₂=-0.2，B₃=-0.126，B₄=0

Table 4 Drift flux models

模型	公式
Nicklin^[41]	$α = J G / 1.2 J G + J L + 0.35 g D$
Hughmark^[42]	$α = J G / 1.2 J G + J L$
Gregory^[43]	$α = J G / 1.19 J G + J L$
Rouhani^[44]	$α = x ρ G C 0 x ρ G + 1 - x ρ L + U g m G - 1$ $U g m = 1.18 ρ L g σ ρ L - ρ G 0.25$ 如果 $α ≤ 0.1$ ， $C 0 = 1 + 0.2 1 - x$ 如果 $α ≥ 0.1$ ， $C 0 = 1 + 0.2 1 - x g D 0.25 ρ L G 0.5$
Bonnecaze^[45]	$α = J G / 1.2 J G + J L + 0.35 g D 1 - ρ G ρ L$
Dix^[46]	$α = J G / J G 1 + J L J G ρ L ρ G 0.1 + 2.9 g σ ρ L - ρ G ρ L 2 0.25$
Mattar^[47]	$α = J G / 1.3 J G + J L + 0.7$
Greskovich^[26]	$α = J G / J G + J L + 0.71 g D s i n θ 0.263$
Sun^[48]	$α = J G / 0.82 + 0.18 P P c r - 1 J G + J L +$ $1.41 g σ ρ L - ρ G ρ L 2 0.25$
Jowitt^[49]	$α = J G / 1 + 0.796 e x p - 0.061 ρ L ρ G J G + J L + 0.034 ρ L ρ G - 1$
Kokal^[50]	$α = J G / 1.2 J G + J L + 0.345 g D ρ L - ρ G ρ L$
Bestion^[51]	$α = J G / J G + J L + 0.188 g D ρ L - ρ G ρ G$

Table 4 Drift flux models

模型	公式
Nicklin^[41]	$α = J G / 1.2 J G + J L + 0.35 g D$
Hughmark^[42]	$α = J G / 1.2 J G + J L$
Gregory^[43]	$α = J G / 1.19 J G + J L$
Rouhani^[44]	$α = x ρ G C 0 x ρ G + 1 - x ρ L + U g m G - 1$ $U g m = 1.18 ρ L g σ ρ L - ρ G 0.25$ 如果 $α ≤ 0.1$ ， $C 0 = 1 + 0.2 1 - x$ 如果 $α ≥ 0.1$ ， $C 0 = 1 + 0.2 1 - x g D 0.25 ρ L G 0.5$
Bonnecaze^[45]	$α = J G / 1.2 J G + J L + 0.35 g D 1 - ρ G ρ L$
Dix^[46]	$α = J G / J G 1 + J L J G ρ L ρ G 0.1 + 2.9 g σ ρ L - ρ G ρ L 2 0.25$
Mattar^[47]	$α = J G / 1.3 J G + J L + 0.7$
Greskovich^[26]	$α = J G / J G + J L + 0.71 g D s i n θ 0.263$
Sun^[48]	$α = J G / 0.82 + 0.18 P P c r - 1 J G + J L +$ $1.41 g σ ρ L - ρ G ρ L 2 0.25$
Jowitt^[49]	$α = J G / 1 + 0.796 e x p - 0.061 ρ L ρ G J G + J L + 0.034 ρ L ρ G - 1$
Kokal^[50]	$α = J G / 1.2 J G + J L + 0.345 g D ρ L - ρ G ρ L$
Bestion^[51]	$α = J G / J G + J L + 0.188 g D ρ L - ρ G ρ G$

Table 5 Empirical formula models

模型	公式
Sterman^[52]	$α = 0.2 J G 4 ρ G 0.6 ρ L - ρ G 0.4 g σ 0.2 d 1 D 0.25$ $d 1 = 260 ρ G 0.2 ρ L - ρ G 0.7 σ g 0.5$ ,如果 $d 1 D > 1$ ，则 $d 1 D = 1$
Flanigan^[53]	$α = 1 / 1 + 3.063 J G - 1.006$
Neal^[54]	$α = 1.25 J G J G + J L 1.88 J L 2 g D 0.2$
Walli^[55]	$α = 1 + X t t 0.8 - 0.38$ ， $X t t = 1 - x x 0.9 ρ G ρ L 0.5 μ L μ G 0.1$
El-Boher^[56]	$α = 1 / 1 + 0.27 x 1 - x × ρ L ρ G - 0.69 ×$ $F r - 0.177 μ L μ G 0.378 R e L W e L 0.067$ $F r = J L 2 g D$ ， $R e L = ρ L J L D μ L$ ， $W e L = ρ L J L 2 D σ$
Huq^[57]	$α = 1 - 2 1 - x 2 1 - 2 x + 1 + 4 x 1 - x ρ L ρ G - 1 0.5$
Graham^[58]	$α = 1 + 1 F t + 1 X t t - 0.321$ ， $F t = G 2 x 3 1 - x ρ G 2 g D 0.5$
Cioncolini^[59]	$α = h x n 1 + h - 1 x n$ ， $h = - 2.129 + 3.129 ρ G ρ L - 0.2186$ ， $n = 0.3487 + 0.6513 ρ G ρ L 0.515$

Table 5 Empirical formula models

模型	公式
Sterman^[52]	$α = 0.2 J G 4 ρ G 0.6 ρ L - ρ G 0.4 g σ 0.2 d 1 D 0.25$ $d 1 = 260 ρ G 0.2 ρ L - ρ G 0.7 σ g 0.5$ ,如果 $d 1 D > 1$ ，则 $d 1 D = 1$
Flanigan^[53]	$α = 1 / 1 + 3.063 J G - 1.006$
Neal^[54]	$α = 1.25 J G J G + J L 1.88 J L 2 g D 0.2$
Walli^[55]	$α = 1 + X t t 0.8 - 0.38$ ， $X t t = 1 - x x 0.9 ρ G ρ L 0.5 μ L μ G 0.1$
El-Boher^[56]	$α = 1 / 1 + 0.27 x 1 - x × ρ L ρ G - 0.69 ×$ $F r - 0.177 μ L μ G 0.378 R e L W e L 0.067$ $F r = J L 2 g D$ ， $R e L = ρ L J L D μ L$ ， $W e L = ρ L J L 2 D σ$
Huq^[57]	$α = 1 - 2 1 - x 2 1 - 2 x + 1 + 4 x 1 - x ρ L ρ G - 1 0.5$
Graham^[58]	$α = 1 + 1 F t + 1 X t t - 0.321$ ， $F t = G 2 x 3 1 - x ρ G 2 g D 0.5$
Cioncolini^[59]	$α = h x n 1 + h - 1 x n$ ， $h = - 2.129 + 3.129 ρ G ρ L - 0.2186$ ， $n = 0.3487 + 0.6513 ρ G ρ L 0.515$

Table 6 The MARD of k-β models

模型	MARD/%
模型	弹状流	泡状流	搅混流	环状流	总体
Armand^[23]	15.0	21.2	8.6	9.4	11.9
Massena^[24]	15.0	21.2	8.5	9.1	11.8
Nishino^[25]	34.8	27.9	18.6	9.2	23.0
Greskovich^[26]	15.6	27.5	10.3	10.7	13.7
Chisholm^[27]	16.2	19.5	9.9	7.5	12.4
Czop^[28]	37.0	59.3	16.4	11.4	26.3
Hajal^[29]	11.5	27.3	8.8	7.6	11.4

Table 7 The MARD of slip ratiomodels

模型	MARD/%
模型	弹状流	泡状流	搅混流	环状流	总体
Lockhart^[30]	37.7	21.8	24.0	13.1	26.2
Fauske^[31]	89.3	92.1	75.5	52.7	78.1
Thom^[32]	51.3	55.6	25.3	6.7	33.5
Zivi^[33]	71.7	76.9	47.3	21.0	53.9
Turner^[34]	80.5	80.3	67.8	50.8	70.5
Baroczy^[35]	44.8	37.2	26.8	12.2	31.1
Smith^[1]	18.6	17.5	11.1	7.4	13.4
Chisholm^[36]	16.1	19.5	9.8	7.4	12.4
Spedding^[37]	34.0	17.1	20.9	10.8	22.9
Chen^[38]	18.1	18.2	12.2	7.8	13.9
Hamersma^[39]	38.9	25.2	24.0	12.3	26.8
Petalaz^[40]	42.0	181.0	15.9	23.6	42.5

Table 8 The MARD of drift flux models

模型	MARD/%
模型	弹状流	泡状流	搅混流	环状流	总体
Nicklin^[41]	21.0	20.5	11.1	10.1	14.8
Hughmark^[42]	15.0	21.4	8.5	9.4	11.9
Gregory^[43]	14.4	21.8	8.1	9.0	11.5
Rouhani^[44]	19.0	20.9	10.1	9.6	13.8
Bonnecaze^[45]	21.0	20.5	11.1	10.1	14.8
Dix^[46]	41.0	19.2	22.3	17.1	26.6
Mattar^[47]	20.9	20.5	11.0	10.1	14.8
Greskovich^[26]	16.2	27.5	10.2	10.5	13.9
Sun^[48]	16.8	31.8	17.4	19.1	19.0
Jowitt^[49]	20.9	20.2	11.4	10.7	15.0
Kokal^[50]	40.5	20.1	18.6	11.4	24.1
Bestion^[51]	58.2	29.0	29.1	12.7	35.2

Table 9 The MARD of empirical formula models

模型	MARD/%
模型	弹状流	泡状流	搅混流	环状流	总体
Sterman^[52]	37.1	67.3	73.1	179.2	77.0
Flanigan^[53]	58.0	23.5	27.9	14.0	34.2
Neal^[54]	25.4	16.0	20.6	14.4	20.6
Wallis^[55]	21.9	57.5	39.5	39.9	36.5
El-Boher^[56]	30.0	49.1	32.6	42.8	35.1
Huq^[57]	21.0	16.1	12.5	7.9	14.7
Graham^[58]	21.9	39.4	11.3	11.6	17.5
Cioncolini^[59]	8.7	55.6	8.5	8.6	13.7

Fig.4 The prediction errors distribution of different models under different flow patterns

Fig.5 Relationship between void fraction and dimensionless parameter (JL/JG)/FrLv of bubble flow and slug flow

Fig.6 Comparison of experimental data and model prediction results

Fig.7 Comparison of experimental data and model prediction results under different amplitudes and frequencies

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