旋转流场流态预测模型验证及其速度分量选择的差异性

doi:10.16085/j.issn.1000-6613.2020-1257

摘要/Abstract

摘要：

鉴于目前高速旋流场中的流体流态判定准则不统一、预测模型契合度不高的问题，依据流体力学基本原理及管道、缝隙流场的判定方法，本文对经典一维雷诺数及二维流量因子预测模型进行了理论重构，并尝试提出了适用于旋转流场中流体流态判定和预测的椭球模型。文章首先根据经典雷诺数模型和流动因子模型，对仿真计算和椭球模型进行了理论验证；然后对不同介质和工况参数下的速度场进行了分析计算，并与相关文献进行对比研究；最后结合对旋转流场中拐点的理论剖析，对椭球模型的合理性和科学性进行了论证，并对模型中速度分量的选择及差异性进行了讨论。结果表明：椭球模型对管道流动的预测结果与经典雷诺数模型完全一致，新模型对旋转流场中转折点的预测值较传统模型明显偏低，与实际工况更加贴近；根据椭球模型进行旋转流场的流态判定时，应选择平均直径处的线速度为剪切平均速度、进出口径向速度平均值为径向平均速度及最大轴向速度为模型输入因子。椭球模型的提出，为旋转流场在理论计算时如何科学判定流体流态提供了新的思路和判定方法。

关键词: 旋转流场, 流态, 模型验证, 速度分量, 差异性

Abstract:

In view of the problems of inconsistent criteria for determining fluid flow regime and poor agreement of prediction models in high-speed rotating flow field, according to the basic principles of fluid mechanics and the determination methods of pipe and clearance flow field, the classical one-dimensional Reynolds number and two-dimensional flow factor prediction models are reconstructed theoretically. Meanwhile, an ellipsoid determination model suitable for determining and predicting fluid flow regime in rotating flow field is proposed. Firstly, according to the classical Reynolds number model and flow factor model, the simulation calculation method and ellipsoid model are theoretically verified. Secondly, the velocity field under different media and working condition parameters is analyzed, and the results are compared with the relevant literature. Finally, the rationality and scientific of the ellipsoid model are demonstrated based on the theoretical analysis of the turning point in the rotating flow field. The selection of velocity components in the model and the differences produced are discussed. The results show that the prediction results of the pipe flow based on the ellipsoid model are completely consistent with the classical Reynolds number model, and the predicted values of the transition point in the rotating flow field by the new model is obviously lower than that of the traditional model, which is closer to the actual working condition. When determining the flow regime of the rotating flow field according to the ellipsoid model, the linear velocity at average diameter should be selected for average shear velocity, the average value of inlet and outlet radial velocity for radial average velocity and the maximum axial velocity for the input factors of the model. The proposed ellipsoid model provides a new idea and method for determining the flow regime scientifically in the theoretical calculation of rotating flow field.

Key words: rotating flow field, flow regime, model validation, velocity component, difference

中图分类号:

TH117

王衍, 曹志康, 王英尧, 胡琼, 胡鹏, 肖业祥. 旋转流场流态预测模型验证及其速度分量选择的差异性[J]. 化工进展, 2021, 40(5): 2389-2400.

WANG Yan, CAO Zhikang, WANG Yingyao, HU Qiong, HU Peng, XIAO Yexiang. Validation of flow regime prediction model and differences of velocity component selection for rotating flow field[J]. Chemical Industry and Engineering Progress, 2021, 40(5): 2389-2400.

图/表 23

图1 管流雷诺数判定模型

图2 平板缝隙流动

图3 流动因子判定模型

图4 管流和平板流的速度场分析

图5 典型旋转流的速度场

图6 高速波动时旋转流的速度场

图7 水力直径计算模型

图8 椭球判定模型

表1 三类速度分量的选择方式

速度

分量

V ˉ c = N × π × 2 r o + r i 2 × 10 - 3 60

V c = V m a x 2 - V r 2

—

径向速度

V ˉ r - i n

V ˉ r - o u t

V ˉ r = V ˉ r - i n + V ˉ r - o u t 2

轴向速度

V ˉ a

V_a-max

—

表1 三类速度分量的选择方式

速度

分量

方式一

方式二

方式三

剪切速度

V ˉ c = N × π × 2 r o + r i 2 × 10 - 3 60

V c = V m a x 2 - V r 2

—

径向速度

V ˉ r - i n

V ˉ r - o u t

V ˉ r = V ˉ r - i n + V ˉ r - o u t 2

轴向速度

V ˉ a

V_a-max

—

图9 两类旋转流场中剪切速度Vˉc的差异性

图10 两类旋转流场中径向速度Vˉr的差异性

图11 轴向速度Va的差异性

表2 管流模型验证的相关参数

管长l/mm	管径d/mm	介质	密度/kg·m^-3	黏度/Pa·s
800	20	水	1000	0.001
		空气	1.29	1.86×10^-5

表3 管流中三类模型判定值对比（水）

$V ˉ c$ /mm·s^-1	$V ˉ r$ /mm·s^-1	$V ˉ a$ /mm·s^-1	Re	λ	说明
0.0014	0.0024	50	1000	0.25	Re_a<2300，层流区
0.0018	0.0037	60	1200	0.30
0.0022	0.0051	70	1400	0.35
0.0027	0.0067	80	1600	0.40
0.0031	0.0082	90	1800	0.45
0.0035	0.0098	100	2000	0.50
0.0040	0.0115	110	2200	0.55
0.0044	0.0131	120	2400	0.60	2300≤Re_a≤4000 过渡区
0.0047	0.0147	130	2600	0.65	2300≤Re_a≤4000 过渡区
0.0050	0.0164	140	2800	0.70
0.0054	0.0180	150	3000	0.75
0.0057	0.0197	160	3200	0.80
0.0059	0.0213	170	3400	0.85
0.0062	0.0229	180	3600	0.90
0.0065	0.0245	190	3800	0.95
0.0067	0.0261	200	4000	1.00
0.0069	0.0277	210	4200	1.05	Re_a>4000湍流区
0.0072	0.0293	220	4400	1.10
0.0074	0.0309	230	4600	1.15

表3 管流中三类模型判定值对比（水）

$V ˉ c$ /mm·s^-1	$V ˉ r$ /mm·s^-1	$V ˉ a$ /mm·s^-1	Re	λ	说明
0.0014	0.0024	50	1000	0.25	Re_a<2300，层流区
0.0018	0.0037	60	1200	0.30
0.0022	0.0051	70	1400	0.35
0.0027	0.0067	80	1600	0.40
0.0031	0.0082	90	1800	0.45
0.0035	0.0098	100	2000	0.50
0.0040	0.0115	110	2200	0.55
0.0044	0.0131	120	2400	0.60	2300≤Re_a≤4000 过渡区
0.0047	0.0147	130	2600	0.65	2300≤Re_a≤4000 过渡区
0.0050	0.0164	140	2800	0.70
0.0054	0.0180	150	3000	0.75
0.0057	0.0197	160	3200	0.80
0.0059	0.0213	170	3400	0.85
0.0062	0.0229	180	3600	0.90
0.0065	0.0245	190	3800	0.95
0.0067	0.0261	200	4000	1.00
0.0069	0.0277	210	4200	1.05	Re_a>4000湍流区
0.0072	0.0293	220	4400	1.10
0.0074	0.0309	230	4600	1.15

表4 管流中三类模型判定值对比（空气）

$V ˉ c$ /mm·s^-1	$V ˉ r$ /mm·s^-1	$V ˉ a$ /mm·s^-1	Re	λ	说明
0.0189	0.1360	700	970.97	0.24	Re_a<2300，层流区
0.0275	0.1067	900	1248.39	0.31
0.0363	0.2875	1100	1525.81	0.38
0.0449	0.2299	1300	1803.23	0.45
0.0534	0.2814	1500	2080.65	0.52
0.0616	0.4879	1700	2358.06	0.59	2300≤Re_a≤4000 过渡区
0.0687	0.5708	1900	2635.48	0.66
0.0755	0.3491	2100	2912.90	0.73
0.0815	0.3629	2300	3190.32	0.80
0.0871	0.4347	2500	3467.74	0.87
0.0923	0.5172	2700	3745.16	0.94
0.0972	0.6076	2900	4022.58	1.01	Re_a>4000 湍流区
0.1018	0.7070	3100	4300.00	1.08
0.1063	0.8353	3300	4577.42	1.14
0.1105	0.9367	3500	4854.84	1.21
0.1147	1.0440	3700	5132.26	1.28
0.1190	1.1777	3900	5409.68	1.35

表4 管流中三类模型判定值对比（空气）

$V ˉ c$ /mm·s^-1	$V ˉ r$ /mm·s^-1	$V ˉ a$ /mm·s^-1	Re	λ	说明
0.0189	0.1360	700	970.97	0.24	Re_a<2300，层流区
0.0275	0.1067	900	1248.39	0.31
0.0363	0.2875	1100	1525.81	0.38
0.0449	0.2299	1300	1803.23	0.45
0.0534	0.2814	1500	2080.65	0.52
0.0616	0.4879	1700	2358.06	0.59	2300≤Re_a≤4000 过渡区
0.0687	0.5708	1900	2635.48	0.66
0.0755	0.3491	2100	2912.90	0.73
0.0815	0.3629	2300	3190.32	0.80
0.0871	0.4347	2500	3467.74	0.87
0.0923	0.5172	2700	3745.16	0.94
0.0972	0.6076	2900	4022.58	1.01	Re_a>4000 湍流区
0.1018	0.7070	3100	4300.00	1.08
0.1063	0.8353	3300	4577.42	1.14
0.1105	0.9367	3500	4854.84	1.21
0.1147	1.0440	3700	5132.26	1.28
0.1190	1.1777	3900	5409.68	1.35

表5 旋转流模型验证相关参数

外径r_o

/mm

内径r_i

/mm

膜厚h

/μm

介质压力

/MPa

环境压力

/MPa

介质

密度

/kg·m^-3

黏度

/Pa·s

图12 旋转流场

表6 上游泵送机械密封相关参数

外径r_o

/mm

内径r_i

/mm

槽深h_g

/mm

膜厚h

/mm

介质

压力p_o

/MPa

环境

压力p_i

/MPa

转速N

/r·min^-1

介质

密度

/kg·m^-3

黏度

/Pa·s

图13 上游泵送机械密封

表7 干气密封相关参数

外径r_o

/mm

内径r_i

/mm

槽深h_g

/μm

膜厚h

/μm

介质

压力p_o

/MPa

环境

压力p_i

/MPa

转速N

/r·min^-1

介质

密度

/kg·m^-3

黏度

/Pa·s

图14 干气密封

图15 不同密封形式的宏观特性变化

表8 对应工况下的模型判定结果

模型	上游泵送临界转速/10³r·min^-1		干气密封临界转速/10⁴r·min^-1
模型	层流	湍流	层流	湍流
Re	18	31	39	67
ξ	7	13	15	27
λ	—	—	0.5	0.8

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