Validation of flow regime prediction model and differences of velocity component selection for rotating flow field

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

Abstract

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

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

CLC Number:

TH117

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.

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.

Figures/Tables 23

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

—

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

—

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

$V ˉ c$ /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

$V ˉ c$ /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

$V ˉ c$ /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

$V ˉ c$ /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

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

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

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

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

References 29

1	BRUNETIERE N, TOURNERIE B, FRENE J. Influence of fluid flow regime on performances of non-contacting liquid face seals[J]. Journal of Tribology, 2002, 124(3): 515-523.
2	丁雪兴, 富影杰, 张静, 等. 基于CFD的螺旋槽干气密封端面流场流态分析[J]. 排灌机械工程学报, 2010, 28(4): 330-334.
	DING Xuexing, FU Yingjie, ZHANG Jing, et al. Fluid state analysis on flow field of gas seal with spiral groove based on CFD[J]. Journal of Drainage and Irrigation Machinery Engineering, 2010, 28(4): 330-334.
3	陈汇龙, 王强, 李雯瑜, 等. 基于Fluent的螺旋槽上游泵送机械密封三维微间隙流场数值模拟[J]. 润滑与密封, 2012, 37(2): 16-18.
	CHEN Huilong, WANG Qiang, LI Wenyu, et al. Numerical simulation of 3-D flow in upstream pumping mechanical seals with spiral grooves based on Fluent[J]. Lubrication Engineering, 2012, 37(2): 16-18.
4	XU J, PENG X D, BAI S X, et al. CFD simulation of microscale flow field in spiral groove dry gas seal[C]//Proceedings of the Mechatronics and Embedded Systems and Applications IEEE/ASME International Conference, Suzhou, 2012.
5	FAIRUZ Z M, JAHN I. The influence of real gas effects on the performance of supercritical CO₂ dry gas seals[J]. Tribology International, 2016, 102: 333-347.
6	MAYER E. 机械密封[M]. 6版. 北京: 化学工业出版社, 1981: 170-173.
	MAYER E. Mechanical seal[M]. 6th ed. Beijing: Chemical Industry Press, 1981: 170-173.
7	马纲, 赵伟, 沈心敏. 螺旋槽气膜密封微间隙流场的三维数值模拟[J]. 润滑与密封, 2012, 37(3): 7-11.
	MA Gang, ZHAO Wei, SHEN Xinmin. Three dimensional numerical simulation of micro-gap flow field in spiral groove membrane seal[J]. Lubrication Engineering, 2012, 37(3): 7-11.
8	YASUNA J A, HUGHES W F. Squeeze film dynamics of two-phase seals: part Ⅱ—turbulent flow[J]. Journal of Tribology, 1994, 114(3): 479-488.
9	RANSOM D L, ANDRES L S. Identification of force coefficients from a gas annular seal-effect of transition flow regime to turbulence[J]. Tribology Transactions, 1999, 42 (3): 487-494.
10	SHAHIN I, GADALA M, ALQARADAWI M, et al. Three dimensional computational study for spiral dry gas seal with constant groove depth and different tapered grooves[J]. Procedia Engineering, 2013, 68(12): 205-212.
11	SUN J J, MA C B, YU Q P, et al. Numerical analysis on a new pump-out hydrodynamic mechanical seal[J]. Tribology International, 2017, 106: 62-70.
12	JIANG J B, PENG X D, LI J Y, et al. A comparative study on the performance of typical types of bionic groove dry gas seal based on bird wing[J]. Journal of Bionic Engineering, 2016, 13(2): 324-334.
13	WANG Y M, YANG H X, WANG J L, et al. Theoretical analyses and field applications of gas-film lubricated mechanical face seals with herringbone spiral grooves[J]. Tribology Transactions, 2009, 52(6): 800-806.
14	SU H, RAHMANI R, RAHNEJAT H. Thermohydrodynamics of bidirectional groove dry gas seals with slip flow[J]. International Journal of Thermal Sciences, 2016, 110: 270-284.
15	WANG B, ZHANG H Q, CAO H J. Flow dynamics of a spiral-groove dry-gas seal[J]. Chinese Journal of Mechanical Engineering, 2013, 26(1): 78-84.
16	丁雪兴, 张鹏高, 黄义仿, 等. 螺旋槽干气密封微间隙流场的CFD数值模拟[J]. 化工机械, 2008, 36(5): 287-290.
	DING Xuexing, ZHANG Penggao, HUANG Yifang, et al. Numerical simulation of computational fluid dynamics(CFD) of the micro-scale flow field in the spiral groove dry gas seals[J]. Chemical Engineering & Machinery, 2008, 36(5): 287-290.
17	FELDMAN Y, KLIGERMAN Y, ETSION I, et al. The validity of the reynolds equation in modeling hydrostatic effects in gas lubricated textured parallel surfaces[J]. Journal of Tribology, 2006, 128(2): 345-350.
18	张鸣远. 高等工程流体力学[M]. 北京: 高等教育出版社, 2012: 324-325.
	ZHANG Mingyuan. Advanced engineering fluid mechanics[M]. Beijing: Higher Education Press, 2012: 324-325.
19	张兆顺. 流体力学[M]. 3版. 北京: 清华大学出版社, 2015: 317-319.
	ZHANG Zhaoshun. Fluid mechanics[M]. 3rd ed. Beijing: Tsinghua University Press, 2015: 317-319.
20	陈卓如. 工程流体力学[M]. 3版. 北京: 高等教育出版社, 2013: 248-259.
	CHEN Zhuoru. Engineering fluid mechanics[M]. 3rd ed. Beijing: Higher Education Press, 2013: 248-259.
21	杜建军, 刘暾, 张国庆, 等. 带有圆周方向均压槽的静压气体止推轴承的气锤自激[J]. 润滑与密封, 2010, 35(1): 9-12.
	DU Jianjun, LIU Tun, ZHANG Guoqing, et al. Study of self-excited vibration for externally pressurized gas thrust bearing with circumferential groove[J]. Lubrication Engineering, 2010, 35(1): 9-12.
22	叶燚玺. 超精密运动平台中气浮支承振动特性的研究[D]. 武汉: 华中科技大学, 2010.
	YE Yixi. Vibration characteristics of ultra precision motion platform in the floating support[D]. Wuhan: Huazhong University of Science and Technology, 2010.
23	张鸣, 朱煜, 段广洪. 超精密气浮工件台的微振动及其抑制[J]. 制造技术与机床, 2005(11): 47-49.
	ZHANG Ming, ZHU Yu, DUAN Guanghong. Micro-vibration of ultra-precision gas bearing linear motion stage and its elimination[J]. Manufacturing Technology & Machine Tool, 2005(11): 47-49.
24	CHEN X D, HE X M. The effect of the recess shape on performance analysis of the gas-lubricated bearing in optical lithography[J]. Tribology International, 2006, 39(11): 1336-1341.
25	王衍, 葛云路, 黄国庆, 等. 干气密封旋转流场的宏观特性与介观速度场的逻辑关系研究[J].摩擦学学报, 2020, 40(3): 377-390.
	WANG Yan, GE Yunlu, HUANG Guoqing, et al. Study on the logic relationship between macroscopic characteristics and mesoscopic velocity field of high-speed rotating flow field of dry gas seal[J]. Tribology, 2020, 40(3): 377-390.
26	WANG Y, GE Y L, HUANG G Q, et al. Microscale flow field analysis and flow prediction model exploration of dry gas seal[J]. IEEE Access, 2020, 8: 52663-52675.
27	王衍, 胡琼, 肖业祥, 等. 超高速干气密封扰流效应及抑扰机制[J]. 航空学报, 2019, 40(10): 116-125.
	WANG Yan, HU Qiong, XIAO Yexiang, et al. Turbulence effect and suppression mechanism of dry gas seal at ultra-high speeds[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(10): 116-125.
28	江锦波. 高速干气密封端面型槽仿生设计理论与实验研究[D]. 杭州：浙江工业大学, 2016.
	JIANG Jinbo. Theoretical and experimental study of the bionic design of grooved surface of a high speed dry gas seal[D]. Hangzhou: Zhejiang University of Technology, 2016.
29	王衍, 孙见君, 陶凯, 等. T型槽气膜密封数值分析及槽型优化[J]. 摩擦学学报, 2014, 34(4):420-427.
	WANG Yan, SUN Jianjun, TAO Kai, et al. Numerical analysis of T-groove dry gas seal and groove optimization[J]. Tribology, 2014, 34(4): 420-427.

[1]	QI Liang, ZHANG Bo, SHANG Qinyu, WANG Yanbing, CAO Zhikai, LI Wei, ZHOU Hua. A novel method for solution of the one-dimensional dynamic mathematical model of PFR [J]. Chemical Industry and Engineering Progress, 2019, 38(s1): 70-76.
[2]	Jinyuan QIAN, Xiaojuan LI, Zan WU, Minrui CHEN, Zhijiang JIN, Bengt SUNDÉN. Research progress on flow regimes and mass transfer of liquid-liquid two-phase flow in microchannels [J]. Chemical Industry and Engineering Progress, 2019, 38(04): 1624-1633.
[3]	Ning JIANG, Fengyuan GUO, Wenqiao HAN, Huajing LIU, Lu LIN. 3E Optimization of heat exchanger network system based on non-counterflow heat transfer [J]. Chemical Industry and Engineering Progress, 2019, 38(02): 761-771.
[4]	YAO Yuting, LI Shiyu. A study on high flux heat exchanger used for low-temperature cogeneration system [J]. Chemical Industry and Engineering Progress, 2018, 37(10): 3737-3743.
[5]	TU Gongyi, ZONG Hongyuan, ZHONG Siqing, XU Jun, ZHOU Jing, XIN Zhong. Experimental study on flow characteristics of gas-solid of powdered coal in a fluidized-bed [J]. Chemical Industry and Engineering Progress, 2017, 36(S1): 180-186.
[6]	XU Dehua, JIN Hu, XU Xueqing, QIU Xiaozhong, HE Xinhua, FU Xiaoyi. Preparation and characterization of smart building paints with multiple functions [J]. Chemical Industry and Engineering Progress, 2017, 36(09): 3388-3394.
[7]	HUANG Zhixian, LIN Yixiong, WANG Hongxing, YE Changshen, LI Ling. Numerical simulation of single droplet motion in a high density difference system [J]. Chemical Industry and Engineering Progree, 2016, 35(S2): 61-67.
[8]	ZHANG Chunwei, CUI Guomin, CHEN Shang. A performance evaluation factor of heat exchanger network based on field synergy [J]. Chemical Industry and Engineering Progree, 2016, 35(12): 3825-3829.
[9]	HONG Yongqiang, CHEN Guifang, MAO Yanpeng, MA Chunyuan. Distillation characteristics of wet flue gas desulfurization serosity [J]. Chemical Industry and Engineering Progree, 2016, 35(08): 2561-2568.
[10]	WEI Dan, SONG Huaping, ZHAO Jun. Numerical simulation of interior flow field in new type pressure regulating valve [J]. Chemical Industry and Engineering Progree, 2015, 34(05): 1264-1268.
[11]	ZHANG Shenglin，CHEN Yongxiang，LI Shuangyue. Effects of process parameters on particle size distribution and productivity of narrow level product in turbo air classifier [J]. Chemical Industry and Engineering Progree, 2014, 33(05): 1113-1117.
[12]	WAN Yiqun，CUI Guomin，FANG Dajun，PENG Fuyu. Uniformity factor of heat flux in heat exchanger networks [J]. Chemical Industry and Engineering Progree, 2013, 32(09): 2043-2048.
[13]	DENG Xianhe 1，HONG Yuxiang 1，LIU Haimin 2. Study on improvement of effective heat transfer temperature difference and enhancement of compound heat transfer in laminar flow [J]. Chemical Industry and Engineering Progree, 2012, 31(11): 2390-2394.
[14]	ZHAO Ye，SUN Lin，LUO Xionglin. Research advances in pinch technology and the synthesis of multipass heat exchanger networks [J]. Chemical Industry and Engineering Progree, 2012, 31(08): 1685-1689.
[15]	HUA Ben，WU Hao，LIU Erheng. Exergy-economics based method about optimal temperature difference in heat-exchanger [J]. Chemical Industry and Engineering Progree, 2009, 28(7): 1142-.