基于实验数据的湍流扩散POD模态分析

doi:10.11949/0438-1157.20210304

摘要/Abstract

摘要：

采用粒子成像测速（PIV）和激光诱导荧光（LIF）技术同时测量了水平通道中湍流扩散过程的流速和荧光剂浓度的瞬时分布，并利用实验数据，通过本征正交分解（POD）模态分析方法，实现了湍流条件下荧光剂扩散过程中浓度分布的数值重构。该方法应用于瞬时浓度分布的特征分析中，得到了瞬时分布的各阶模态，并分析各阶模态空间分布特征及其所含能量。结果表明，浓度分布在距离荧光剂入口较近的区域具有较强的周期性，且低阶POD模态能量占主导地位。应用POD分析得到的模态可以较准确地重构距离荧光剂入口较近区域的浓度分布的基本特征，相对误差主要集中于距离荧光剂入口较远的区域，表明本文提出的基于POD模态分析的湍流条件下浓度场的数值重构更适用于周期性较强的系统，为预测未知时刻的湍流扩散浓度分布提供了基础。

关键词: 湍流扩散, POD分析, 粒子成像测速, 激光诱导荧光

Abstract:

In this paper, velocity and concentration distributions of fluorescent agent in turbulent liquid flow in a horizontal channel were experimentally measured by simultaneous use of particle image velocimetry (PIV) and laser induced fluorescence (LIF) technologies. Then an approach to numerical reconstruction of the concentration distribution by using the proper orthogonal decomposition (POD) analysis based on the experimental data was developed. For doing this, the POD method was applied to analyze instantaneous concentration distribution characteristics, and obtain different modes of the concentration distribution, and the spatial characteristics of the modes and their energy were analyzed. The results show that the concentration distribution in the area close to the phosphor inlet has a strong periodicity, and the low-order POD mode energy is dominant. The modalities obtained by applying POD analysis can more accurately reconstruct the basic characteristics of the concentration distribution in the area closer to the phosphor inlet, and the relative error is mainly concentrated in the area which is far from the injection mouth. This suggests that the POD analysis approach proposed in the present paper is suitable for numerical reconstruction of concentration distribution in the turbulent flow systems with periodicity, and thus lays a foundation for effective prediction of concentration distribution in turbulent diffusion processes.

Key words: turbulent diffusion, POD analysis, PIV, LIF

中图分类号:

TQ 021.4

王芳,贾胜坤,张会书,袁希钢,余国琮. 基于实验数据的湍流扩散POD模态分析[J]. 化工学报, 2021, 72(9): 4531-4543.

Fang WANG,Shengkun JIA,Huishu ZHANG,Xigang YUAN,Kuotsung YU. POD modal analysis of turbulent diffusion based on experimental data[J]. CIESC Journal, 2021, 72(9): 4531-4543.

图/表 15

图1 实验装置1,2—储水槽;3—潜水泵;4—荧光素钠溶液;5—隔膜泵;6,12—转子流量计;7—Nd:YAG激光器;8—片状透镜;9—反射镜;10—格栅;11—流体通道;13,14—CCD相机;15—计算机

Fig.1 Schematic diagram of experimental apparatus

图2 荧光强度-荧光素钠浓度标定曲线

Fig.2 Calibration curve between fluorescence intensity and C20H10Na2O5 concentration

图3 LIF图像处理流程图

Fig.3 Flow diagram for LIF image processing

图4 荧光素钠在湍流水中扩散过程的不同时刻荧光素钠浓度分布（中心位置z=0）

Fig.4 Concentration distribution during diffusion process at different times (central position z=0)

图5 平均浓度分布和平均速度分布（中心位置z =0）

Fig.5 Mean concentration and velocity distribution(central position z =0)

图6 不同切面位置平均浓度分布

Fig.6 Mean concentration distribution of different section positions

图7 不同切面平均浓度分布轴向方向距离入口0~50 mm处平均浓度变化

Fig.7 The mean concentration distribution of different sections at 0 to 50 mm away from the outlet in the axial direction

图8 截取后的瞬时浓度分布（t=10 s）

Fig.8 Instantaneous concentration field after interception(t=10 s)

图9 POD前4阶模态θ值的分布

Fig.9 Distribution of θ of the first 4 POD modes

图10 平均时间系数

Fig.10 Mean temporal coefficient

图11 POD模态能量（A和B区）

Fig.11 POD modal energy (A and B regions)

图12 POD模态重构

Fig.12 POD modal reconstruction

图13 不同轴向位置的模态重构和原始浓度分布

Fig.13 Modal reconstruction and original concentration distribution of different coaxial positions

图14 模态重构相对误差

Fig.14 Relative error of modal reconstruction

图15 模态重构平均相对误差（A和B区）

Fig.15 Mean relative error of modal reconstruction (A and B regions)

参考文献 33

1	余国琮, 袁希钢. 化工计算传质学导论[M]. 天津: 天津大学出版社, 2011: 263-327.
	Yu G C, Yuan X G. Introduction to Computational Mass Transfer [M]. Tianjin: Tianjin University Press, 2011: 263-327.
2	Lemoine F, Wolff M, Lebouché M. Experimental investigation of mass transfer in a grid-generated turbulent flow using combined optical methods[J]. International Journal of Heat and Mass Transfer, 1997, 40(14): 3255-3266.
3	Lemoine F, Antoine Y, Wolff M, et al. Some experimental investigations on the concentration variance and its dissipation rate in a grid generated turbulent flow[J]. International Journal of Heat and Mass Transfer, 2000, 43(7): 1187-1199.
4	Funatani S, Fujisawa N, Ikeda H. Simultaneous measurement of temperature and velocity using two-colour LIF combined with PIV with a colour CCD camera and its application to the turbulent buoyant plume[J]. Measurement Science and Technology, 2004, 15(5): 983-990.
5	Sheng J, Meng H, Fox R O. A large eddy PIV method for turbulence dissipation rate estimation[J]. Chemical Engineering Science, 2000, 55(20): 4423-4434.
6	Lemoine F, Antoine Y, Wolff M, et al. Mass transfer properties in a grid generated turbulent flow: some experimental investigations about the concept of turbulent diffusivity[J]. International Journal of Heat and Mass Transfer, 1998, 41(15): 2287-2295.
7	Sun Z M, Yu K T, Yuan X G, et al. A modified model of computational mass transfer for distillation column[J]. Chemical Engineering Science, 2007, 62(7): 1839-1850.
8	Liu G B, Yu K T, Yuan X G, et al. A numerical method for predicting the performance of a randomly packed distillation column[J]. International Journal of Heat and Mass Transfer, 2009, 52(23/24): 5330-5338.
9	Dong B, Yuan X G, Yu K T. Determination of liquid mass-transfer coefficients for the absorption of CO₂ in alkaline aqueous solutions in structured packing using numerical simulations[J]. Chemical Engineering Research and Design, 2017, 124: 238-251.
10	Zhang C, Yuan X G, Luo Y Q, et al. Prediction of species concentration distribution using a rigorous turbulent mass diffusivity model for bubble column reactor simulation (Ⅰ): Application to chemisorption process of CO₂ into NaOH solution[J]. Chemical Engineering Science, 2018, 184: 161-171.
11	Taira K, Kunihiko T, et al. Proper orthogonal decomposition in fluid flow analysis(Ⅰ): Introduction[J]. Journal of Japan Society of Fluid Mechanics(Nagare), 2011, 30(2):115-123.
12	Rowley C W. Model reduction for fluids, using balanced proper orthogonal decomposition[J]. International Journal of Bifurcation and Chaos, 2005, 15(3): 997-1013.
13	Kerschen G, Golinval J C, Vakakis A F, et al. The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: an overview[J]. Nonlinear Dynamics, 2005, 41(1/2/3): 147-169.
14	Zhang Q S, Liu Y Z. Influence of incident vortex street on separated flow around a finite blunt plate: PIV measurement and POD analysis[J]. Journal of Fluids and Structures, 2015, 55: 463-483.
15	Lacassagne T, Simoëns S, Hajem M EL, et al. POD analysis of oscillating grid turbulence in water and shear thinning polymer solution[J]. AIChE Journal, 2021, 67(1): e17044.
16	Taira K, Hemati M S, Brunton S L, et al. Modal analysis of fluid flows: applications and outlook[J]. AIAA Journal, 2020, 58(3): 998-1022.
17	Simoens S, Ayrault M. Concentration flux measurements of a scalar quantity in turbulent flows[J]. Experiments in Fluids, 1994, 16(3/4): 273-281.
18	Chang K C, Lee K H. Determination of mixing length in turbulent mixing layer on basis of vorticity field[J]. International Journal of Heat and Fluid Flow, 2017, 66: 121-126.
19	Hjertager L K, Hjertager B H, Deen N G, et al. Measurement of turbulent mixing in a confined wake flow using combined PIV and PLIF[J]. The Canadian Journal of Chemical Engineering, 2003, 81(6): 1149-1158.
20	傅强, 张会书, 胡楠, 等. 水溶解CO₂过程界面对流现象的PIV/LIF测量及传质系数预测[J]. 化工学报, 2018, 69(2): 586-594.
	Fu Q, Zhang H S, Hu N, et al. Simultaneous PIV/LIF measurements of interfacial convection during CO₂ dissolution in water and prediction of mass transfer coefficient[J]. CIESC Journal, 2018, 69(2): 586-594.
21	曹艳华. 四维变分资料同化的降维方法及在海洋资料同化中的应用[D]. 北京: 首都师范大学, 2006.
	Cao Y H. Reducing dimension method of four dimensional variational data assimilation data assimilation and application in ocean data assimilation[D]. Beijing: Capital Normal University, 2006.
22	邱翔, 刘宇陆. 湍流的相干结构[J]. 自然杂志, 2004, 26(4): 187-193.
	Qiu X, Liu Y L. Turbulent coherent structure[J]. Nature Magazine, 2004, 26(4): 187-193.
23	Qin W J, Xie M Z, Jia M, et al. Large eddy simulation and proper orthogonal decomposition analysis of turbulent flows in a direct injection spark ignition engine: cyclic variation and effect of valve lift[J]. Science China Technological Sciences, 2014, 57(3): 489-504.
24	de Lamotte A, Delafosse A, Calvo S, et al. Analysis of PIV measurements using modal decomposition techniques, POD and DMD, to study flow structures and their dynamics within a stirred-tank reactor[J]. Chemical Engineering Science, 2018, 178: 348-366.
25	Taira K, Brunton S L, Dawson S T M, et al. Modal analysis of fluid flows: an overview[J]. AIAA Journal, 2017, 55(12): 4013-4041.
26	Hall K C, Thomas J P, Dowell E H. Proper orthogonal decomposition technique for transonic unsteady aerodynamic flows[J]. AIAA Journal, 2000, 38(10): 1853-1862.
27	Graftieaux L, Michard M, Grosjean N. Combining PIV, POD and vortex identification algorithms for the study of unsteady turbulent swirling flows[J]. Measurement Science and Technology, 2001, 12(9): 1422-1429.
28	Rowley C W, Colonius T, Murray R M. Model reduction for compressible flows using POD and Galerkin projection[J]. Physica D: Nonlinear Phenomena, 2004, 189(1/2): 115-129.
29	Towne A, Schmidt O T, Colonius T. Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis[J]. Journal of Fluid Mechanics, 2018, 847: 821-867.
30	Berger J, Guernouti S, Woloszyn M. Evaluating model reduction methods for heat and mass transfer in porous materials: proper orthogonal decomposition and proper generalized decomposition[J]. Journal of Porous Media, 2019, 22(3): 363-385.
31	赵朋龙, 陈耀慧, 董刚, 等. 基于本征正交分解的湍流边界层中条带结构实验研究[J]. 南京理工大学学报(自然科学版), 2019, 43(6):752-758.
	Zhao P L, Chen Y H, Dong G, et al. Experimental study on streaky structures in turbulent boundary layer based on POD[J]. Journal of Nanjing University of Science and Technology, 2019, 43(6):752-758.
32	Berkooz G, Holmes P, Lumley J L. The proper orthogonal decomposition in the analysis of turbulent flows[J]. Annual Review of Fluid Mechanics, 1993, 25(1): 539-575.
33	Colonius T, Freund J B. Reconstruction of large-scale structures and acoustic radiation from a turbulent M = 0.9 jet using proper orthogonal decomposition[C]//Ninth European Turbulence Conference. 2002.

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