Simulation of a jet under the combined action of waves and currents using a momentum integral model

Chen Yongping; Li Xingfei; Fang Shuqiao; Xu Zhenshan; Chen Yuhang; Ebenezer Otoo

doi:10.12284/hyxb2024025

Volume 46 Issue 2

May 2024

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Chen Yongping，Li Xingfei，Fang Shuqiao, et al. Simulation of a jet under the combined action of waves and currents using a momentum integral model[J]. Haiyang Xuebao，2024, 46(2)：1–13 doi: 10.12284/hyxb2024025

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Simulation of a jet under the combined action of waves and currents using a momentum integral model

doi: 10.12284/hyxb2024025

Chen Yongping^{1, 2
,},
Li Xingfei^{1, 2},
Fang Shuqiao^{3, 4},
Xu Zhenshan^{1, 2},
Chen Yuhang^{1, 2},
Ebenezer Otoo^{1, 2}

1.
The National Key Laboratory of Water Disaster Prevention, Hohai University, Nanjing 210098, China
2.
College of Harbor, Coastal and Offshore Engineering, Hohai University, Nanjing 210098, China
3.
Second Institute of Oceanography, Ministry of Natural Resources, Hangzhou 310012, China
4.
Key Laboratory of Ocean Space Resource Management Technology, Ministry of Natural Resources, Hangzhou 310012, China

Received Date: 2023-01-09
Rev Recd Date: 2023-09-21

Available Online: 2024-05-31

Publish Date: 2024-05-29

Abstract

Abstract

Wastewater is usually discharged into the sea in the form of jet, and its dilution process is the result of the interaction of jet, wave and tidal current. In this study, based on the reasonable assumptions, the governing equations are integrated to the form of ordinary differential equations. According to the hydrodynamic characteristics of the jet in the wavy current environment, the entrainment and drag force functions of the jet are introduced to close the governing equations, thus the integral model for the turbulent jet under the combined action of waves and currents is established. Through comparison and verification, it is confirmed that the integral model can accurately simulate the time average movement and dilution process of the near-field jet under the wavy current environment. It is found that compared with a pure current environment, the influence range of jet on the surrounding water is larger than that in a wavy current environment, and the dilution capacity of jet can be remarkably enhanced by the wave effect. Based on the momentum integral simulation results, the empirical fitting formulas for the position of the jet cross-sectional trajectory line and the minimum dilution in the wavy current environment are established. The developed model could be served as an efficient and accurate tool to assess the environmental impacts of submarine outfalls on the surrounding waters.
- combined wave and current environment,
- turbulent jet,
- momentum integral simulation,
- jet trajectory,
- dilution

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References(27)

References

[1]	郭振仁. 污水排放工程水力学[M]. 北京: 科学出版社, 2001. Guo Zhenren. Hydraulics of Polluted Water Discharge Engineering[M]. Beijing: Science Press, 2001.
[2]	Choi K W, Lee J H. Distributed entrainment sink approach for modeling mixing and transport in the intermediate field[J]. Journal of Hydraulic Engineering, 2007, 133(7): 804−815. doi: 10.1061/(ASCE)0733-9429(2007)133:7(804)
[3]	徐振山, 陈永平, 张长宽. 海岸动力环境下射流运动研究综述[J]. 水科学进展, 2012, 23(3): 438−444. Xu Zhenshan, Chen Yongping, Zhang Changkuan. Review of hydrodynamics of jet flow in coastal waters[J]. Advances in Water Science, 2012, 23(3): 438−444.
[4]	姜国强, 李炜. 横流中有限宽窄缝射流的旋涡结构[J]. 水利学报, 2004, 35(5): 52−57, 63. Jiang Guoqiang, Li Wei. Vortex structure of slot turbulent jets in cross-flow[J]. Journal of Hydraulic Engineering, 2004, 35(5): 52−57, 63.
[5]	姜国强, 李炜, 陶建华. 动水环境中有限宽窄缝湍射流的水力特性研究[J]. 水利学报, 2004, 35(12): 51−55, 61. Jiang Guoqiang, Li Wei, Tao Jianhua. Study on vertical turbulent slot jet impinging into cross flow[J]. Journal of Hydraulic Engineering, 2004, 35(12): 51−55, 61.
[6]	周丰, 孙昭晨, 梁书秀. 波浪环境中圆形垂向射流的试验研究[J]. 水利学报, 2007, 38(8): 981−985, 990. Zhou Feng, Sun Zhaochen, Liang Shuxiu. Experimental study on vertical round jet discharged into wave environment with definite depth[J]. Journal of Hydraulic Engineering, 2007, 38(8): 981−985, 990.
[7]	Anghan C, Bade M H, Banerjee J. A review on fundamental properties of the jet in the wave environment[J]. Ocean Engineering, 2022, 250: 110914. doi: 10.1016/j.oceaneng.2022.110914
[8]	Anghan C, Bade M H, Banerjee J. Direct numerical simulation of turbulent round jet released in regular waves[J]. Applied Ocean Research, 2022, 125: 103248. doi: 10.1016/j.apor.2022.103248
[9]	Abdel-Rahman A A, Eleshaky M E. Diffusion characteristics of a plane jet discharged in a wavy crossflowing stream[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2004, 218(4): 411−423.
[10]	袁丽蓉. 波流环境中垂向紊动射流的数值模拟研究[D]. 大连: 大连理工大学, 2006. Yuan Lirong. Numerical study on vertical turbulent jet in waves and currents[D]. Dalian: Dalian University of Technology, 2006.
[11]	鲁俊, 王玲玲, 曹小红. 横流中射流及其温度标量输运大涡模拟[J]. 水利水电科技进展, 2013, 33(2): 26−31. Lu Jun, Wang Lingling, Cao Xiaohong. Large eddy simulation of jets with and without temperature scalar in a current[J]. Advances in Science and Technology of Water Resources, 2013, 33(2): 26−31.
[12]	王娅娜. 波流环境下垂向射流水动力及稀释特性实验研究[D]. 南京: 河海大学, 2015. Wang Yana. Experimental study on hydrodynamics and initial dilution of a vertical jet in wavy cross-flow environment[D]. Nanjing: Hohai University, 2015.
[13]	Xu Zhenshan, Chen Yongping, Tao Jianfeng, et al. Three-dimensional flow structure of a non-buoyant jet in a wave-current coexisting environment[J]. Ocean Engineering, 2016, 116: 42−54. doi: 10.1016/j.oceaneng.2016.02.022
[14]	Xu Zhenshan, Chen Yongping, Wang Yana, et al. Near-field dilution of a turbulent jet discharged into coastal waters: effect of regular waves[J]. Ocean Engineering, 2017, 140: 29−42. doi: 10.1016/j.oceaneng.2017.05.003
[15]	Xu Zhenshan, Chen Yongping, Pan Yi. Initial dilution equations for wastewater discharge: example of non-buoyant jet in wave-following-current environment[J]. Ocean Engineering, 2018, 164: 139−147. doi: 10.1016/j.oceaneng.2018.06.021
[16]	Chin D A. Model of buoyant-JET-surface-wave interaction[J]. Journal of Waterway, Port, Coastal, and Ocean Engineering, 1988, 114(3): 331−345. doi: 10.1061/(ASCE)0733-950X(1988)114:3(331)
[17]	Jirka G H. Integral model for turbulent buoyant jets in unbounded stratified flows. Part I: single round jet[J]. Environmental Fluid Mechanics, 2004, 4(1): 1−56. doi: 10.1023/A:1025583110842
[18]	周连伟. 三维非恒定流场中圆形浮射流的数值模拟研究[D]. 大连: 大连理工大学, 2004. Zhou Lianwei. Numerical study on round buoyant jet in 3D unsteady flow[D]. Dalian: Dalian University of Technology, 2004.
[19]	Lin Yingpin, Hsu H C, Chen Y Y. Theoretical analysis of a buoyant jet interacting with small amplitude waves[J]. China Ocean Engineering, 2009, 23(1): 73−84.
[20]	胡飞, 陈永平, 徐振山, 等. 波浪环境下垂直射流动量积分模型[J]. 水利学报, 2013, 44(9): 1058−1063, 1070. Hu Fei, Chen Yongping, Xu Zhenshan, et al. A momentum integral model for vertical jet in wavy environment[J]. Journal of Hydraulic Engineering, 2013, 44(9): 1058−1063, 1070.
[21]	Lai A C H, Law A W K, Adams E E. A second-order integral model for buoyant jets with background homogeneous and isotropic turbulence[J]. Journal of Fluid Mechanics, 2019, 871: 271−304. doi: 10.1017/jfm.2019.269
[22]	Shrivastava I, Lai A C H, Adams E E. Numerical model for unidirectional diffuser in a crossflow[J]. Journal of Hydraulic Engineering, 2022, 148(7): 04022010. doi: 10.1061/(ASCE)HY.1943-7900.0001987
[23]	He Zhiguo, Lou Yingzhong. Integral model for multiple forced plumes arranged around a circle in a linearly stratified environment[J]. Physical Review Fluids, 2019, 4(12): 123501. doi: 10.1103/PhysRevFluids.4.123501
[24]	Chen Yanan, He Zhiguo, Lou Yingzhong, et al. Experimental study of horizontal heated buoyant jets in a linearly stratified ambience[J]. Physics of Fluids, 2021, 33(4): 047116. doi: 10.1063/5.0045906
[25]	He Zhiguo, Zhang Han, Chen Yanan, et al. Hydrodynamics of horizontal heated buoyant jet in linearly stratified fluids[J]. Physics of Fluids, 2022, 34(2): 025108. doi: 10.1063/5.0077726
[26]	方树桥. 波流环境中射流动量积分通用模型研究及应用[D]. 南京: 河海大学, 2020. Fang Shuqiao. Study and application of general momentum integral model for a jet in wavy current environment[D]. Nanjing: Hohai University, 2020.
[27]	Xu Zhenshan, Chen Yongping, Jiang Dongbo. Experimental study on a buoyant jet in wavy crossflow[C]//Proceedings of the 28th International Ocean and Polar Engineering Conference. Sapporo: International Society of Offshore and Polar Engineers, 2018: 891−897.