Simulation of a jet under the combined action of waves and currents using a momentum integral model
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摘要: 污水通常以射流的形式向海排放，其在海洋环境水体中的稀释过程是射流与波浪、潮流共同作用的结果。本文基于合理的假设条件，对射流运动的控制方程进行积分处理，结合波流环境下射流的结构特征，引入射流卷吸与拖曳力函数，结合必要的边界条件，形成封闭的控制方程组，建立波流环境下射流动量积分模型。通过与实验资料的对比分析可以看出，该模型可以准确模拟波流环境下射流在近区段的时均运动与稀释过程；相较于单一的横流作用，波流共同作用下射流对周边水体的影响范围更大，射流初始稀释能力更强。基于多个组次的动量积分模拟实验，通过无量纲分析与最小二乘拟合，建立了波流共同作用下射流轨迹中心线位置及最小稀释度的经验公式。相关成果可为排海污水环境影响评估提供快速、准确的分析手段。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.
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图 1 使用全局坐标系和局部坐标系的射流排放到波流环境中的示意图（修改自方树桥[26]）
Fig. 1 Schematic diagram of a jet discharge into a wave current environment with global and local coordinate systems
图 2 波流环境下射流最小稀释度垂向位置和最小稀释度物理与数值结果对比
Fig. 2 Comparison of physical and numerical results of the vertical position of minimum dilution and the minimum dilution of jets in wavy crossflow environments
图 3 波流环境下浮射流最小稀释度垂向位置和最小稀释度物理与数值结果对比
Fig. 3 Comparison of physical and numerical results of the vertical position of minimum dilution and the minimum dilution of buoyant jets in wavy crossflow environments
图 4 波流环境下射流在一个波周期内的浓度云图（以 D1 为例）
Fig. 4 Concentration distributions within one wave period of a jet (taking D1 for example) in a wavy crossflow environment
图 5 波流与横流环境下射流平均浓度等值线的对比（以D1为例）
Fig. 5 Comparison of contour lines of average concentration for a jet (taking D1 for example) in wavy crossflow and crossflow only environments
图 6 波流环境下浮射流在不同α2值（0.3、0.6、0.8）下的最小稀释度和垂向位置的模型预测与实验数据的比较
Fig. 6 Comparison of minimum dilution and vertical location of model prediction with experimental data for different values of α2 (0.3, 0.6, 0.8) for buoyant jets in wavy crossflow environments
图 7 波流环境下射流在不同α3值（0.025、0.055、0.075）下的最小稀释度和垂向位置的模型预测与实验数据的比较
Fig. 7 Comparison of minimum dilution and vertical location of model prediction with experimental data for different values of α3 (0.025, 0.055, 0.075) for jets in wavy crossflow environments
图 8 波流环境下射流在不同α4值（0.2、0.5、0.7）下最小稀释度和垂向位置的模型预测与实验数据的比较
Fig. 8 Comparison of minimum dilution and vertical location of model prediction with experimental data for different values of α4 (0.2, 0.5, 0.7) for jets in wavy crossflow environments
图 9 波流环境下射流轨迹中心线位置沿下游距离的变化关系
Fig. 9 The variation relationship of the centerline position of jet trajectory along the downstream distance for jets in wavy crossflow environments
图 10 波流环境下射流最小稀释度与下游距离的变化关系
Fig. 10 The variation relationship of the minimum dilution along the downstream distance for jets in wavy crossflow environments
表 1 波流环境下非浮力射流实验组次条件
Tab. 1 Experimental conditions of non-buoyant jets in wavy crossflow environments
组次 射流初速度
u0/(m·s−1)横流速度
ua/(m·s−1)波浪周期
T/s波浪波高
H/cmRw A1 0.499 0.038 6 1.0 3.0 19.1 A2 0.499 0.038 6 1.4 3.0 11.2 B1 0.760 0.038 6 1.0 3.0 29.1 B2 0.760 0.038 6 1.4 3.0 17.0 C1 1.017 0.038 6 1.0 3.0 39.0 C2 1.017 0.038 6 1.4 3.0 22.7 D1 0.499 0.077 6 1.0 3.0 19.1 D2 0.499 0.077 6 1.4 3.0 11.2 E1 0.760 0.077 6 1.0 3.0 29.1 E2 0.760 0.077 6 1.4 3.0 17.0 F1 1.017 0.077 6 1.0 3.0 39.0 F2 1.017 0.077 6 1.4 3.0 22.7 
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表 2 波流环境下浮力射流实验组次条件
Tab. 2 Experimental conditions of buoyant jets in wavy crossflow environments
组次 射流初速度
u0/(m·s−1)横流速度
ua/(m·s−1)波浪周期
T/s波浪波高
H/cm无量纲密度差
Δρ/ρ0Rw JB1 0.180 0.025 1 1.0 3.0 0.7% 6.89 JB2 0.180 0.026 4 1.0 3.0 1.3% 6.89 JB3 0.180 0.038 0 1.0 3.0 0.7% 6.89 JB4 0.180 0.041 7 1.0 3.0 1.3% 6.89
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表 3 波流环境下射流数值实验组次
Tab. 3 Numerical experiments of jets in wavy crossflow environments
数值
组次射流速度
u0/(m·s−1)横流速度
ua/(m·s−1)波周
期T/s波高
H/cm射流横流
速度比R波浪横流
速度比Rwa斯特劳哈
尔数StJ1 0.72 0.06 1.0 1.035 12 0.15 0.17 J2 0.72 0.06 1.5 0.568 12 0.15 0.11 J3 0.72 0.06 2.0 0.486 12 0.15 0.083 J4 0.72 0.06 1.0 2.415 12 0.35 0.17 J5 0.72 0.06 1.5 1.326 12 0.35 0.11 J6 0.72 0.06 2.0 1.128 12 0.35 0.083 J7 0.72 0.06 1.0 3.795 12 0.55 0.17 J8 0.72 0.06 1.5 2.083 12 0.55 0.11 J9 0.72 0.06 2.0 1.773 12 0.55 0.083 J10 0.60 0.06 1.0 1.035 10 0.15 0.17 J11 0.60 0.06 1.5 0.568 10 0.15 0.11 J12 0.60 0.06 2.0 0.486 10 0.15 0.083 J13 0.60 0.06 1.0 2.415 10 0.35 0.17 J14 0.60 0.06 1.5 1.326 10 0.35 0.11 J15 0.60 0.06 2.0 1.128 10 0.35 0.083 J16 0.60 0.06 1.0 3.795 10 0.55 0.17 J17 0.60 0.06 1.5 2.083 10 0.55 0.11 J18 0.60 0.06 2.0 1.773 10 0.55 0.083 J19 0.48 0.06 1.0 1.035 8 0.15 0.17 J20 0.48 0.06 1.5 0.568 8 0.15 0.11 J21 0.48 0.06 2.0 0.486 8 0.15 0.083 J22 0.48 0.06 1.0 2.415 8 0.35 0.17 J23 0.48 0.06 1.5 1.326 8 0.35 0.11 J24 0.48 0.06 2.0 1.128 8 0.35 0.083 J25 0.48 0.06 1.0 3.795 8 0.55 0.17 J26 0.48 0.06 1.5 2.083 8 0.55 0.11 J27 0.48 0.06 2.0 1.773 8 0.55 0.083
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