Numerical Study of Multiple Momentum Jets in a Vegetated Crossflow

Abstract

Vertically discharged multiple jets in crossflow is a common form of wastewater discharge. The presence of vegetation in the flow channel complicates the hydraulic characteristics of jets. The realizable k-ε turbulent model is used to simulate the flow, turbulence, and vortex characteristics of multiple jets with different spacing and jet-to-crossflow velocity ratios, to study the flow characteristics and vortex structure of multiple jets in a vegetated channel. The results reveal that vegetation inhibits the development of a counterrotating vortex pair. The jets with a low jet-to-crossflow velocity ratio are concentrated near the flow symmetry profile by the dual constraints of ambient flow and vegetation. The jets gradually spread outward and the counterrotating vortex pair become more obvious when the jet-to-crossflow velocity ratio increases. Vegetation reduces the shading effect of the front jet on the rear jet by accelerating the dissipation of shear layer vortices. The influence of the front jet on the rear jet decreases as the spacing increases.

1. Introduction

The urban areas along rivers and coasts discharge a large amount of domestic and industrial sewage through pipes into rivers, lakes, and oceans, and this is generally considered as jet flow [1,2,3,4,5]. The sewage discharged into the receiving water body should be highly diluted in a small area near the jet to reduce its impact on the surrounding water ecosystem, this is a better way of sewage treatment [6,7,8]. Vegetation can often be seen in natural water bodies, which not only purifies the river and improves its ability to drain flood water and sediments [9,10,11], but also complicates the characteristics of the jet [12,13,14,15]. Therefore, it is crucial for ecological purposes to study the characteristics of jet flow in vegetated channels.

The jet and the ambient fluid become mixed because of the initial momentum of the jet and a strong shear effect occurs in the ambient fluid. Thus, the jet absorbs the surrounding ambient fluid. The cross-section of the jets expands, whereas the concentration dilutes. Recently, many scholars have studied this issue. Wright et al. [16] studied circular buoyant jets in the crossflow by a systematic dimensional analysis and derived approximate solutions for the jet trajectory and jet dilution in a density-stratified crossflow. Malcangio et al. [13], Ben Meftah et al. [12], and Mossa et al. [5] investigated the effect of rigid vegetation on bottom-buoyant jets in a flowing environment through a series of flume experiments. The experiments demonstrated the influence of the turbulent structure generated by rigid vegetation on jet diffusion and its internal structure, which revealed the turbulent structure near the jet and the interaction characteristics between jets and the vegetation. Based on the experiments of Malcangio et al. [13] and Ben Meftah et al. [12], Gao et al. [7] and Xiao et al. [17] analyzed the spatial and temporal evolution of the vortex and the influence of dominant frequency on the vortex structure by using the large eddy simulation (LES) model, which further illustrated the role of vegetation on jet development. Teng et al. [18,19] investigated the effect of different vegetation arrangements on the lateral emission jet by using the particle image velocimetry (PIV) technique. Their experiments revealed the diamond-shaped arrangement of vegetation to have a stronger deceleration effect than the other arrangements.

The aforementioned studies mainly focused on the characteristics of a single jet in the vegetated channel. Multiple jets can disperse the total flow into multiple parts, which increases the contact area between the jet and the environmental flow. The roll-suction effect results in the formation of a strong mixing zone between the jets. The dilution and diffusion effects of the jets become more obvious, and hence, multiple jets are more widely used. The flow form is much more complex than that of a single jet due to the mutual adsorption effect between the two adjacent strands of multiple jets. This effect directly affects the subsequent flow development. Numerous studies have been conducted by many scholars on the flow and turbulence characteristics of multiple jets in unvegetated channels. Based on the experiments of Ali et al. [20], Lai et al. [21] formulated a general semi-analytical model for multiple tandem jet interaction in a crossflow and successfully predicted the reduction in rear jet effective velocity. Yu et al. [22] proposed a model to predict the trajectories of multiple jets by investigating the effect of the jet-to-crossflow velocity ratio on the effective jet lateral flow velocity and concentration dilution characteristics, using PIV and laser-induced fluorescence (LIF) techniques. Li et al. [23] used the realizable k-ε turbulent model to numerically simulate multiple jets in crossflows with a jet spacing that is five times the orifice diameter (S = 5D), and obtained the jet concentration trajectory line, concentration half-width, as well as the variation patterns of flow velocity decay and dilution on the concentration trajectory line. Zhang et al. [24] investigated the dilution mechanism in the near zone of a multi-porous diffuser in a wide and shallow channel by field dye experiments and derived an analytical model for the concentration field of multiple jets after it reaches the water surface.

The experimental results of many scholars have revealed the significant effect of vegetation on the jet. However, few studies related to multiple jets under the action of vegetation are available. Numerical simulations can provide more complete data and a better visualization of turbulent flows, which are difficult to measure accurately in experimental studies [25,26,27,28,29,30]. This study employs the numerical simulation method and determines the effects of jet spacing and jet-to-crossflow velocity ratio on the flow and turbulence characteristics of multiple jets in the vegetated channel.

2. Model and Validation

2.1. Calculation Model Layout

The flume experiments conducted by Ben Meftah et al. [12] and Malcangio et al. [13] have been recognized by many scholars [15,17,18,31,32,33]. In this study, the model used is similar, but with reasonable adjustments on the models of Ben Meftah et al. [12] and Malcangio et al. [13], as presented in Figure 1. Tandemly arranged multiple jets (flow velocity U_j) are located in the center of the vegetated area and flowed into the ambient fluid (flow velocity U_a) along the vertical direction. The ratio of jet flow velocity to ambient flow velocity is α = U_j/U_a = 10.53~31.58, and the ambient fluid depth is 0.3 m. With the same vegetation setup as in the experiments of Ben Meftah et al. [12], cylinders with a diameter D of 3 mm were used to simulate the vegetation in a regular arrangement with a horizontal and longitudinal spacing of 16.7D. The scale of the model in the flow direction (x), spreading direction (y), and vertical direction (z) is 333D × 133D × 110D, respectively, of which the length of the vegetation area is 225D. Jet holes with a diameter of D the same as the diameter of the vegetation were set in the vegetated area, where each jet hole was arranged in the middle of two vegetation plants equidistant from the front and rear vegetation. The distance of the first jet from the model inlet is 150D. For a convenient analysis, the center of the first jet orifice is defined as the coordinate origin (0, 0, 0).

The effects of vegetation, distance between jets, and the jet-to-crossflow velocity ratio α on multiple jets were clarified with several sets of calculation runs: two jets with shorter distances in the unvegetated channel (runs N31 to N33), two jets with shorter distances in the vegetated channel (runs N2V1 to N2V3), two jets with longer distances in the vegetated channel (runs F2V1 to F2V3), and three jets with shorter distances in the vegetated channel (runs N3V1 to N3V3). Information such as the number of jets n, the ambient flow depth H, the jet spacing S, the jet velocity U_j, the ambient flow velocity U_a, the jet-to-crossflow velocity ratio α (α = U_j/U_a), the channel Reynolds number Re_a (based on the hydraulic radius R and the ambient flow velocity U_a), and the jet inlet Reynolds number Re_j (based on the jet velocity U_j and the jet hole diameter D) are presented in

Table 1. Initial conditions and parameters of the different calculational runs.

Runs	n	H(m)	S/D	Uj (m/s)	Ua (m/s)	α	Rej	Rea
N31	3	0.3	-	2	0.19	10.53	6721	26,282
N32	3	0.3	-	3.83	0.19	20.16	12,871	26,282
N33	3	0.3	-	6	0.19	31.58	20,164	26,282
N2V1	2	0.3	16.7	2	0.19	10.53	6721	26,282
N2V2	2	0.3	16.7	3.83	0.19	20.16	12,871	26,282
N2V3	2	0.3	16.7	6	0.19	31.58	20,164	26,282
F2V1	2	0.3	33.4	2	0.19	10.53	6721	26,282
F2V2	2	0.3	33.4	3.83	0.19	20.16	12,871	26,282
F2V3	2	0.3	33.4	6	0.19	31.58	20,164	26,282
N3V1	3	0.3	16.7	2	0.19	10.53	6721	26,282
N3V2	3	0.3	16.7	3.83	0.19	20.16	12,871	26,282
N3V3	3	0.3	16.7	6	0.19	31.58	20,164	26,282

.

2.2. Governing Equations

When multiple jets penetrate into the ambient flow, strong shear and admixture occur between the jets as well as between the jets and the ambient flow. A fluent software was adopted to simulate the motion of the jet. The realizable k-ε turbulent model proposed by Shih et al. [34] has been employed by many scholars for its more accurate description of these phenomena by introducing strain and rotation tensors in the calculation of turbulent viscosity [23,35,36,37]. Therefore, this model is chosen for numerical calculations in this study. The governing equations of the realizable k-ε turbulent model are as follows:

Continuity equation:

$$\frac{\partial \rho }{\partial t}+\frac{\partial (\rho u_i)}{\partial x_i}=0$$

(1)

Momentum equation:

$$\frac{\partial \left(\rho u_i\right)}{\partial t}+\frac{\partial \left(\rho u_i{u}_j\right)}{\partial x_j}=-\frac{\partial p}{\partial x_i}+\frac{\partial }{\partial x_j}\left[(\mu +{\mu }_t)\times (\frac{\partial u_i}{\partial x_j}+\frac{\partial u_j}{\partial x_i})\right]$$

(2)

Turbulent kinetic energy (k) equation:

$$\frac{\partial \left(\rho k\right)}{\partial t}+\frac{\partial }{\partial x_j}\left(\rho u_{j}k\right)=\frac{\partial }{\partial x_j}\left[\left(\mu +\frac{{\mu }_t}{{\sigma }_k}\right)\frac{\partial k}{\partial x_j}\right]+G_k+G_b-\mathsf{\rho }\mathsf{\epsilon }-Y_M+S_k$$

(3)

Turbulent dissipation rate (ε) equation:

$$\frac{\partial \left(\rho \epsilon \right)}{\partial t}+\frac{\partial }{\partial x_j}\left(\rho u_j\epsilon \right)=\frac{\partial }{\partial x_j}\left[\left(\mu +\frac{{\mu }_t}{{\sigma }_{\epsilon }}\right)\frac{\partial \epsilon }{\partial x_j}\right]+\rho C_1{S}_{\epsilon }-\rho C_2\frac{{\epsilon }^2}{k+\sqrt{\mathsf{\nu }\mathsf{\epsilon }}}+C_{1\epsilon }\frac{\epsilon }{k}{C}_{3\epsilon }{G}_b+S_{\epsilon }$$

(4)

where u_i is the average velocity in the directions x, y, and z, respectively. μ and μ_t are the viscosity coefficient and the turbulent vortex viscosity coefficient, respectively. ρ is the density and P is the time-averaged pressure. G_k and G_b denote the turbulent kinetic energy due to the mean velocity gradient and buoyancy, respectively. Y_M denotes the effect of fluctuating expansion on the overall dissipation rate in compressible turbulence. α_k and α_ε denote the inverse effective Prandtl number of k and ε. S_k and S_ε are user-defined source terms.

Multi-phase flow is modeled using the VOF model, which captures the water–air interface by calculating the volume fraction of the water or gas phase of the grid with a time-averaged control equation of

$$\frac{\partial \gamma }{\partial t}+\nabla ·\left(\overline{u}\gamma \right)=0$$

(5)

$$\phi =\gamma {\phi }_w+\left(1-\gamma \right){\phi }_g$$

(6)

where γ (0 < γ < 1) is the volume fraction of the water phase. φ_w and φ_g are the physical quantities of the water and gas phases, which are compressible in the model in accordance with the ideal gas theorem and whose local density is determined by the local air pressure.

2.3. Solution Methods and Boundary Condition

In this study, a transient solver is used for calculation, the control equations are discretized by the finite volume method, the space is discretized by the second-order windward interpolation method, and the SIMPLEC scheme is used for the pressure–velocity coupling. All equations are converged with a control accuracy of 1 × 10⁵.

The velocity-inlet boundary is adopted to the inlet of the ambient flow and jet, and the pressure-inlet boundary is used for the air portion. The air–water intersection is set to the standard atmospheric pressure, whereas the outlet of the channel is set to the pressure-outlet. All sidewalls are adopted with non-slip boundary conditions, and the standard wall function is adopted near the sidewalls.

2.4. Model Validation and Mesh Sensitivity Analysis

In the previous study, the experiments of Malcangio et al. [13] were reproduced by using the realizable k-ε turbulent model, and the numerical calculations were in good agreement with the experimental results. This indicated that the realizable k-ε turbulent model can describe the motion of the jet in the crossflow well. The literature [38] can be consulted for model validation.

In this study, the hexahedral mesh was used as the computational mesh because of its significant advantages of computational accuracy, distortion resistance, and convergence speed [39,40]. The model was divided into several parts and meshed separately to save calculation time while keeping calculation accuracy, similar to the meshing methods of Xiao et al. [17] and Etminan et al. [41]. The flow field becomes complicated when it is near the jet hole and vegetation. The jet hole has a very small diameter and the grid has to be encrypted. Hence, the grid scale of the vegetation area is smaller. However, the grid is relatively sparse and the grid scale is larger near the inlet and outlet of the channel, where it is far from the jet hole. The specific grid layout with a total number of 1.39 million grids is illustrated in Figure 2.

Run CV4 from the experiments conducted by Ben Meftah et al. [12] was simulated with an intermediate grid of 1.39 million, a coarse grid of 0.63 million and a fine grid of 1.67 million to verify whether the mesh density meets the requirements of computational accuracy. Figure 3 presents the comparison results of the trajectory of jet for different numbers of grids. The jet trajectories are normalized by D with the locus of maximum V_xz (V_xz = (u² + w²)^1/2; u and w are the velocity components in the flow and vertical directions, respectively) and obtained in the plane at y/D = 0. The calculations of the realizable k-ε turbulent model with fine and intermediate grids are less different from the experimental results, and the difference between the intermediate grid results and the fine grid results is insignificant. Overall, the results simulated by using the realizable k-ε turbulent model in this study are similar to the calculated data of Xiao et al. [17], who adopted the LES. It is reasonable to choose the intermediate grid for the simulation because of the cost-effectiveness of computational resources.

3. Results

3.1. Mean Velocity Field

Figure 4a,b exhibit the V_xz/U_a contour plots of the three jets in the center plane (y/D = 0) for runs N32 and N3V2. It can be seen that the penetration height of the three jets increases successively when there is no vegetation in the channel. The jet penetration height shows the same pattern when in the vegetated channel, but the degree of jet development is different from that when there is no vegetation. The first jet in run N3V2 grows at a higher height than in run N32, yet it differs less from the next two jets. It suggests that vegetation has an important effect on the jet trajectory. The penetration height of the single jet is greater in the vegetated channel than in the unvegetated channel [9], which is also confirmed by the comparison of the first jet trajectory in Figure 4. This phenomenon is caused by the presence of vegetation that reduced the ambient flow velocity [42,43,44], which led to an increase in the jet-to-crossflow velocity ratio and reduced the deflection effect of the ambient fluid on the jet. However, this rule does not apply to the jets located in the rear of multiple jets, such as the third jet in run N3V2, which has a smaller penetration height than the third jet in run N32. The rear jets not only affected by ambient flow, but also the front jets and the vortex structure generated by the vegetation. These effects increase turbulence and accelerates energy dissipation, resulting in a reduction in the penetration height of the rare jets.

Figure 5 presents the along-range variation of u/U_a, v/U_a, and w/U_a in the y/D = 1.67 plane for the three jets in runs N32 and N3V2. The variation of u/U_a, v/U_a, and w/U_a at each position in run N3V2 is smaller than that of run N32. In Figure 5a, there are multiple extremes of u/U_a along the z-axis at various locations in run N32. The first maximum and minimum values from bottom to top are due to the filling of the negative pressure zone caused by the crossflow from the wake vortex [45]. The second maximum value is due to the volume suction of the jet that results in a larger flow at this location, and the second minimum value is due to the shading of the previous jet [23]. However, the variation of u/U_a caused by these phenomena is not obvious in run N3V2. In Figure 5b,c, the magnitude of the variation of v/U_a and w/U_a along the water depth at each position is greater for run N32 than for run N3V2. In particular, in Figure 5c, the peak of w/U_a of the run N3V2 is smaller, but possesses a greater range of increase in the z-direction, which suggests that the vegetation promotes the diffusion of the jet in the z-direction. Figure 6a,b demonstrate the jet streamlines of runs N32 and N3V2, respectively. The color of the streamlines indicates the magnitude of the velocity. It can be found that the jets in the unvegetated channel will be obviously deflected and move outward after rising to a certain height, and then a spiral flow is formed because the surrounding water is affected by the abovementioned jet. At this time, it will form an obvious reverse vortex pair CVP [46], which dissipates slowly along the course. However, in the vegetated channel, the obstructive effect of the vegetation on the jet and the Carmen vortex street generated by the cylindrical bypass flow in the vegetation area accelerate the dissipation of the CVP, and jets are clustered into bundles, flowing downstream rather than the spiral flow seen in unvegetated channel.

Three sets of runs were compared to examine the impact of the distance between jets on multiple jets in the vegetated channel: two jets with larger spacing, two jets with smaller spacing, and three jets with smaller spacing. Figure 7a–c illustrate the along-range variation of u/U_a, v/U_a, and w/U_a in the y/D = 1.67 plane for runs N2V2 to N3V2, respectively. The variation of u/U_a, v/U_a, and w/U_a along the water depth is almost the same for runs N2V2, F2V2, and N3V2 at x/D = 10, which is located at the rear side of the first jet hole, and the variation of u/U_a, v/U_a, and w/U_a along the water depth is almost the same for runs N2V2 and N3V2 at x/D = 27. This indicates that the rear jet has no obvious effect on the front jet, which contradicts the findings of Li et al. [23] about multiple jets in an unvegetated environment. In their study, only ambient crossflow was present, and the jet spacing was 5D, which made the coiled suction effect between the front and rear jets more intense and increased the negative pressure on the rear side of the front jet. However, the distances between the jet holes in this study are larger, 16.7D and 33.4D, respectively, while the vegetation accelerates the dissipation of jet energy. Therefore, the influence of the rear jet on the front jet is relatively weak and can be ignored.

The distributions of u/U_a and v/U_a are highly similar at each position, but w/U_a differs greatly. w/Ua is mainly influenced by the jet flow velocity and can reflect the jet diffusion in the vertical direction. The peak of w/U_a decreases along the range and appears at an increasing position, which is consistent with the developmental trajectory of the jet. At the position x/D = 43, the peaks of w/U_a for runs N2V2 and F2V2 appear at different locations and have different magnitudes, but their locations and values are reflected in run N3V2, which suggests that there is a limited interaction between the first two jets and the last one in run N3V2. The along-water depth distribution of w/U_a in run N3V2 is similar to run F2V2 in the lower layer (Z/H < 0.3) and to that of run N2V2 in the upper layer (Z/H > 0.7). The larger w/Ua in the middle layer (0.4 ≤ Z/H ≤ 0.7) is caused by the coiled suction effect between the first two jets and the last one. When the w/U_a distributions of runs N2V2 and F2V2 at x/D = 27 and x/D = 43 are compared, they reveal that the peak of w/U_a appears higher in run N2V2 and penetrates a deeper ambient flow. The influence of the front jet on the rear jet is smaller in run F2V2 with larger spacing because distance between the jets influences the front and rear jets interact in the vertical direction.

Figure 8 illustrates the jet trajectory from the jet hole to 15D downstream for all vegetated runs in the center plane (y/D = 0). The trajectories are defined in accordance with the maximum value of the resultant velocity V_xz over the flow symmetry profile and are dimensionless as V_xz/U_a. The figure reveals the trajectory of each jet with the same jet-to-crossflow velocity ratio to be highly similar to the lower layer (Z/H < 0.5) and to change significantly at the higher layer (Z/H ≥ 0.5). The reason for this phenomenon is that the jet diffuses obliquely upward. Hence, the main factor that affects the jet trajectory in the lower layer is the jet-to-crossflow velocity ratio, whereas in the higher layer, it is affected by multiple influences of ambient flow, vortices, and other jets. The bending amplitude of the jet with a low jet-to-crossflow velocity ratio is greater when compared to the trajectories of different jet-to-crossflow velocity ratios, and the jet flow direction gradually turns similar to the ambient flow direction. When V_xz and U_a directions are similar, the jet trajectory is affected by vegetation and bends downward, and the bending degree decreases with the increase in the jet-to-crossflow velocity ratio.

As given in Figure 9a–c, with the increase in the jet-to-crossflow velocity ratio, the variation of u/U_a, v/U_a, and w/U_a at each position along the y/D = 1.67 plane becomes larger for all runs, for example, run N3V3 has multiple extreme values at positions x/D = 10, x/D = 27, and x/D = 43. As shown in Figure 10a–c, the streamlines of the jets in runs N3V1, N3V2, and N3V3 depict that the jet diffusion is not obvious at low jet-to-crossflow velocity ratios that gather near the flow symmetry profile, and that the development of CVP is inhibited by both ambient fluid and vegetation. As the jet-to-crossflow velocity ratio increased, the jet flow to the outside and the CVP gradually developed. The multi-peak of u/U_a also comes to the fore because of the mixing effect between the jet and ambient flow as well as the roll absorption effect between the jets.

3.2. Turbulent Kinetic Energy

Turbulent kinetic energy (TKE) reflects the three-dimensional turbulence characteristics of the fluid, which can be calculated by Equation (7). To analyze the effects of the distance between jets and the jet-to-crossflow velocity ratio on TKE, several locations in the y/D = 1.67 plane were selected to show the distribution of TKE along the water depth, as presented in Figure 11. For display purposes, TKE is dimensionless as TKE/U_a².

$$TKE=\frac{1}{2}({u^{\prime }}^2+{v^{\prime }}^2+{w^{\prime }}^2)$$

(7)

where u′, v′, and w′ represent the fluctuating flow velocity in the x, y, and z directions, respectively.

Figure 11 demonstrates an increase in the peak of TKE/U_a² with an increase in the jet-to-crossflow velocity ratio and the location of the peak. The distribution of TKE/U_a² in the runs of three jets with different jet-to-crossflow velocity ratios was compared. The results reveal that TKE/U_a² in run N3V1, which has a smaller velocity ratio, increases gradually when it runs to the back of the downstream jet. Whereas in run N3V2, which has a larger velocity ratio, TKE/U_a² tends to increase first and then decrease, and the trend becomes more obvious as the velocity ratio continues to increase. A flow velocity field analysis reveals that the smaller the jet-to-crossflow velocity ratio, the stronger the inhibitory effect of the ambient flow on the jet. Therefore, the jet is concentrated near the flow symmetry profile, but breaks through the ambient flow constraint to spread outward at larger jet-to-crossflow velocity ratios. This trend makes sense because the large-flow-ratio jet diffuses to the sides and displaces the surrounding fluid as it moves downstream. This results in a relative decrease in the pulsating flow velocity on the flow symmetry profile. This phenomenon is not obvious between the two jets with a small distance, but very significant between the two jets with a large distance. For example, TKE/U_a² in the two jets with a small distance that runs N2V1, N2V2, and N2V3 from the back side of the first jet to the back side of the second jet shows an increasing trend, whereas in the two jets with a large distance that runs F2V1, F2V2, and F2V3, TKE/U_a² still shows an increasing trend in the small-flow-rate ratio. However, in the largest jet-to-crossflow velocity ratio, run F2V3 shows a decreasing trend, and even TKE/U_a² in the back side of the second jet is smaller than the back side of the first jet in this run.

The distribution of TKE/U_a² along the water depth on the back side of the first jet is almost the same in all runs by the same jet-to-crossflow velocity ratio, which can be seen in Figure 11a. The rear jet has no significant effect on the turbulent kinetic energy distribution at the rear side of the front jet, whereas on the back side of the second jet (compare runs N2V1, N2V2, N2V3 in Figure 11b and runs F2V1, F2V2, F2V3 in Figure 11c), a significant difference appears. In the two jets with smaller spacing, TKE/U_a² on the back side of the second jet is significantly larger than that in the two jets with larger spacing, and the location of the peak of TKE/U_a² is higher. The larger TKE/U_a² and higher location of the TKE/U_a² peak indicate that when the front jet runs above the rear jet, it has a more intense entrainment and mixing effect with the rear jet. The TKE/U_a² distribution on the back side of the front and the rear jets with different spacing was compared. Here, the influence of the front jet on the rear jet decreased with the increase in jet spacing, and the influence of the rear jet on the front jet was inconspicuous under larger spacing. This is consistent with the conclusion obtained in the previous section.

3.3. Vortex Field Structure

The distribution of vortex W_y in the flow symmetry plane (y/D = 0) for runs N33, N2V3, F2V3, and N3V3 are demonstrated in Figure 12. Positive and negative values represent the direction of rotation of the vortex, and the absolute value represents the intensity of the vortex. The common boundary formed by the two parts of the crossflow and the jet with different velocities is known as the flow shear layer. Figure 12 also reveals an obvious large-scale vortex, namely the shear layer vortex, on the windward side upstream of the jet. It starts near the jet orifice, exists on the windward side of the jet, and gradually develops upward. Under the effect of the crossflow, the shear layer vortex develops toward the back of the jet and delivers part of the vortex volume to the CVP, and finally, sheds off in the crossflow along the flow direction. A comparison of Figure 12a,d depicts the vortex field of run N3V3 to be messier than that of run N33. The shear layer vortex before the first jet of run N3V3 has a higher development height, whereas the last two jets are lower than that of run N33. The ambient flow velocity before the first jet in run N3V3 is smaller than that before the first jet in run N33 because of the disturbance of vegetation. Hence, the shear layer vortex before the first jet in run N3V3 is less curved. The shear layer vortex in run N3V3 dissipates quickly after passing through the vegetation and its intensity is significantly reduced by the time it reaches above the next jet. As a result, the shading effect of the front jet on the rear jet is reduced and the development height of the shear vortex layer is lower than in the run without vegetation. This is because vegetation has the same disturbance effect on the shear layer vortex. The comparison of Figure 12b,c depicts that the dissipation of the shear layer vortex of run F2V3 is faster than that of run N2V3, owing to the reduced shading effect caused by the increased spacing.

When the shear layer vortex breaks, the velocity of its inner fluid decreases, bends under the action of the crossflow, and moves along the direction of the jet trajectory. When the inverse pressure gradient acts on the leeward side of the jet, the shear layer vortex breaks up to form a CVP. Figure 13 displays the along-range distribution of axial vortex W_x for runs N33, N2V3, F2V3, and N3V3. The process of CVP formed by shear layer vortex rupturing in run N33 is given in Figure 13a. The CVP height rises in the direction of flow development, which is consistent with the evolution of the jet trajectory. But as the distance from the jet hole grew, the CVP intensity decreased and the shape standardized. This means that the jet gradually merged with the mainstream along the flow direction and attained consistency. Simultaneously, the flow field inside the jet also gradually stabilized. Figure 13b–d demonstrate that the CVP formed by the interaction between the jet and the ambient fluid in the vegetated channel was suppressed, which had a narrow CVP morphology with a small diffusion range in the y direction and a larger diffusion range in the z direction. The diffusion range of the CVP in the vegetated channel increased with the increase in the jet-to-crossflow velocity ratio. However, the diffusion in the y direction was always smaller than that in the unvegetated channel, and the dissipation along the course was also faster. The along-range variation phenomenon of the CVP in runs N33 and N3V3 is similar to the along-range variation patterns of v/U_a and w/U_a in Figure 5. This further indicates that the vegetation inhibits the development of the CVP in the spreading direction and accelerates the along-range dissipation of the CVP, and thus, suppresses the diffusion of the jet.

4. Conclusions

In this study, the realizable k-ε turbulent model was used to investigate the hydrodynamic characteristics of multiple jets with different jet spacing and jet-to-crossflow velocitty ratio in a straightforward vegetated channel. The conclusions are as follows:

(1)

Both the obstructive effect of vegetation on the jet and the Carmen vortex street generated by the crossflow passing through the vegetation interfere with the jet. Vegetation inhibits the diffusion of jets in the spreading direction while promoting the diffusion of jets in the vertical direction. For the same jet-to-crossflow velocity ratio, the CVP generated by the jet were more pronounced in the unvegetated environment.

(2)

For multiple jets, vegetation reduces the shading effect of the forward jet on the backward jet by accelerating the dissipation of the shear layer vortices, inhibiting the penetration height of the backward jet in the ambient flow.

(3)

When the jet spacing is greater than a certain value, the influence of the rear jet on the front jet is not obvious, while the front jet still experiences a coiled suction effect with the rear jet when it runs above the rear jet, and its influence on the rear jet decreases as the spacing increases.

This study aims to analyze the flow behavior of multiple jets in the vegetated crossflow channel. In general, the vegetation hinders the lateral spreading of the jet while facilitating its vertical diffusion. The smaller the distance between the jet holes, the stronger the entrainment effect between the jets. Moreover, ecological vegetation can adsorb harmful substances in water. Therefore, suitable ecological vegetation can be planted in the polluted river, which is conducive to the restoration of the water environment, and can increase the river appreciation function.