Experimental Investigation of Positively Buoyant Surface Jet in Confluence Regions

doi:10.21203/rs.3.rs-4870938/v1

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Experimental Investigation of Positively Buoyant Surface Jet in Confluence Regions

https://doi.org/10.21203/rs.3.rs-4870938/v1

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Understanding the influence of ambient currents and jet discharge characteristics on warm polluted outfall performance is crucial for mitigating the ecological impact of effluents discharged from a diffuser in a confluence region. To this end, laser-induced fluorescence (LIF) experiments were conducted to investigate the combined effects of jet strength and nozzle location on the mixing of a positive or neutral jet issuing into a plane perpendicular to the crossflows. The trajectory and mixing within a channel junction of surface crossflow jets is investigated. Two different nozzle discharge locations and velocities were studied to assess the 3D jet trajectory and concentration distribution. The investigations revealed that a jet issued into the main channel mixes more effectively with wider dispersion compared with a jet issued in the tributary. This is due to the shear layer in the main channel, which restricts the jet in tributary to a narrower width, limiting its ability to mix effectively with ambient water.

Positively Buoyant Jet

Surface Jet

laser-induced fluorescence

LIF

The study examines the influence of ambient currents and jet discharge characteristics on warm polluted outfall
Laser-induced fluorescence (LIF) experiments were conducted to investigate the combined effects of jet strength and nozzle location on the mixing of a positive or neutral jet.
The results demonstrated that the discharge rate and buoyancy influenced both the jet trajectory and dilution, with increased velocity and buoyancy leading to enhanced mixing and a wider dispersion of the jet.

Urban development near rivers has led to the increased release of municipal and industrial wastewater into water bodies. Although several studies have explored wastewater movement in rivers, further investigation is needed to understand the impact of effluent discharge on river health [1], [2]. The discharge of effluent into flowing water, termed jet in crossflow, has applications in industry, hydraulics, and the environment [3], [4], [5], [6].

The hydrodynamics of a jet in crossflow is inherently complex, especially when the jet is released in areas of the river with complex structures, such as a confluence channel junction. To the best of the authors’ knowledge, the mixing of a jet in a confluence zone has never been investigated. This study aims to investigate effluent discharges released in confluence areas to examine the effect of the junction on the outfall. First, the hydrodynamics of both jets in crossflow and confluences are reviewed briefly in the following sections.

Jet in crossflow

When a less-dense discharge is introduced into a denser fluid, it gives rise to a positive buoyant jet. Specifically, a positive buoyant surface jet is formed when discharged near the free surface. This phenomenon is commonly observed in both natural and industrial settings, such as the release of heated cooling water [7] and discharge of treated wastewater into water bodies [8]. This method is the most traditional and economical method for releasing pollutants into rivers or coastal areas. Due to their limited dilution factor, usually ten or below, surface discharges tend to pose greater environmental risks compared to submerged alternatives [9].

The dilution factor is a measure of the amount of pollution that has been diluted or reduced in concentration. The dilution factor is calculated using the following equation.

$$\:Dilution\:Factor=\frac{Volume\:of\:initial\:Concentration}{Volume\:of\:final\:Concentration}$$

In Eq. (1), "Volume of Initial Solution" refers to the volume of the concentrated pollution before dilution, and "Volume of Final Solution" refers to the total volume of the diluted pollution after dilution.

The trajectory of the jet is established by connecting the points with the maximum time-averaged concentration in each cross section (Fig. 1). The angle 𝜃 represents the inclination angle of the jet, signifying the direction angle of the instantaneous velocity along the central axis in relation to the crossflow direction (𝜃_𝑜 is the initial angle, while 𝜃 denotes angles along the trajectory). Theoretically, 𝜃 reaches zero degrees at the end of the trajectory.

The length-scale parameters for buoyant surface jet classifications were introduced by Jirka et al. [10], and Chu and Jirka [11] provided an initial classification for buoyant surface jets in crossflows. A comprehensive classification system by Jones et al. [9] categorized surface jets into four main classes as either free jets, shoreline-attached jets, wall jets, or upstream intruding plumes, using the parameters defined in Tables 1 and 2 where a₀ is the cross-sectional area of the jet, g is the gravitational acceleration, ρ is the water density, and Δρ₀ is the difference in discharge density (Δρ₀ = ρ_a − ρ₀).

Table 1

Dynamic length scales of jets
Discharge length scale	$\:{L}_{Q}={Q}_{0}/{M}_{0}^{1/2}$
Jet-to-plume length scale	$\:{L}_{M}={M}_{0}^{3/4}/{J}_{0}^{1/2}$
Jet-to-crossflow length scale	$\:{l}_{m}={M}_{0}^{1/2}/\stackrel{-}{{u}_{a}}$
Plume-to-crossflow length scale	$\:{l}_{b}={J}_{0}/{\stackrel{-}{{u}_{a}}}^{3}$

Table 2

Flow characteristics of jets
Jet flow rate	$\:{Q}_{0}=\stackrel{-}{{u}_{0}}{a}_{0}$
Jet momentum flux	$\:{M}_{0}=\stackrel{-}{{u}_{0}}{Q}_{0}$
Jet buoyancy flux	$\:{J}_{0}={Q}_{0}\:{g}_{0}^{{\prime\:}}$
Discharge buoyant acceleration	$\:{g}_{0}^{{\prime\:}}=g(\varDelta\:{\rho\:}_{0}/{\rho\:}_{0})$

A crossflow buoyant jet can be categorized into four distinct asymptotic regimes based on whether buoyancy, momentum, or crossflow primarily influences the jet's mixing characteristics (Fig. 1) [12]:

Momentum Dominated Near-Field (y/l_m < < 1): This regime occurs when the initial jet momentum significantly influences the jet discharge.
Momentum Dominated Far-Field (y/l_m > > 1): In this regime, the crossflow effects become significant in the jet discharge.
Buoyancy Dominated Near-Field (y/l_b < < 1): This regime is characterized by the initial plume buoyancy playing a crucial role in the plume discharge.
Buoyancy Dominated Far-Field (y/l_b > > 1): The crossflow effects become prominent in the plume discharge.

where y represents the cross-channel distance, and l_m and l_b are the lengths of the near-field for a momentum-dominated jet or buoyancy-dominated plume, respectively (Fig. 1).

Early investigations into surface thermal discharge patterns were initiated by Dunn et al. [13], followed by computational modeling using mathematical models and turbulence closure techniques [14]. In the 1960s, research focused on surface buoyant jets, prompted by concerns over the environmental impact of heated cooling water discharges from power plants. Notable contributions during this period were laboratory experiments and integral jet models [10].

A surface jet discharging into a crossflow transition along its trajectory. In the "zone of flow establishment" immediately following the nozzle, the flow undergoes a transformation into a sheared jet-like velocity distribution. In this region, buoyancy has a minimal impact, and the flow is primarily governed by the momentum of the jet, conforming to a Gaussian distribution. As the momentum diminishes, the jet shifts towards the crossflow, entering a plume-like condition. Mixing in this zone is influenced by buoyancy effects and secondary flows, which collectively form a near-field zone. In the far field, mixing is predominantly governed by buoyant spreading or passive diffusion (Fig. 1) [8], [9].

Researchers have explored surface jets to enhance understanding of these phenomena. Anwar [15] conducted experiments to assess the vertical and horizontal isotherms of warm surface jets (73 ^◦C) discharged from a rectangular channel into a cold crossflow (15 ^◦C). The study revealed a strong depth dependence of the jet axis, and the mutual interaction between the buoyant surface jet and crossflow generated a zone with overshoot velocity at the outer edge of the jet. Additionally, a slow-moving zone was observed on the lee side of the buoyant jet, along with a return flow closer to the inner wall (near the discharge point) of the flume. Gawad et al. [16] investigated the effects of horizontal surface and submerged jets in crossflows, highlighting similar Gaussian distributions in the excess jet velocity and concentration in both the lateral and vertical directions for cases without strong bank reattachment and recirculation.

Gharavi et al. (2020) [8] conducted experimental measurements of the 3-D velocity field to enhance the understanding of the flow structure of surface jets under crossflow conditions. Stereoscopic Particle Image Velocimetry (PIV) was employed to measure the instantaneous spatial and temporal velocity distributions in a measurement zone downstream of the jet discharge point. This study identified the formation and evolution of vortices in the flow structure. This vortex in the surface jet in crossflow exhibited similarities to one half of the counter-rotating vortex pair (CVP) typical of submerged jets in crossflows. It was inferred that the water surface behaved as a plane of symmetry (Fig. 2).

Confluence Hydrodynamics

Channel confluences are hydrological systems in which two or more channels converge, resulting in complex flow structures. These structures can be challenging to understand and model due to the complexity of the flow physics involved. Over the years, researchers have attempted to gain a better understanding of the behavior of open-channel confluences using experimental methods [17], [18], [19], [20], [21], numerical methods [31], [32], [33], [34], and field experiments [26], [27], [28], [29]. Best (1987) [30] proposed a generalized model for river confluences that included six different zones (Fig. 3). These zones are characterized by different flow patterns and velocities. The first zone is the stagnation zone, where water from the tributary branch river is impeded by the main river, causing a build-up of water. The second zone is the deflection zone, where the flow from the branch river changes direction to align with that of the main river channel. The third zone is the separation zone, which is the area immediately after the junction close to the inner bank of the main river. The velocity in this zone is usually low, yet highly turbulent with flow recirculation. The fourth zone is the maximum velocity zone, which occurs in the contraction or acceleration zone between the shear layer and outer and inner banks of the main river. The fifth zone is the flow recovery zone, in which the flow begins to recover from the turbulence generated in the shear plane. The sixth and final zone is the shear plane, which occurs at the branch river entrance to the main river and is the primary source of turbulence generation due to differences in their velocity fields.

After the confluence junction, various river characteristics change significantly, including alterations in water surface and bed level. Additionally, a range of phenomena can be observed, such as the transport of sediment, dispersion of pollutants, erosion and deposition processes, and river migration [31].

Several key elements, such as junction angle, ratio of discharge or momentum between the main channel and tributary flows, bed level (accordant or discordant), channel geometry, and any differences in density between the incoming flows, can affect the morphodynamics of a confluence [32], [33], [34], [35]. While channel confluences have been studied for several decades, it is evident that examination of these details continues to accelerate [36], [37], [38], [39]. Significant research efforts have focused on investigating the phenomenon of flow mixing at confluences [27], [40], [41]. Furthermore, there has been considerable interest in studying the relationship between sediment transport and the morphology of river systems [29], [42], [43].

According to previous studies, confluences can be categorized based on their width-to-depth ratio as either small (W/H < 10), medium (10 < W / H < 50), or large scale (W / H > 50) [29], [33]. Recently, researchers have explored the possibility of applying findings from small laboratory and field experiments to large rivers, thus this scaling categorization should be considered [44]. It has been suggested that for large width-to-depth ratios, the influence of secondary currents is diminished due to increased roughness caused by the shape of the riverbed. Consequently, it may be challenging to extend observations from small to large-scale confluences [33].

Objective

Despite numerous investigations into confluence channels or jets in crossflow, there is still a gap in existing studies. To the best of the authors’ knowledge, no prior study has explored the dynamics of positively buoyant surface jets in confluence regions. Recognizing this research gap, our study aims to provide a comprehensive investigation of the behavior and characteristics of positively buoyant surface jets in the complex context of confluence regions. We inspect not only the fundamental features of these jets but also their concentration patterns and trajectories within the intricate dynamics of river confluences. Different jet in cross flow categories that can occur when a buoyant surface jet is discharged into a confluence are examined, by considering variable jet location, momentum, and buoyancy. Specifically, laboratory flume experiments were conducted in an open-channel confluence with injection of an effluent jet into either the tributary or main channel upstream of the confluence zone. For various jet and confluence flow scenarios, laser-induced fluorescence was utilized to evaluate the mixing of the effluent within the confluence zone. Through a systematic exploration of this uncharted territory, we seek to contribute valuable insights into the understanding of the flow patterns, turbulence, concentration dynamics, and trajectory behaviors associated with positively buoyant surface jets in confluence areas.

2.1. Experimental Setup and Flume Configuration

The experiments were conducted at the Water Resources Engineering Laboratory of the University of Ottawa using a flume designed to simulate confluence-flow scenarios. The flume was 8 m in length, 1.1 m in width, and 0.6 m in depth (Fig. 4a). Within the flume, a confluence channel was meticulously designed to replicate river confluence dynamics with the convergence of the two channels positioned 1.1 m downstream of the flume entrance. The upstream main channel and tributary channel were specifically configured with widths of 0.20 m and 0.15 m, respectively. The downstream channel maintained a width of 0.20 m, ensuring a coherent representation of channel dimensions within the experimental setup. The angle between the two channels was set at 30°, which falls within the natural range of observed confluence angles [45]. The flow depth was kept at 10 cm in both channels. For better visualization, the side walls and bottom of the flume were made of tempered glass. Three adjustable speed pumps in parallel were installed under the flume to recirculate water from the flume outlet tank to the flume inlet tank, facilitating controlled flow conditions.

The experimental setup facilitated the discharge of buoyant surface thermal jets into the confluence flow. The jet discharge nozzle was connected to a constant-head tank positioned above the flume. The constant head tank was raised to a height of 0.8 meters above the nozzle tip to maintain a consistent hydraulic driving head for the discharge. Jet flow control was achieved using two valves and the flow rate was quantified using a flowmeter. (Fig. 4b). Two distinct scenarios were considered for the surface thermal jet discharge location: one in the main upstream channel, and the other in the tributary channel (Fig. 4a). Both scenarios involved initiating the thermal jet through round nozzles with a diameter (d) of 4 mm, approximately 200 mm upstream of the confluence junction, specifically at the water surface, to investigate the influence of the channel hydrodynamics and geometry on the jet behavior.

2.2. Experimental Parameters

In this study, a range of jet and ambient conditions was systematically investigated using a nozzle diameter (D) of 4 mm. The jet densiometric Froude number (Fr) (Eq. 2) was varied from 2 to 5.4. Table 3 lists the experimental conditions for each test case, emphasizing the key parameters considered in this study. The effluent used in the experiments represents the thermal jet discharge. Fresh tap water was used to simulate ambient conditions within the flume. Control over effluent temperature and density variations was meticulously maintained to replicate realistic thermal jet scenarios. Temperature adjustments were made to ensure a constant temperature between 15 and 25°C for the source discharge and 15°C for the ambient water. The discharge densities ranged from 997 to 999.1 kg/m³, reflecting the variability of the thermal buoyancy effects in the positively buoyant surface jets. The discharge rate from the nozzle was measured using a flowmeter to monitor and control thermal jet characteristics.

$$\:Fr=\frac{{u}_{j}}{\sqrt{{g}_{0}^{{\prime\:}}\times\:D}}$$

Where u_j is jet velocity and D is nozzle diameter.

Table 3

Experimental conditions
	Q (L/h)	u_j (m/s)	u_{a_m} (m/s)	u_{a_b} (m/s)	u_r=u_a/u_j	Jet Density (Kg/m³)	Crossflow Density (Kg/m³)	g'₀	Fr	L_Q	L_M
R₁(Jet1)	2.50	0.06	0.10	0.02	1.81	997.05	999.70	0.03	5.42	0.004	0.02
R₂(Jet2)	2.50	0.06	0.10	0.02	0.36	997.05	999.70	0.03	5.42	0.004	0.02
R₃(Jet1)	1.00	0.02	0.10	0.02	4.52	996.52	999.61	0.03	2.01	0.004	0.001
R₄(Jet2)	1.00	0.02	0.10	0.02	0.90	996.52	999.61	0.03	2.01	0.004	0.001
R₅(Jet1)	2.50	0.06	0.10	0.02	1.81	997.77	997.77	0.00		0.004
R₆(Jet2)	1.00	0.02	0.10	0.02	4.52	997.77	997.77	0.00		0.004
R₇(Jet1)	1.00	0.02	0.10	0.02	0.90	997.77	997.77	0.00		0.004
R₈(Jet2)	2.50	0.06	0.10	0.02	0.36	997.77	997.77	0.00		0.004
R₉(Jet1)	2.50	0.06	0.10	0.00	1.81	997.05	999.70	0.03	5.42	0.004	0.02
R₁₀(Jet2)	2.50	0.06	0.10	0.00	0.00	997.05	999.70	0.03	5.42	0.004	0.02

Ambient Velocity (u_a): General ambient velocity in the experimental setup.

Main Channel Velocity (u_a−m): Velocity in the main channel.

Tributary Channel Velocity (u_a−b): Velocity in the tributary channel.

Velocity Ratio (u_r): The ratio of ambient velocity to jet velocity.

2.3. Flow Visualization Techniques

To enhance the visualization of the flow patterns, 0.04 gram of Rhodamine 6G dye was added to the source discharge tank containing warm water. This dye serves as a tracer, emitting a longer wavelength of incident light to improve visibility. A diode-pumped solid-state (DPSS) continuous-wave green laser with an output power of 10 W and wavelength of 532 nm was employed to induce fluorescence in the dye throughout a horizontal laser sheet (Fig. 4b). The flow dynamics and interactions within the confluence flow were captured using a high-speed charge-coupled (CCD) camera positioned above the flume (Fig. 4b). Operating at 100 frames per second, this camera ensured that consecutive frames were uncorrelated, offering a comprehensive view of the flow fields. The camera boasted a resolution of 2336 × 1728 pixels and provided detailed, high-quality imagery. A C-mount 12 mm lens with an f/1.4 aperture was employed to increase the coverage area. Continuous acquisition was maintained, and the exposure time was set to 1/4000 for effective capture of the dynamic behavior of the thermal jets. The captured images were stored with a Mono8 bit resolution, utilizing 256 grayscale levels. This setup enhanced the quality and contrast of the obtained images, ensuring accurate and detailed visualization of the flow phenomena. The camera was connected to a computer through a PCI frame grabber facilitated by two attached camera-link cables. This connection allows for efficient data transfer and real-time monitoring of the flow dynamics. Figure 5 shows a raw image captured by the camera. This configuration rendered the jet flow bright against a dark background, with each pixel's light intensity level ranging from pure black to pure white. Thus, recorded images provided a detailed representation of the flow characteristics. The concentration of the tracer dye was linearly correlated with the light intensity [46], facilitating quantitative analysis of the thermal jet concentration within the flow. Pure white was associated with the initial concentration (C_o), and pure black with zero concentration.

2.4. Processing and Data Analysis

Before initiating the jet discharge, a preliminary set of approximately 100 images capturing only the background, devoid of Buoyant Jets, was recorded and time averaged. This process aims to eliminate extraneous light sources unrelated to the jet fluid concentration. Upon achieving steady flow conditions, a series of 3,000 images was recorded, encompassing the jet discharge phase. Subsequently, the background image was subtracted from the images containing the jet to eliminate background light interference.

The post-processing of the captured images was conducted using MATLAB code tailored to the experimental requirements. This code analyzes grayscale images pixel-by-pixel to determine tracer concentrations and subsequently converts them into color-coded represent3ations. A statistical analysis, including time-averaged images and their variance, was performed by analyzing consecutive frames. After this analysis, the concentration distribution fields and contours were generated based on the nondimensionalized C/C₀ parameter, where C₀ represents the initial discharge concentration. These visualizations elucidate the degree of mean concentration reduction, providing insights into the dilution level compared to the initial concentration.

Visualizing intricate flow patterns within a flume is a critical aspect of this study. To determine the dilution levels, the experimental setup incorporated a horizontal laser sheet positioned at the nozzle level. The image processing procedure illustrated in Fig. 4b elucidates the precise location of the trajectory and facilitated a comprehensive analysis of dilution within the confluence flow. This approach provided insight into the dispersion characteristics of thermal jet discharge under varying conditions.

Sequentially altering the vertical position of the laser sheet emission across the flume width allowed for the creation of eight distinct slices, each spaced approximately 25 mm apart. These slices provided a detailed cross-sectional view of the flow dynamics. The captured frames from these slices were subsequently compiled using ParaView visualization software tools, enabling the generation of both 2D and 3D representations of the mean flow fields.

3.1. General Observations

3.1.1. Instantaneous Visualization

Figure 6 provides detailed visualizations of the instantaneous concentration flow fields for two experimental cases, R3 and R4, which differ in their discharge locations, allowing us to compare the impacts on jet flow in the confluence channels.

In Case R3, the jet reached the confluence and encountered the shear layer, which pushed it away from the inner bank. This deviation alters the trajectory, enhancing its mixing efficiency with the ambient flow. The broader exposure of the jet to the surrounding fluid allows for a dynamic interaction between the jet momentum and varying velocities at the confluence. The presence of rotating tracer bundles, marked by blue rectangles, indicates the active mixing and redistribution of fluid properties, contributing to a diversified flow pattern. This scenario underscores the beneficial effects of strategic jet placement in promoting effective mixing within a channel. Conversely, Case R4 presents a scenario in which the jet is discharged into a narrower section of the channel closer to the inner bank. This proximity causes part of the jet to be trapped in a separation zone, thereby limiting its initial mixing. However, as the jet progresses into the recovery zone, it begins to spread more evenly across the channel width. Despite the delayed start, the jet in R4 eventually achieves a broad distribution of fluid, though the initial confinement affects the efficiency and pattern of mixing.

A comparison of Cases R3 and R4 highlights the profound impact of discharge locations on fluid dynamics within the confluence channels. In Case R3, the jet is effectively pushed away from the inner bank, thereby facilitating early and efficient mixing. This is attributed to the increased interaction with the surrounding fluid dynamics, which promotes the development of Kelvin-Helmholtz instabilities and enhances the mixing process. In contrast, the positioning in Case R4 restricts the initial spread of the jet, leading to a more confined flow pattern that only begins to disperse upon reaching a recovery zone.

These observations emphasize the critical role of the discharge location in influencing the development of flow instabilities and the overall effectiveness of mixing processes in confluence channels. Understanding these dynamics is essential for optimizing fluid mixing and management strategies for engineering and environmental applications.

3.1.2. Timed-averaged Visualization

The time-averaged flow depictions of the jets were visualized using the ParaView software tool, as illustrated in Fig. 7. When the jet is introduced into the main channel, it initially travels close to the channel wall until it reaches the junction. At this point, the jet encounters the shear layer created by the confluence, which pushes it away from the wall. As the jet progresses into the recovery zone, it is redirected back towards the wall, resuming its movement near the channel boundary.

In the tributary channel discharge scenario, the movement of the jet mimics some aspects of its behavior in the main channel, but within a more confined space. Initially, the jet travels close to the channel wall. Upon reaching the junction, it encounters the confluence shear layer, which compels the jet to remain near the wall but with a narrower width than the main channel discharge case. Additionally, a part of the jet becomes trapped in the separation zone at this point, which restricts its initial ability to mix with the surrounding water.

Cases R3 and R4 represent specific instances within a broader array of scenarios explored in this study. Although these cases provide insights into the spatial dynamics and immediate effects of jet behavior in confluence channels, they serve as a preliminary focus. The subsequent sections of this paper delve into additional variables that significantly influence jet dynamics, such as temperature and velocity. The effects of these factors on jet penetration and overall fluid interaction within different the confluence zone are thoroughly discussed.

3.1.3. Visualization of the Case of Stagnant Flow Conditions in the Tributary Channel

This section explores the dynamics of a jet when introduced into a channel system in which one part, the tributary, is under stagnant flow conditions. Under these conditions, the behavior of the jet can vary significantly depending on its point of release, either into the main channel or directly into the tributary. By investigating these scenarios, we aim to understand the fluid mechanics and flow behaviors that emerge when a moving jet encounters a stagnant tributary (or a large embayment), thereby providing insights into the complexities of fluid dynamics in engineered and natural waterways. The following analysis details how the jet behaves in each scenario, as illustrated in Fig. 8, and discusses the implications of these behaviors for fluid mixing and channel flow management.

When the jet is released into the main channel under conditions where the tributary channel is stagnant, the jet behaves similarly to its behavior in a simple, unobstructed channel. However, a portion of the jet diverges into the tributary channel. This diversion occurs primarily due to the formation of a shear layer between the main flow and the stagnant zone. This shear layer creates instabilities and turbulence, which enhance mixing and facilitate the penetration of the jet into the stagnant zone. The absence of opposing flow in the tributary further reduces hydrodynamic resistance, allowing part of the jet to "spill" into the tributary. This phenomenon can be visualized as the jet exploiting the path of least resistance, where stagnant water does not provide the usual dynamic pressure or velocity profiles that would otherwise influence and restrict the flow direction.

In the second scenario, where the jet is released directly into the stagnant tributary, a shear layer forms at the junction between the tributary and main channel. This shear layer is crucial because it acts as a dynamic boundary that governs flow characteristics. The presence of the shear layer at the junction results in the jet being initially confined within the tributary due to the differences in velocity and momentum between the jet and stagnant flow conditions. Over time, the jet gradually penetrated into this shear layer, slowly diffusing and releasing into the main channel. This slower release is characterized by the gradual mixing of the jet with the main channel's flow, The shear-induced turbulence at the junction enhances mixing and facilitates the transition into broader channel dynamics. This phenomenon of shear-induced turbulence and enhanced mixing also occurs when the jet is discharged into the main channel, highlighting the critical role of shear layers in influencing fluid dynamics and mixing efficiency in both scenarios.

3.2. Jet Trajectory

3.2.1. Jet-1 Trajectory

The trajectory of a jet can be described as the path along which the concentration is the highest [47]. For non-dimensionalization, the jet diameter was used as the length scale, and the mixing behavior was analyzed up to the distance of 200 jet diameters downstream. Figure 9 illustrates the paths of the surface jets within the channel at the confluence. It is evident that the trajectories are influenced by the Froude number (Fr), which varied across different scenarios. This variation suggests that the dynamic interplay between the buoyancy of the flow and the channel geometry shapes the jet behavior. Notably, the figures reveal a slight difference in the trajectory between positive and neutral jets when released at the surface. This divergence is primarily due to buoyancy differences. Positive jets, which are lighter than the ambient fluid, tend to rise due to the buoyant forces. Because they are released near the surface, the surface acts as a symmetry plane and further influences their upward movement. Conversely, neutral jets, which are buoyancy-neutral relative to the surrounding fluid, follow a more level trajectory, influenced not by buoyancy but by the prevailing flow dynamics within the channel. This leads to observed variations in how each jet navigates the confluence zone, reflecting the subtle yet substantial impact of buoyancy on jet behavior. Additionally, R1 and R5 have bigger velocities compared to R3 and R7, further affecting the trajectory and dynamics of the jets in the channel.

3.2.2. Jet-2 Trajectory

Figure 10 depicts the trajectory of jet-2 within the tributary channel under various scenarios. It is evident from this figure that the jet is constrained by the shear layer of the channel, preventing it from spreading across the channel width. Consequently, the jet follows a path of limited width, remaining close to the inner bank of the channel. The same situation occurs for either positive or neutral jets released into the tributary. Positive jets, although lighter and typically rising above the surrounding fluid, find their upward movement blocked by their release near the surface. This confinement near the surface restricts their ability to rise, causing them to exhibit behavior similar to that of neutral jets under these specific conditions. Both types of jets, despite their inherent differences in buoyancy, are influenced significantly by the shear layer and proximity to the surface, which together dictate a similar trajectory along a narrow path within the tributary channel.

3.2.3. Jet Trajectory in the Case of Stagnant Flow Conditions in the Tributary Channel

Figure 11 illustrates the trajectory of the jets when the discharge from the tributary is zero. A key observation from the R10 experiment is that, because of the shear layer of the main channel, the discharge becomes temporarily trapped within the tributary. As the jet concentration increases, it begins to release from upstream of the tributary into the main channel at the point known as the stagnation zone. In addition, when the jet is released from the main channel in this situation, it moves near the inner bank and behaves similarly to a jet in a simple channel. This positioning near the inner bank reflects a typical jet trajectory in less complex channel configurations, highlighting how the dynamics of the main channel continue to influence the jet behavior even in the absence of active discharge from the tributary.

3.3. Cross-sectional distributions and Jet Widening

Analyzing the expansion of the jet along its path provides valuable insights into the development of the jet and emphasizes the influence of both the discharge rate and placement of the discharge on the effectiveness of mixing and dilution. This section provides a better understanding of how these factors contribute to the overall performance of the jet in terms of enhancing the fluid integration and reducing the concentration gradients within the flow. By examining the growth of the jet and its interaction with the surrounding fluids, one can better comprehend the mechanisms that drive its integration and dispersion.

The normalized concentration profiles across various downstream cross-sections perpendicular to the central trajectory of the jet are depicted in Fig. 12 considering different discharge ratios and densities. The parameter "b_c" denotes the distance from the jet centerline to the point where the concentration falls to 𝑒⁻¹𝐶_𝑚𝑎𝑥, with 𝐶_𝑚𝑎𝑥 representing the peak tracer concentration along the centerline. Analysis of these profiles enables comparison of the expansion of each jet at consistent cross-sectional points, demonstrating how variations in jet velocity and location affect the jet widening. Notably, a jet with the same velocity, when released in the main channel, exhibits a wider spread than a jet in the tributary (compare R1 versus R2, and R3 versus R4). This difference is primarily because the jet in the tributary is constrained by the shear layer, limiting its widening compared to the jet in the main channel. Furthermore, jets released from the same location but at different velocities demonstrate that a jet with higher velocity is wider than one with lower velocity (compare R1 versus R3, and R2 versus R4). This widening disparity can be attributed to the higher initial momentum of the faster jet. Additionally, in all cases, particularly near the jet nozzle, the widening of the half of the jet closest to the inner wall is less than the other half due to the wall’s restrictive influence on the fluid flow.

Figure 13 shows the jet widening at 2.5 cm below the surface for two tests: one with a positively buoyant jet (R1) and one with a neutral jet. Comparing the figures indicates that the neutral jet has a wider distribution at this level.

3.4. Variance of Concentration

The investigation of concentration fluctuations facilitates a deeper understanding of the differential mixing dynamics occurring at the interface regions between the injected jet and ambient flow. The quantification of these fluctuations is expressed through the non-dimensional variance of concentrations, denoted as $\:{{\sigma\:}}^{2}/{\text{C}}_{\text{m}\text{a}\text{x}}^{2}$, where 𝜎 represents the standard deviation of the concentration values. This variance metric is systematically evaluated at several downstream cross-sections orthogonal to the central trajectory of the jet, as demonstrated for experimental cases R1 and R3 in Fig. 14. This analysis not only provides insights into the spatial distribution and intensity of mixing of the jet as it interacts with the confluence flow at various distances from the point of discharge but also underscores the variability of mixing efficiency dependent on the initial conditions and configuration of the jet.

According to the findings, the variance profiles exhibit a bimodal distribution with a notable minimum along the jet centerline, indicating reduced mixing within the jet core itself. In contrast, dual peaks in the variance profiles are prominent, located at both the inner and outer edges of the jet's shear trajectory. Notably, the peak at the outer edge consistently surpasses that at the inner edge across all cases examined. This asymmetry is primarily attributed to the formation and subsequent disruption of Kelvin-Helmholtz (KH) instability structures, as documented in references [47], [48].These instabilities play a pivotal role in enhancing turbulent mixing, particularly at the upper edge, where the differential velocity between the jet and the ambient fluid maximizes shear, thereby intensifying the mixing processes. As the trajectory progresses, the bimodal distribution of the variance profiles gradually smoothens and eventually converges into a single line. This transition indicates an increasing uniformity in mixing along the jet's path, as initial variations in concentration diminish and the fluid elements from the jet and ambient flow become more homogeneously mixed. This phenomenon typically results from the enhanced turbulence and diffusive processes that effectively redistribute the momentum and mass as the flow moves downstream. Moreover, comparisons of the variance profiles across different scenarios reveal that the variance levels are consistently lower when the jet is positioned in the main channel. This is because, when the jet is in the main channel, it can distribute over a wider width, allowing it to dilute better. This is consistent with the results of the widening and concentration distribution presented above.

As highlighted in the introduction, several confluence features significantly influence the mixing dynamics. These include the angle between the converging channels and flow ratios of the approaching streams. In our analysis, we focused on specific instances involving one angle and one flow ratio. However, it is important to note that variations in these factors can dramatically alter the jet behavior. For instance, increases in the confluence angle can enlarge the separation zone, trapping more of the discharge within it, particularly when the jet is discharged in the tributary channel. Similarly, an increase in the velocity of the tributary flow tends to push the shear layer towards the outer bank, compelling the jet in the main channel to navigate through a narrower width while increasing the turbulence in the shear layer.

Further complexities arise when considering additional scenarios that can affect jet mixing. These might include differences in channel depth, physical properties of the fluids involved, and environmental variables such as temperature gradients. Each of these factors can potentially alter flow dynamics and mixing efficiency in diverse ways. A comprehensive examination of these scenarios will provide deeper insights into the interplay between confluence features and their cumulative effects on jet behavior and fluid mixing in hydraulic systems, which is beyond the scope of this paper.

For the effective management of effluent discharges in river confluences, it is paramount to comprehend the factors influencing jet dynamics and mixing processes. This study explored the combined effects of varying the discharge velocities, buoyancy, and confluence geometries on the performance of surface jets. Through a series of Laser-Induced Fluorescence (LIF) experimental tests, the trajectories and concentration distributions of jets in complex flow environments were examined. The experiments focused on different scenarios in which confluence discharge and ambient flow conditions were systematically varied to assess their impact on jet behavior and mixing efficacy.

Instantaneous and time-averaged flow visualizations captured via LIF experimentation revealed various parameters such as jet trajectory, spread, and dilution rates. The results demonstrated that both the jet trajectory and dilution were influenced by the discharge rate and buoyancy, with increased velocity and buoyancy leading to enhanced mixing and a wider dispersion of the jet.

The study further highlighted that higher ambient flow velocities relative to jet speed (characterized by the parameter u_r) resulted in more dynamic interactions between the jet and ambient water, promoting greater entrainment and dilution. This was particularly evident in scenarios where the jet was discharged into the main channel, showing deviations in the jet trajectory and an increased dilution effect compared with jets in tributary channels.

In conclusion, this research provides substantial evidence that the design and placement of effluent discharges can be optimized by considering the detailed dynamics of jet behavior in confluence regions. These findings offer valuable management for environmental practices, suggesting that strategic positioning and orientation of discharges can significantly enhance the mixing and dilution of effluents, thereby minimizing their ecological impact. The insights gained from this study are not only applicable to the design of new discharge systems, but also to the improvement of existing installations in urban and industrial landscapes. Future work will aim to integrate these findings into computational models to further refine the predictions and enhance the design of effluent management systems in complex riverine environments.

Acknowledgments

The research was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC).

Author contributions:

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Ehsan Behzad, Abdolmajid Mohammadian and Colin D. Rennie. The first draft of the manuscript was written by Ehsan Behzad and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Competing interest reported. Please avoid assigning the following reviewers due to potential conflicts of interest:

George Serban Constantinescu IIHR – Hydroscience and Engineering The University of Iowa, Iowa City, IA 52242 Phone: (319) 384-0630 or (319) 594-2817 Email: [email protected]

Dr. Alexander Sukhodolov Research Group Leader Department 1: Ecohydrology and Biogeochemistry Email: [email protected] Phone: +49 (0)30 64181 675 Fax: +49 (0)30 64181 663 Office: Room 407 Address: Müggelseedamm 310, 12587 Berlin

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You are reading this latest preprint version

Experimental Investigation of Positively Buoyant Surface Jet in Confluence Regions

Status:

Version 1

Abstract

Figures

Highlights

1. Introduction

2. Methodology

2.1. Experimental Setup and Flume Configuration

2.2. Experimental Parameters

2.3. Flow Visualization Techniques

2.4. Processing and Data Analysis

3. Results and Discussion

3.1. General Observations

3.1.1. Instantaneous Visualization

3.1.2. Timed-averaged Visualization

3.1.3. Visualization of the Case of Stagnant Flow Conditions in the Tributary Channel

3.2. Jet Trajectory

3.2.1. Jet-1 Trajectory

3.2.2. Jet-2 Trajectory

3.2.3. Jet Trajectory in the Case of Stagnant Flow Conditions in the Tributary Channel

3.3. Cross-sectional distributions and Jet Widening

3.4. Variance of Concentration

4. Conclusions

Declarations

Acknowledgments

References

Additional Declarations

Status:

Version 1

Discharge length scale	\(\:{L}_{Q}={Q}_{0}/{M}_{0}^{1/2}\)
Jet-to-plume length scale	\(\:{L}_{M}={M}_{0}^{3/4}/{J}_{0}^{1/2}\)
Jet-to-crossflow length scale	\(\:{l}_{m}={M}_{0}^{1/2}/\stackrel{-}{{u}_{a}}\)
Plume-to-crossflow length scale	\(\:{l}_{b}={J}_{0}/{\stackrel{-}{{u}_{a}}}^{3}\)

Jet flow rate	\(\:{Q}_{0}=\stackrel{-}{{u}_{0}}{a}_{0}\)
Jet momentum flux	\(\:{M}_{0}=\stackrel{-}{{u}_{0}}{Q}_{0}\)
Jet buoyancy flux	\(\:{J}_{0}={Q}_{0}\:{g}_{0}^{{\prime\:}}\)
Discharge buoyant acceleration	\(\:{g}_{0}^{{\prime\:}}=g(\varDelta\:{\rho\:}_{0}/{\rho\:}_{0})\)