Trajectory of Particulate Waste Transported by Artificial Upwelling

Abstract

The feeding activities of fish in marine aquaculture have raised concerns about severe benthic pollution within the cage area. This paper suggests removing particulate waste from the cage area through the implementation of artificial upwelling (AU), a method likely to alleviate the organic burden within the cultivation area. A numerical model was developed to simulate AU-induced particulate matter transport under different operating conditions, with the majority of simulation results validated through flume experiments. The influence of particle characteristics, environmental conditions, and engineering parameters of AU on organic matter transport are discussed. In particular, our study offers a detailed analysis of the minimum initial upwelling velocity required to transport particulate waste to a designated distance. It also recommends situating the bottom of the cage above the maximum height of the waste plume to effectively segregate fish from the waste carried by the upwelling.

1. Introduction

The global expansion of mariculture, driven by the increasing world population and the subsequent surge in seafood demand, has witnessed considerable scale and production increases [1,2,3]. Mariculture is distributed worldwide, with production concentrated in countries such as China, India, and Indonesia. Among them, China stands out as the largest producer, reaching 22.75 million tons in 2022. While mariculture plays a pivotal role in contributing to food security and supplying ample nutrition for humanity [4], it confronts several challenges concerning sustainable development. One of the major concerns is the presence of particulate organic waste originating from fish cage culture [5]. This waste, consisting mainly of unconsumed feed and fecal matter, sinks into the water and accumulates on the seafloor, leading to benthic organic enrichment [6]. As a result, this phenomenon promotes the eutrophication of the water column and instigates significant modifications in the physical and chemical attributes of the benthic environment [7,8]. To achieve the long-term goal of sustainable development, various measures have been implemented to address aquaculture pollution, including the regulation of aquaculture capacity, rational feeding, and multi-trophic aquaculture [9,10]. Nonetheless, highly efficient treatment mechanisms targeting organic particulates directly have yet to be developed.

As a geoengineering tool, artificial upwelling (AU) emerges as a viable strategy to bring cold, nutrient-rich deep ocean water to the surface, realizing ocean fertilization sustainably. This process, in turn, fosters the proliferation of phytoplankton and promotes mariculture growth [11,12]. Over the past few decades, significant advancements have been made in the development of various AU devices, with several undergoing successful testing [13]. In 1997, a density current generator [14] was installed in Gokasho Bay, Japan, significantly reducing the incidence of red tide in the area [15]. More recently, in 2002, an artificial upwelling experiment utilizing a bubble curtain was conducted in the inner part of Amafjord, Norway, leading to a significant increase in the biomass of non-toxic algae and a complete reduction in the growth of toxic algae [16]. Continuing the trend of innovation, in 2018, Fan et al. implemented an artificial upwelling sequestration demonstration project in Aoshan Bay, China, which more than doubled the biomass and carbon removal of cultivated seaweeds [17]. Extensive research has demonstrated its positive effects, although uncertainties related to potential impacts on ecosystems have not been resolved. Currently, researchers are actively exploring diverse application scenarios for AU in marine ecological regulation. This includes its potential role in reducing hypoxia and facilitating surface seawater cooling [13]. These ongoing efforts highlight the continuous exploration and development of AU as a powerful tool for sustainable marine ecosystem management.

Air-lift AU, which induces the upwelling of deep ocean water through the injection of compressed air into an underwater nozzle [18], holds the potential to alleviate the contamination issues caused by particulate organic waste. As illustrated in Figure 1, within a crossflow scenario, the behavior of AU mirrors that of a diverted buoyant plume proficient in elevating particulate waste and conveying it beyond the cultured confines into the expanse of the open ocean. The transport of particulate waste is regulated by the initial upwelling velocity, with the velocity and direction of the crossflow—governed by tidal forces—playing a pivotal role. The challenge lies in discerning the optimal initial upwelling velocity, ensuring the conveyance of particulate waste beyond the aquacultural confines without inducing disturbance to the piscine inhabitants. Hence, studying the trajectory of particulate waste carried by AU is of significant importance.

The hydrodynamic performance of air-lift AU has been well studied. Liang et al. derived the velocity and flow rate of AU in stagnant water based on the jet flow theory [18]. Qiang et al. [19] devised a model predicting the AU trajectory in a crossflow drawing using the algebraic approach proposed by Ansong [20]. Yao et al. formulated a model predicting the maximum height of AU [21]. Despite these advancements, it is worth noting that no studies have specifically focused on the movement of particulate waste transported by AU.

In this study, particle-loaded artificial upwelling was subjected to both experimental and numerical simulation. The characteristics of the flow field and particle dynamics were scrutinized within a simplified two-dimensional (2D) model through numerical simulations and physical experiments. Furthermore, in this paper, the control methods in engineering applications are discussed.

2. Mathematical Model

2.1. Dynamic Analysis of Particulate Organic Waste Transported by AU

The upwelling plume can deliver particulate organic waste, and its deflection in the crossflow determines the transport and fate of the particles. Particulate waste typically does not follow the movement path of the upwelling plume precisely; its movement is affected by multiple factors, including the density, shape, and size of the particulate waste [22]. Generally, smaller and lighter particles can be transported over more extensive distances within the plume.

2.2. Simplified 2D Numerical Model

The AU originating from the nozzle could be considered as a steady turbulent round jet in the z-direction, as shown in Figure 2. For the simplicity of the considered problem, we assumed a uniform and unidirectional crossflow. The water body was divided into bottom water and ambient water, with the former having a density greater than the latter. For this setup, AU was characterized as a negatively buoyant plume. To solve the flow field in the plume region and the trajectories of particles, a 2D numerical model was established based on Lagrangian integration techniques.

In the Lagrangian framework, the AU plume consisted of a series of noninterfering elements moving along the AU trajectory. The mean velocity of water in the element was denoted by $\overrightarrow{u}$, so the element thickness was h = u∆t ($u=\left|\overrightarrow{u}\right|$) and its mass was m = ρπb²h, where ρ and b are the mean density of water in the element and half-width of the element, respectively, and ∆t is the time step. According to the conservation principles of mass, momentum, heat content, and salt content, the plume’s governing equations were as follows [23,24]:

$$\frac{dm}{dt}={\rho }_a{Q}_e$$

(1)

$$\frac{d\left(m\overrightarrow{u}\right)}{dt}=\overrightarrow{u_a}\frac{dm}{dt}-m\frac{{\rho }_a-\rho }{\rho }\overrightarrow{g}$$

(2)

$$\frac{d\left(m{C}_{p}T\right)}{dt}=C_p{T}_a\frac{dm}{dt}$$

(3)

$$\frac{d\left(mS\right)}{dt}=S_a\frac{dm}{dt}$$

(4)

where T and S represent the temperature and salinity of the plume and ρ_a, $\overrightarrow{u_a}$, T_a, and S_a represent the density, velocity, temperature, and salinity of the ambient water, respectively; C_p represents specific heat (assumed to be constant).

Furthermore, the geometry of the AU trajectory was defined as below:

$$\frac{\overrightarrow{ds}}{dt}=\overrightarrow{u}$$

(5)

In Equations (3) and (4), we neglected the losses in heat and salinity caused by turbulent diffusion since the Peclet number Pe = LU/D—where L is the characteristic length scale, U is the velocity magnitude, and D is the characteristic diffusion coefficient—is actually greater than 1 for typical AU motion scales.

Q_e was the volume flux of ambient water entrained by the plume due to shear-induced entrainment Q_s and forced entrainment Q_f [23,25]. The first one arose from shear between the plume and the ambient and was present even in the absence of ambient current. The latter was caused by the advection of the ambient current into the plume.

The shear-induced entrainment was defined as follows:

$$Q_s=2\pi bh\alpha \left|u-u_a\cos \varphi \right|$$

(6)

where $\varphi$ is the angle between the plume axis and the horizontal plane and $u_a\cos \varphi$ denotes the component of crossflow velocity in the direction of the plume axis. α is the entrainment coefficient, which is related to the local densimetric Froude number F [23,26]:

$$\alpha =\sqrt{2}\frac{0.057+\frac{0.554\sin \varphi }{F^2}}{1+5\frac{u_a\cos \varphi }{\left|u-u_a\cos \varphi \right|}}$$

(7)

$$F=E\frac{\left|u-u_a\cos \varphi \right|}{{\left(g\frac{\left|{\rho }_a-\rho \right|}{\rho }b\right)}^{1/2}}$$

(8)

where E = 2 is a proportionality constant obtained by comparing the results of the numerical model with the asymptotic solutions of basic jet flow [24].

The form of forced entrainment was as follows:

$$Q_f=u_a\left[2bh\sin \varphi +\pi b\cos \varphi \frac{\partial b}{\partial s}h-\frac{\pi }{2}{b}^2\sin \varphi \frac{\partial \theta }{\partial s}h\right]$$

(9)

Equation (9) consists of three contributions: the first term represents the forced entrainment due to the projected plume area normal to the crossflow; the second term is a correction due to the growth of the plume radius; and the third term is a correction due to the curvature of the trajectory.

The governing equations required for simulating AU could be completed by including a state equation, as indicated in Equation (10), which describes the density variations caused by temperature and salinity. Specifically, the UNESCO (1981) state equation was adopted [27].

$$\rho =\rho \left(T,S\right)$$

(10)

Based on the Gaussian profiles, the velocity and density distribution functions of the plume cross-section were specified by the following equations [27]:

$$u_f=u_c\exp (-r^2/{b_g}^2)+u_a\cos \varphi$$

(11)

$$\frac{{\rho }_a-{\rho }_f}{{\rho }_a-{\rho }_c}=\exp (-r^2/{(\lambda b_g)}^2)$$

(12)

where subscript c denotes the value at the center of the plume cross-section, subscript f denotes any point on the plume cross-section, and r represents the distance from any point on the plume cross-section to the center of the section. b_g is a measure of the plume width, where the excess velocity is e⁻¹ = 37% of the center value, and $b=\sqrt{2}{b}_g$. λ = 1.2 is the ratio of widths of density and velocity profiles.

Integrating Equations (11) and (12) on the plume cross-section, the total volume flux Q, axial momentum flux M, and buoyancy flux J could be obtained as follows:

$$Q=\pi {b_g}^2(u_c+2u_a\cos \varphi )$$

(13)

$$M=\frac{1}{2}\pi {b_g}^2{(u_c+2u_a\cos \varphi )}^2$$

(14)

$$J=\pi {b_g}^2\left(\frac{{\lambda }^2}{1+{\lambda }^2}{u}_c+{\lambda }^2{u}_a\cos \varphi \right)\frac{({\rho }_a-{\rho }_c)g}{{\rho }_{ref}}$$

(15)

Q, M, and J could also be obtained by the mean velocity u and mean density ρ:

$$Q=\pi b^{2}u$$

(16)

$$M=\pi b^2{u}^2$$

(17)

$$J=\pi b^{2}u\frac{({\rho }_a-\rho )g}{{\rho }_{ref}}$$

(18)

According to Equations (13)–(18), the velocity and density at the center of the plume cross-section could be related to the mean values over the cross-section:

$$u_c=\frac{2M}{Q}-2u_a\cos \varphi =2u-2u_a\cos \varphi$$

(19)

$$\begin{array}{l}{\rho }_c={\rho }_a-\frac{b^{2}u({\rho }_a-\rho )}{{b_g}^2\left(\frac{{\lambda }^2}{1+{\lambda }^2}{u}_c+{\lambda }^2{u}_a\cos \varphi \right)}\\ ={\rho }_a-\frac{b^{2}u({\rho }_a-\rho )}{{b_g}^2\left(\frac{{\lambda }^2}{1+{\lambda }^2}(2u-2u_a\cos \varphi )+{\lambda }^2{u}_a\cos \varphi \right)}\end{array}$$

(20)

Substituting Equations (19) and (20) into Equations (11) and (12), respectively, then combining them with $b=\sqrt{2}{b}_g$, the expressions for u_f and ρ_f became the following:

$$u_f=\left(2u-2u_a\cos \varphi \right)\exp (-2r^2/b^2)+u_a\cos \varphi$$

(21)

$${\rho }_f={\rho }_a-\frac{2u({\rho }_a-\rho )}{\frac{{\lambda }^2}{1+{\lambda }^2}\left(2u-2u_a\cos \varphi \right)+{\lambda }^2{u}_a\cos \varphi }\exp (-2r^2/{\lambda }^2{b}^2)$$

(22)

Equations (21) and (22) gave profiles of amplitude u_f and ρ_f with respect to the axis of the plume. The direction of the velocity in the same plume cross-section was considered to be the same, so the projection of the velocity at any point in the x and z directions were respectively $u_f\cos \varphi$ and $u_f\sin \varphi$.

The properties of particulate organic waste could change due to degradation and decomposition, but we treated them as rigid spheres in solving their motion equations. Particle collision was ignored in the dilute particle-laden flows.

The particle’s motion equations were given by [28,29,30] the following:

$$\begin{array}{l}\frac{\overrightarrow{d{u}_p}}{dt}=\left(1-\frac{{\rho }_s}{{\rho }_p}\right)\overrightarrow{g}+\frac{3C_d{\rho }_s}{4d_p{\rho }_p}\left|\overrightarrow{u_s}-\overrightarrow{u_p}\right|\left(\overrightarrow{u_s}-\overrightarrow{u_p}\right)+\frac{{\rho }_s}{{\rho }_p}\frac{d\overrightarrow{u_s}}{dt}\\ +\frac{{\rho }_s}{2{\rho }_p}\left(\frac{d}{dt}(\overrightarrow{u_s}-\overrightarrow{u_p})\right)+\frac{9{\rho }_s\sqrt{\pi v_s}}{\pi {\rho }_p{d}_p}{\displaystyle {\int }_0^t\frac{\frac{\overrightarrow{d{u}_s}}{d\tau }-\frac{\overrightarrow{d{u}_p}}{d\tau }}{\sqrt{t-\tau }}}\end{array}$$

(23)

$$\frac{\overrightarrow{d{x}_p}}{dt}=\overrightarrow{u_p}$$

(24)

The terms on the right-hand side of Equation (23) respectively represent gravity, drag, pressure gradient, virtual mass, and Basset history term. Subscripts p and s denote particles and surrounding fluid, respectively; u is the velocity, ρ is the density, d_p is the particle diameter, C_d is the drag coefficient, and g is the gravitational acceleration.

The drag coefficient was determined by the Reynolds number Re_p [31]:

$$C_d=\left\{\begin{array}{l}\frac{24}{{\mathrm{Re}}_p}\left(1+0.15{{\mathrm{Re}}_p}^{0.687}\right),{\mathrm{Re}}_p\le 1000\\ 0.44,{\mathrm{Re}}_p>1000\end{array}\right.$$

(25)

with the Reynolds number Re_p defined as

$${\mathrm{Re}}_p=d_p\left|\overrightarrow{u_f}-\overrightarrow{u_p}\right|/\upsilon$$

(26)

Utilizing the proposed model, a computer program was developed to study the flow field of AU and the trajectories of transported particulate waste. The governing equations of the AU control body were discretized through numerical techniques, specifically employing the finite difference method. Simultaneously, the motion equations dictating the particle’s trajectory were effectively solved using the fourth-order Runge-Kutta method. In the numerical computations, the initial position of the particles was set as the central point of the nozzle, while the initial velocity was prescribed as 0 m/s. The computation was terminated as the particle left the plume region or settled onto the ground. The flow field parameters on the particle trajectory were updated at every time step.

3. Experimental Setup

The experiments were conducted in a transparent flume (5 m long, 0.4 m wide, and 0.5 m deep) in the PIV Laboratory of Hainan Institute, Zhejiang University. The flume was equipped with a flow generation system with a continuously adjustable flow rate to achieve a crossflow velocity of up to 0.15 m/s. AU was simulated by discharging a saline solution vertically upwards from the bottom of the flume. For the discharge of the saline solution, a stable upwelling device was designed [32], as shown in Figure 3, which mainly consisted of a saline solution vessel, a separator vessel, an overflow collector, and a U-like nozzle. The liquid in the separator vessel could be steadily injected into the flume vertically upwards under the effect of water pressure difference through the U-like nozzle.

In the stable upwelling device, different initial upwelling velocities were obtained by varying the water pressure difference, i.e., the distance between the overflow surface of the separator vessel and the water surface in the flume. The liquid held in the saline solution vessel was weighed before and after discharging the saline solution, and the difference between the two weighings was recorded as M_o. The weight of the liquid collected by the overflow collector was also weighed after discharge and recorded as M_c. Additionally, the duration T_inj of discharge needed to be recorded. Then, the total mass of liquid injected into the flume from the U-like nozzle was ∆M = M_o − M_c and the mean velocity at the outlet of the U-like nozzle could be expressed as $u_0=4\mathsf{\Delta }M/(\rho \pi D^2{T}_{inj})$.

The experimental setup is shown in Figure 4a. The operation procedure of the experiments was as follows:

• Merge industrial salt with freshwater to concoct a saline solution. Employ a thermo-salinity meter (WS-100s) to measure its temperature and salinity. The obtained numerical values can be utilized to determine density based on the seawater equation of state. Introduce a dye as a tracer by adding it to the saline solution for tracking purposes.
• Fill the flume with water and set the crossflow velocity with the flow controller.
• Inject the saline solution into the separator vessel until the water level reaches the overflow surface. Then, open the upper valve and employ peristaltic pumps (ZP300-S48, Lei Rong Fluid Technology (Shanghai) Co., Ltd., Shanghai, China, ZP600-S64, Lei Rong Fluid Technology (Shanghai) Co., Ltd., Shanghai, China) to continuously supply the saline solution to the saline solution vessel, maintaining the separator vessel in an overflow state.
• Open the lower valve, allowing the saline solution to be ejected from the U-like nozzle into the ambient water in the flume, creating an artificial upwelling plume. As the injection rate exceeds the discharge rate, the separator vessel should remain in an overflow state, maintaining a constant water level. The change in ambient water level induced by the discharged saline solution should be less than 1 × 10⁻⁴ m, resulting in a minimal alteration in plume velocity, less than 0.044 m/s. Therefore, it can be assumed that the outlet velocity of the U-like nozzle remains constant during the emission of the plume.
• In particle transport experiments, simulate particulate organic waste using glass beads. Using a funnel, seed the glass beads into the discharged fluid from the top of the separator vessel to ensure a uniform velocity distribution of particles at the U-like nozzle outlet. Illuminate the vertical cross-section through the center of the U-like nozzle outlet with a laser sheet generated by a Nd:YAG solid-state laser (Beamtech Optronics Co., Ltd., Bei**g, China) to observe the particle distribution, as shown in Figure 4b.
• Use a high-speed CMOS camera to capture images of the artificial upwelling plume and particle dispersion.

Water depth was maintained at 0.4 m for all experimental conditions. The U-like nozzle, with a diameter of 6 mm, was positioned at a depth of 35 cm below the water surface. Throughout the experiments, the density of the saline solution was carefully adjusted to 1012 kg/m³, while the density of the surrounding ambient water was determined to be 996 kg/m³. The experimental parameters for a total of 16 tests are detailed in

Table 1. Experimental parameters for a total of 16 tests.

Test No.	D (mm)	ua (m/s)	uo (m/s)	dp (mm)	ρp (kg/m3)
101	6	0.031	0.284	-	-
102	6	0.031	0.419	-	-
103	6	0.031	0.511	-	-
104	6	0.031	0.568	-	-
105	6	0.031	0.645	-	-
201	6	0.062	0.284	-	-
202	6	0.062	0.419	-	-
203	6	0.062	0.511	-	-
204	6	0.062	0.568	-	-
205	6	0.062	0.645	-	-
P101	6	0.031	0.511	0.070	2450
P102	6	0.031	0.511	0.100	2450
P103	6	0.031	0.511	0.125	2450
P201	6	0.062	0.511	0.070	2450
P202	6	0.062	0.511	0.100	2450
P203	6	0.062	0.511	0.125	2450

, categorized into groups with and without particles.

4. Results

4.1. Model Validations

A snapshot of the artificial upwelling plume is shown in Figure 5. The plume with initial momentum ascended first and deflected downstream under the influence of crossflow. Due to the negative buoyance, the plume in the ambient water eventually descended after reaching a specific height. The plume trajectories thus had a parabolic shape. Model–data comparisons are given in Figure 6. When the crossflow velocity was 0.03 m/s, the numerically simulated plume descended more rapidly compared to the experimental results. However, as the crossflow velocity was increased to 0.06 m/s, the numerically simulated plume appeared to descend more slowly. This discrepancy was attributed to the model neglecting heat and salinity losses caused by turbulent diffusion, resulting in an overestimation or underestimation of plume density. The average relative errors in plume height at the two crossflow velocities were 2.5% and 6.7%, respectively. Overall, the model predicted the trajectory of the plume fairly well.

Further model–data comparisons of plume half-widths are shown in Figure 7. The width of the plume gradually expanded along its trajectory and underwent gentler changes near its peak. It is noteworthy that the variance in half-width between different initial upwelling velocities was pronounced near the plume’s peak, but gradually converged as the plume descended. Model predictions and experimental results showed the same trend and were in general agreement.

Figure 8 shows a comparison between the numerically calculated particle trajectories (white lines) and the experimentally taken particle dispersion images. The instantaneous plume velocity contained the time-averaged velocity and its fluctuations, i.e., the pulsating velocity. The numerical model only considered the time-averaged flow field of the plume to obtain the mean trajectory of the particles. In contrast, the experimentally recorded particle dispersion contained turbulent diffusion characteristics of particles deviating from the mean trajectory under the influence of pulsating velocity.

The particle sizes in Figure 8 range from 0.07 mm at the top to 0.1 mm in the middle and 0.125 mm at the bottom, exhibiting a gradual increase in brightness within the image. Another factor that contributed to the augmented brightness was the utilization of a basic funnel for particle release during the experiment, a method that may have led to an increased particle concentration. For tests p101, p102, p201, and p202, the numerically calculated particle trajectories all correlated well with the actual particle dispersion. For tests p103 and p203, on the other hand, the actual particle dispersion deviated from the mean trajectory to a greater extent, probably due to the high particle concentration, which led to the excessive influence of particle–particle interaction and particle motion on the plume flow field. Improved particle release methods are needed to address this issue. Even if the turbulence effect has a large influence on particle transport, the particle mean trajectory can still be used as an important reference for the design of engineering applications.

4.2. Effect of Particle Characteristics

As illustrated in Figure 9a, increased particle density led to a shorter traveling distance of particles. This implies that higher particle density made it more difficult for particles to track the plume, decreasing their horizontal transport distance and maximum height. Figure 9b illustrates how the plume-driven particle horizontal transport distance and maximum height varied with an increase in particle density from 1100 kg/m³ to 2500 kg/m³. Particles with minimal density could ascend to 4.5 m and traverse horizontally for a considerable 77 m. Conversely, particles with the maximal density underwent a vertical ascent of 2 m and exhibited a meager horizontal transport distance of merely 5.9 m. The correlation between the horizontal transport distance of particles and particle density generally aligned with an exponential function that was similar for the maximum height.

An increase in particle size also led to a shorter transport distance of the particles, as shown in Figure 9c. Under the conditions illustrated in Figure 9d, particles with sizes ranging from 0.5 to 7 mm exhibited dispersion across distances ranging from 2 to 42 m from the nozzle. Particles smaller than 1.5 mm were transported beyond 10 m. The dependence of horizontal transport distance and maximum height on particle size was well-fitted by power law functions.

4.3. Effect of Environmental Conditions

Figure 10a illustrates the trajectories of the same particles under different crossflow velocities. An increase in crossflow velocity led to a decrease in the maximum height to which particles ascended with the plume, but their horizontal transport distance increased. This indicates that higher crossflow velocities are more conducive to particle transport. The effect of a crossflow velocity of 0.2~1 m/s is shown in Figure 10b. The horizontal transport distance of particles exhibited a linear increase with the augmentation of crossflow velocity, while the maximum height showed an inverse correlation with crossflow velocity, fitting well with the exponential function.

From Figure 10c, it is discernible that fluctuations in the density difference between bottom water and ambient water exerted a relatively modest impact on particulate transport, albeit influencing the buoyancy of the plume. The horizontal transport distance of particles and the maximum height exhibited a linear inverse correlation with the density difference, as depicted in Figure 10d.

4.4. Effect of Engineering Parameters of AU

The trajectories of the same particles at different initial upwelling velocities are shown in Figure 11a. By increasing the initial upwelling velocity, the plume could lift the particles higher and transport them farther. Figure 11b examines the effect of initial upwelling velocities of 0.4~2 m/s. With the augmentation of the initial upwelling velocity, the maximum height demonstrated power law expansion, whereas the horizontal transport distance manifested linear progression. Under the conditions depicted in Figure 11b, particles with a 1 mm size required a minimum initial upwelling velocity of 1 m/s to be transported beyond 10 m and at least 1.6 m/s to be transported beyond 15 m.

The impact of nozzle diameter on particle trajectories was analogous to that of the initial upwelling velocity, as illustrated in Figure 11c. The linear increase in both the horizontal transport distance of particles and the maximum height with the augmentation of nozzle diameter is evident, as depicted in Figure 11d. The augmentation of either nozzle diameter or initial upwelling velocity served to amplify the initial momentum of the plume, thereby enhancing the motion of particles.

5. Discussion

The efficient removal of particulate waste from mariculture sites, while ensuring the preservation of aquatic life, is beneficial in alleviating the degradation of the aquatic environment within mariculture sites and mitigating the decline in ecological carrying capacity. A key question to consider is how large initial upwelling velocity is needed to transport particles beyond a specified distance. Additionally, the maximum height of lifted particulate waste is important in deciding the distance between the bottom of the fish cage and the seabed. This effectively separates fish feeding in deeper water from the waste plume caused by upwelling.

Suppose here a typical scenario in the aquaculture area: a fish cage normally has a radius of 10 m; the predominant dimensions of particulate waste within the aquaculture zone are less than 2 mm with a density of 1100 kg/m³, and there is a density difference of about 1 kg/m³ between the bottom water and the ambient water. Figure 12 and Figure 13 show the results of the minimum upwelling velocity required and the maximum height, respectively, under different crossflow velocities and nozzle diameters. As an example, we take D = 0.8 m and u_a = 0.3 m/s, and the results suggest a minimum upwelling velocity of 1.25 m/s for a target transport distance of 2 times the radius of the fish cage. To prevent fish from being affected by the lifted particulate waste, the base of the cage should be set at least 4.21 m above the seabed.

Figure 12 indicates that conducting particle transport at lower crossflow velocities necessitates a greater initial upwelling velocity, implying the need to supply more energy to the artificial upwelling device. Additionally, the maximum height of lifted particulate waste increases, necessitating an elevation of the base of the cage. When the crossflow velocity increases from 0.2 m/s to 0.4 m/s, the minimum initial upwelling velocity decreases by 32% for a target transport distance of 2 times the radius of the fish cage, and the corresponding maximum height decreases by 70%. It is advisable to perform particle transport at higher crossflow velocities whenever possible to reduce the energy consumption of the artificial upwelling device.

According to Figure 13, an increase in nozzle diameter contributes to a reduction in both the minimum initial upwelling velocity and the maximum height reached by ascending particulate waste. With a nozzle diameter of 0.6 m, the minimum initial upwelling velocity is recorded at 1.4 m/s for a target transport distance of 2 times the radius of the fish cage. Upon an increase in nozzle diameter to 1 m, the minimum initial upwelling velocity diminishes to 0.8 m/s. Moreover, the maximum height experiences a decrease from 2.9 m to 2.1 m. In practical engineering, the design of nozzle dimensions must also take into account the constraints imposed by environmental conditions.

6. Conclusions

This study helps the conservation of mariculture sites by decreasing the load of particulate waste under the cages. A numerical model was established to simulate the process of AU-induced particulate waste transport, with the validation of its efficacy achieved through empirical investigations in a hydraulic flume. Subsequently, the model was utilized to explore the potential of the proposed methodology.

The numerical computations and experimental findings indicate that crossflow velocity, initial upwelling velocity, nozzle diameter, and particle characteristics exert significant influences on particle transport. By adjusting the initial upwelling velocity, it becomes feasible to transport particulate waste beyond specified target distances. In scenarios presented in this paper, the minimum initial upwelling velocity required to transport particles (d_p < 2 mm, ρ_p = 1100 kg/m³) beyond distances of 10 m to 25 m ranges from 0.35 to 1.95 m/s. The maximum height of particle ascent is approximately 12 m and, consequently, the base of the cage should be set at least 12 m above the seabed. In this way, by efficiently transporting particulate matter to reduce the accumulation of organic waste, AU has the potential to improve the environmental conditions in aquaculture areas and facilitate ecological restoration.