Optimization and Verification of the Spreading Performance of a Pneumatic Pond Feeder Using a Coupled CFD–DEM Approach

Abstract

As a key device for precise feeding in aquaculture, feeders directly affect feed utilization efficiency and farming profitability; however, pneumatic pond feeders commonly exhibit poor spreading uniformity and low feed utilization. In this study, a dual-sided air intake structure incorporating a triangular flow-splitter plate was added inside the feed chamber, and the spreading process was simulated using a coupled computational fluid dynamics–discrete element method approach to analyze the motion mechanisms of feed pellets within the feeding device. A rotatable orthogonal composite experimental design was employed for the multiparameter collaborative optimization of the feed chamber height ($h$), the triangular flow-splitter plate width ($d$), and its inlet angle ($\alpha$). The results demonstrated that the triangular flow-splitter plate renders the velocity field within the device chamber more uniform and reduces the coefficient of variation ($CV$) of circumferential pellet distribution to 18.27%, a 22.19% decrease relative to the unmodified design. Experimental validation using the optimal parameter combination confirmed a mean $CV$ of 17.02%, representing a 24.45% reduction compared with the original structure. This study provides a theoretical foundation and reliable technical solution for precise feeding equipment in aquaculture.

1. Introduction

Pneumatic feeders are widely adopted in large-scale aquaculture because of their advantages, such as extensive operational coverage, high feeding efficiency, and low labor costs [1,2]. However, during actual operation, influenced by the coupled effects of blower performance, structural parameters, and material characteristics, these feeders commonly suffer from low spreading uniformity and unstable airflow distribution. These issues cause feed wastage—raising aquaculture costs and increasing residual feed—triggering water eutrophication and making fish more susceptible to disease, thereby severely constraining the improvement of aquaculture profitability [3]. Therefore, optimizing the spreading performance of feeders to achieve precise and uniform feed distribution is a critical issue that demands urgent resolution in the current field of aquaculture equipment [4,5].

Existing feeder designs predominantly rely on empirical trial-and-error: single structural parameters are iteratively adjusted, prototypes are fabricated, and field tests are conducted. This approach lacks quantitative analysis grounded in gas–solid coupling mechanisms, and the manufacture and testing of prototypes extend the optimization cycle, increasing costs [6]. In recent years, the coupled computational fluid dynamics (CFD) and discrete element method (DEM) approach has provided an effective tool for investigating gas–solid two-phase flow mechanisms and offers theoretical support for analyzing the interaction mechanisms between airflow and feed pellets within pneumatic feeders [7,8,9]. Domestic and international scholars have applied this methodology to the optimization of agricultural machinery design. Zhao et al. [10] employed the coupled EDEM–Fluent method to analyze the motion trajectories of feed pellets and the airflow distribution within the throwing disc, optimizing gas–solid mixture uniformity through improvements to the feed chamber. This also provided a new approach for feeder design and testing; however, they did not present a quantitative characterization of the radial distribution of pellets. Yang et al. [11] utilized a parametric CFD–DEM-coupling simulation to reveal the influence mechanisms of the distributor’s rotating cover cone angle and bellow diameter on airflow pressure, velocity, and pellet distribution. This methodology of dual-parameter optimization coupled with gas–solid simulation overcomes the limitations of traditional single-factor experiments, providing a methodological reference for the design of complex agricultural equipment. However, the study’s validation relied primarily on bench tests, and it did not further measure the spatial distribution of particles from their exit from the device to deposition on the soil surface. Existing research primarily focuses on simulating either fluid or particle motion. The application of the CFD–DEM-coupling model to optimize the spreading performance of feeders remains insufficient; particularly, systematic research on structural parameter optimization, operational parameter matching, and multiobjective performance validation is lacking [12,13,14].

In summary, this study addresses the multiphysics coupling problem inherent in the operation of pneumatic feeders. We construct a CFD–DEM-based particle–airflow coupling simulation model. Through parametric design, we investigate the influence mechanisms of key parameters–including the internal structure of the feed chamber and throw chamber and the inclination angle of the diversion device—on the motion trajectory and spatial distribution of feed pellets. The reliability of the simulation results is validated via physical prototype experiments [15]. This study aims to establish a set of optimization methods for pneumatic feeder spreading performance based on gas–solid coupling theory, providing a theoretical foundation and technical support for the intelligent and precise design of aquaculture equipment.

2. Materials and Methods

2.1. Structure and Working Principle of the Pneumatic Feeder

The pneumatic feeder primarily comprises discharge tubes, a throw chamber, a feed chamber, an electric motor, and a support frame, as illustrated schematically in Figure 1a. The operational site of the pneumatic feeder is shown in Figure 1b.

The spreading process of the pneumatic feeder achieves precise feeding through the synergistic action of aerodynamic forces and mechanical mechanisms. The specific workflow is as follows: Feed pellets enter the conveying tube from the feed hopper and are mixed with air by the airflow generated by the blower, forming a suspended flow. Driven by differential pressure, the mixture is rapidly transported into the cavity formed between the feed chamber and throw chamber. With the combined forces of centrifugal energy from the throw chamber’s high-speed rotation and pneumatic pressure, pellets are propelled centrifugally through the discharge tubes into the air. Subsequently, they follow a parabolic trajectory before settling onto the water surface, thereby completing the discharge process.

As shown in the cross-sectional schematic of the feeding device in Figure 2, the structure primarily consists of four discharge tubes, a throw chamber, and a feed chamber. The discharge tubes are connected to the throw chamber via bolted joints, while the throw chamber and feed chamber are interfitted to form a feeding cavity. These components are linked by a motor shaft, which drives the throw chamber in rotary motion to generate centrifugal force.

The gas–solid two-phase flow, formed by the interaction of air and pellets within the cavity, is distributed into the four discharge tubes under differential pressure when passing through the throw chamber [11] before being ejected outward via the tubes. As indicated by the arrow direction in Figure 2, which illustrates the flow path of the gas–solid mixture, the stability and distribution uniformity of the mixture within the cavity critically influence the spatial uniformity of pellets settling on the water surface [16].

2.2. Feeder Structural Design Optimization of the Triangular Flow-Splitter Plate in the Feed Chamber

The pneumatic feeder used in this study is a medium-size unit uniformly manufactured by Nanjing Tongwei Co., Ltd. in China. It floats with an above-water height of approximately 1.1 m and can cover a circular feeding area with a diameter of 40 m.

The feed chamber structure was redesigned to address the issue of uneven pellet distribution in pneumatic feeders. In the traditional configuration, a single circular duct directs airflow unidirectionally into the feed chamber. This design causes pellets to impact the exposed motor shaft and opposite chamber wall under aerodynamic force, disrupting pellet distribution and compromising flow field homogeneity. This study introduced a triangular flow-splitter plate to replace the single duct, creating two opposing square inlets that deliver airflow symmetrically from both sides of the feed chamber. This design buffers impact forces and optimizes flow distribution. As shown in the schematic of the improved feed chamber (Figure 3b, red-highlighted area), pellets enter symmetrically with the airflow, achieving enhanced gas–solid dispersion. The mixture is then conveyed to the throw chamber and finally accelerated along the discharge tube walls for ejection.

Measurements show that the feed chamber height of the prototype feeding device is 80 mm, the inner diameter of the feed chamber is 84 mm, and the wall thickness is 5 mm. The circular duct connected to the feed chamber has an inner diameter of 54 mm and an inclination of about 20°. Referencing the dimensions of the conventional device and ensuring unimpeded structural assembly, this study preliminarily designed the feed chamber height ($h$) as 80 mm, the triangular flow-splitter plate width ($d$) as 60 mm, and its inlet angle ($\alpha$) as 40°. The remaining dimensions should be consistent with those of the prototype device. Meanwhile, the airflow velocity should be stabilized before reaching the feed chamber, according to the following continuity equation:

$$A_1{v}_1=A_2{v}_2$$

(1)

where $A_1$, $A_2$ are the cross-sectional areas of the inlet duct; $v_1$ is the fluid flow velocity at cross section $A_1$; and $v_2$ is the fluid flow velocity at cross section $A_2$. For maintaining consistent flow velocity between the circular duct and dual inlets, the square inlet channels were designed with a width of 21.2 mm and a height matching the circular duct diameter of 54 mm. All other dimensions remained identical to the prototype. The Reynolds number is expressed as follows:

$$R_e={\displaystyle \frac{{\rho }_a{v}_{a}L}{{\mu }_a}}$$

(2)

where ${\rho }_a$ is the air density, $v_a$ is the air flow velocity, $L$ is the characteristic length, and ${\mu }_a$ is the dynamic viscosity coefficient of air. According to this equation, the airflow state transitions to turbulence when $v_a$ > 2 m/s. Turbulent vortices and velocity pulsations effectively disperse pellets, preventing localized accumulation or sedimentation, and thereby significantly enhancing spreading uniformity [17].

2.3. Analysis of Granular Material Kinetics

2.3.1. Motion Analysis in Discharge Tubes

After being conveyed by airflow in the feed chamber, pellets enter the throw chamber and discharge tubes. The aerodynamic force acting on pellets within the discharge tubes is negligible compared with the centrifugal force generated by tube rotation [10]. As shown in Figure 4, the throw chamber drives the discharge tubes to rotate around the vertical axis $O_z$ at an angular velocity $\omega$, with an inclination angle $\theta$ = 60° between the tubes and $O_z$. Given pellets as rigid point masses of mass $m$, the centrifugal force $F_c$ in this coordinate system is as follows:

$$F_c=m{\omega }^{2}s\left(t\right)·sin\theta$$

(3)

where $s$(t) is the axial displacement of the pellets along the tubes. The Coriolis force $F_{cor}$ acting on the pellets is as follows:

$$F_{cor}=2m\omega \dot{s}·sin\theta$$

(4)

During rotation, the lateral supporting force $F_N$ exerted by the tube wall on the pellets is as follows:

$$F_N=\sqrt{{\left(m{\omega }^{2}s\right(t)·sin\theta cos\theta )}^2+{(2m\omega \dot{s}·sin\theta )}^2}$$

(5)

The axial dynamic equation along the discharge tubes is as follows:

$$m\ddot{s}=F_{c}sin\theta -\mu F_{N}sign\left(\dot{s}\right)$$

(6)

where $\mu$ is the friction coefficient between pellets and the tube wall.

Combining Equations (3)–(6) and simplifying them yields the following axial pellet dynamic equation:

$$\ddot{s}=0.75{\omega }^{2}s- \mu \omega \sqrt{{\displaystyle \frac{3{\omega }^2{s}^2}{16}}+{\dot{s}}^2}·sign\left(\dot{s}\right)$$

(7)

As a single-axis equation of motion, it shows that the pellet’s axial acceleration results from the combined effects of wall interactions and rotational motion. Initial conditions $s\left(0\right)=0$ and $\dot{s}\left(0\right)=0$ are substituted, Equation (7) is solved, and the equation for pellet motion within the tubes under low-friction conditions ($\mu <0.2$) is provided as follows:

$$s\left(t\right)\approx {\displaystyle \frac{0.75{\omega }^2}{16{\mu }^2}}\left(e^{\omega \sqrt{0.75}t}-1-\omega \sqrt{0.75}t\right)$$

(8)

It is an idealized equation under specified initial conditions that provides closed-form estimates of the axial residence time and the exit velocity in the discharge tube, forming the basis for subsequent analysis of pellet motion after leaving the discharge tube.

By analyzing the forces on, and the kinematics of, pellets within the discharge tube, the above equation enables a theoretical prediction of the spreading behavior and informs the subsequent arrangement of the computational grid.

2.3.2. Postejection Motion Analysis of Granular Materials

After exiting the discharge tubes, pellets follow a parabolic trajectory under gravity and aerodynamic drag before settling on the water surface. The air resistance $F_d$ acting on a pellet is as follows:

$$F_d={\displaystyle \frac{1}{2}}{C}_d{\rho }_a\pi {r_p}^2{v}^2$$

(9)

where $C_d$ is the air resistance coefficient, $r_p$ is the equivalent radius of the pellet material, and $v$ is the relative velocity between the pellet and air.

Setting the exit point of a discharge tube as the coordinate origin, the equations of motion in three dimensions are as follows:

$$\left\{\begin{array}{c}\ddot{x}=-{\displaystyle \frac{C_d{\rho }_a\pi {r_p}^2}{2m}}{v}_x\sqrt{v_x^2+v_y^2+v_z^2}\\ \ddot{y}=-{\displaystyle \frac{C_d{\rho }_a\pi {r_p}^2}{2m}}{v}_y\sqrt{v_x^2+v_y^2+v_z^2}\\ \ddot{z}=-g-{\displaystyle \frac{C_d{\rho }_a\pi {r_p}^2}{2m}}{v}_z\sqrt{v_x^2+v_y^2+v_z^2}\end{array}\right.$$

(10)

The analysis of the pellet’s motion within the discharge tube revealed that its ejection velocity depends on the rotational speed of the throw chamber, the length of the discharge tube, and the initial contact position between the pellet and the tube. This ejection velocity fundamentally determines key operational parameters of the feeder, such as the maximum throwing distance and distribution area. For ensuring that improvements in distribution uniformity do not compromise these core operational parameters—thereby meeting the requirements of practical working conditions and feeder standards regarding basic performance—the rotational speed and length of the discharge tubes must be maintained as constant boundary conditions in EDEM–Fluent simulations [18]. The pellet’s motion is a composite of rotation about the axis and sliding along the tube wall. Theoretical analysis indicated that after leaving the throw chamber, the pellet should follow a parabolic trajectory. Pellets ejected from discharge tubes of identical length should exhibit a quasi-normal spatial distribution. The finding from the analysis of the pellet’s trajectory upon leaving the tube and its resulting spatial distribution can be compared and validated against the trajectories and distributions obtained from CFD–DEM simulations.

2.4. Simulation Experiment Design

To validate the consistency between theoretical pellet motion analysis and actual discharge dynamics, as well as the structural rationality of the feeder, this study employed Ansys Fluent 2021 R1 and EDEM 2022 for CFD–DEM bidirectional coupling simulations of the feeding process. This validation ensures that the optimized feeder meets practical requirements in aquaculture operations.

2.4.1. Construction of a 3D Simulation Model

For subsequent analysis, Ansys SpaceClaim 2021 R1 was utilized to extract the fluid domain of the feeding cavity. Its parametric modeling and efficient geometry repair capabilities efficiently handle fluid domain extraction from complex mechanical structures [19]. The 3D solid model of the feeder was imported into SpaceClaim, retaining key structures containing airflow channels. On the basis of the continuum assumption, the enclosed geometry of the internal flow field was volumetrically extracted. Boolean subtraction along mechanical wall surfaces using splitting tools precisely defined the fluid domain topology [20,21]. The fluid domain models before and after optimization are shown in Figure 5.

Subsequently, adaptive meshing of the extracted fluid domain model was performed using Fluent’s Meshing Capabilities. Employing an element size of 3 mm, the final mesh comprised approximately 700,000 computational cells, which satisfied the grid resolution requirements for simulating coupled rotating flow field and particle motion. The surfaces of the divided mesh were appropriately assigned: the yellow surfaces in Figure 6 represent the inlet and outlet surfaces, while the remaining light purple surfaces were set as walls. After updating the mesh, it was imported into EDEM, with the wall material defined as steel.

2.4.2. Physical Property Parameters of Granular Materials

This study utilized enhanced Type 153 feed pellets produced by Tongwei Co., Ltd. for analyzing the spreading performance of the pneumatic feeder. Measurements indicated a quasi-cylindrical shape with approximate dimensions of $\varnothing 3\times 4$ mm. The remaining physical property parameters of the pellets were determined based on the relevant research and experimental methods described in References [22,23], as listed in

Table 1. Pellet feed characteristic parameters.

Parameter	Pellet Feed	Feeding Device
Poisson’s ratio	0.23	0.3
Density/(kg·m−3)	1200	7800
Shear modulus/(MPa)	9.74	70,000
Coefficient of restitution (w/feeder)	0.35	0.39
Static friction coefficient (w/feeder)	0.34	0.17
Rolling friction coefficient (w/feeder)	0.16	0.02

.

In the feeding device, the gas phase is air and is modeled as incompressible turbulent flow, with the outlet pressure set to standard atmospheric pressure. The solid phase is treated as a discrete assembly of individual pellets whose motion obeys Newton’s second law. The standard k–ε model was employed to solve the continuous-phase airflow field via Ansys Fluent’s Navier–Stokes equations, with discrete-phase pellet dynamics simulated in EDEM using the Hertz–Mindlin contact model. Consistent with the kinematic analysis in prior sections, and for preserving fundamental operational parameters, the throw chamber’s rotational speed was fixed at 24 r/s, the inlet airflow velocity at 24 m/s [10], and a particle factory was set at the inlet to generate pellets at a rate of 1500 particles per second. These settings ensured that the simulation parameters reflected actual pond operations for enhanced accuracy. Temporal resolution specifications included an EDEM time step of $5\times {10}^{-5}$ s and a Fluent time step of $5\times {10}^{-3}$ s, with the latter being an integer multiple of the former; 4 s total simulation duration equivalent to 800 Fluent steps; maximum iterations per time step limited to 20; and data output intervals of 0.001 s for comprehensive particle trajectory extraction [24,25].

2.4.3. Uniformity Evaluation Metrics

The coefficient of variation ($CV$) for the circumferential distribution of feed pellets was employed as the core quantitative indicator of spreading uniformity to systematically evaluate the spreading performance of the pneumatic feeder. This metric characterized particle spatial distribution using statistical methods. Centered on the rotational axis of the feeder’s throw chamber, six arcuate computational grid planes were positioned at 2 m intervals along each of eight circumferential directions spaced at 45° intervals around the feeder. Each grid plane spanned an angular range of 20°. Within EDEM, utilizing the Selection module in postprocessing, this study statistically analyzed the total mass of pellets falling within each computational grid. The $CV$ for the circumferential distribution of pellets was calculated as follows:

$$CV={\displaystyle \frac{\sigma }{M_0}}\times 100\%$$

(11)

where $\sigma =\sqrt{{\displaystyle \frac{1}{n-1}}\sum _{i=1}^n{(M_i-M_0)}^2}$ is the standard deviation of pellet density; and $M_0={\displaystyle \frac{1}{n}}\sum _{i=1}^n{M}_i$ is the mean mass of pellets collected by the grids within the collection domain.

3. Results and Analysis

3.1. Simulation Results and Analysis

3.1.1. EDEM Particle Simulation Analysis

An EDEM–Fluent coupled simulation was executed by employing the aforementioned software configurations to validate the feeding performance reliability of the model. Figure 7a,b illustrates the motion characteristics of pellets within the traditional chamber structure, where color gradients represent instantaneous particle velocities, and streamlines depict trajectory paths. The simulated motion patterns align with theoretical kinematic analysis: Centrifugal forces drive pellets along the discharge tube walls in high-speed helical paths, acquiring initial velocity before ejection. Upon exiting the feeding mechanism, particles follow parabolic trajectories before settling on the water surface. Airflow effects dominate pellet behavior during feed chamber entry, concentrating particles toward the side opposite the feeding direction. Within the discharge tubes, aerodynamic influences diminish significantly as centrifugal force becomes the predominant influence. This transition creates discernible variations in particle trajectory density, evidenced by nonuniform streamline distribution patterns.

Figure 7c,d shows the EDEM simulation results for the optimized feeding device. Compared with those in the original device, the pellet trajectory streamlines in the optimized structure exhibit a more uniform distribution, without the pronounced sparse/dense variations. The dual-side feeding configuration also promotes more uniform pellet mixing within the chamber. The pellets are distributed evenly to all four discharge tubes under the action of the airflow, effectively resolving the hybrid flow bias issue inherent in the traditional single-side feeding approach.

3.1.2. Analysis of Pellet Distribution Uniformity Results

Figure 8 illustrates the EDEM simulation setup with eight circumferential directions (labeled A through H at 45° intervals), each containing six arcuate grid planes. Directional differentiation employs distinct colors, while radial positioning is indicated by numerical sequencing from innermost plane 1 to outermost plane 6. Figure 9a displays the pellet distribution pattern for the traditional structure. Given that the outermost grids exceed the feeder’s maximum throwing range and the innermost grids fall outside operational zones—both exhibiting negligible pellet deposition—this study utilized data from 32 effectively covered grid planes to calculate circumferential distribution $CV$. The pellet distribution conforms to theoretical expectations, demonstrating a bimodal profile with dual concentration peaks. The calculated $CV$ reaches 40.46%, with 62.13% of total pellet mass concentrated in directions A, B, G, and H. This directional bias aligns with physical observations: Pellets accumulate toward one side within the throw chamber before being ejected predominantly toward specific directions during discharge tube rotation. Consequently, ensuring uniform pellet conveyance into the discharge tubes emerges as the core solution to distribution nonuniformity, with the feed chamber and flow deflector structures identified as critical control elements for airflow distribution and particle dispersion within the cavity.

Figure 9b presents the optimized pellet distribution profile. The circumferential distribution $CV$ for the enhanced feeding mechanism calculated using 32 inner-grid planes within the effective coverage zone is 18.27%. The pellet distribution demonstrates a uniform radial progression with balanced directional dispersion, in which mass fractions consistently hover around 12%. Compared with the preoptimized configuration, distribution heterogeneity is substantially reduced by 22.19 percentage points, implying significantly improved alignment with operational demands for pneumatic feeding systems.

3.1.3. Contour Analysis of Fluid Domain Simulation

The simulation results for the velocity and pressure fields within the fluid domain are shown in Figure 10. Five horizontal cross sections (P1–P5) were uniformly extracted longitudinally through the feed chamber to display contour plots of velocity and pressure. Observation reveals significant interlayer variations in the velocity field across the feed chamber sections during the distribution process. In the top section (P1), large low-velocity regions appear in the flow field. Near the bottom sections (P4, P5), extensive low-velocity vortex zones are present in the flow field. This nonuniformity in the interlayer flow field indicates distinct hydrodynamic deficiencies in the preoptimized chamber structure. That is, the structure fails to ensure uniform flow distribution, thereby adversely affecting feeding uniformity.

The simulation results for the velocity and pressure fields in the optimized fluid domain are shown in Figure 11. Contour plots of the velocity and pressure fields on horizontal cross sections taken at the same five locations within the feed chamber are displayed. The velocity fields across the chamber sections in the optimized structure tend to converge, exhibiting insignificant interlayer differences. The flow distribution is considerably more uniform, demonstrating higher homogeneity compared with that in the preoptimized chamber flow field. This finding indicates that the optimized structure effectively improves the velocity field distribution within the feed chamber, significantly contributing to pellet distribution uniformity.

Although the opposed inlets lead to a modest rise in chamber pressure in the optimized fluid domain, the simulations showed no effect of pressure on spreading uniformity. Using steel for the internal structures also maximizes durability. In Figure 11, at section P5, a small low-pressure spot appears, likely caused by pellet-induced perturbations of the airflow in the coupled simulation; in the bottom region, where pellet concentration is higher, gas–solid momentum exchange may further amplify local pressure fluctuations.

3.2. Orthogonal Regression-Based Central Composite Simulation Optimization

Building upon the coupled CFD–DEM simulation, a central composite design based on orthogonal regression was employed to perform multiobjective optimization of the key structural parameters of the pneumatic feeder. On the basis of the optimized throwing structure, this study investigated the influence of three critical design parameters—feed chamber cavity height, triangular flow-splitter plate width, and triangular flow-splitter plate inlet angle—on the throwing performance. The analysis aimed to identify the optimal parameter combination for the feed chamber. In consideration of practical assembly and operational requirements, the factor value ranges were determined as follows: feed chamber cavity height $h$ = 70–90 mm; triangular flow-splitter plate width $d$ = 50–70 mm; and triangular flow-splitter plate inlet angle $\alpha$ = 35–45°. The $CV$ for the circumferential pellet distribution was adopted as the quantitative evaluation metric. A rotatable central composite design with quadratic regression was constructed for three factors via Design-Expert 13 software. For a test with $k$ factors, the coded value $\beta$ for the axial distance from the center point was given as follows:

$$\beta ={\left(2^k\right)}^{\frac{1}{4}}$$

(12)

The experimental design employed a three-factor, five-level coding method. The corresponding relationships between the coded levels and the actual factor values are presented in

Table 2. Coding of factors.

Coding	Factors
	$\mathbf{Feed} \mathbf{Chamber} \mathbf{Cavity} \mathbf{Height} \mathit{h}$/mm	$\mathbf{Splitter} \mathbf{Plate} \mathbf{Width} \mathit{d}$/mm	$\mathbf{Splitter} \mathbf{Plate} \mathbf{Inlet} \mathbf{Angle} \mathit{\alpha }$/(°)
−1.68179	70	50	35
−1	74	54	38
0	80	60	42.5
1	86	66	47
1.68179	90	70	50

. This experimental methodology facilitated the establishment of a multivariate nonlinear regression model, enabling effective analysis of the influence patterns of individual parameters and their interactions on throwing uniformity. It thereby provided a theoretical basis for determining the optimal parameter combination for the throwing mechanism [26,27].

3.2.1. Analysis of Experimental Results

Multivariate regression analysis was applied to fit the experimental data. The test plan and results are presented in

Table 3. Test plan and results.

Run	Factor			$\mathit{C}\mathit{V}$
	$\mathit{h}$/mm	$\mathit{d}$/mm	$\mathit{\alpha }$/(°)
1	80	60	42.5	16.39
2	86	66	47	18.35
3	70	60	42.5	22.24
4	80	60	50	17.57
5	74	54	38	24.81
6	80	60	42.5	17.02
7	74	54	47	21.8
8	86	54	47	18.24
9	80	60	42.5	15.89
10	80	60	42.5	17.19
11	80	60	35	23.87
12	80	70	42.5	17.95
13	90	60	42.5	17.13
14	86	66	38	20.91
15	80	60	42.5	16.67
16	74	66	38	20.38
17	80	60	42.5	16.07
18	80	50	42.5	21.34
19	74	66	47	19.86
20	86	54	38	22.3

. The quadratic regression model demonstrates high statistical significance (F = 29.41, p < 0.0001). In the lack-of-fit test, the lack-of-fit term yields p = 0.1297 (>0.05) with an F-value of 2.96, confirming that no systematic bias exists in the model. This finding verifies that the regression surface accurately characterizes parameter–response relationships within the design space [28]. After stepwise regression screening to eliminate nonsignificant cross terms, the quadratic polynomial regression equation for $CV$ concerning feed chamber height, triangular flow-splitter plate width, and inlet angle was obtained as follows:

$$CV=635-6.24h-6.56d-7.16\alpha +0.018hd-0.015h\alpha +0.019d\alpha +0.035h^2+0.035d^2+0.081{\alpha }^2$$

(13)

This equation clearly reveals the nonlinear influence of structural parameters on distribution uniformity. The parameter significance test results further provide a reliable mathematical foundation for subsequent response surface optimization.

Table 4. Analysis of variance for circumferential distribution $CV$.

Source	Sum of Squares	df	Mean Square	F	p
Model	136.95	9	15.22	29.41	<0.0001
$h$	17.81	1	17.81	34.41	0.0002
$d$	13.15	1	13.15	25.41	0.0005
$\alpha$	31.66	1	31.66	61.19	<0.0001
$hd$	3.18	1	3.18	6.14	0.0327
$h\alpha$	1.23	1	1.23	2.38	0.1538
$d\alpha$	2.04	1	2.04	3.94	0.0752
$h^2$	22.14	1	22.14	42.79	<0.0001
$d^2$	21.64	1	21.64	41.82	<0.0001
${\alpha }^2$	37.14	1	37.14	71.78	<0.0001
Residual	5.17	10	0.5175
Lack of Fit	3.87	5	0.7733	2.96	0.1297
Pure Error	1.31	5	0.2617
Cor Total	142.13	19

presents the analysis of variance for circumferential distribution $CV$s. Factors $h$, $d$, and $\alpha$, together with their quadratic terms $h^2$, $d^2$, and ${\alpha }^2$, respectively, exhibit highly significant effects (p < 0.01) on $CV$. Interaction terms $hd$ and $d\alpha$ also show significant influence (p < 0.05). The order of factor impact magnitude is $\alpha$ > $h$ > $d$.

.

3.2.2. Response Surface Analysis

The analysis of the data in Table 4 reveals that the interaction terms $hd$ and $d\alpha$ significantly affect the circumferential distribution $CV$s, whereas the $h\alpha$ interaction exhibits no significant influence. Consequently, this study focused on analyzing the effects of $hd$ and $d\alpha$ interactions on $CV$. Figure 12a presents the response surface plot for the interaction between feed chamber height $h$ and triangular flow-splitter plate width $d$ at a fixed inlet angle $\alpha$ = 42.5°. The plot demonstrates that within the $h$ range of 70–85 mm, $CV$ decreases with increasing $h$; by contrast, within 85–90 mm, this trend reverses. Similarly, for splitter width $d$ within 50–60 mm, $CV$ decreases with increasing $d$, but this relationship inverts in the 60–70 mm range. Minimal $CV$ values are consistently observed when the splitter width $d$ ranges between 58 and 62 mm and the chamber height $h$ falls within 80–85 mm.

Figure 12b illustrates the response surface for the interaction between triangular flow-splitter plate width $d$ and inlet angle $\alpha$ at a fixed chamber height $h$ = 80 mm. The analysis reveals that when $\alpha$ ranges from 35° to 45°, $CV$ decreases with increasing $\alpha$, whereas this trend reverses within the 45–50° range. Minimal $CV$ values occur when the splitter width $d$ falls between 60 and 65 mm, with the inlet angle $\alpha$ operating within 42.5–46.25°.

To identify the optimal design parameter combination minimizing the circumferential distribution $CV$ for feed pellets, this study implemented the central composite design-based response surface methodology in Design-Expert 13 for parameter optimization. Afterward, constrained by the factor ranges specified in Table 4, and utilizing the $CV$ regression equation (Equation (13)) as the objective function, this study computationally solved the minimum value. The optimized solution yields a theoretical minimum $CV$ of 15.81% at the following predicted parameter combination: feed chamber height $h$ = 82.26 mm, triangular flow-splitter plate width $d$ = 61.54 mm, and triangular flow-splitter plate inlet angle $\alpha$ = 44.06°.

3.3. Experimental Verification

The feeding device was manufactured using the optimized design parameters determined through our analysis, with the structurally enhanced feed chamber illustrated in Figure 13. Fixed-point pellet dispersion performance testing was conducted at the open, level, hardened ground experimental site of Nanjing Agricultural University’s Binjiang Campus under windless conditions. Tongwei Company’s Enhanced Type-153 pellets, with 12.9% moisture content consistent with simulation parameters, were used. Collection boxes measuring 400 × 300 mm were uniformly arranged along concentric circles with radii of 7, 11, 15, and 19 m, centered on the pneumatic feeder using an equidistant placement method at approximately 800 mm arc length intervals. The corresponding angular spacings were 10° at 7 m radius, 6.3° at 11 m, 4.6° at 15 m, and 3.6° at 19 m, as depicted in the experimental site layout shown in Figure 13.

Following the experiments, the total feed mass in each collection box was recorded, and the $CV$ for pellet distribution was calculated. Three replicated experiments were conducted for the preoptimized and optimized devices. For the preoptimized device, the $CV$s are 39.61%, 41.96%, and 42.85%, yielding a mean of 41.47% with an average relative error of 3.91%. For the optimized device, the $CV$s are 16.42%, 17.61%, and 17.04%, resulting in a mean of 17.02% with an average relative error of 7.67%. The experimental outcomes broadly match the simulation predictions, confirming the accuracy of the software-optimized parameters and the feasibility of the structural enhancements.

4. Conclusions

This study implemented structural modifications and simulation tests on a pneumatic fishpond feeder, improving the uniformity of pellet spreading. The modified feeder effectively addresses the problem of nonuniform feeding and increases feed utilization efficiency, providing theoretical foundations and technical support for the development of aquaculture equipment:

(1)

The triangular flow-splitter plate design splits and recombines the gas–solid mixed flow within the feed chamber, thereby improving the homogeneity of the flow field. The feeding process of the pneumatic feeder was simulated using the coupled EDEM–Fluent method. Comparative analysis of feeding performance before and after optimization established the efficacy of the structural improvements to the feed chamber.

(2)

This study employed a 32-grid computational model to evaluate pellet dispersion uniformity. The results show that the optimized feeder achieved a dispersion $CV$ of 18.27%, representing a 22.19% improvement in performance over the conventional design. Subsequent central composite design with response surface analysis yielded a prediction for the optimal parameter combination, that is, chamber height $h$ = 82.26 mm, splitter width $d$ = 61.54 mm, and inlet angle $\alpha$ = 44.06°, theoretically predicting a minimum $CV$ of 15.81%.

(3)

Pellets were collected at the test site to validate the actual performance of the pneumatic feeder. The results indicate a $CV$ of 17.02% under optimal parameter combinations, which is generally in good agreement with the simulation results. This finding verifies the reliability of the feeder simulation and demonstrates that the structural improvements to the feed chamber can significantly enhance the uniformity of pellet dispersion.

Most coupled simulation studies on distribution devices have been developed for open-field agricultural scenarios, which limits their study objects and applicability. Building on a pond environment, this work extends and supplements that of the literature and offers a measure of novelty. However, we did not consider ambient wind and water-surface fluctuations as factors affecting spreading uniformity; dedicated experiments on these influences remain to be conducted. Likewise, any impacts associated with the increased pressure observed in the feed chamber could not be substantiated within short-term trials and will require longer-term testing. More uniform feeding can effectively prevent localized over- or under-feeding, safeguard water quality, and support stable fish growth, thereby improving economic returns for producers. In our future work, we will not only incorporate more parametric variables as influencing factors to conduct more systematic simulation analysis on spreading uniformity, but also carry out further in-depth investigation into the service life of the device, thereby enhancing its applicability and reliability.