Water, particularly in arid and semi-arid environments, is acknowledged as an exceedingly vital resource (Elkamhawy et al., 2021; Alrowais et al., 2023a). Thus, the imperative task of safeguarding water resources from pollution necessitates reducing contamination levels and enhancing water quality to align with international standards and curtail the environmental dissemination of contaminants (El-Saiad et al., 2021; Abd-Elhamid et al., 2022; Alrowais et al., 2023b). Pollutants, such as pesticides, herbicides, fertilizers, and industrial wastewater, are discharged into different drains of water, rendering them unfit for human consumption (Elkamhawy et al., 2021; Fan et al., 2018). The safeguarding of water resources mandates the prevention of pollution by curtailing the discharge of contaminants into water bodies. Achieving this involves the enforcement of regulations and policies that restrict the amount of pollutants industries can release into different water bodies. Eliminating water pollution is essential for preserving biodiversity, providing safe drinking water, and promoting sustainable development through diverse treatment methods like sedimentation, filtration, and disinfection (Saravanan et al., 2021; Alrowais et al., 2024a). These procedures play a pivotal role in purging pollutants, ensuring water safety for consumption. The efficacy of treatment technologies in eliminating an extensive array of contaminants from water resources underscores the importance of investing in these technologies to shield and conserve water resources for future generations (National Research Council, 1999). This crisis underscores the urgency of developing effective and sustainable methods for water treatment to ensure the availability of clean water resources.

The demand for water is increasing due to population growth, agricultural expansion, and industrial development. Agriculture consumes about 70% of the world’s water, followed by 20% for industry and 10% for municipalities; in addition water demand is projected to rise by 55% by 2050 (Abd-Elhamid et al., 2022). Recycling agricultural drainage water for irrigation is a cost-effective solution, but this water is often polluted by fertilizers, herbicides, and pesticides (Alrowais et al., 2023b). Water pollution is worsened by untreated wastewater discharge, especially in developing nations. Improving water quality and adhering to international standards is crucial to minimize environmental contamination (El-Saiad et al., 2021; El-Agha et al., 2011).

Traditional water treatment technologies, such as physical, chemical, and biological processes, frequently rely on energy-intensive, chemically driven procedures, which can have negative environmental consequences and might not be practicable in remote, isolated, or economically disadvantaged areas (El-Saiad et al., 2021; Abdel Daiem et al., 2021). The essential advancement of eco-friendly technologies is vital for protecting both human health and environment, with the goal of reducing the pollution of natural water sources (Çinar et al., 2006; Liu et al., 2020; Md Anawar and Chowdhury, 2020). Predominantly, adsorption/bio-adsorption serve as one of the primary and effective mechanisms for removing both inorganic and organic pollutants from water solutions that could combine biological and physiochemical adsorption in a bioreactor, contributing to enhanced self-decontamination and improved water quality from both economic and environmental perspectives (Alrowais et al., 2023c; Alrowais et al., 2024b; El-Shatoury et al., 2014). Bioreactors, including gravel filters, are emerging as a promising sustainable alternative that use the natural, biological, and low maintenance processes to remove different pollutants from drainage water with a resilient ecosystem via diverse microbial communities and self-regulation. Moreover, a sustainable, and renewable bioreactor system can be put together using biodegradable and local bio-filter media, such as sand, gravel, peat, carbon material, and compost (Abdel Daiem et al., 2021; Çinar et al., 2006; Alrowais et al., 2023c; Alrowais et al., 2024b; El-Shatoury et al., 2014; Ramírez-Baca et al., 2005; El Monayeri et al., 2007; Braschi et al., 2022; Aljubiri et al., 2024). In addition to providing a low-energy, eco-friendly alternative to traditional treatment systems by using passive energy, renewable energy is considered as sludge reduction reactor. Furthermore, the longevity and durability of bio-filters contribute to their sustainability. With proper design and maintenance, bio-filters can function effectively for many years (El-Saiad et al., 2021; Abdel Daiem et al., 2021). The concept of self-purification in watercourses, wherein the natural ecosystem progressively breaks down contaminants, is improved through the judicious use of bioreactors. These systems rely on microorganisms in the filter media to break down organic pollutants, trap suspended particles and neutralize hazardous compounds (Abdel Daiem et al., 2021; El-Shatoury et al., 2014). Therefore, numerous studies have delved into bioreactor media, concentrating on assessing the impact of different media on the efficient removal of various contaminants from water bodies (Abdel Daiem et al., 2021; Çinar et al., 2006; El Monayeri et al., 2007; EL-Gohary, 2007).

While submerged bioreactors exhibit effectiveness in contaminant removal, their installation in open channels may introduce hydraulic impacts that influence water flow and quality. Previous studies have highlighted the need for a comprehensive hydraulic investigation to understand these impacts and optimize bioreactor deployment (Alrowais et al., 2023a; El-Saiad et al., 2021; Abd-Elhamid et al., 2022). Treating bioreactors as porous media allows the application of established studies (EL-Gohary, 2007; Mulqueen, 2005; Tao et al., 2011) to forecast the hydraulic features of watercourse flow in their installation vicinity. Abd-Elhamid et al. (2022) and El-Saiad et al. (2021) experimentally studied the hydraulic characteristics induced by bioreactor installation in an open waterway. These studies investigated different operational parameters, such as water flow, water height, and various bioreactor specifications, including relative heading up on the performance of bioreactors. Numerical simulation is considered an essential tool in engineering applications, as it allows for the analysis of complex systems and the accurate prediction of their behavior, helping to improve designs and save time and costs (Burgan, 2021). The use of computational fluid dynamics (CFD) has become integral in simulating and analyzing the hydraulic behavior of water flow in open channels. This approach allows for the creation of three-dimensional numerical models to assess the effects of bioreactor placement on flow velocity, turbulence, and shear stress (Alrowais et al., 2023a).

The aim of this study was to numerically investigate the influence of different arrangements of bioreactors within an open water channel on the hydraulic characteristics of a channel. Different Froude’s numbers, which reflect the various hydraulic conditions of various drain flow regimes, were used to conduct the investigation of relative heading up. Notably, this study uniquely focused on directing the whole flow of open drains through the bio-filter, distinguishing it from most previous studies that primarily dealt with submerged bioreactors for which only a portion of the discharge passes through, and the rest flows over the submerged bioreactor. The use of CFD modeling can help to optimize the design and operation of bioreactors in waterways. Overall, the hydraulic impact of bioreactors on contaminated waterways needs to be carefully evaluated to ensure effective treatment of the contaminated water while minimizing any negative impacts on the water courses and surroundings.

The purpose of this study was to understand and reduce the hydraulic effects that gravel bio-filters have on watercourses by numerically simulating them under various scenarios. The scenarios were investigated as follows: The first scenario examined at various discharges, which led to varying velocities and, as a result, varied Froude’s values that represented the drains’ true domain. The second scenario relied on the use of a 1.20 m fixed length bio-filter with different numbers of rounded shapes at the inlet of the bio-filter. Additionally, different numbers of triangular shapes at the inlet of the bio-filter were investigated. Both scenarios two and three were utilized to identify the effect of inlet shape on the hydraulic performance of bio-filter. The fourth scenario was applied to check the effect of changing the U.S. face angle with respect to horizontal direction (i.e., four angles: 0°, 15°, 30°, and 45° where the angle measuring direction is counterclockwise from horizontal direction) of the bio-filter at its inlet. The final scenario was based on changing the U.S. face angle with respect to the vertical direction (i.e., four angles: 0°, 15°, 30°, and 45° where the angle measuring direction is clockwise from vertical direction) of the bio-filter at its inlet. Figure 1 shows the summarized methodology for this study.

The dimensions of the numerical model were as follows: The total length of the model was 10.0 m in the X-direction. The mesh block was divided into three zones using four mesh planes at intervals of 0.0, 4.40, 5.60, and 10.0 m. The total width of the model was 1.0 m in the Y-direction. The block of mesh was surrounded by two mesh planes at 0.0 m and 1.0 m intervals. The total height of the model was 1.0 m in the Z-direction. The mesh block was divided into three zones using four mesh planes at intervals of 0.0, 0.60, 0.78, and 1.0 m. Finally, the mesh block was created using the same cell size of 0.035 m in the three model directions.

The current study was performed using one of the most powerful CFD FLOW-3D software packages (FLOW-3D, 2025). A CAD program was also used to create the geometry of the bio-filter and export it to FLOW-3D by stereolithographic (STL) format as shown in Figure 2. As shown in Equations 1, 2, the Reynolds-averaged Navier-Stokes equations (RANS) are the primary equations that regulate the flow in three directions during the numerical simulation. The finite volume method (FVM) is employed in FLOW-3D to solve the governing equations. The unknown values are calculated at various nodes in the mesh geometry of the finite volume method, which is described as a Eulerian method for defining, analyzing, and transforming partial differential equations to algebraic form (Patankar, 2018). This method expresses a small volume surrounding each node point on a mesh structure using the divergence theorem to transform volume integrals into surface integrals. These terms are then evaluated as fluxes at the surface of each finite volume.

The continuity equation: ∂ u i ∂ x i = 0 (1)

The momentum equation: ∂ u i ∂ t + 1 V F u j ∂ u i ∂ x j = 1 ρ ∂ ∂ x j ‐ p δ ij + ν ∂ u i ∂ x j + ∂ u j ∂ x i ‐ ρ u i ′ u j ′ ¯ (2) where u is time-averaged velocity (m/s), ν is kinematic viscosity (m²/s), V F is fractional volume open to flow, p is averaged pressure (N/m²), and − u i ′ u j ′ ¯ are components of Reynold’s stress

The volume of fluid (VOF) algorithm presented by Hirt and Nichols (1981) was utilized to perform the free surface profile. The function (F) displays the fluid occupancy of a grid cell. F has a value between zero and unity, where zero indicates that no fluid is present in the grid cell and unity indicates that the fluid fills the grid cell to the fullest. Equation 3 shows the free surface forms for grid cells whose (F) values range from zero to unity. ∂ F ∂ t + 1 V F ∂ ∂ x F A x u + ∂ ∂ y FA y v + ∂ ∂ z FA z w = 0 (3) where (A_x, A_y, A_z) are the area fractions and (u, v, w) are the velocity components in (x, y, z) coordinates, respectively.

To increase the accuracy of the numerical model outputs, it is crucial to precisely define the boundary conditions. To shorten the simulation’s runtime, one mesh block was selected. The mesh block’s 3D boundary conditions were ascertained as follows: the X-direction’s inlet was identified as the volume flow rate, and the outlet as a designated pressure with a fluid elevation assigned to 0 points 6 m. The two sides of the mesh block were identified as a wall in the Y-direction. The bottom was identified as a wall in the Z-direction, and the top was identified as a given pressure with a given atm as depicted in Figure 3. The configuration, temperature, velocity, and pressure distributions are the initial conditions of the numerical model. The geometry of the waterway dictated the fluid configuration. During the simulation, the specific mass was set to a standard 1,000 kg/m³, the temperature was set to a standard 25°C. Furthermore, 0.0 m/s was chosen as the starting velocity. Hydrostatic pressure was the final pressure distribution to be established.

FLOW-3D reduces required memory, streamlines mesh creation, and increases numerical accuracy using simple rectangular orthogonal elements in planes and hexahedral elements in volumes. To optimize the numerical model’s accuracy and efficiency, a grid convergence test was utilized to determine the optimal mesh size. The grid convergence test indicated that 0.035 m was the ideal cell size. A Courant number was used to determine the maximum time-step size. This number controls the maximum flow distance allowed at each time step in the simulation. To avoid the flow passing through more than 1 cell in a time step, the Courant number was set to 0.25 in this study. Depending on the Courant number, 0.00075 s was the maximum time step value.

Turbulence is the chaotic, unstable moving fluid that occurs when there are insufficient stabilizing viscous forces. The two-equation (k - ε) model, the two-equation (k - ω) models, and the renormalization-group (RNG) model are some of the turbulence behavior models in FLOW-3D that are most often used. Flow motion is represented using the RNG model as it more accurately replicates motion behavior than the (k - ε) and (k - ω) models (Alemi and Maia, 2018). The turbulent kinetic energy K T and its dissipation ε T are represented by Equations 4, 5, respectively, and are the primary equations in the RNG model. ∂ k T ∂ t + 1 V F u A x ∂ k T ∂ x + v A y ∂ k T ∂ y + w A z ∂ k T ∂ z =   P T + G T + Diff K T ‐ ε T (4) ∂ ε T ∂ t + 1 V F u A x ∂ ε T ∂ x + v A y ∂ ε T ∂ y + w A z ∂ ε T ∂ z = C 1 . ε T K T P T + c 3 . G T + Diff ε ‐ c 2 ε T 2 k T (5) In Equations 4, 5, K T is the turbulent kinetic energy (m²/s²), P T is the turbulent kinetic energy production (m²/s²), G T is the buoyancy turbulence energy (m²/s²), ε T is the turbulent energy dissipation rate, D i f f K T and D i f f ε are terms of diffusion, c 1 = 1.42 , c 2 and c 3 = 0.2 are dimensionless parameters, c 1 and c 3 have constant values, but c 2 is computed from the turbulent kinetic energy ( K T ) and turbulent production ( P T ) terms.

The model of the porous media is employed for calculating the drag and capillary pressure impacts in porous media such as soils, cracked rock, sponges, and paper. Solid materials that have linked interstitial spaces that allow fluid to pass through are referred to as porous media. When the pores of a material like sandstone or gravel are significantly smaller than the control volume, the porous media model makes sense. A porous medium’s porosity is calculated by dividing its open volume by its overall volume. Porosity, as defined in Equation 6, is equivalent to volume fraction V f in the terminology used in FLOW-3D. Porosity  n = V f (6)

Materials with porosities close to 1.0, such as metallic foam filters, are entirely open. The gravel bio-filter’s porosity utilized was 39%, even though depending on the packing configuration, the porosity of closely packed spheres, or gravel ranges from 25% to 47%. After building the porous material’s continuum model and averaging each control volume, the standard preservation equations were derived. Equation 7 expresses conservation of mass: ∂ ρ f ∂ t + ∇ ⋅ ρ f U = 0 (7) where U is the microscopic flow velocity (m/s) and ρ f is the fluid density (kg/m³).

Utilizing Henry Darcy’s (1856) discovery that the unidirectional flow rate via porous medium is directly related to the applied pressure differential, one may determine the momentum equation in porous media. Equation 8 expresses this relationship, V f U = ‐ K μ ⋅ ∂ P ∂ x (8) where μ is the dynamic viscosity (N·s/m²) and K is the material’s coefficient of permeability

For gravel, the values of K are (10^–7 to 10^–9) m², while for clay, they are in the range (10^–13 to 10^–16) m². The resistance to flow increases with decreasing permeability. Drag is the term used to describe this resistance in porous medium modelling. Equation 9 illustrates how the drag term proportional to the velocity in the Navier-Stokes equations represents the porous medium’s flow resistance, b =   F d ⋅ U (9) where F d is the drag coefficient for porous mediums

The microscopic velocity in a porous media containing coarse particles or fibers can be rather high, and the resulting flow losses can be both linear and proportional to the flow velocity square. Equation 10 provides the pressure decrease in Forchhemer’s equation, ∂ P ∂ x = μ K U + ρ K 2 U U (10) where K₂ is the non-Darcian or inertial permeability.

A single expression for F _d may be obtained by combining the linear Darcian and quadratic non-Darcian flow loss equations, as shown in Equation 11, F d = μ ρ 1 ‐ V f V f a 1 ‐ V f V f + b R eP D (11) where a  and  b are constant coefficients, R e P is the Reynolds number, and D is the particle diameter (mm).