Micro-Hydropower Generation Using an Archimedes Screw: Parametric Performance Analysis with CFD

Abstract

Micro-hydropower technologies are increasingly attracting attention due to their potential to contribute to sustainable energy generation. With the growing global demand for electricity, it is essential to research and innovate in the development of devices capable of harnessing hydroelectric potential through such technologies. In this context, the Archimedes screw generator (ASG) stands out as a device that potentially offers significant advantages for micro-hydropower generation. This study aimed, through a simplified yet effective method, to analyze and determine the simultaneous effects of the number of blades, inclination angle, and flow rate on the torque, mechanical power, and efficiency of an ASG. Computational Fluid Dynamics (CFD) was employed to obtain the torque and perform the hydrodynamic analysis of the devices, in order to compare the results of the optimal geometric and operational characteristics with previous studies. This proposal also helps guide future work in the preliminary design and evaluation of ASGs, considering the geometric and flow conditions that take full advantage of the available water resources. Under the specific conditions analyzed, the most efficient generator featured three blades, a 20° inclination, and an inlet flow rate of 24.5 L/s, achieving a mechanical power output of 117 W with an efficiency of 71%.

1. Introduction

Access to electricity is essential for the development of any nation or community, enabling better health services, education, water supply, food security, and access to information technology. However, due to the rising global energy demand, it is crucial to adopt renewable energy sources for power generation, preferably located near consumption sites or integrated into the national electricity transmission network. According to the International Energy Agency [1], approximately 745.7 million people worldwide, primarily in Africa, still lack access to electricity.

In the Latin American and Caribbean region, more than 16.2 million people, primarily in rural communities of developing countries, lack electricity in their homes, according to the Latin American Energy Organization (OLADE) [2]. A feasible solution to this challenge is to generate energy as close as possible to the point of consumption using renewable resources, thereby reducing environmental pollution. One promising alternative is harnessing hydroelectric potential through micro power plants, as they are considered clean, reliable, and cost-effective technologies capable of competing with market energy prices [3,4].

The Archimedes screw generator (ASG) is capable of operating with hydraulic heads of up to 10 m and flow rates from 0.01 m³/s to 10 m³/s [5], which makes it suitable for micro-scale hydropower plants (<1 MW). It has even been suggested that these devices can operate without hydraulic head, relying solely on the kinetic energy of the flow [6]. Figure 1 presents the range of hydraulic head and flow rate associated with the power output of different turbines, including the ASG. Additionally, the operational range of commercial ASG models, such as the PicoPica10 and PicoPica500 [7] can also be observed.

This device consists of an axis carrying helical propellers, typically installed in a semicircular channel [9]. Originally used as a pump for centuries [10] it was patented in 1992 by Karl-August Radlik for the purpose of generating electrical energy [11]. The operating principle of the ASG involves water entering from the top and moving along its length, applying hydrostatic pressure to the flights, which induces their rotation. By connecting the screw shaft to an electric generator, electrical energy can be produced. Figure 2 illustrates the basic design of the ASG and its main components.

The ASG is classified as a quasi-steady-state pressure device, like water wheels [12], because its operation relies on the difference in hydrostatic pressure generated by the weight of the water acting through its blades [13]. Consequently, the conversion of torque is primarily driven by hydrostatic pressure [14]. However, other researchers, such as Okot [15], classify it as a reaction turbine. ASGs are typically installed in run-of-river hydroelectric generation schemes, reducing their environmental impact [14].

These devices are noteworthy for addressing the three pillars of sustainable development proposed by René Passet in 1979 [12].

Table 1. Technical, economic, social, and environmental advantages of using the ASG.

Type	Advantages
Technical	✓ Can operate under hydraulic heads ranging from 0.1 to 10 m [16]. ✓ Can function with flow rates between 0.1 and 10 m3/s [16]. ✓ Typically achieves efficiencies between 60% and 80% [16]. ✓ Operates without the need for large reservoirs [12]. ✓ Can operate effectively under flows with high sediment contamination [17]. ✓ Can generate electricity from untreated wastewater [17,18]. ✓ May be installed in series or parallel configurations to enhance electricity production [14,19] ✓ Offer a potential alternative to traditional energy-dissipating hydraulic structures by recovering flow energy and enhancing power generation [20]. ✓ Offer a broader operational envelope compared to other technologies with similar operational ranges [14].
Economic	✓ Requires minimal maintenance, making it suitable for developing countries and isolated, remote regions. ✓ Overall operation and maintenance costs are expected to be lower than those of other turbines under similar operating conditions [21]. ✓ Installation investments are approximately 22% lower than those for a Kaplan turbine [22] ✓ Enables electricity generation in locations where large dams cannot be constructed. ✓ Can be integrated with existing flood control infrastructure or former mill sites, reducing civil construction costs [14].
Social	✓ Can be locally manufactured, thereby promoting employment opportunities [22]. ✓ Its use can help reduce diesel and kerosene for lighting, refrigeration, and cooking, thereby lowering the risk of fires and indoor air pollution. ✓ The absence of a need for a large, actively controlled reservoir minimizes land flooding and soil degradation [23]. ✓ The simplicity of this technology, combined with low maintenance requirements and costs, makes ASG suitable even for remote or developing areas with limited or expensive access to the electrical grid [12].
Environmental	✓ Does not obstruct fish migration, allowing passage through the blades: Passage through the ASG does not interfere with fish swimming speed (salmon in this case) [24]. Fish mortality is higher in Francis turbines compared to passage through an ASG [24]. The ASG does not interfere with eel migration and has no impact on their mortality [25]. Passage through an ASG exposes fish to a gradual and mild pressure drop, minimizing the risk of injuries such as barotrauma [25]. ASG are among the safest turbines for aquatic life [26,27,28,29]. ✓ Allows the passage of sediments and floating debris [30].

summarizes the advantages of the ASG as an electricity-generating device.

The main geometric parameters of the ASG are outer diameter ($D_o$), inner diameter ($D_i$), pitch ($S$), number of blades ($N$), length ($L$), and inclination angle ($\beta$) [31]. These parameters, along with the channel and its key characteristics—such as the inlet section, slope (s), and gap (G)—are presented in Figure 3. To enhance the design of these devices, several optimal geometric relationships have been identified, which are presented in

Table 2. Geometric relationships of the ASG reported in the literature.

Geometric Parameter or Relationship	Nomenclature	Recommended Value of the Geometric Parameter or Relationship	Reference
Diameter ratio	$\delta =D_i/D_o$	From 0.4 to 0.6	[32]
		From 0.45 to 0.55	[33]
		0.532	[14]
		0.5	[20,34,35]
Pitch ratio	$\sigma =S/D_o$	1	[14,32,33,35,36]
		1.2 when β < 30°, 1 when β = 30° and 0.8 when β > 30°	[34]
Length ratio	$L/S$	3.84	[14]
Inclination angle	$\beta$	20° to 25°	[16]
		20° to 35°	[12,20]
		22°	[34]
		18° to 36°	[37]

.

Regarding the number of blades ($N$), most full-scale ASG installations consist of three to four blades [18,21,34,38]. Specifically, Lyons [39] and Songin [40] reported that experimental observations did not show a significant increase in the efficiency of Archimedes screw generators for $N>3$. This finding is supported by Dragomirescu [41], who reported $N=3$ as the optimal number of blades. Conversely, Shahverdi [42] recommended a two-bladed screw due to material savings; however, based on experimental tests, Lyons [39] reported a considerable reduction in the performance of two-bladed screws.

Regarding the mathematical models developed to estimate the efficiency of the ASG, Müller and Senior [9] presented a simplified model based on the hydrostatic pressure along the screw surface. This model assumes that the efficiency of device is not influenced by rotational speed, meaning that frictional losses are neglected. However, although their approach aims to derive a concise equation for efficiency prediction, the geometric simplification of the screw becomes so pronounced that it is no longer practical as a design tool.

More complex mathematical models have since been developed. In these models, the main assumption is that the water level in each bucket reaches the maximum height at which no flow occurs into the next compartment over the inner cylinder [43]. Regarding the flow conditions in the ASG, Dellinger et al. [5] developed a mathematical model to estimate the appropriate submergence level of the ASG by controlling the downstream water level. Optimal submergence values were found to be between 0.5 and 0.6 times the ASG diameter. It is important to note that this value varied depending on the ASG inclination angle (tested at 20°, 24°, and 28°); lower inclination angles resulted in higher optimal submergence, and vice versa. These results were experimentally validated using a screw with an outer radius of 0.096 m, a length of 0.4 m, three blades, and a pitch of 0.192 m. Both theoretical and experimental efficiencies exceeded 80% at the optimal submergence level, leading to the conclusion that an incorrect submergence level can result in up to 20% efficiency losses in the ASG.

Additionally, one of the most extensively studied geometric parameters, both theoretically and experimentally, is the optimal inclination angle of the ASG. Erinofiardi et al. [44] constructed a single-blade ASG with an outer diameter of 0.142 m, a length of 0.646 m, and a pitch of 0.054 m. A constant flow rate of 1.2 3 L/s was supplied, and three inclination angles were tested: 22°, 30°, and 40°. The results showed that the ASG rotated faster at higher inclination angles. However, this increased rotational speed did not lead to greater energy generation but rather to higher frictional losses. The study concluded that the optimal operating angle was 22°, as the highest device efficiency was achieved at this inclination.

On the other hand, Shahverdi et al. [31] compared various geometric parameters of the ASG using a mathematical model aimed at optimizing and properly designing the ASG for installation in place of the energy dissipation structures in the Aghili canal, located in Khuzestan Province, Iran. The authors reported theoretical efficiencies exceeding 90%. In their study, screws with lengths of 4, 5, 6, and 7 meters were tested, with the number of blades ranging from 1 to 5, and inclination angles between 15° and 35°. Overall, screws of all lengths achieved better efficiencies within the 20–30° inclination range (efficiencies around 80%), as well as with ASGs featuring 2 or 3 blades.

YoosefDoost and Lubitz [45] developed an equation to estimate the flow rate through an ASG, taking into account variables such as water inlet level, ASG rotational speed, and screw geometry. The model is applicable to both laboratory-scale prototypes and full-scale ASGs. To estimate the coefficients of the general model with good accuracy, the authors employed a genetic algorithm.

In this context, YoosefDoost and Lubitz [33] proposed an analytical model for the rapid geometric estimation of an ASG based on the inlet flow rate. This mathematical formulation allows the determination of the outer diameter of the ASG as a function of flow rate under various geometric conditions. The model was compared against 48 industrial ASG designs operating in hydropower applications and achieved a Pearson correlation coefficient of 91.8%, demonstrating that the proposed method has sufficient accuracy to be used for geometric screw design, eliminating iterative loops and lengthy design processes.

Shahverdi [20] developed a model to predict the efficiency of the ASG by applying Buckingham π theorem to describe the dimensionless relationships between independent and response parameters. Based on this, a series of CFD simulations were conducted, enabling the development of a mathematical model using the software Design-Expert v11. It is worth noting that this model is valid only for laboratory-scale ASGs.

Regarding the design of multi-screw plants, the only reported study is that of YoosefDoost and Lubitz [19], who proposed a simple method for rapid, approximate estimation of the number and geometry of ASG, considering site-specific conditions, river flow characteristics, and certain technical considerations.

In a more recent study, Simmons et al. [14] proposed a set of mathematical relationships to estimate the torque of an ASG, considering various geometric parameters: outer diameter, number of blades, filling level, inclination angle, and surface roughness. The proposed model was based on full-scale ASGs, and CFD simulations were conducted to evaluate different scenarios, enabling the derivation of the final mathematical formulation.

On the other hand, the use of numerical simulation through Computational Fluid Dynamics (CFD) has been recognized as a valuable tool for enhancing the design of these devices [14,46,47,48,49,50,51,52]. It allows for significant savings in time, human resources, and economic investments in such analyses. To date, two simulation methods have been employed for evaluate ASGs. The first method considers a steady-state model of the ASG, where the flow completely fills the channel [46,47,48,49], allowing for the evaluation of pressure and velocity at different sections of the ASG. The second method simulates real operating conditions, with the screw in motion and the water in the channel modeled as a free surface flow [14,50,51,52].

Regarding the first simulation method, Rosly et al. [46] conducted CFD simulations of an ASG with several configurations. They observed that a maximum efficiency of 81% was achieved with a 3-blade screw having three turns per blade. These results were validated using a previously proposed mathematical model [9]; however, it was concluded that the calculated efficiency might be overestimated compared with real-world performance [43].

Khan et al. [49] also used CFD simulations to study the effect of blade number on screw efficiency, finding a maximum efficiency of 87% with a 5-blade screw, although these results were not experimentally validated. Similarly, Maulana et al. [48] investigated the impact of blades number on pressure distribution along the ASG. They concluded that a 2-blade screw exhibited a more constant pressure drop, leading to improved torque and ASG stability.

Other studies have taken a different approach by simulating the moving screw and channel with free surface flow. In this context, Dellinger et al. [35] investigated the effects of pitch and blades number on power output, concluding that a ASG with 5-blade minimized leakage losses and that the optimal pitch angle varied depending on the number of blades. On the other hand, Espinosa [53] evaluated the efficiency and torque of the screw under different flow conditions and rotation speed, concluding that a lower rotation speed resulted in a more uniform torque and better efficiency. However, he also observed an overestimation in the ASG rotation speed under the proposed flow conditions.

Reis and Carvalho [54] used the OpenFOAM numerical simulation tool to evaluate the influence of various parameters, such as rotation speed, internal diameter, pitch, and screw inclination, on the device performance, resulting in a maximum efficiency of 86%. Furthermore, they observed that reducing the pitch and internal radius increased the efficiency of the three-bladed ASG. For their part, Shahverdi et al. [31] evaluated various parameters, such as screw rotation speed, flow rates in the channel, and ASG inclination angles. They compared the results with experimental data, determining a relative error of 0.69% for a flow rate of 1.13 L/s, an angular velocity of 10 rad/s, and an inclination of 24.9°. On the other hand, Abbas et al. [51] used the ANSYS-Fluent numerical simulation model to evaluate the feasibility of using ASG for electricity generation at sites in rural areas of Pakistan with water head of less than 1 m. These authors obtained the highest power values for a screw with an external diameter of 0.12 m, a pitch of 0.13 m, and a length of 0.850 m.

In this study, numerical simulations were used to evaluate ASGs with 1, 2, and 3 blades, inclination angles of 20°, 24°, and 28°, and inlet flow rates of 16.5, 24.5, 32.9, 40.9, and 47.9 L/s. The ASGs were evaluated using ANSYS Fluent 2022R2 with a steady-state simulation scheme, which offers low computational costs and allows for the evaluation of a wider range of conditions in a short time. The objective of this study was to analyze and determine the influence of the number of blades, inclination angle, and flow rate on three key response variables: torque, mechanical power, and efficiency of an ASG, using Computational Fluid Dynamics (CFD). This methodology enabled the simultaneous evaluation of various hydrodynamic parameters, including pressure, flow velocity, and turbulent kinetic energy. It should be noted that, as this is a simplified numerical model, the results are to be considered a preliminary analysis, providing an approximate estimation of the studied variables alongside a detailed hydrodynamic assessment of the device. This approach helps to reduce the number of viable configurations requiring high-fidelity analysis, which involves multiphase simulations and models such as sliding mesh for the final design.

2. Materials and Methods

This section describes the different phases carried out during the research. Figure 4 provides an overview of the proposed analysis method.

2.1. Geometric Design Parameter for ASG

The geometric dimensions of the device were selected based on two main objectives: (1) to design a device that is easy to transport for future field validation, and (2) to ensure that the dimensions are suitable for experimental tests in future studies at the Inter-American Institute of Technology and Water Sciences (IITCA-UAEMéx).

Table 3. Constant geometric parameters of the ASG used in this research.

Geometric Characteristic	Dimension or Shape
$\mathrm{Outer} \mathrm{diameter} {(D}_o)$	0.494 m
$\mathrm{Inner} \mathrm{diameter} {(D}_i)$	0.247 m
Pitch (S)	0.494 m
Length (L)	2 m
$\mathrm{Gap} (G$)	0.003 m
Channel geometry	circular
Channel diameter	0.50 m

summarizes the geometric parameters selected for the device. The ASG diameter was chosen to fit a semicircular channel with a diameter of 0.5 m, and to ensure free movement, a gap of 3 mm was established between the channel and the ASG. Additionally, the geometric relationships recommended in Table 2 were considered: $\delta =0.5$, $\sigma =1$ and $L/D_o=4$.

The variable geometric parameters are presented in

Table 4. Variable geometric parameters used in this research.

Geometric Characteristic	Dimension
Inclination angle	20°, 24° and 28°
Number of blades	1, 2 and 3

. The evaluation range for the inclination angle was determined based on the recommendations provided in Table 2. Lyons et al. [39] and Songin [40], based on experimental observations, reported that increasing the number of blades beyond three does not result in a significant improvement in the efficiency of Archimedes screw generators. Consequently, this study focuses on evaluating ASG configurations with 1, 2, and 3 blades.

Five flow rates were evaluated corresponding to water depths of 20, 25, 30, 35 and 40 cm at the canal entrance. According to the literature [5], the optimal immersion level for the ASG ranges from 0.5 to 0.6 times its diameter, corresponding to water depths of 25 to 30 cm in this case. However, it was of interest to observe and demonstrate the ASG performance under operating conditions different from the optimal range suggested so far.

Regarding the inlet flow conditions, it is assumed that an intake structure upstream of the ASG ensures a uniform flow with the corresponding water depths. Given that the inlet channel has a constant cross-sectional area, each proposed water depth corresponds to a different flow rate, which was calculated for the section shown in Figure 3b. The flow velocity was determined using the Manning equation $\left(v={\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}{R}_h^{{\displaystyle \frac{2}{3}}}{s}^{{\displaystyle \frac{1}{2}}}\right)$, with the specified water depth used to calculate the hydraulic radius $R_h$. A Manning roughness coefficient of n = 0.010 was applied for the acrylic channel. Additionally, a slope (s) of 0.0001 m/m and a constant water depth in the inlet channel were assumed. It should be noted that alternative methods are available to estimate the operating flow rate of ASG based on geometry, inlet water level, and rotational speed [33,45].

Once the flow velocity at the inlet channel was determined, the inlet flow rate was calculated using the continuity equation.

$$Q={\displaystyle \frac{vA}{1000}}$$

(1)

where Q is the flow rate in L/s, v is the velocity in m/s, and A is the cross-sectional area of the inlet channel in m² (in this case, the hydraulic area).

Once the factors and levels of analysis were determined, a total of 45 simulation scenarios were proposed using a multi-level factorial experimental design (

Table 5. Factors and levels of analysis for multi-level factorial analysis.

Factors	Levels of Analysis
ASG inclination	20°, 24° and 28°
Number of blades	1, 2 and 3
Inlet flow rate (L/s)	16.54, 24.54, 32.98, 41.10 and 47.98

).

2.2. CFD Simulation

Computational Fluid Dynamics (CFD) is based on the approximate and iterative solution of the Navier–Stokes equations, which describe the conservation of mass, momentum, and energy [55], along with turbulence models, multiphase models, and others. In the simulations performed in the present study, the software iteratively solved the conservation equations of mass and momentum, together with the Shear Stress Transport (SST) $k-\omega$ turbulence model. The governing equations employed are detailed below to provide the mathematical framework of the numerical approach.

Mass conservation equation:

$$\rho \left({\displaystyle \frac{\partial }{\partial t}}+{\displaystyle \frac{\partial \left(u\right)}{\partial x}}+{\displaystyle \frac{\partial \left(v\right)}{\partial y}}+{\displaystyle \frac{\partial \left(w\right)}{\partial z}}\right)=0$$

(2)

Momentum equations:

$$\rho \left({\displaystyle \frac{\partial \left(u\right)}{\partial t}}+u{\displaystyle \frac{\partial \left(u\right)}{\partial x}}+v{\displaystyle \frac{\partial \left(u\right)}{\partial y}}+w{\displaystyle \frac{\partial \left(u\right)}{\partial z}}\right)=-{\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\partial p}{\partial \left(x\right)}}+v{\displaystyle \frac{{\partial }^2\left(u\right)}{\partial x^2}}+v{\displaystyle \frac{{\partial }^2\left(u\right)}{\partial y^2}}+v{\displaystyle \frac{{\partial }^2\left(u\right)}{\partial z^2}}$$

(3)

$$\rho \left({\displaystyle \frac{\partial \left(v\right)}{\partial t}}+u{\displaystyle \frac{\partial \left(v\right)}{\partial x}}+v{\displaystyle \frac{\partial \left(v\right)}{\partial y}}+w{\displaystyle \frac{\partial \left(v\right)}{\partial z}}\right)=-{\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\partial p}{\partial \left(y\right)}}+v{\displaystyle \frac{{\partial }^2\left(v\right)}{\partial x^2}}+v{\displaystyle \frac{{\partial }^2\left(v\right)}{\partial y^2}}+v{\displaystyle \frac{{\partial }^2\left(v\right)}{\partial z^2}}$$

(4)

$$\rho \left({\displaystyle \frac{\partial \left(w\right)}{\partial t}}+u{\displaystyle \frac{\partial \left(w\right)}{\partial x}}+v{\displaystyle \frac{\partial \left(w\right)}{\partial y}}+w{\displaystyle \frac{\partial \left(w\right)}{\partial z}}\right)=-{\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\partial p}{\partial \left(z\right)}}+v{\displaystyle \frac{{\partial }^2\left(w\right)}{\partial x^2}}+v{\displaystyle \frac{{\partial }^2\left(w\right)}{\partial y^2}}+v{\displaystyle \frac{{\partial }^2\left(w\right)}{\partial z^2}}$$

(5)

where $x, y, z$ are the axes of the coordinate system, $u, v, w$ are the radial, tangential, and vertical components of velocity, $\rho$ is the fluid density and $\upsilon$ is the kinematic viscosity of the fluid.

SST $k-\omega$ turbulence model equations [56]

$${\displaystyle \frac{\partial \left(\rho k\right)}{t}}+{\displaystyle \frac{\partial \left(\rho U_{i}k\right)}{\partial x_i}}={\tilde{P}}_k-{\beta }^{\ast }\rho k\omega +{\displaystyle \frac{\partial }{\partial x_i}}\left[\left(\mu +{\sigma }_k{\mu }_t\right){\displaystyle \frac{\partial k}{\partial x_i}}\right]$$

(6)

$${\displaystyle \frac{\partial \left(\rho \omega \right)}{t}}+{\displaystyle \frac{\partial \left(\rho U_i\omega \right)}{\partial x_i}}=\alpha \rho J^2-\beta {\rho \omega }^2+{\displaystyle \frac{\partial }{\partial x_i}}\left[\left(\mu +{\sigma }_{\omega }{\mu }_t\right){\displaystyle \frac{\partial \omega }{\partial x_i}}\right]+2(1-F_1)\rho {\sigma }_{\omega 2}{\displaystyle \frac{1}{\omega }}{\displaystyle \frac{\partial k}{\partial x_i}}{\displaystyle \frac{\partial \omega }{\partial x_i}}$$

(7)

$${\nu }_t={\displaystyle \frac{a_{1}k}{\mathrm{m}\mathrm{a}\mathrm{x}(a_1\omega ,J{F}_2)}}$$

(8)

$$F_1=tanh\left({\left[min\left(max\left({\displaystyle \frac{\sqrt{k}}{{\beta }^{\ast }\omega y}},{\displaystyle \frac{500\nu }{y^2\omega }}\right),{\displaystyle \frac{4{\rho \sigma }_{\omega 2}k}{{CD}_{k\omega }{y}^2}}\right)\right]}^4\right)$$

(9)

$$F_2=tanh\left({\left[max\left({\displaystyle \frac{2\sqrt{k}}{{\beta }^{\ast }\omega y}},{\displaystyle \frac{500\nu }{y^2\omega }}\right)\right]}^2\right)$$

(10)

$${CD}_{k\omega }=max\left(2{\rho \sigma }_{\omega 2}{\displaystyle \frac{1}{\omega }}{\displaystyle \frac{\partial k}{\partial x_i}}{\displaystyle \frac{\partial \omega }{\partial x_i}},{10}^{-10}\right)$$

(11)

$$P_k={\mu }_t{\displaystyle \frac{\partial U_i}{\partial x_j}}\left({\displaystyle \frac{\partial U_i}{\partial x_j}}+{\displaystyle \frac{\partial U_j}{\partial x_i}}\right) \to {\tilde{P}}_k=\min \left(P_k, 10{\beta }^{\ast }\rho k\omega \right)$$

(12)

$$\alpha ={\alpha }_{1}F+{\alpha }_2(1-F)$$

(13)

where $k$ is the turbulent kinetic energy, $\omega$ is the specific dissipation rate, ${\mu }_t$ is the turbulent eddy viscosity, $F_1$, $F_2$ and ${CD}_{k\omega }$ are blending functions, $J$ is the invariant measure of the strain rate, $y$ denotes the distance to the nearest wall and $P_k$ is a production limiter. The constants for this model are ${\beta }^{\ast }=0.09$, ${\alpha }_1=5/9$, ${\beta }_1=3/40$, ${\sigma }_{k1}=0.85$, ${\sigma }_{\omega 1}=0.5$, ${\alpha }_2=0.44$, ${\beta }_2=0.0828$, ${\sigma }_{k2}=1$ and ${\sigma }_{\omega 2}=0.856$.

The Navier–Stokes equations are nonlinear coupled partial differential equations and are among the best-known and most challenging equations in engineering sciences. From these equations, mathematical models for special cases (steady-state, two-dimensional flow) can be derived by applying the appropriate simplifications for the problem under analysis. Because the equations are highly complex, finding an analytical solution is extremely challenging, making it necessary to use numerical methods to obtain an approximate solution [57]. The CFD simulation process primarily consists of five stages, as shown in Figure 5.

2.2.1. Conceptual Model

Regarding the conceptual model, an example is shown in Figure 6, where the fluid domain, together with the boundaries and sections of interest, may be observed.

2.2.2. Mesh Configuration

The mesh facilitates the discretization of the domain to be modeled. An unstructured tetrahedral mesh was used because of its adaptability to complex geometries. Before running the simulations, a mesh independence analysis was conducted to ensure that the results were not dependent on the mesh. To do this, the velocity and pressure in the fluid domain were compared for each of the meshes used.

Regarding the mesh quality analysis, the orthogonality criterion was considered, and a visual inspection was performed to ensure that the elements could capture the gap between the ASG and the channel. Additionally, the simulation time was compared. In all simulations, several variables (mass flow, velocity, and pressure within the domain) were monitored to ensure convergence and the final flow state.

2.2.3. Simulation Scheme

In this stage, ANSYS was used to define water as the working fluid. The solution scheme was based on pressure, and the flow was considered steady-state. The SST $k-\omega$ turbulence model (shear stress transport) was applied, with the ASG modeled as static. This turbulence model was selected because it combines the robustness of the $k-\epsilon$ formulation with the accuracy of the $k-\omega$ model, making it applicable to a wide range of flows [58]. On the other hand, this type of simulation was used to compare results with other studies that employed a similar analysis method to the one developed in this work [46,47,48,49]. Furthermore, this approach makes it possible to approximate the torque generated by the ASG and to evaluate its hydrodynamics.

To ensure the convergence of the numerical solution and the stability of the final flow state, representative variables of the physical phenomenon under study were monitored. These included mass flow rates at the inlet and outlet to verify continuity; flow velocity at the outlet and within the fluid domain to confirm the steady-state condition; pressure distribution within the fluid domain and on the ASG blades; and torque exerted on the blades. Additionally, residuals were monitored throughout the simulation to ensure they reached values on the order of 1 × 10⁻³.

The solution methods involved the use of a coupled scheme. Spatial discretization of the gradient was carried out using the Least Squares Cell-Based method. Second-order discretization schemes were applied for pressure, momentum, turbulent kinetic energy, and specific dissipation rate.

2.2.4. Efficiency and Mechanical Power Estimation

In the post-processing stage, the velocity and pressure fields in the domain were obtained, along with the torque on each of the ASGs analyzed. This data is essential for calculating the mechanical power generated using the following expression [44]:

$$P_{mechanical}={\omega }_{t}T$$

(14)

where $P_{mechanical}$ is the mechanical power of the ASG (W), ${\omega }_t$ is the angular velocity of the ASG (rad/s), and $T$ is the torque (N-m).

To obtain the angular velocity, the model proposed by Alberto [59] was used, as follows:

$${\omega }_t= {\displaystyle \frac{Qtan\left(\alpha \right)}{1000A_m{y}_c}}$$

(15)

where ${\omega }_t$ is the angular velocity of the ASG in rad/s, $Q$ is the inlet flow rate in L/s, $A_m$ is the wetted cross-sectional area of the screw in m², $y_c$ is the location of the centroid of the wetted area of the screw cross-section, and $\alpha$ is the blade inclination angle.

To calculate efficiency, it is necessary to determine the hydraulic power, which is obtained using the following expression [43]:

$$P_{hydraulic}=\left(\rho gQH\right)/1000$$

(16)

where $P_{hidraulic}$ is the hydraulic power (W), $\rho$ is the water density (kg/m³), $g$ is the acceleration due to gravity (m/s²), $Q$ is the flow rate (L/s), and $H$ is the net available water head (m).

Finally, to obtain the efficiency of the ASG (${\eta }_{turbine}$) [44], the following equation is used:

$${\eta }_{turbine}={\displaystyle \frac{P_{mechanical}}{P_{hydraulic}}}$$

(17)

In the final stage of the study, various ASG selection criteria, commonly used in another study, were evaluated. A compilation of these criteria was made to generate a more comprehensive evaluation and interpretation. The evaluated factors were torque, mechanical power, efficiency, and the behavior of pressure, velocity, and turbulence kinetic energy along the screw [46,47,48,49]. Additionally, main effect plots were created for the response variables—torque, power, and efficiency—while varying the flow rate, number of blades, and inclination angle.

3. Results and Discussion

This section presents and analyzes the results obtained from numerical simulations, aiming to evaluate the behavior of the ASG under different geometric configurations and operating conditions. The analysis focuses on the main effects of the number of blades, inclination angle, and inlet flow rate on three fundamental response variables: torque, mechanical power, and hydraulic efficiency. The results are interpreted based on the underlying hydrodynamic principles and compared with previous studies to validate the adopted approach and support future design strategies.

3.1. Boundary Conditions

For the simulation of the ASG, the flow velocity at the ASG inlet was defined as a boundary condition. Following the procedure described in the previous section, the velocities shown in

Table 6. Hydraulic conditions at the inlet channel (boundary conditions).

Flow Depth (cm)	Velocity (m/s)	Flow Rate (L/s)
20	0.226	16.54
25	0.250	24.54
30	0.268	32.98
35	0.280	41.10
40	0.285	47.98

were obtained. Atmospheric pressure was applied as the outlet condition.

3.2. Mesh Independence and Quality Analysis

The mesh independence analysis was carried out for three configurations: the first corresponding to the ASG with a single blade inclined at 28°, the second to the ASG with two blades inclined at 24°, and the third to the ASG with three blades inclined at 20°. All cases were evaluated at an inlet velocity of 0.268 m/s, corresponding to an inlet discharge of 32.98 L/s. The characteristics of each mesh evaluated are presented in

Table 7. Characteristics of the meshes used for the mesh independence analysis.

Characteristics of the ASG	Element Size	Average Orthogonal Quality	Number of Elements	Simulation Time
$N=1$ $\beta =28°$	25 mm	0.76	416,469	30 min
	20 mm	0.78	625,306	45 min
	15 mm	0.79	1,254,499	1 h 15 min
	12 mm	0.79	2,342,542	1 h 50 min
	10 mm	0.79	3,970,235	6 h
$N=2$ $\beta =24°$	25 mm	0.75	567,248	24 min
	20 mm	0.77	743,356	30 min
	15 mm	0.78	1,318,988	55 min
	12 mm	0.79	2,352,757	1 h 37 min
	10 mm	0.79	3,914,504	8 h
$N=3$ $\beta =20°$	25 mm	0.75	712,914	50 min
	20 mm	0.76	848,227	1 h
	15 mm	0.77	1,352,373	1 h 30 min
	12 mm	0.78	2,298,113	3 h
	10 mm	0.79	3,756,286	6 h

.

According to the orthogonality criterion [60] for mesh quality assessment, a ‘very good quality’ rating was achieved for all five cases evaluated. In all simulations, the residual values were confirmed to remain on the order of 1 × 10⁻³, thereby ensuring convergence of the results. In addition, the computation time was recorded to evaluate the feasibility of each mesh. The simulations were performed on a computing system equipped with an AMD Ryzen 74800H processor, 16 GB of RAM, and eight processing cores, provided by the Instituto Interamericano de Tecnología y Ciencias del Agua, Toluca, México.

Figure 7 and Figure 8 show the pressure distribution within the fluid domain and the velocity at the ASG outlet, respectively, as a function of the mesh element count, demonstrating that no significant differences were observed in the results obtained. It may therefore be inferred that any of the proposed meshes yield reliable outcomes, with preference given to the one requiring the shortest simulation time. However, since ASG operation depends on pressure differences, it was observed that the pressure field stabilized from the 15 mm mesh onwards. This mesh was therefore considered the most suitable for the present study, as it combined high quality with an acceptable simulation time.

To ensure convergence of the results, the residual values were verified to decrease between iterations until reaching values below 1 × 10⁻³, as recommended by ANSYS Inc. [60], with license provided by the Instituto Interamericano de Tecnología y Ciencias del Agua, Toluca, México. In addition, several variables were monitored to confirm the final flow state, including the mass flow rate at the inlet and outlet of the domain, together with the velocity and pressure within the fluid domain. Figure 9 shows these plots for the case of the ASG with one blade, inclined at 28°, and an inlet flow velocity of 0.268 m/s. Nevertheless, this analysis and verification were performed for all 45 simulations.

With regard to continuity, the ANSYS Fluent Manual [60] recommends verifying that the difference between the inlet and outlet does not exceed 1%. In this case, the differences ranged from 0.00001% to 0.3091%, thereby ensuring both the continuity of the system and the reliability of the results obtained across the evaluated scenarios.

3.3. Torque, Mechanical Power, and Hydraulic Efficiency Estimation

One of the most important parameters evaluated in the ANSYS Fluent 2022R2 simulations was the torque, as it enabled the determination of the mechanical power and efficiency of the devices.

For data analysis, a multilevel factorial design of experiments was proposed (Table 5), Subsequently, the main effects on the three response variables under study—torque, mechanical power, and efficiency—were analyzed.

3.3.1. Torque Analysis

Table 8. Torque of the ASG for different geometric and flow conditions in N-m.

1-Blade
Inclination	Flow (Q)
	16.5 L/s	24.5 L/s	32.9 L/s	40.9 L/s	47.9 L/s
20°	7.92	11.60	15.40	17.80	20.56
24°	7.70	11.66	15.10	17.64	20.20
28°	7.49	11.29	14.90	17.65	20.08
2-Blades
Inclination	Flow (Q)
	16.5 L/s	24.5 L/s	32.9 L/s	40.9 L/s	47.9 L/s
20°	14.94	22.07	29.23	33.65	36.58
24°	14.94	21.97	28.76	33.23	36.14
28°	14.98	21.68	28.29	33.07	35.53
3-Blades
Inclination	Flow (Q)
	16.5 L/s	24.5 L/s	32.9 L/s	40.9 L/s	47.9 L/s
20°	22.59	33.66	43.31	49.87	52.06
24°	21.13	33.37	42.83	49.51	52.16
28°	20.97	32.87	42.11	48.69	51.62

presents the torque values obtained for the 45 simulation scenarios. Additionally, Figure 10 illustrates the torque behavior as a function of the flow rate for ASGs with 1, 2, and 3 blades, considering an inclination angle of 20°. For this inclination angle, the highest torques values were observed across all simulated scenarios, indicating higher power output. Furthermore, Figure 10 shows that increasing the number of blades leads to higher torque, as it allows a greater volume of flow to be retained between the blades, thereby increasing pressure within the ASG. Notably, a greater pressure difference between the ASG inlet and outlet results in a higher energy transfer between the fluid and the machine, leading to increased torque.

The primary objective of the main effects analysis was to identify the conditions that produce the highest torque, as it is directly related to mechanical power output. This analysis is presented in Figure 11, where it can be observed that the factors with the greatest influence on torque are the number of blades and the inlet flow rate to the ASG. Increasing the number of blades enhances torque by providing a larger contact surface between the ASG and the fluid. Conversely, increasing the inclination angle results in a slight decrease in torque, making it the factor with the least influence on the response variable. This observation agrees with the experimental study conducted by Erinofiardi et al. [44], which reported a similar trend. Lastly, increasing the inlet flow rate raises the generated torque, as a greater volume of water accumulates between the blades.

In this case, to maximize torque, the optimal conditions are an ASG with three blades, an inclination angle of 20°, and a flow rate of 47.9 L/s.

3.3.2. Mechanical Power Estimation

To calculate the mechanical power, the angular velocity for each ASG was determined as a function of the water inlet height, flow rate, and inclination angle. The results are presented in

Table 9. Angular velocity of the ASG as a function of inlet flow rate and inclination angle (rad/s).

Water Inlet Height (cm)	Flow Rate (L/s)	Inclination
		20°	24°	28°
20	16.5	3.42	3.26	3.06
25	24.5	3.48	3.29	3.13
30	32.9	3.49	3.18	2.99
35	40.9	3.01	2.52	2.34
40	47.9	2.37	2.25	2.13

.

Table 10. Mechanical power of the ASG for different geometric and flow conditions in Watts.

1-Blade
Inclination	Flow (Q)
	16.5 L/s	24.5 L/s	32.9 L/s	40.9 L/s	47.9 L/s
20°	27.07	40.37	53.69	54.47	48.82
24°	25.08	38.30	48.04	44.42	45.54
28°	37.75	35.27	44.51	41.31	42.85
2-Blades
Inclination	Flow (Q)
	16.5 L/s	24.5 L/s	32.9 L/s	40.9 L/s	47.9 L/s
20°	51.05	76.85	101.90	102.97	86.85
24°	48.66	72.20	91.47	83.70	81.45
28°	45.87	67.76	84.52	77.40	75.81
3-Blades
Inclination	Flow (Q)
	16.5 L/s	24.5 L/s	32.9 L/s	40.9 L/s	47.9 L/s
20°	77.20	117.18	151.00	152.60	123.61
24°	68.79	109.65	136.23	124.69	117.57
28°	64.22	102.73	125.80	113.98	110.15

presents the mechanical power values, with a notable increase in power observed at a flow rate of 32.9 L/s and an inclination angle of 20°. Figure 12 shows the mechanical power as a function of the flow rate for ASGs with different numbers of blades and a 20° inclination. It is important to highlight that the highest power values are obtained within the flow rate range of 32.9 to 40.9 L/s, which correspond to inlet heads of 30 to 35 cm, respectively.

The main effects on mechanical power are shown in Figure 13. It can be seen that the number of blades and the inlet flow rate are the factors with the greatest influence on mechanical power. Increasing the number of blades raises mechanical power, as it is directly proportional to torque. Similarly to the torque analysis, mechanical power decreases as the inclination angle increases; however, this factor has the least influence on the response variable, with an average variation of 15%. Regarding the inlet flow rate, mechanical power increases within the flow range of 16.5 to 32.9 L/s, reaching its maximum at the latter. Beyond this point, there is an average decrease of 12% for the flow rate of 47.9 L/s.

Based on the results obtained, the optimal scenario for maximizing mechanical power was found to be an ASG with 3 blades, an inclination angle of 20°, and a flow rate of 32.9 L/s.

3.3.3. Hydraulic Efficiency Estimation

Table 11. Efficiency of the ASG for different geometric and flow conditions.

1-Blade
Inclination	Flow (Q)
	16.5 L/s	24.5 L/s	32.9 L/s	40.9 L/s	47.9 L/s
20°	24%	25%	24%	20%	15%
24°	19%	20%	18%	14%	12%
28°	15%	16%	14%	11%	10%
2-Blades
Inclination	Flow (Q)
	16.5 L/s	24.5 L/s	32.9 L/s	40.9 L/s	47.9 L/s
20°	46%	47%	45%	37%	27%
24°	37%	37%	34%	26%	21%
28°	30%	30%	27%	20%	17%
3-Blades
Inclination	Flow (Q)
	16.5 L/s	24.5 L/s	32.9 L/s	40.9 L/s	47.9 L/s
20°	70%	71%	66%	55%	38%
24°	52%	56%	50%	38%	31%
28°	42%	46%	40%	30%	25%

shows a maximum efficiency of 71% for the ASG with 3 blades, a 20° inclination, and an inlet flow rate of 24.5 L/s. Additionally, Figure 14 presents efficiency as a function of flow rate for ASGs with different numbers of blades and a 20° inclination, which was the angle that achieved the best efficiencies. This figure demonstrates that increasing the number of blades improves the energy utilization of the flow, resulting in higher efficiencies for the same flow rates. For the flow rate of 24.5 L/s, the ASG with 3 blades shows a 64.7% increase in efficiency compared to the ASG with a single blade.

The main effects on efficiency are shown in Figure 15. It is worth noting that the graph represents the average values of the response variable for the different levels of each factor. Therefore, these values do not represent maximum or minimum efficiency but rather highlight the trend for each factor. This approach aims to generally determine the influence of the independent variables on the response variable. In this case, it can be observed that the most influential factor is the number of blades. Increasing the number of blades improves efficiency, as more blades result in higher torque and mechanical power, optimizing the energy utilization from the flow. In contrast, the inclination angle and inlet flow rate have the same level of influence on the response variable. Increasing the inclination angle leads to a decrease in efficiency, establishing that a 20° angle is optimal for this case study.

On the other hand, regarding the inlet flow rate, it can be observed that the highest efficiencies are achieved in the range of 16.5 to 32.9 L/s, with a maximum of 71% at a flow rate of 24.5 L/s. This flow rate corresponds to an inlet head of 25 cm, which translates to an immersion level of 0.5. This aligns with the study conducted by Dellinger et al. [35], which reported that the optimal immersion level lies in the range of 0.5 to 0.6. The optimal values of the independent variables for achieving a maximum ASG efficiency of 71% are as follows: a ASG with 3 blades, a 20° inclination angle, and a flow rate of 24.5 L/s.

Based on these analyses, it was concluded that the factor with the greatest influence on the response variables (torque, mechanical power, and efficiency) is the number of blades. Additionally, it was determined that the optimal inclination angle for this case is 20°, as increasing this angle leads to a decrease in the values of the response variables. Regarding the inlet flow rate, the optimal values varied for each response variable. However, it is worth noting that the best efficiencies and maximum mechanical powers were achieved within the range of 16.5 to 32.9 L/s.

Table 12. Values of the independent variables that maximize the response variables.

Response Variables	Response Variable Values	Independent Variables
		Number of Blades	Inclination Angle	Flow Rate (L/s)
Torque	52.06 N-m	3	20°	47.9
Mechanical power	151 W	3	20°	32.9
Efficiency	71%	3	20°	24.5

presents the optimal values for the number of blades, inclination angle, and inlet flow rate to maximize each response variable. The results presented in this summary table are consistent with those reported in the specialized literature. Regarding the number of blades, it was determined that three blades ($N$ = 3) maximize the three response variables analyzed—torque, mechanical power, and hydraulic efficiency. This finding agrees with Dragomirescu [41], who identified $N$ = 3 as the optimal number of blades, and with Rosly et al. [46], who, based on CFD simulations, concluded that screws with three helical turns and three blades exhibit the highest efficiency. Likewise, studies such as those by Lyons [39] and Songin [40] confirm that no significant increase in efficiency is observed for values of $N$ > 3, whereas $N$ = 2 results in a marked reduction in the performance of the ASG.

With respect to the inclination angle (β), the present study determined that a value of 20° allows the three response variables to be maximized. This result is consistent with the range 20° ≤ β ≤ 22° widely reported in the literature. For instance, Erinofiardi et al. [44] experimentally determined an optimal angle of 22°, while Simmons et al. [16] observed that most ASGs in operation are installed with inclination angles between 20° and 25°. Furthermore, studies by Lashofer et al. [34] and Dellinger et al. [35] confirm that inclinations below 20° increase the screw length, whereas values above 30° considerably reduce its conveying capacity.

Taken together, these results strengthen the validity of the method employed for the evaluation of the ASG in this study, demonstrating that the observed trends accurately reproduce the physical behavior reported by various authors. This suggests that the simplified model and simulation procedure used are suitable for the preliminary analysis of the performance of Archimedes screw generators under different geometric configurations and operating conditions.

3.3.4. Validation

To validate the developed ASG simulation, experimental and model data was used. The screw specification used in Lubitz et al. [43] model is given in

Table 13. Experimental screw specification used for validation [43].

Parameter	Value
Slope (β)	24.9°
Outer diameter ($D_o$)	0.146 m
Inner diameter ($D_i$)	0.0803 m
Pitch $\left(P\right)$	0.146 m
Number of flights $\left(N\right)$	3
Screw length ($L$)	0.584 m
Gap width ($G_w$)	0.762 mm
Rotation speed (${\omega }_m$)	10 rad/s
Flow rate ($Q$)	1.13 L/s
Head ($H$)	0.25 m

.

Additionally,

Table 14. Comparison of the mechanical power obtained with numerical simulation and the data reported by Lubitz et al. [43].

Model	Mechanical Power	Absolute Error	Relative Error
Numerical simulation	2.54 W	---	---
Model data by Lubitz et al. [43]	2.50 W	0.04 W	1.6%
Experimental data by Lubitz et al. [43]	2.20 W	0.34 W	15.4%

presents the results obtained from the numerical simulation, compared with both the experimental data and the model proposed by Lubitz et al. [43]. The differences amount to 1.6% with respect to the model and 15.4% relative to the experimental data. These discrepancies are mainly attributed to the simplifications adopted in the numerical simulation; in particular, the ASG domain was considered stationary, leading to an underestimation of friction losses compared to those occurring under real operating conditions. Nevertheless, the proposed model provides a useful reference for the preliminary design of this type of ASG, requiring low computational resources while allowing the visualization and quantification of relevant hydrodynamic variables.

3.4. Hydrodynamic Analysis

The CFD simulation enabled the analysis of various variables, such as the pressure on the blades, the fluid velocity along the screw, and the turbulence, to obtain a detailed and comprehensive understanding of the screw hydrodynamics. For this analysis, screws with a 20° inclination, 1, 2, and 3 blades, and a flow rate of 24.5 L/s were considered, as this scenario resulted in the highest efficiency. This analysis complements the previous one by allowing both qualitative and quantitative observation of the ASG behavior when varying the number of blades.

3.4.1. Blade Pressure Analysis

The ASG, being a quasi-steady-state pressure turbine, operates based on the pressure difference between the front and rear faces of its blades. This is supported by the analysis of the static and dynamic pressure in the fluid domain of the ASG (

Table 15. Static and dynamic pressure in ASGs with different number of blades, flow rate of 24.5 L/s and 20° inclination.

Blades	Total Pressure (Pa)	Static Pressure (Pa)	Dynamic Pressure (Pa)
1	320	234	86
2	328	241	87
3	340	253	87

), where the static pressure contribution is greater than 70% in all cases.

Figure 16 shows the total pressure contours for ASGs with 1, 2, and 3 blades at a 20° inclination, operating with a flow rate of 24.5 L/s. It can be observed that the highest pressure occurs at the ASG inlet, due to the increased contact area between the fluid and the ASG. Comparing the pressure at the inlet of the 1-blade ASG with that of the 3-blade ASG, the latter exhibits pressures around 500 Pa, while the 1-blade ASG has a pressure of approximately 425 Pa. Increasing the number of blades leads to higher inlet pressure, allowing each space between blades to accumulate a larger water volume. These conditions are not observed in ASGs with fewer blades, as the reduced contact area results in less water volume accumulation and, consequently, lower pressure. Unlike the findings reported by Maulana et al. [48], the pressure contours in this study do not show pressure peaks at the blade tips, which translates to improved hydrodynamic behavior, as well as enhanced stability and uniformity in the energy transfer between the fluid and the ASG. This difference can be attributed to the fact that for the design of this ASG, a diameter ratio ($D_i/D_o$) of 0.5 was considered, which falls within the recommended range (see Table 2).

3.4.2. Blade Number and Turbulence Relationship

For the turbulence analysis, a plane was defined along the central axis of the ASG (Figure 17). As observed, turbulence is generated at the inlet and outlet of the ASG due to changes in flow direction. The ASG with the most turbulence is the one with 1-blade, indicating greater instability and potential vibrations. This turbulence effect decreases as the number of blades increases, as seen in the 3-blade ASG, where turbulence occurs only at the inlet and outlet, rather than throughout the entire fluid domain as in the 1-blade ASG.

3.4.3. Blades and Velocity Relationship

Unlike pressure, the fluid velocity tends to increase as it passes through the ASG. In other words, the flow velocity at the ASG outlet is expected to be higher than at the inlet, serving as an indicator of the energy transfer between the fluid and the screw (Figure 18). This effect has also been observed in studies such as that of Maulana et al. [48]. According to the velocity scale, the 3-blade screw showed a less abrupt change in velocity compared to the 1- and 2-blade ASGs, which, similar to the pressure evaluation, indicates greater stability in the ASG operation.

4. Conclusions

A total of 45 simulations were carried out using CFD to determine the effect of the number of blades, inclination angle, and inlet flow rate on the torque, mechanical power output, and efficiency of the Archimedes screw generator (ASG), as well as on the flow hydrodynamics through the device. The analysis included configurations with 1, 2, and 3 blades; inclination angles of 20°, 24°, and 28°; and flow rates of 16.5, 24.5, 32.9, 40.9, and 47.9 L/s. The results obtained from these simulations enabled the application of a multifactorial main-effects analysis.

For this case study, the optimal inclination angle was 20°, as it produced the highest torque, mechanical power, and efficiency. Furthermore, it was determined that the factors with the greatest influence on power generation and efficiency are the number of blades and the inlet flow rate. In particular, a higher number of blades resulted in greater mechanical power, while operating at a flow rate of 24.5 L/s yielded the best efficiency. The highest efficiency, 71%, corresponded to the ASG configuration featuring three blades, a 20° inclination angle, and an inlet flow rate of 24.5 L/s, delivering a mechanical power output of 117 W. This finding supports the idea that the optimal operating flow rate is associated with an ASG immersion level between 0.5 and 0.6 m, which is consistent with that reported in other studies.

The simulations were performed under steady-state conditions to reduce computational time, making this a preliminary study aimed at evaluating key variables such as torque, mechanical power, and efficiency of an ASG as a function of blade number, inclination angle, and operating flow rate. The advantage of the method employed lies in its ability to provide a rapid estimation of mechanical power in a relatively short time. However, certain simplifications were made that do not consider free-surface effects or the losses associated with friction generated by screw movement, leading to an overestimation of power output by approximately 15%. For final design purposes, it is necessary to refine the simulations by incorporating transient-state conditions and free-surface flow scenarios to adjust torque values. This simulation approach would provide a more realistic estimation of mechanical power output.

The steady-state ASG simulation also enabled the simultaneous evaluation of other criteria, including the pressure distribution along the screw. The results indicated that the geometric characteristics and relationships employed in the design were appropriate, as no significant pressure fluctuations were observed in any of the evaluated sections. This ensures device stability and torque uniformity. Additionally, the effect of geometric conditions on flow velocity and turbulence was assessed.

The proposed methodology may serve as a starting point for future studies analyzing devices of different dimensions. Nonetheless, it is worth noting that the geometric relationships employed resulted in uniform pressure and velocity distributions; therefore, it is advisable to maintain these relationships among length, pitch, and diameter. Moreover, flow rates associated with immersion levels between 0.5 and 0.6 m should be considered to maximize the mechanical power and efficiency of the device.