Optimization of screw turbine design parameters to improve the power output and efficiency of micro-hydropower generation

Abstract

Micro-hydropower is one of the renewable energy sources that can be used to electrify the off-grid rural areas. Archimedes screw is a potential machine element that can be used as the micro-hydropower screw turbine for efficient generation of electricity at low head run-rivers, and surface irrigation sites. It is crucial to consider an optimization design approach to determine the optimum parameters of the Archimedes screw to increase the power output and efficiency. Different researches are ongoing to use Archimedes screw as a micro-hydropower turbine, however, the optimization of the Archimedes screw parameters are untouched yet. The aim of this research is to design and optimize the Archimedes screw to increase the power output and efficiency of screw turbine by using theoretical analysis, ANSYS CFD, and ANSYS Workbench response surface optimization methodology. In this research, the performance of Archimedes screw is investigated for a range of flow rates (0.01 m³/s, 0.015 m³/s, and 0.02 m³/s) and heads (0.5 m to 1 m) with various additional parameters such as pitch of screw, inner diameter of screw, and number of screw blades. The optimum design was obtained at a flow rate of 0.015 m³/s, water head of 0.7 m, and inclination angle of 35° that increased the efficiency of the screw turbine from 55.4% to 92.9% compared to the reference geometry. And also, at the optimum design parameters, the maximum power output is increased from 57.07 Watt to 95.69 Watt.

Keywords:

• Archimedes screw turbine
• micro-hydropower
• modeling and optimization
• CFD analysis
• response surface methodology

Review Editor:

• D T Pham, University of Birmingham, United Kingdom

Subjects:

• Mechanical Engineering
• Mechanical Engineering Design
• Power & Energy
• Technology
• Clean Tech

1. Introduction

Hydropower is the most abundantly available renewable energy source that can be used for electricity generation for many nations. It is the leading source of renewable energy worldwide covering half of all renewable energy productions. As a general definition, hydropower electricity is generated when water turning the power wheel at a rate such that the development of power can be accomplished most efficiently and economically (Abdullah et al., 2020). Micro-hydropower plants are sustainable development technologies to generate electricity for both developing and developed countries (YoosefDoost & Lubitz, 2020). Micro-hydropower plant is a small-scale hydropower plant that uses water sources from small-size flowing water bodies such as irrigation drains, small rivers, and waterfalls. Micro-hydropower generation has three main components: water, turbine, and generator (Erinle et al., 2020; Weking & Sudarmojo, 2019). One of the most important components of micro-hydropower is the turbine that can be used to convert the potential energy and kinetic energy of water to mechanical energy. There are different turbine types which can be used for micro-hydropower generation and one of the most commonly used turbine is screw turbine (Alonso-Martinez et al., 2020; Weking & Sudarmojo, 2019). Most commonly, a central hollow screw shaft with a helical thread profile is used to pressurize water for micro-hydropower generation (Lee & San Lee, 2021). Water at higher elevations moving down along the length of the screw can be translated to the rotation of the screw due to the hydrostatic forces of the fluid on the surfaces of the screw threads that drives a generator to develop efficient, cost-effective, and clean electricity (Dedić-Jandrek & Nižetić, 2019; Rorres, 2000; Taylor et al., 2010). Generally, there are two overall categories of modern hydropower turbines such as impulse and reaction turbines. The Archimedes screw turbines (ASTs) cannot be categorized as either an impulse or reaction mechanisms due to its different power generation mechanism that is by using pressure differences across the blades created by the weight of the water. Therefore, ASTs can be considered as a quasi-static pressure machines.

Screw turbine can be easily installed to open channel water sources such that running-rivers and irrigation channels (Nuernbergk & Rorres, 2013). The typical water-to-wire efficiency of ASTs is as high as 60% to 80% (Alonso-Martinez et al., 2020). Screw turbine can be also applied on the running-rivers with low heads ranging from 0.1 m to 1 m and flowing at low flow rates ranging from 0.01 m³/s to 10 m³/s (YoosefDoost & Lubitz, 2020). A significant advantage of screw turbines from other types of turbines is that they can generate relatively high torque at low running frequency of blades (Platonov et al., 2019). Archimedes screw is considered as potential tool for the efficient generation of electricity at low head and flow rate sites (Kumar et al., 2016; Rorres, 2000). Furthermore, the most advantage of the screw is its simplified civil engineering work which can reduce the construction cost significantly (Charisiadis, 2015). In addition to that, several studies indicated that the use of screw turbine could reduce the negative impacts on wildlife and aquatic species. For example, in some fish farms, fishes can pass easily through the screw helix with 98–99% unharmed during the passage (Lavrič et al., 2018; Nuramal et al., 2017).

Numerical simulation can be used to obtain the proper blade configurations of the screw turbine, and to predict the pressure changes that occur along the turbine blades (Maulana et al., 2018). The first attempt was made to model the power output of ASTs with a simplified two-dimensional geometry of the screw’s helical planes at steady-state flow conditions and by neglecting hydraulic energy losses and mechanical frictional losses (Taylor et al., 2010). For double ASTs, the combination of different blade angles give lower rotational speed than uniform blade angles (Syam et al., 2019). For a single screw turbine, the highest rotational speed and power can be attained at low flow rates (Syam et al., 2019). Furthermore, the effect of the pitch length and the number of blades were studied and the torque was seen increased with increasing the pitch length of the two blades screw. The combined effects of helix turns and number of blades have been evaluated by using computational fluid dynamics (CFD) technique with constant boundary conditions (Siswantara et al., 2019; Williamson et al., 2019). CFD is also used to evaluate the design of non-uniform screw blade geometry to capture the flow fields correctly. The performance characteristics of the micro-hydropower screw turbine can cover wide range of volumetric flow rates (0.1 m³/s to 0.6 m³/s) and rotational speeds (Shahverdi et al., 2020). Archimedes screw turbine commonly rotate at around 26 rpm, however, the top of the screw can be connected to a gearbox to increase the rotational speed in the range of 750 to 1500 rpm to make it compatible with standard generators (Maulana et al., 2018). The output torque of screw turbine with varying diameter ratios, length, and number of blades has been evaluated using CFD analysis. However, as indicated in the previous CFD analysis results, the torque did not vary when the length of the screw is increased because the head difference remained constant within each bucket (Dellinger et al., 2018; Nuramal et al., 2020). The torque is increased with increasing the pitch length, and decreased with increasing of the number of blades. Even though longer screw meant more overall buckets, and more opportunity to create power, there is also the introduction of friction loss with a longer screw. Ideally, there is a peak value where the screw is long enough to create the highest power, but without developing high friction loss. However, as the pitch ratio increased, larger volume of water can provide pressure on a single blade to rotate the screw. In addition to that, if there is more water in a single bucket, there will be less opportunity for the development of friction loss. Therefore, the number of blades has little effects on the torque output of the screw. Simulated ASTs experiments using open source CFD model with different flow rates, and variable rotational speeds showed that water at the outlet of the screw had significant effect on the screw performance (Nishi et al., 2019; Zitti et al., 2020).

The suitability of screw turbine for efficient generation of electricity at low head sites in run-rivers and irrigation systems is under investigation. However, the computations of optimum parameters of screw turbine have not been investigated yet. The aim of this work is to optimize screw turbine geometrical parameters to improve the efficiency and power output for micro-hydropower generation by considering the potential resources of small run-rivers, and irrigation canals. In this research, the application of screw turbine for micro-hydropower generation is investigated and the screw parameters are optimized at 0.01 m^3/s, 0.015 m^3/s and 0.02 m³/s flow rates to improve the performance of screw geometry using ANSYS Workbench CFD analysis. The optimization of the reference geometry of screw turbine was applied by using ANSYS Workbench Response Surface Optimization (RSO) technique. The results are expected to provide better electricity generation alternatives for the remote and rural areas with affordable and reasonable prices for lighting, mobile charging, radio and television, and clean cooking applications. Therefore, the objective of the work is to apply the analysis and optimization techniques using response surface method (RSM), and ANSYS CFD analysis approaches to:

1. Identify initial design parameters of the screw geometry

2. Develop screw turbine 3D Models

3. Analyze and determine screw turbine design parameters to calculate the output power and efficiency

4. Determine the final optimum design parameters and comparison of the power output and efficiency with the reference screw geometry results

2. Methodology

2.1. Design parameter identification

For screw turbine there are two types of geometrical parameters: external and internal parameters (Simmons et al., 2021). The external parameters are the outer radius (R₀), total length (L), and slope (K) of the screw turbine, and the internal parameters are inner cylinder radius (R_i), pitch of the blade (P), and number of blades (N) of the screw turbine. The values of external parameters depend on the flow rate, location of site, and construction materials of the turbine. The values of internal parameters depend on values of external parameter. The operating parameters of screw turbine are the volume of water flow between two successive blades buckets (Vb), the flow discharge (Q), the angular speed (ω), and the water head (H) (Dellinger et al., 2018). The maximum volume of water in one cycle rotation of the screw ($V_u)$ can be represented in terms of outer radius and pitch of screw as shown in Eq. (1)(1) $$V_u=\pi {R_0}^{2}p$$(1) (Simmons et al., 2021). (1) $$V_u=\pi {R_0}^{2}p$$(1)

Volume of one chute (the region bounded between two adjacent blades and inner and outer radii of the screw) is expressed by ($V_C$) as shown in Eq. (2)(2) $$V_C=\frac{\left(\pi \left({R_0}^2-{R_i}^2\right)L\right)}{N}$$(2) . (2) $$V_C=\frac{\left(\pi \left({R_0}^2-{R_i}^2\right)L\right)}{N}$$(2)

Bucket is the maximum connected region occupied by the trapped water within any one chute and expressed as shown in Eq. (3)(3) $$V_b=\frac{V_u}{N}$$(3) . (3) $$V_b=\frac{V_u}{N}$$(3)

To simplify the design calculations, three dimensionless parameters such as radius ratio ($\rho$), pitch ratio ($\lambda$), and volume ratio ($\nu$) have been considered (Kotronis, 2016) where $\mathrm{\rho }=\frac{\mathrm{\text{Ri}}}{\mathrm{\text{Ro}}},(0\le \mathrm{\rho }\le 1),$ $\mathrm{\lambda }=\frac{\mathrm{\text{PK}}}{\text{πDo}},(0\le \mathrm{\lambda }\le 1),$ and $\mathrm{v}=\frac{{\mathrm{V}}_{\mathrm{u}}}{\mathrm{\pi }{{\mathrm{R}}_0}^2\mathrm{P}},(0\le {\mathrm{v}}_{\mathrm{u}}\le 1)$ (Table 1). From dimensionless parameters the value of $V_u$ can be represented in terms of pitch ratio and volume ratio as shown in Eq. (4)(4) $$V_u=\frac{2{\pi }^2{R_0}^3}{K}\lambda \nu$$(4) . (4) $$V_u=\frac{2{\pi }^2{R_0}^3}{K}\lambda \nu$$(4)

Table 1. Parameters of Archimedes screw for different number of blades (Rorres, 2000).

Number of blades (N)	Radius ratio (ρ)	Pitch ratio (λ)	Volume per turn ratio (λ.ν)	Volume ratio (ν)
1	0.5358	0.1285	0.0361	0.2861
2	0.5369	0.1863	0.0512	0.2747
3	0.5357	0.2217	0.0588	0.2697

The gap width between screw turbine and the diameter of screw enclosure can be calculated by using Eqs. (5)(5) $$\mathit{\text{Gw}}=0.0045\sqrt{\mathit{\text{Do}}}\mathrm{ }m$$(5) and (6)(6) $$\mathrm{\text{De}}=\mathrm{\text{Do}}+2\mathrm{G}\mathrm{w}$$(6) respectively. (5) $$\mathit{\text{Gw}}=0.0045\sqrt{\mathit{\text{Do}}}\mathrm{ }m$$(5) (6) $$\mathrm{\text{De}}=\mathrm{\text{Do}}+2\mathrm{G}\mathrm{w}$$(6)

To calculate the water debit, we can use Eq. (7)(7) $$Q=\mathit{\text{AV}}$$(7) (Charisiadis, 2015). Testing of water debit is required to know how much water flow per unit time. (7) $$Q=\mathit{\text{AV}}$$(7)

Therefore, the hydraulic power is determined from the flowing water at a specified height by using Eq. (8)(8) $$P=\rho \mathit{\text{gQH}}$$(8) (Nuramal et al., 2017). (8) $$P=\rho \mathit{\text{gQH}}$$(8) where, P = hydraulic power (Watt); $\rho$ = water density (kg/m³); Q = water flow rate (m³/s); H = head or height of water drop (m); g = gravitational acceleration (m/s²).

Furthermore, the speed of screw turbine can be calculated in terms of the volume flow rate and total volume of screw in one revolution by using Eq. (9)(9) $$n=\frac{60Q}{V_u}$$(9) (Charisiadis, 2015). (9) $$n=\frac{60Q}{V_u}$$(9)

However, the recommended rotational speed of screw turbine should be within the limits as shown in Eq. (10)(10) $$n\le \frac{50}{{D_O}^{\frac{2}{3}}}$$(10) . (10) $$n\le \frac{50}{{D_O}^{\frac{2}{3}}}$$(10)

2.2. Mechanical power and efficiency

The mechanical power available at the turbine shaft can be determined by measuring the torque (T) at a orresponding angular speed (ω) as shown in Eq. (11)(11) $$\mathit{\text{Pm}}=T\omega$$(11) . (11) $$\mathit{\text{Pm}}=T\omega$$(11)

Finally, the mechanical efficiency of the turbine describes how effectively the available kinetic energy of the water is transformed into turbine motion and generates the mechanical power as shown in Eq. (12)(12) $${\mathrm{ɳ}}_m=\frac{\mathit{\text{Pm}}\mathrm{ }}{P}$$(12) . (12) $${\mathrm{ɳ}}_m=\frac{\mathit{\text{Pm}}\mathrm{ }}{P}$$(12)

2.3. Design of the screw geometry

The design of external parameters of the screw turbine was based of the small-rivers and irrigation canals water flow rates and heads (Williamson et al., 2019; YoosefDoost & Lubitz, 2020). The small-rivers and irrigation canals with a capacity of water flow rate of 0.01 m³/s, 0.015 m³/s, and 0.02 m³/s, and water heads of 0.1 m to 1 m were used. By considering the turbine maximum angular speed and volume of water in one revolution, the outer radius of the turbine can be calculated in terms of flow rate and volume of water in one cycle of screw rotation as shown in Eq. (13)(13) $$R_{\mathit{\text{out}}}={\left(\frac{\mathit{\text{Qtan}}\alpha }{\mathit{\lambda }v}\frac{6\sqrt[3]{4}}{10{\pi }^2}\right)}^{\frac{3}{7}}$$(13) . (13) $$R_{\mathit{\text{out}}}={\left(\frac{\mathit{\text{Qtan}}\alpha }{\mathit{\lambda }v}\frac{6\sqrt[3]{4}}{10{\pi }^2}\right)}^{\frac{3}{7}}$$(13)

As shown in Table 2, by taking N = 1, Q = 0.01 m³/s, K (slope) = tan30°= 0.577, and the total screw length (L) = 1 m, the external and internal screw radii can be calculated ${\mathrm{R}}_{\mathrm{\text{out}}}=167.3\text{mm Ri}=89.4\mathrm{\text{mm}}$ respectively. Similarly, the pitch of the screw, the maximum volume of water in one cycle of the screw rotation, volume of one chute, the volume of one bucket, the gap width between screw and enclosure, the diameter of the screw enclosure, the speed of screw turbine, and the recommended rotational speed of screw turbine can be calculated as 0.2341 m, $5.783\mathrm{x}{10}^{-3}\mathrm{ }{\mathrm{m}}^3,$ $0.0199\mathrm{ }{\mathrm{m}}^3,$ $5.783\mathrm{x}{10}^{-3}\mathrm{ }{\mathrm{m}}^3,$ $2.6\mathrm{x}{10}^{-3}\mathrm{ }\mathrm{m},$ $0.3392\mathrm{m},$ $103.75\mathrm{\text{rpm}},$ and $103.8657 \mathit{\text{rpm}}$ respectively by using the previous equations. By considering the recommended calculated value and standards of the rotational speed of the standard screws, 104 rpm has been selected for the screw turbine.

Table 2. The screw geometry external parameters at L = 1 m, Q = 0.01 m³/s and inclination angle of 30⁰.

Number of blades (N)	Outer diameter (DO) mm	Inner diameter (Di) mm	Pitch (p) mm	Rotational speed (N) rpm
1	334	178	234	104
2	288	154	292	115
3	272	146	328	119

The hydraulic power can be calculated from the flowing water at different flow rates and water heads as shown in Table 3. The hydraulic power is used as an input power for screw turbine to generate the mechanical power. For the given external and internal parameters, the minimum hydraulic power at the minimum flow rate and head can be calculated as $P=\rho \mathit{\text{gQH}}=1000\mathrm{\hspace{0.17em}\times \hspace{0.17em}}9.81\mathrm{\hspace{0.17em}\times \hspace{0.17em}}0.01\mathrm{\hspace{0.17em}\times \hspace{0.17em}}0.5=49.05 \mathit{\text{watt}}.$

Table 3. Hydraulic power of flowing water for range of flow rate and heads.

Water flow rate (m^3/s)	Net head (m)	Hydraulic power of water (Watt)
0.01	0.5	49.05
	0.6	58.86
	0.7	68.67
	0.8	78.48
	0.9	88.29
	1	98.1
0.015	0.5	73.575
	0.6	88.29
	0.7	103.005
	0.8	117.72
	0.9	132.435
	1	147.15
0.02	0.5	98.1
	0.6	117.72
	0.7	137.34
	0.8	156.96
	0.9	176.58
	1	196.2

2.4. Computational fluid dynamics (CFD) modeling and analysis

ANSYS Computational Fluid Dynamics (CFD) package was used to model the screw geometry by using the calculated values of external and internal parameters. During modeling, stationary domain, rotating domain, and interface boundary conditions were considered with steady state simulation condition. The stationary domain contains both the inlet and outlet conditions. The inlet is used for mass flow rate boundary condition and the outlet is used for pressure-based boundary condition. In order to setup the rotating frame of reference, the turbine was set as a rotating, and no slip wall. The surrounding wall of the enclosure was setup with the same condition except a wall speed that serves as a counter rotating wall, which can be treated as stationary with respect to the rotating domain. Furthermore, interfaces were required for this setup to connect the stationary domain to the rotating turbine domain. The interfaces were treated by the frame change model of Frozen Rotor as the rotating and stationary domains share the fixed wall; however, the frame of reference is changing due to the movement of the rotating domain. The design and modeling of the screw turbine was performed for three different number of blades (1, 2, and 3), as shown in Figure 1. To simulate the water flow moving into and out of the turbine, the sections of inlet, outlet and wall were created using ANSYS design modeler which is defined as enclosure as shown in Figure 2. The clearance between screw blade and enclosure has been calculated in the theoretical section by using equation five (Alonso-Martinez et al., 2020) which is equal to 2 mm.

Figure 1. 3D model of (a) single blade, (b) double blade, and (c) triple blade screw turbines.

Figure 2. Screw enclosure (a) and mesh generation (b).

2.4.1. Mesh sensitivity analysis

The creation of the mesh size requires the finite element analysis approach to determine the optimum elements size and number with greater accuracy of results. Therefore, it is important to conduct a mesh sensitivity analysis to determine the convergence point where increasing the number of elements or reducing element size have insignificant effects on results. As shown in Figure 3, the convergence point was determined with 5 mm element size, 4193541 numbers of elements, and 2844816 numbers of nodes.

Figure 3. Mesh sensitivity analysis.

The ANSYS Workbench graphical user interface (GUI) with CFX solver and MPI local parallel run mode platform were used to create four partitions. The CFD simulations were conducted starting from the initial geometry setup to evaluate the improvement and effectiveness of results. The CFD analysis of fluid flow was done by considering turbulence modeling to include the effects of fluctuations on the flow behavior. The consideration of the turbulence effect can be used to predict the onset and amount of flow separation accurately. The SST k-ɛ model has been used to solve the fluid flow. The use of SST k- ɛ model has advantage for the formulation of free-stream at near-wall domain with low Reynolds number. Furthermore, optimization of the screw turbine geometry was applied by using response surface methodology (RSM).

3. Results and discussion

3.1. Screw turbine geometry and working parameters

Before starting applying the screw geometry optimization process, single blade reference screw geometry has been created to evaluate the reference power output and to analyze the effects of working parameters on the power output as shown in Figure 5. The results of the reference geometry were used to setup a starting point to compare with the new optimization results. As shown in Figure 4(a), there is an area of high speed flow as the inlet section of the turbine and ass the fluid exits the turbine the flow becomes highly turbulent forming a spiral wake flow. As shown in Figure 4 (b), the pressure distribution at the inlet of the turbine blade is maximum, and the areas with the highest-pressure values are observed to occur close to the leading edge of the turbine blade where the flow first comes into contact with the screw. Furthermore, Figure 5(a, b, and c) indicates the effects of individual, and combined design parameters such as angle of inclination, head, and flow rate on the power output of the turbine. The power output was recorded from CFD post-processing results. In this work, the main monitored component is torque developed by the turbine and the power is calculated using the value of torque at rotating turbine and angular speed. $$\mathrm{\text{Torque}}\times ()@\text{turbine}=\left[\mathrm{J}\right]$$ $$\text{Angular speed}=[\text{radian s}^\hspace{0.17em}-1]$$ $$\mathrm{\text{Power}}=\text{torque}\times \left(\right)@\text{turbine*angular speed}.$$

Figure 4. ANSYS CFD modeling of single blade turbine (a) streamline of the flow, and (b) pressure distributions contour over the turbine length.

Figure 5. The power output of single blade turbine (a) at a flow rate of 0.01 m³/s, (b) at a flow rate of 0.015 m³/s, and (c) at a flow rate of 0.02 m³/s for different angle of inclination and head.

From the results obtained, it is clearly seen that at a higher flow rate the power output has been seen significantly increased for increased inclination angle and head. At low flow rate, there is a slight increase of the power output at a higher inclination angle and head with randomly fluctuating patterns. As shown in Figure 5(a), around 45 Watt power output is recorded at 1 m head, 0.01 m³/s minimum flow rate, and 40° inclination angle. In general, the results included in Figure 5(a, b and c) indicate that the possible power output can be achieved at a 1 m head independent of the angle of inclinations and flow rates. However, the values of power output can be increased when the flow rate is increased for the given 1 m head as shown in Figure 5(b and c).

Figure 6 indicates the effects of the number of blades on the flow speed of the fluid at a flow rate of 0.015 m³/s. It is clearly indicated in Figure 6(a and b) that as the number of blades are increased from two to three, the maximum flow speed has been increased from 1.152 m/s to 1.907 m/s at the inlet of the screw turbine. And also, the pressure distributions have been decreased from 55700 MPa to 22020 MPa when the number of blades are increased from two to three as shown in Figure 7 (a and b). However, increasing of the number of blades has not a significant effect on the power output as shown in Figure 7. There is a slight increment of the power output in the ranges of 25–40° angles of inclinations for a single blade screw turbine. However, when we consider the average values, the two blade screw turbine has the highest power output as shown in Figure 8. In general, Figure 8 showed that when a number of blades are increased the power output of a turbine was decreased. The results obtained pointed out that even though more buckets were created at higher number of blades, additional power losses were introduced subsequently and power losses were associated with the inlet impact losses which can be resulted from the deceasing of flow speed, larger bearing losses, and more internal fluid friction losses.

Figure 6. The streamline for (a) two blades turbine and (b) three blades turbine.

Figure 7. The pressure distributions for (a) two blades turbine and (b) three blades turbine.

Figure 8. The effect number of blades on the power output of turbine at different angle of inclination.

3.2. Design parameters optimization by using response surface optimization (RSO)

As shown in the preference screw geometry evaluations, even though there is slight increment of the power output for different combinations of the design parameters, the results showed inconsistent and very low power output. Therefore, it is important to determine the optimum combinations of design parameters to harvest the maximum possible power output. To reduce the computation time and over estimation, the optimization of parameters is performed at a flow rate of 0.015 m³/s, a head of 0.7 m, and a rotational speed of 104 rpm. The number of iterations (41) was determined based on the random trials using ANSYS Workbench RSO package. As shown in Table 4, the internal radius and pitch size have been considered as input parameters to determine the optimum torque for the given flow rate, head, and speed.

Table 4. Input parameters for the response surface optimization at a flow rate of 0.015 m³/s, a head of 0.7 m, and a rotational speed of 104 rpm.

Iteration	Inner radius (mm)	Pitch (mm)	Torque (Nm)
1	17.9525	385.4125	8.0541
2	20.4575	321.9125	8.12224
3	22.9625	353.6625	8.23594
4	25.4675	390.1625	8.29485
5	27.9725	319.5375	8.66841
6	30.4775	356.0375	7.19336
7	32.9825	287.7875	6.51579
8	35.4875	424.2875	5.42203
9	37.9925	202.475	5.89079
10	40.4975	338.975	7.49302
11	43.0025	270.725	6.54969
12	45.5075	407.225	5.54255
13	48.0125	236.6	5.696
14	50.5175	373.1	5.45412
15	53.0225	304.85	4.68205
16	55.5275	441.35	3.26962
17	58.0325	193.9438	4.82688
18	60.5375	330.4438	5.46401
19	63.0425	262.1938	7.34276
20	65.5475	398.6938	5.594698
21	68.0525	228.0688	6.36434
22	70.5575	364.5688	6.118347
23	73.0625	296.3188	2.51368
24	75.5675	432.8188	3.35155
25	78.0725	211.0063	4.51412
26	80.5775	347.5063	7.383713
27	83.0825	279.2563	2.98261
28	85.5875	415.7563	6.71406
29	88.0925	245.1313	5.97277
30	89	233	5.18868
31	90.5975	381.6313	−2.68162
32	93.1025	313.3813	−3.68406
33	95.6075	449.8813	−5.17897
34	98.1125	189.6781	−8.27939
35	100.6175	326.1781	−5.28199
36	103.1225	257.9281	−1.12198
37	105.6275	394.4281	−6.0761
38	108.1325	223.8031	−7.9192
39	110.6375	360.3031	−8.00849
40	113.1425	292.0531	−8.50434
41	115.6475	428.5531	−8.23568

Table 4 and Figure 9 showed the patterns of torque and power output results respectively for different inner radius. Figure 9 showed that as the inner radius is increased, the power output of the turbine has been decreased, which indicates the existence of optimum inner radius to generate high power output. It is also clear to see that the minimum inner radius has improved the power output as shown in Figure 9. As the water travelled down along the length of the screw, the interaction of the fluid is expected to be mainly with the screw’s blades and trough, which can improve the rotation and reduce frictional power losses. As the inner diameter of the screw turbine is decreased, the interaction between the incoming fluid flow and the central shaft become decreased allowing the development of greater hydrostatic forces on the turbine blades to effectively rotate the screw turbine. Furthermore, a screw with a smaller radius can creates a larger bucket volume. As the diameter ratio increases, the maximum volume of water within the turbine will decrease and leads to less force to be applied on blades. This is especially important when the turbine is operating horizontally without the hydrostatic force created by the angle of inclination.

Figure 9. The effect of inner radius on the power output at a flow rate of 0.015 m³/s, a head of 0.7 m, and a rotational speed of 104 rpm.

The data in Figure 10 shows the relations between the pitch of screw and the power output. As shown in the figure, at 316 mm pitch of screw, the power output was increased significantly. However, increasing the pitch above 316 mm decreased the power output due to the decreasing of the number of buckets in the screw. A smaller pitch allows more buckets to exist in the screw, but small pitch can also develop more power loss due to the internal fluid frictions. Furthermore, when a screw has more buckets, there will be a larger surface area that creates interactions between the fluid molecules in the screw and helical planes. Theoretically, more buckets are expected to produce more power, however, with every new bucket the involvement of additional internal fluid friction forces reduces the power output. And also, smaller buckets may not contain the ideal volume of water to sufficiently rotate the screw. The higher speeds and low flow rate did not allow enough water across each bucket to efficiently operate the screw.

Figure 10. The effect of pitch of screw on the power output at a flow rate of 0.015 m³/s, a head of 0.7 m, and a rotational speed of 104 rpm.

Figures 11 and 12 showed the combined effects of inner radius and pitch of screw on the power and torque outputs. A combination of small inner radius and medium (316 mm) pitch size indicate the maximum power and torque generations. Based on the results obtained as shown in Tables 5 and 6, the optimization process can be used to determine the optimum design parameters that can give the maximum power output. Table 5 indicates the comparison of screw turbine reference and optimized screw geometry initial and design optimum design parameters. The optimum inner radius is four times lower than the initial inner radius. The effects of the values of inner radius on the power output can be clearly seen in Figure 11. The power output at the optimum parameters have been improved by two times of the initial reference geometry parameters as shown in Table 5. The optimum pitch size has been increased to 316 mm within the given limits of evaluation ranges. Similarly, Table 6 indicates the improved mechanical power output without varying the hydraulic power output. Therefore, the efficiency of the optimized geometry (92.9%) is double compared to the reference geometry and it is the maximum result compared to the previous works as shown in Figure 13.

Figure 11. The combined effects of inner radius and pitch of screw on the power output at a flow rate of 0.015 m³/s, a head of 0.7 m, and a rotational speed of 104 rpm by using ANSYS Workbench RSO.

Figure 12. The combined effects of inner radius and pitch of screw on the torque output at a flow rate of 0.015 m³/s, a head of 0.7 m, and a rotational speed of 104 rpm by using ANSYS Workbench RSO.

Figure 13. The comparison of the final power output of the reference and optimized screw turbine geometry corresponding to the standard heads of micro-hydropower turbine.

Table 5. Comparison of the initial and optimal design parameters of screw turbine.

Name	Inner Radius (mm)	Pitch (mm)	Radius ratio	Pitch ratio	Torque (Nm)	Power (Watt)
Optimized geometry	23.201	316	0.14	0.174	8.6996	95.6956
Reference geometry	89	233	0.5369	$0.1285$	5.18868	57.07548

Table 6. Comparison of the power output and efficiency of the reference and optimized screw turbine geometry.

Geometry	Torque (Nm)	Angular speed (rad/s)	Mechanical power (Watt)	Hydraulic power (Watt)	Efficiency %
Reference geometry	5.18868	11	57.07548	103.005	55.4
Optimized geometry	8.6996	11	95.6956	103.005	92.9

Before starting applying the screw geometry optimization process, a single blade reference screw geometry was created to evaluate the reference power output and to analyze the effects of working parameters on the power output and efficiency based on the literature then the optimization is performed using ANSYS Response Surface methodology. As shown in Table 4, by varying the turbine geometrical parameter at a water flow rate of 0.015 m³/s, a head of 0.7 m and a rotational speed of 104 rpm, high power was produced. Based on the results and the optimization design processes, a final optimal papermeters were determined with high power production.

4. Conclusion

In this work, Archimedes screw geometrical parameters optimization has been applied to produce the maximum possible power by using reproducible methods. The optimum Archimedes screw turbine parameters have been determined using CFD analysis. From the results obtained, it is possible to conclude that the use of Archimedes screw turbine with optimum parameters in the micro-hydropower generation is a feasible solution for the rural lighting electrification application. The optimum design of the screw with the diameter ratio (0.14 m), pitch ratio (0.174) and length of screw turbine (1 m) can give the maximum power output at a flow rate of 0.01 m^3/s, 0.015 m^3/s and 0.02 m³/s. Furthermore, the 1 m head, 316 mm pitch, and 1 or 2 number of blades are recommended to produce the maximum power output. From the results obtained it is also observed that increasing the angle of inclinations have a significant effect on the performance of the screw turbine power generation for different flow rates and heads. Finally, the optimized geometries have increased the power output and efficiency of the screw turbine two times of the reference geometry and the obtained results indicate that the optimized power output is much enough for lighting purposes. It is recommended for further investigation to reduce power loss due to environmental effect and structure of the turbine. In addition to that it is recommended to manufacture the developed screw turbine model and test it in the real conditions to evaluate the performance of the machine.

Acknowledgment

Does not apply.

Data availability

The data supporting this research work is available on reasonable request from the corresponding author.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Haymanot Beza Lamesgin

Haymanot Beza Lamesgin is the Lecturer of Mechanical Engineering specialized in Mechanical Design at Bahir Dar Institute of Technology, Bahir Dar University, Bahir Dar, Ethiopia. She completed her MSc. And BSc. Degree at the faculty of Mechanical and Industrial Engineering, Bahir Dar Institute of Technology, Bahir Dar University.

Addisu Negash Ali

Dr. Addisu Negash Ali is an Associate Professor of Mechanical Engineering specialized in Mechanical Design at Bahir Dar Institute of Technology, Bahir Dar University, Bahir Dar, Ethiopia. He completed his PhD, MSc. And BSc. Degree at the National Taiwan University of Science and Technology, Addis Ababa University, and Arba Minh University respectively. Currently, he is the Chair of Mechanical Design at the Faculty of Mechanical and Industrial Engineering, Bahir Dar Institute of Technology, Bahir Dar University.