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

Figures & data

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

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

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

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).

Figure 3. Mesh sensitivity analysis.

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.

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.

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

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.

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.

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

Rorres, C. (2000). The turn of the screw: Optimal design of an Archimedes screw. Journal of Hydraulic Engineering, 126(1), 72–80. https://doi.org/10.1061/(ASCE)0733-9429(2000)126:1(72)

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Data availability

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