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Numerical Optimization Study of Archimedes Screw Turbine (AST): A case study
Renewable Energy 145 (2020) 2130e2143
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Numerical Optimization Study of Archimedes Screw Turbine (AST): A case study K. Shahverdi a, b, *, R. Loni c, B. Ghobadian c, S. Gohari a, S. Marofi d, Evangelos Bellos e a
Department of Water Science Engineering, Bu-Ali Sina University, Hamedan, Iran Department of Water Structures Engineering, Tarbiat Modares University, Tehran, Iran c Department of Biosystems Engineering, Tarbiat Modares University, Tehran, Iran d Water Research Institute, Bu-Ali Sina University, Hamedan, Iran e Thermal Department, School of Mechanical Engineering, National Technical University of Athens, Greece b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 November 2018 Received in revised form 12 March 2019 Accepted 27 July 2019 Available online 29 July 2019
The use of renewable energies including hydropower energy is growing throughout the world. Among the existing hydropower technologies, small-scale hydropower technologies are popular due to easy accessibility and availability in different locations. Recently, Archimedes Screw Turbines (ASTs) as a new technology have been considered. The main objective of this research is the structural optimization of an AST for substituting in irrigation canals instead of existing check structures. For this purpose, the AST performance model was numerically developed for screw performance optimization in MATLAB 2013a environment. The developed model was validated using experimental data. Different structural parameters were optimized to design an appropriate AST for replacing instead of check drop-1 in the east Aghili canal in Khuzestan province (Iran). The canal was simulated using the ICSS hydrodynamic model. The results of the developed model showed a good agreement with reported experimental data. The highest efficiency was obtained 90.83% for the screw length of 6 m, the inclination angle of 20 , and the flight number of 1 at the design flow rate. Based on the findings, the suggested system can be used instead of the canal structures without considerable change in the hydraulic and performance of the canal. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Archimedes screw turbine Numerical optimization Power generation East Aghili canal
1. Introduction Nowadays, producing sustainable energy is one of the main challenges throughout the world. The fossil fuel resources decreasing, CO2 increasing, environmental pollution and global warming cause researchers to find other resources of energies ([1,2]). Renewable energies such as solar, wind, geothermal and hydropower energies as popular kinds of renewable energy resources can be found throughout the world ([3e6]). Among the mentioned resources, hydropower energies have been used widely as large-scale hydropower plants in large dams. Although almost all of the large-scale hydropower opportunities have already been exhausted, there is a strong potential for small-scale hydropower (micro hydropower) resources to be exploited. Some
* Corresponding author. Department of Water Science Engineering, Bu-Ali Sina University, Hamedan, Iran. E-mail address: [email protected] (K. Shahverdi). https://doi.org/10.1016/j.renene.2019.07.124 0960-1481/© 2019 Elsevier Ltd. All rights reserved.
of these resources are small rivers, irrigation systems, drinking water networks, wastewater networks, cooling systems, etc. In hydropower plants, the hydraulic power of water is converted to mechanical power using a turbine in order to electricity generation. Recently, inverse use of the conventional Archimedes screw pump is considered as a popular technology to be used as a turbine for electricity generation from flowing water, named Archimedes Screw Turbine (AST). Traditionally, the Archimedes screw was used for pumping water from a lower to a higher level or conveying liquid or solid materials in a horizontal or inclined plane [7]. There are different types of turbine for electricity generation including Kaplan, Pelton, etc. Comparing the relative costs of an AST and the more common Kaplan turbine for a small-scale hydropower site showed that for an energy output of about 15% more, the AST cost is about 10% less, and its annual capital cost 22% cheaper [8]. In addition, the AST is an environmental and fish friendly structure which needs low civil works for installation in even existing structures [9]. Previous researches showed screw
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efficiency decreases when rotation speed increases at higher speed because the friction forces become unexpectedly large [10]. Numeric researches on the real performance of ASTs are limited. Rorres [11] derived relationships using analytical and numerical analysis for the water levels, flow rates and flow leakages based on actual Archimedes screw pump geometry with modern computing techniques. Due to the importance of flow leakage of hydraulic machinery on their performance, flow leakage of hydraulic machinery was investigated experimentally and numerically in Refs. [12,13], and [14]. The design and optimization of hydraulic machinery were investigated in Ref. [15] based on the flow rate, head and rotational speed, and in Ref. [16] based on experimental and numerical analysis. Müller and Senior [17] presented a simple two-dimensional theory of the Archimedes screw. They developed a model based on the geometry parameters of the Archimedes screw. They assumed the hydrostatic pressure creates torque and causes the screw rotation. Questionnaire investigation on about 400 installed ASTs in Europe showed that outer diameter is equal to pitch, and the inner diameter is half the outer diameter in most of the installed screws. Also, the mean and max electrical efficiencies of ASTs were calculated as 69% and 80%, respectively [18]. The effect of the upstream canal water level on the screw diameter was considerable, and for the screw inclination angle of 34.8ᵒ, the AST electrical efficiency has reported 84% [19] which is a high efficiency. C Zafirah and Nurul Suraya [20] investigated the helix turns and a number of flights to optimize the AST performance using CFD (Computational Fluid Dynamic) method. The results showed that the highest performance of 81% could be obtained for a screw with flights number of 3 and the helix turns of 3. Also, the screw with flights number of 2 has higher performance than flights number of 3 for any helix turns. Stergiopoulos et al. [21] studied screw performance with horizontal, vertical and inclined axes using CFD and explained the methodology, but they did not present any results about screw performance. Lashofer et al. [22] tested both screws with rotating trough meaning the trough is fixed to the flights and screw with the fixed trough. They found that the screw with fixed trough has higher efficiency than that of for rotating trough. They investigated screw efficiency for a wide range of geometry parameters and reported the efficiency of up to 90%. Also, the Ritz-Atro company in Germany reported the screw efficiency of up to 90% (www.ritz-atro. de). However, increasing AST efficiency is being studied. Dellinger et al. [23] developed a theoretical model in which screw performance was investigated as a function of screw geometry and flow condition. The flow leakage, friction, and outlet submersion losses were all included and the fill factor was variable. They installed an experimental device in the laboratory and conducted some experiments on the screw used in the theoretical model investigation. The results of the theoretical and experimental models showed good agreements for the calculated torque and efficiency with those of in the experiment. Since flow motion in ASTs are three-dimensional and occurred phenomena are complex, Dellinger et al. investigated screw performance using CFD method, OpenFOAM software, in different flow conditions and rotation speeds of the screw. The validation data for the OpenFOAM simulations were collected using a laboratory set up. The screw computational domain grids were defined about 5 million meshes used for the calculations. Initial and boundary conditions were defined and simulations were then performed. They resulted in that a three-dimensional simulation is a powerful tool in order to investigate the ASTs performance. However, they suggested more studies for the different inclination angle of the screw and various flow condition [24]. A more complete performance model of ASTs was described in
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Refs. [25,26]. In the first work, the ideal model of an AST was numerically developed. Also, the screw performance was investigated experimentally. The numeric developed model was validated using experimental data. The validated model was used for screw efficiency prediction. The predicted mechanical power and efficiency showed good agreements with associated experimental results. Moreover, the maximum efficiency was approximately 80%. Kozyn and Lubitz [26] developed a complete power losses model to real screw efficiency prediction. The complete model was implemented in MATLAB. In that research, the ideal power and efficiency were predicted using Lubitz et al. [25] ideal model, and then real mechanical power and efficiency experimentally estimated. Using ideal and real mechanical power and efficiency difference, all power losses were calculated. Finally, each power loss was estimated using the developed power losses model. This model validated using an installed AST in Waterfored, Ontario, Canada. Most of the studies until now, on the screw performance, are experimentally, and in some cases both numerically and experimentally, but they are not in a real case study and in micro hydropower resources like irrigation canals. Irrigation canals are one of the best micro hydropower resources because they have many energy dissipater structures to reduce the hydraulic energy of flowing water. Some of these structures are drops, chutes, settling basin, etc. which dissipate excess energy of water as usually heat losses. The excess energy of flowing water in such structures can be converted to electricity. Considering ASTs are an efficient, fish friendly, environmentally friendly device, and have low civil works for substituting in existing structures, they could be a good candidate for this purpose. East Aghili canal in Khuzestan province (Iran) is a good case for studying and optimizing an AST performance because it has many check structures which may be substituted with appropriate ASTs. Also, its hydraulic and physical data exist due to previous studies [27,28]. Although, the use of the AST to generate electricity is growing, there are no references dealing with their optimum design and application in irrigation canals throughout the world. It is necessary to exploit these energy sources by designing and applying an appropriate AST instead of irrigation canal structures. The main objectives of this paper are to recognize places which have potential hydraulic energy in the east Aghili canal by ICSS (Irrigation Canal System Simulation) hydrodynamic simulation, and to develop a numerical model of ASTs. Finally, an optimum AST instead of the first check structure (check drop-1) in east Aghili canal was designed using developed model. 2. Modeling and methodology 2.1. General modeling description In this research, a numerical model of an AST system was developed for the estimation of power generation in irrigation canals. This research was conducted for the optimization of the AST for the east Aghili canal as a case study. For this goal, in the first stage, ICSS hydrodynamic model was used for simulating the east Aghili canal and then available head and hydraulic power of water flow in the canal were calculated. In this software, experimental data of the east Aghili canal were used. In the next stage, an advance hydraulic model was developed using hydraulic relationships in the AST systems. All of the codes were written in the MATLAB 2013a. It should be mentioned that all of the hydraulic losses were assumed in the developed model and the results of the modeling were validated using the reported experimental data. Finally, the optimum structural parameters of the AST including the flight numbers, screw length, and screw inclination angle, as well as the performance parameters including water depth and flow were
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optimized for the east Aghili canal. A summary of the investigated methodology in the current study is presented in Fig. 1.
2.2. AST components An AST exploits the kinetic and potential energies of a liquid in places with very low head or nearly zero head. The kinetic and the potential energy of a liquid are transformed into mechanical work for rotating the screw and generating a torque. A coupled generator to the screw converts the mechanical energy into the electrical one. The potential sites for AST installing like rivers, irrigation systems such as canals and conduits, stormwater systems and water distribution systems, drinking water networks, wastewater networks, cooling systems and even a desalination plant, etc. with nearly zero to 6.5 m head and flow rate of fewer than 6.5 m3/s are the most common places. The schematic of AST components is shown in Fig. 2. Based on Fig. 2, an AST system consists of different parts including screw, trough, upstream canal and downstream canal. Water inflows from upstream canal to the screw inlet and causes the screw to rotate and a torque is generated. As the water reaches to the screw end, it inters to the downstream canal which has a constant water level. In the AST system, water is supplied by an upper resource to the inlet of the inclined AST. Water moving down from upstream of the screw to the downstream is entrapped between two adjacent screw flights. Water level difference between the upstream and downstream elevation of either side of the flights creates pressure force acting on the flights and creating a torque that causes mechanical rotation of the screw. Finally, flow is entered into the lower reservoir. The hydraulic and mechanical parameters can be used for computing the mechanical power and efficiency. It should be mentioned, a bucket is a volume of water trapped between two successive flights. There is a gap between the flights and the fixed trough, named as Gap width (Gw ). The gap width allows the screw to rotate freely within the trough, and it causes a gap leakages. The geometrical parameters of an AST are shown in Fig. 3. They are outer diameter (Do ), inner diameter (Di ), the pitch of the screw (S), total length (L), number of flights (N), and screw inclination angle (b). These parameters should be optimized for any values of the net water head (H) and the total volume flow rate flowing through the system (Qt ).
Fig. 1. A summary of the investigated methodology in the current study.
Fig. 2. Schematic of AST components.
Fig. 3. Geometrical parameters of an AST.
2.3. AST model developing As shown in Fig. 4, consider an AST with an inclination angle of b (related to the horizontal axis and in a cylindrical coordinate system) in which w is aligned with screw centerline, r is the radial position of the considered element from the centerline and q is the angular position of the element from the centerline in the w axis. Steady-state flow condition (constant rotation speed u and volume flow rate Qt ) was assumed for hydraulic modeling. An individual bucket was considered to calculate its torque (Tb ) and volume (Vb ) using numerical integration. All buckets were assumed to have the same behavior; therefore, total torque and volume flow rate can be calculated using single bucket torque and volume. The flow chart of the mechanical power and efficiency calculation is shown in Fig. 5 described as follow.
Fig. 4. Coordinate system of a rotating screw.
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2.3.1. Geometric parameters calculation According to the geometry of the screw, geometric parameters are defined as below [26]:
wðrÞ ¼ r
qðwÞ ¼ 2p
(1) w S
z1 ¼ r cosðqÞcosðbÞ
(2)
Sq sinðbÞ 2p
z2 ¼ r cosðqÞcosðbÞ ð
Sq S ÞsinðbÞ 2p N
(3)
(4)
in which z1 and z2 are the vertical positions of any point (r q) on the downstream and upstream surfaces of the flights, respectively. Also, the minimum (zmin ) and maximum (zmax ) value of vertical point occur at the downstream and upstream surfaces of the flights, respectively (Fig. 6). For a bucket, q ranges between 0 and 2p, and r ranges between Di =2 andDo =2; therefore, by substituting q ¼ p , r ¼ Do = 2 in Equation (3), and q ¼ 2p, r ¼ Di =2 in Equation (4), zmin and zmax can be calculated as following Equations:
Do S cosðbÞ sinðbÞ zmin ¼ 2 2
zmax ¼
Do S cosðbÞ sinðbÞ 2 2
(5)
(6)
Introducing fill factor f as relative depth in the screw section, the actual water level can be defined as follows:
zwl ¼ zmin þ f ðzmax zmin Þ
(7)
If f ¼ 0 then z ¼ zmin and the bucket is empty. Whenf ¼ 1, water level reaches to the top point of the central shaft of the screw and z ¼ zmax . The volume of water in a bucket (Vb ) can be calculated by numerical integration of dV, Equation (8), for q between 0 and 2p, and r between Di =2 andDo =2.
Fig. 6. Position of the minimum (zmin ) and maximum (zmax ) value of the vertical point.
z2 > zwl ; z1 > zwl
0 z z1 S ð wl Þ rdrdq dV ¼ f z2 z1 N S rdrdq N
z2 > zwl ; z1
(8)
z2 < zwl ; z1 > zwl
2.3.2. Ideal power calculation The geometric parameters are used for calculating ideal power (no flow leakages or power losses) generated within an AST. The hydrostatic pressure created at points z1 and z2 due to the weight of water within a bucket are calculated using Equations (9) and (10), respectively, as follow:
0
z1 > zwl z1 < zwl
(9)
0
z2 > zwl z2 < zwl
(10)
p1 ¼ f
rgðzwl z1 Þ
p2 ¼ f
rgðzwl z2 Þ
in which p1 and p2 are the hydrostatic pressure downstream and upstream surfaces of the flights, respectively. The bucket torque (Tb ) and total generated torque (T) due to the hydrostatic pressure are calculated using Equations (11) and (12), respectively: r¼Do=2 ðp ð q¼2
Tb ¼
ðp1 p2 Þ r¼Di=2 q¼0
T ¼ Tb ð
NL Þ S
S rdrdq 2p
(11)
(12)
Given a constant rotation speed (u), ideal power (Pideal ) in which there are no flow leakages or power losses is calculated by Equation (13):
Pideal ¼ u:T
(13)
When water enters the AST, some flow leakages and some power losses are occurred reducing ideal power. The flow leakages are gap leakage and overflow leakage, and the power losses are bearing power loss, outlet expansion power loss, hydraulic friction power loss and outlet submersion power loss.
Fig. 5. Flow chart of the mechanical power and efficiency calculation.
2.3.3. Flow leakages calculation The gap leakage (Qgl ) is not contributed to the screw torque
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generation. Nagel (1968) suggested an empirical model as Equation (14) to estimate gap leakage when f ¼ 1. This model has been used widely in previous researches. Note that the optimal performance of the screw occurs when f ¼ 1; therefore, this model is used for screw design. Nagel model was used in this research to estimate gap leakage.
Qgl ¼ 2:5Gw D1:5 o
(14)
When fill factor becomes greater than 1, an overflow leakage (Qo ) will occur. This leakage is estimated based on the relation of Vnotch overflow defined by Equation (15) [10].
Qo ¼
4 pffiffiffiffiffiffi 1 þ tanðbÞÞðzwl zmax Þ2:5 m 2gð 15 tanðbÞ
(15)
in which m is the flow coefficient and is equal to 0.537 according to Nuernbergk and Rorres [10]. 2.3.4. Power losses calculation 2.3.4.1. Bearing friction power loss. The bearing friction power loss occurs due to screw rotation. At this point, it is important to state that higher rotation speed leads to higher bearing power loss. Typically, bearing power loss (Pl;b ) is a function of rotation speed given by bearing manufacture. In this research, the screw material was considered as smooth steel with power loss equation as Equation (16):
Pl;b ¼ 0:0003u þ 0:0082
(16)
2.3.4.2. Outlet expansion power loss. When water flows between two different cross-section areas, a power loss occurs, named outlet expansion power loss. Moving water from trough with a lower cross-section area to the receiving outlet canal with a greater crosssection area faces cross-section expansion power loss. The overall outlet expansion power loss (Pl;OE ) can be calculated using BordaCarnot relation defined as Equation (17).
Pl;OE ¼ rgQt :ðzo
v2t Þ 2g
(17)
in which ris water density, g is gravitational acceleration, zo is the Borda-Carnot coefficient and vt is the transport velocity of the buckets along the screw length defined as Equations (18) and (19), respectively:
A zo ¼ ð1 Q Þ2 Ao vt ¼
Su 2p
(18)
(19)
Where Ao is the cross-section area of the downstream canal, and AQ is the average cross-section area within the AST calculated using Equation (20):
AQ ¼ Vb
N S
(20)
water passing through it. These contacts produce some frictions in the transport direction and rotational direction. In the transport direction, the screw flights produce no torque. The shear stresses of the trough (tt ) and central shaft (tcsh ) due to the fluid viscosity can be calculated using Equations (21) and (22), respectively:
tt ¼ lt
rv2t
(21)
8
tcsh ¼ lcsh
rv2t
Where lt and lcsh are Darcy-Weisbach friction factor for the trough and central shaft, respectively. Note that the relationship between the two mentioned friction factor coefficients can be driven using Darcy-Weisbach and Manning equilibrium easily. Shear forces (F) on the wetted area of the trough (Awt ) and central shaft (Awcsh ) can be calculated by Equation (23):
F ¼ tt BAwt þ tcsh BAwcsh
(23)
In which, Bis number of buckets. Finally, overall head loss (hl;ht ) and power loss (Pl;ht ) due to hydraulic friction in the transport direction are given by Equations (24) and (25), respectively:
hl;ht ¼
rBVb g
(24)
FL
Pl;ht ¼ rgQhl;ht
(25)
Hydraulic friction power loss in the rotational direction has two components including friction between water and central shaft and friction between water and flights. The shaft relative velocity (vshaft ), generated shear stress (tshaft ) and power loss (Pl;hshaft ) can be calculated using Equations (26)e(28), respectively:
vshaft ¼
Di u 2
tshaft ¼ lchs
(26)
rv2shaft
(27)
8
Pl;hshaft ¼ lchst
rv2shaft 8
BAshaft
(28)
in which Ashaft is the shaft wetted area. Determining shear stress between water and flights are rather complex. Relative moving of water has two components; the radial component which is orthogonal to the shaft axis and the component parallel to the shaft which causes no friction loss. The relative velocity between water and flights, related shear stress and power loss depend on the radial position of the considered element; therefore, to calculate the power loss due to flights friction (Pl;hflight ), Equation (29) must be integrated from D2i to D2o and radial position from 0 to 2p. Do 2
ð 2ðp
Pl;hflight ¼ B
lf 1 r 8
Di 2
2.3.4.3. Hydraulic friction power loss. Hydraulic friction power loss (Pl;h ) occurs due to fluid motion and its viscosity when it contacts with the screw and trough. In an AST system, a portion of the trough, central shaft and flights are directly in contact with the
(22)
8
0
Do 2
r 3 u3 dAf 1 þ B
ð 2ðp
lf 2 r 8
Di 2
r 3 u3 dAf 2
(29)
0
in which lf 1 and lf 2 are Darcy-Weisbach friction factor for the upstream surface and downstream surface of the flights, and subscriptions 1 and 2 are corresponding to the upstream surface and downstream surface of the flights, respectively. The values of the
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wetted surfaces area of the flights (dAf 1 and dAf 2 ) are calculated using Equations (30) and (31), respectively:
0 ; z1 > zwl pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 4p r þ S rdrdq; z1 zwl 2pr
(30)
0 ; z2 > zwl pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ f 4p2 r 2 þ S2 rdrdq; z2 zwl 2pr
(31)
dAf 1 ¼ f
dAf 2
The total hydraulic friction power loss is calculated using Equation (32)
Pl;h ¼ Pl;ht þ Pl;hshaft þ Pl;hflight
(32)
2.3.4.4. Submersion power loss. To calculate the submersion power loss (Pl;S ), an empirical equation derived from experimental results by Kozyn and Lubitz [26] was used in this research for our allowed submersion ranges defined by Equation (33).
Pl;S ¼ ð0:01765Qnd 0:1397Qnd þ 0:1989Þ:Pideal
(33)
in which Qnd is the non-dimensional flow calculated using Equation (34)
Qnd ¼
uS ðD2 D2i Þ 2pQt o
(34)
2.3.5. Mechanical power calculation Considering the flow leakages and power losses in the ideal power, mechanical power can be calculated by Equation (35).
Pmech ¼ Pideal :ð1
Qgl þ Qo Pl;b þ Pl;OE þ Pl;h þ Pl;S Þ:ð1 Þ Qt Pideal
(35)
Note that generator power loss is not included in the above equation as well as in this research. Finally, screw mechanical efficiency (hmech ) is calculated using Equation (36):
hmech ¼
Pmech Pideal
(36)
Based on the described Equations above, a mathematical model of AST was implemented in MATLAB 2013a environment to design appropriate AST for any condition. As hydraulic parameters like water depths and volume flow rate are calculated using the ICSS model, the AST mathematical model is started to run. To find the optimum values of the radial element (dr) and angular element (dq) for numerical integration, the angular 2p , and several radial elements element was first assumed to be 360 were then investigated. The model convergence results showed that the volume and torque of a single bucket remain constant for dr 0:0075 ; therefore, dr ¼ 0:0075 was selected to the calculations. About ten dr values larger than the optimum value were investigated. 2.4. East Aghili canal specification and its simulation Irrigation canals are conveying water from places with a higher height to those of with a lower height. Water is transformed due to its potential and kinetic energies. There are some energy dissipater
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structures to lose the extra energy of flowing water in some places. These losses are usually as heat losses. Here, this hydraulic energy is used for electricity generation. The ASTs can be used for this purpose, but the existing conditions of the canal must keep without any change. In an irrigation canal, water depth should be controlled at a dead band in order to deliver a constant volume flow rate to the turnouts. The dead band is a margin around target depth (usually ±10%) within which water level variations are accepted. Therefore, substituting existing structures with an AST, water depth must remain within the dead band as much as possible, and an AST in such a condition must be designed. The east Aghili canal, located in Aghili district in Khuzestan province in southwest Iran (Fig. 7) was used in this study. It has 20 rectangular turnouts and 11 check structures. The canal length is 16.215 km, Manning's roughness coefficient is 0.017 and trapezoidal cross-section side slopes is 1:1. The base width of the canal is 1.5 m from 0 to 9.485 km and 1 m from 9.485 to 16.215 km. The bed slope varies along the canal between 0.0001 and 0.0004. The turnouts are rectangular gates with width and height of 0.6 m and 0.6 m, respectively. Also, the width of all check structures are equal to the canal width and their heights are 0.8 m in the first reaches and 0.6 m in the last reaches. A check structure controls water depth within the dead band at the target depth. At least one turnout is located between two successive check structures in this canal. According to the capacity of the turnouts, a fraction of water exists from canal to each turnout for supplying the farmers need; therefore, the volume flow rate decreases along the canal. The volume of water which passes from each check structure is contributed to a corresponding check structure power generation. In some check structures location, there is a drop from which water falls to the next reach to dissipate extra energy of passing water. A view of the investigated canal is shown in Fig. 8. The main parameters of the structures except turnouts are given in Table 1. To exactly deliver water to the turnouts, water depth at upstream of the check structures must remain within the dead band and as much as possible at the target depth. In this research, the first check structure (check drop-1) is only examined to design an appropriate AST for a better explanation of the methodology. In the design stage, water depth at upstream of the check structure is designed exactly at the target depth (design depth); therefore, the total energy value upstream of the check drop-1 is the sum of water height and water depth at this point. To calculate water depth downstream of the check structures at the specified volume flow rate, the ICSS simulations on the canal are needed. The net head H is the difference between the energy at upstream and downstream of the check structure.
2.5. ICSS hydrodynamic model The ICSS 4 (ICSS version 4) software was used in this research as an irrigation canal simulation model for simulating the east Aghili canal. Using the ICSS outputs, available head and hydraulic power can be calculated. This model is a fully hydrodynamic model [29]. It solves partial differential Saint-Venant Equations and simulates an open canal water conveyance system with various structures. Various hydraulic and hydrologic conditions are the model inputs as boundary and initial conditions. This model was widely used in many studies. The inputs to the ICSS model are physical and hydraulic parameters, described in the second paragraph of the previous section as well as Table 1. The ICSS outputs are water depth profile along the canal and volume flow rate of the structures.
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Fig. 7. Location of the east Aghili canal in Aghili district [27].
2.6. Validation To validate the developed Archimedes screw model, Lubitz et al. [25] experimental data was used. The screw specification used in Lubitz et al. [25] model is given in Table 2. The results of the Lubitz et al. [25] experimental model and the developed model in this research are illustrated in Fig. 9. As shown, the model results have good agreement with the experimental data, and could accurately Fig. 8. A view of the east Aghili canal, a) downstream and b) upstream.
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Table 1 The main parameters of the east Aghili canal structures except turnouts. Structure name
Water height at upstream of the structure (m)
Water height at downstream of the structure (m)
Target depth (m)
Passing flow
inlet (reservoir) Check Drop-1 Check-1 Check-2 Check-3 Check Drop-2 Check-4 Check-5 Check-6 Check-7 Check Drop-3 Check-8
195.642 192.304 188.945 188.205 187.263 185.804 183.164 182.404 181.714 180.992 179.646 178.184
195.642 191.194 188.937 188.25 187.22 183.844 182.964 182.254 181.604 180.904 179.244 178.024
1.25 1.25 1.15 1.15 1.05 1.05 1.05 0.95 0.85 0.75 0.75
1.47 1.22 1.07 0.94 0.79 0.67 0.61 0.55 0.48 0.36 0.25 0.15
predict the screw power specifically around optimum point, i.e. for rotation speeds of 7e14 rad/s.
Table 2 Lubitz et al. (2014) experimental screw specification used for validation. Parameter
variable
unit
value
Outer diameter Inner diameter Screw length Pitch Flights Number Rotation speed Volume flow rate head Inclination angle Gap width
Do Di L S N
cm cm cm cm rad/s l/s cm ᵒ cm
14.6 8.03 0.584 0.146 3 10 1.13 25 24.9 0.0762
u Qt H
b Gw
3. Results and discussion In this section, the results of the ICSS hydrodynamic model for prediction of the depth and hydropower potential are first presented. In the next step, the results of the screw performance under variation of screw length, flight number and inclination angle are presented. Finally, the effect of canal volume flow rate and depth are investigated on the screw efficiency. 3.1. ICSS hydrodynamic results
Fig. 9. Model validation using Lubitz et al. (2014) experimental data.
In this section, the results of the ICSS hydrodynamic simulation are presented. As mentioned, when the existing structures are replaced with the desired AST, it must be tried to do this without any considerable changes in the existing conditions of the canal as well as with low civil works. Designed water depths upstream of the check structures were target depths. Water depth downstream of the check structures was simulated for the inlet volume flow rate of 1.47 m3/s which is the design flow of the canal inlet. The design volume flow rate for the check drop-1 is 1.22 m3/s. Available head and hydraulic power in different locations of the east Aghili canal were calculated (Table 3). As seen in Table 3, the overall hydraulic power can be produced in the east Aghili canal is 65.9 kW. In this research, only the check drop-1 have been considered to design an optimum AST using the developed model. The accumulative hydraulic power in the first five reaches of the east Aghili canal is about 77.8% of the total hydraulic power due to large volume flow rates passing the corresponding check structures.
Table 3 Water depths at upstream and downstream of each check structure, available head and hydraulic power. Structure name
Water depth at upstream of the structures (m)
Water depth at downstream of the structures (m)
Available head (m)
Hydraulic power (kW)
inlet (reservoir) Check Drop-1 Check-1 Check-2 Check-3 Check Drop-2 Check-4 Check-5 Check-6 Check-7 Check Drop-3 Check-8 Sum
0.584 1.25 1.25 1.15 1.15 1.05 1.05 1.05 0.95 0.85 0.75 0.75
0.584 0.529 0.717 0.82 0.528 0.588 0.622 0.59 0.529 0.388 0.295 0.249
1.831 0.541 0.285 0.665 2.422 0.628 0.61 0.531 0.550 0.857 0.661
21.9 5.7 2.6 5.2 15.9 3.8 3.3 2.5 1.9 2.1 1.0 65.9
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Fig. 10. Volume flow rate and water depth variations in check drop-1 during the third month of the winter season.
Table 4 The screw specifications for the check drop-1 in the east Aghili canal. Parameter
variable
unit
value
Outer diameter Inner diameter Pitch Gap width Fill factor Volume flow rate Head Water density Gravitational constant
Do Di S Gw f Qt H
m m m mm m2/s m kg/m3 m/s2
1.5 0.75 1.5 0.762 1 1.22 1.831 1000 9.81
r g
Volume flow rate changes during the cultivation season because of different water requests of the farmers. According to the Author investigation and simulations by ICSS, these variations are important in the third month of the winter season, 2011 (Fig. 10), in which crop water requirement and consequently flow variations in the check drop-1 is high. As shown, water depth is always within the dead band by regulating check drop-1 while flow is varying. 3.2. Design criteria To design an appropriate AST for substituting instead of the check drop-1, some considerations were made. Since the canal geometry changes must remain minimum, the outer diameter of the canal was set to be equal to the base width of the canal, i.e. Do ¼ 1.5 m. Based on [18] questionnaire survey on almost 400 installed commercial screws in Europe, the pitch and the outer diameter of the investigated screws were nearly equal, and the inner diameters were half the outer diameters. So, this accepted values for the commercial structures were used for the pitch and inner diameter values. The last ratios, i.e. S ¼ 1.5 m and Di ¼ 0.75 m, were taken in this research. Also, the optimum performance of the ASTs in term of fill factor reported f ¼ 1 was used [25]. The screw parameters for the check drop-1 in the east Aghili canal are presented in Table 4. Several simulations were performed based on the various inclination angles, flights number, and screw lengths to obtain the optimum structure of an AST for using instead of the check drop-1 in the east Aghili canal. The same methodology can be used for designing the optimum structure of an AST for generating with the highest mechanical power in the other structures of the canal. All power losses existed in an AST system were taken into account in the modeling.
Fig. 11. The screw performance for variation of screw length, and inclination angle at N ¼ 1.
3.3. Structural parameters In this section, the AST performance under variation of different structural parameters including screw length, flights number and inclination angle was considered and optimized. Fig. 11 shows the screw efficiency variation under the screw length and inclination angle variations with the flight number of 1. As shown, with an increase of the inclination angle, the screw efficiency increases for all lengths until it reaches the peak point and then it decreases quickly. Since the volume flow rate is constant, the screw rotation speed must increase with the increase of inclination angle and consequently mechanical power will be increased as well as efficiency. After peak point, both hydrostatic pressure and therefore generated torque decrease and friction power losses increase which cause efficiency decreases quickly. Since upstream and downstream water depths are constant, the minimum value of the inclination angle differs for each screw length. The minimum value of inclination angle for the shorter screw is higher than that of for larger screw; therefore, curves move to the left hand with a screw length increase. In case of peak point on the curves, peak point for screw length of 4 m is 44.3%. As screw length increases, bucket numbers and consequently torque, mechanical power and efficiency all increase as well as friction power losses. In screw length of 6 m produced
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mechanical power is highest and friction power losses are not yet dominant in the system. Increasing screw length to the 7 m, mechanical power is still increasing but the values of the friction power losses are very high (friction power loss in the rotational direction is a function of rotation speed with the order of 3), and therefore peak point falls down. As seen in Fig. 11, the highest efficiency was obtained 90.83% for the screw length of 6 m, inclination angle of 20 and flight number of 1. This is the best performance compared to the other investigated screw lengths. Such a high efficiency in the AST system was reported in Ref. [22] and by Ritz-atro company in Germany (www.ritz-atro.de). Since screw length and net head are constant during each modeling, therefore minimum value of the inclination angle for each length is different. For the optimum screw length, efficiency variation under the screw inclination angle and flights number variations were shown in Fig. 12. Inclination angle ranges between 17O and 45O, and flight numbers change from 1 to 5. The Archimedes screw with the flight number of 1 resulted in the best performance of 90.83% atb ¼ 20+ . When flights number increases at a specific screw length, friction losses increase and cause the efficiency to be decreased. Fig. 13 depicts a variation of the mechanical power under variation of flight numbers and inclination angles at the screw length of 6 m. The mechanical power of the point with peak efficiency is 19.9 kW for N ¼ 1 and b ¼ 20+ as efficiency diagram (Fig. 12). Since the hydraulic power is constant and is equal to 21.9 kW, values of the efficiency and mechanical power have the same behavior. Fig. 14 shows the variation of power losses, mechanical power, rotational speed, and torque under variation of inclination angle at L ¼ 6 m and N ¼ 1. It could be seen in Fig. 14 that as the inclination angle increases the screw rotation speed also increases in order to stay a constant volume flow rate passing under the check drop-1 at the design value of 1.22 m3/s. Also, as the inclination angle increases, the screw end is submerged within the outlet receiving canal because screw length and water levels at the upstream canal and downstream receiving canal are all constant. Increasing screw rotation and screw submersion cause bearing power loss, friction power loss and submersion power loss increase and to be dominant in the system. Therefore, efficiency decreases after inclination angle ofb ¼ 20+ . While power losses are increasing, the mechanical power is decreasing. At b ¼ 25:5+ , the mechanical power and sum of all power losses are equal and then power losses are become greater than mechanical power, meaning all powers converted to the power losses.
Fig. 12. Efficiency variation as a function of screw inclination and flights number for screw length of 6 m.
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Fig. 13. Variation of the mechanical power under variation of flight numbers, and inclination angles at screw length of 6 m.
Fig. 15a, b, and c show variation of efficiency investigated under variation of inclination angles, flight numbers for screw length of 4 m, screw length of 5 m, and screw length of 7 m, respectively. Also, Fig. 16a, b, and c show those of for the mechanical power. These behaviors are the same as those of for screw length 6 m, and the same discussion and reasons may be presented. It may only be noticed that for screw lengths of 4 and 5 m, efficiency corresponded to the flight number of 3 are higher. For screw lengths 7 m, this occurred at N ¼ 2. 3.4. Performance parameters Effect of volume flow rate on the AST performance was considered in this section. As said, analysis of the volume flow rate of the canal and the ICSS simulations showed that the water flow ranges between 1.06 and 1.35 m3/s at the check drop-1. Considering the target depth and the dead band values, water depth deviation is between 1.125 and 1.375 m (±10% of the target depth) which are upper and lower limit of the dead band, respectively. In Fig. 17, efficiency and mechanical power of the AST were considered under volume flow rate variations. The optimized AST have the flight number of 1, screw length of 6 m, and the inclination angle of 20, the rotation speed of 9.54 rad/s, upstream water depth of 1.25 m and design flow of 1.22 m3/s. The effect of the flow variations was investigated for the optimized AST (Fig. 17). There are some important points in Fig. 17 as volume flow rate was changed between its maximum (1.35 m3/s) and minimum (1.06 m3/s) values. As an AST is substituted in the canal, water depth upstream of the AST is controlled by AST mechanism. Water depth at the downstream canal is always constant because there is a weir at the end of the downstream canal. As volume flow rate to the check drop-1 is increasing from the lower flow and since rotation speed is constant, the resultant pressure and torque values increase. This fact increases produced mechanical power. Also, the volume flow rate increase causes the hydraulic power to be increased. In this condition, efficiency decreases because the volume flow rate has more impact on the mechanical power than hydraulic power. For lower volume flow rate, the efficiency is higher, but the mechanical power is 17.24 kW. The mechanical power at the optimum point is 19.90 kW and corresponding efficiency is 90.83%. As the maximum point is reached, optimum efficiency and maximum produced mechanical power are reached. Also, the water level is reached to the highest point of the inner cylindrical shaft means fill factor is 1. After this point, the hydraulic power increase will
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Fig. 14. Variation of power losses, mechanical power, rotational speed, and torque under variation of inclination angle at L ¼ 6 m and N ¼ 1.
Fig. 15. Efficiency of the screw under variation of inclination angles, flight numbers, at a) L ¼ 4 m, b) L ¼ 5 m, and c) L ¼ 7 m.
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Fig. 16. Variation mechanical power under variation of inclination angles, flight numbers, at a) L ¼ 4 m, b) L ¼ 5 m, and c) L ¼ 7 m.
Fig. 17. The screw performance for a range of volume flow rate variations.
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Fig. 18. Water depth variation after the optimum designed AST installing.
Table 5 Optimum values of the screw for various flights number.
N¼1 N¼2 N¼3 N¼4 N¼5
Inclination angle (ᵒ)
Screw length (m)
Mechanical power (kW)
Efficiency (%)
20 26 22 26 26
6 6 7 6 6
19.9 19.23 18.06 15.8 13.76
90.83 87.8 82.41 71.2 62.8
continue because volume flow rate increases and contributed water depth in hydraulic power generation is fixed; therefore, overflow leakage will occur and mechanical power is reducing. Design volume flow rate and design head are equal to 1.22 m3/s and 1.25 m respectively. The maximum efficiency is expected to be occurred at the design flow rate and design head. The maximum mechanical power occurred at the design flow rate, but efficiency was not maximum at this point. The reason for this phenomena is that a dead band must be defined in irrigation canals. This causes water depth is not fixed at the target depth exactly, but it is established within the dead band. This causes water height contributed to hydraulic power to be variable and between upper and lower dead band. Depending on the water depth position within the dead band, the hydraulic power and consequently efficiency are variable. Therefore, maximum efficiency does not occur at design flow rate necessarily. The water depth variations in Fig. 17 confirm this claim. Water depth in the presence of the AST was added to Fig. 10 and illustrated in Fig. 18 to have a comparison between flow and water depth variation before and after the AST application. As seen, when volume flow rate variation is significantly higher than design flow, for example, 1.35 m3/s, water depth at upstream of the dead band exceeded upper dead band limit; however, it does not have considerable deviation. Also, water depth decreases for less volume flow rate than design flow and vice versa regardless of the initially established water depth. In could be concluded that mechanical power for the designed AST is between 17.24 kW and 19.90 kW and the canal mechanism remain almost constant for most of the volume flow rate occurred in the canal. There was only a small impact on the water depth for high volume flow rate. Now, ASTs can be suggested to be applied in the irrigation canals guarantying high efficiency. Although N ¼ 1 was investigated as an optimum choice,
efficiency and mechanical power for other values of the flight number were acceptable (Table 5). For example, for N ¼ 3 which is a typical value for the flight number, the mechanical power was obtained 18.06 kW and corresponding efficiency was 82.41%. For real plants, financial efficiency is more important than mechanical efficiency, and these two do not usually occur simultaneously. In a study like this, it is difficult to estimate financial efficiency, because the cost of parts and construction is difficult to estimate. This work only was investigated mechanical power, but not electrical power or financial efficiency. 4. Conclusions In the current study, a numerical model of screw system was developed in MATLAB 2013a to the optimal design of an appropriate AST for substituting instead of irrigation canal structures. This optimization was conducted for a case study in east Aghili canal, Khuzestan province, Iran. The first check structure (check drop-1) was considered for this purpose, and an optimum AST was designed to be substituted instead of check drop-1. The ICSS hydrodynamic model was used for simulating the canal condition including water depth and flow in the structures. To design an optimum AST, different structural parameters of the screw turbine were considered including screw inclination angle, number of flights, and volume flow rate of water. Available head and hydraulic power in different locations of the canal were calculated using ICSS. The overall hydraulic power that can be produced in the canal was obtained 65.9 kW. Hydraulic power existing in check drop-1 was 21.9 kW. Due to existing conditions of the canal and for low civil works, the outer diameter of the screw was chosen equal to the canal width (1.5 m). Also, the inner diameter and pitch of the screw were selected 0.75 m and 1.5 m, respectively.
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The best screw, with the highest efficiency, which can be substituted instead of check drop-1 was a screw with the length of 6 m, inclination angle of 20 , flight number of 1, and the rotation speed of 9.54 rad/s. The highest efficiency was obtained 90.83% for the optimum screw, and corresponding mechanical power was obtained 19.90 kW. The mechanical power for a wide range of the volume flow rate around design flow (1.22 m3/s) occurred in the canal in the third month of the winter season, in 2011, was ranged between 17.24 kW and 19.90 kW. The results showed that the optimum screw designed in this research have no considerable effect in the canal condition and can be substituted successfully instead of the check drop-1. Substituting irrigation canals check structures with an optimum AST which can be designed using this research methodology is recommended for future works. Acknowledgement Reyhaneh Loni, B. Ghobadian, and G. Najafi are grateful to the Tarbiat Modares University (http://www.modares.ac.ir) for financial supports given under IG/39705 grant for renewable Energies of Modares research group. References [1] K. Kusakana, J. Munda, A. Jimoh, Economic and environmental analysis of micro hydropower system for rural power supply, in: Power and Energy Conference, 2008. PECon 2008, IEEE 2nd International, 2008, pp. 441e444. IEEE. [2] S. Khurana, A. Kumar, Small hydro powerda review, Int. J. Tumor Ther. 1 (2011) 107e110. [3] J. Du, H. Yang, Z. Shen, J. Chen, Micro hydro power generation from water supply system in high rise buildings using pump as turbines, Energy 137 (2017) 431e440. [4] M.R.B. Khan, R. Jidin, J. Pasupuleti, S.A. Shaaya, Optimal combination of solar, wind, micro-hydro and diesel systems based on actual seasonal load profiles for a resort island in the South China Sea, Energy 82 (2015) 80e97. [5] H. Lavri c, A. Rihar, R. Fiser, Simulation of electrical energy production in Archimedes screw-based ultra-low head small hydropower plant considering environment protection conditions and technical limitations, Energy 164 (2018) 87e98. [6] E. Tasdemiroglu, Development of small hydropower in Türkiye, Energy 18 (1993) 699e702. [7] A. Kozyn, S. Ash, W. Lubitz, Assessment of archimedes screw power generation potential in Ontario CCTC 2015 paper number 1570095585, in: Climate Change Technology Conference, 2015. Montreal. [8] REN21, Renewables 2013: Global Status Report, Renewable Energy Policy Network for the 21st Century, 2013. [9] L. Lisdiyanti, Y. Hizhar, B. Yulistiyanto, Effect of Flow Discharge and Shaft Slope
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of Archimides (Screw) Turbin on the Micro-hydro Power Plant, 2012. [10] D.M. Nuernbergk, C. Rorres, Analytical model for water inflow of an Archimedes screw used in hydropower generation, J. Hydraul. Eng. 139 (2012) 213e220. [11] C. Rorres, The turn of the screw: optimal design of an Archimedes screw, J. Hydraul. Eng. 126 (2000) 72e80. [12] Y. Liu, L. Tan, Tip clearance on pressure fluctuation intensity and vortex characteristic of a mixed flow pump as turbine at pump mode, Renew. Energy 129 (2018) 606e615. [13] Y. Hao, L. Tan, Symmetrical and unsymmetrical tip clearances on cavitation performance and radial force of a mixed flow pump as turbine at pump mode, Renew. Energy 127 (2018) 368e376. [14] T. Lei, X. Zhifeng, L. Yabin, H. Yue, X. Yun, Influence of T-shape tip clearance on performance of a mixed-flow pump, Proceedings of the Institution of Mechanical Engineers, Part A: Journal of power and energy 232 (2018) 386e396. [15] Y. Wang, X. Huo, Multiobjective optimization design and performance prediction of centrifugal pump based on orthogonal test, Advances in Materials Science and Engineering 2018 (2018). [16] M. Liu, L. Tan, S. Cao, Design method of controllable blade angle and orthogonal optimization of pressure rise for a multiphase pump, Energies 11 (2018) 1048. [17] G. Müller, J. Senior, Simplified theory of Archimedean screws, J. Hydraul. Res. 47 (2009) 666e669. [18] A. Lashofer, W. Hawle, B. Pelikan, State of technology and design guidelines for the Archimedes screw turbine, in: Meeting of Hydro, 2012. [19] O. Dada, I. Daniyan, O. Adaramola, Optimal design of micro hydro turbine (archimedes screw turbine) in arinta water fall in ekiti state, Nigeria, Res. J. Eng. Appl. Sci. 4 (2014) 34e38. [20] R. C Zafirah, A. Nurul Suraya, Parametric study on efficiency of archimedes screw turbine, ARPN Journal of Engineering and Applied Sciences 11 (2016) 10904e10908. [21] А. Stergiopoulou, V. Stergiopoulos, E. Kalkani, Towards a First CFD Study of Innovative Archimedean Kinetic Energy Conversion Systems in Greece, Proceedings of the 5th IC-EpsMsO, 2013, pp. 634e640. [22] A. Lashofer, W. Hawle, B. Pelikan, Betriebsbereiche und Wirkungsgrade der €ge aus Wasserkraftschnecke, Wasserkraftprojekte Band II: Ausgew€ ahlte Beitra der Fachzeitschrift WasserWirtschaft, 2014, p. 154. [23] G. Dellinger, A. Terfous, P.-A. Garambois, A. Ghenaim, Experimental investigation and performance analysis of Archimedes screw generator, J. Hydraul. Res. 54 (2016) 197e209. [24] G. Dellinger, P.-A. Garambois, N. Dellinger, M. Dufresne, A. Terfous, J. Vazquez, A. Ghenaim, Computational fluid dynamics modeling for the design of Archimedes Screw Generator, Renew. Energy 118 (2018) 847e857. [25] W.D. Lubitz, M. Lyons, S. Simmons, Performance model of archimedes screw hydro turbines with variable fill level, J. Hydraul. Eng. 140 (2014), 04014050. [26] A. Kozyn, W.D. Lubitz, A power loss model for Archimedes screw generators, Renew. Energy 108 (2017) 260e273. [27] H. Savari, M. Monem, K. Shahverdi, Comparing the performance of FSL and traditional operation methods for on-request water delivery in the Aghili network, Iran, J. Irrig. Drain. Eng. 142 (2016), 04016055. [28] K. Shahverdi, M.J. Monem, M. Nili, Fuzzy SARSA learning of operational instructions to schedule water distribution and delivery, Irrig. Drain. 65 (2016) 276e284. [29] D.H. Manz, M. Schaaljez, Development and Application of the Irrigation Conveyance System Simulation Model, 1992.
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
Numerical Optimization Study of Archimedes Screw Turbine (AST): A case study K. Shahverdi a, b, *, R. Loni c, B. Ghobadian c, S. Gohari a, S. Marofi d, Evangelos Bellos e a
Department of Water Science Engineering, Bu-Ali Sina University, Hamedan, Iran Department of Water Structures Engineering, Tarbiat Modares University, Tehran, Iran c Department of Biosystems Engineering, Tarbiat Modares University, Tehran, Iran d Water Research Institute, Bu-Ali Sina University, Hamedan, Iran e Thermal Department, School of Mechanical Engineering, National Technical University of Athens, Greece b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 November 2018 Received in revised form 12 March 2019 Accepted 27 July 2019 Available online 29 July 2019
The use of renewable energies including hydropower energy is growing throughout the world. Among the existing hydropower technologies, small-scale hydropower technologies are popular due to easy accessibility and availability in different locations. Recently, Archimedes Screw Turbines (ASTs) as a new technology have been considered. The main objective of this research is the structural optimization of an AST for substituting in irrigation canals instead of existing check structures. For this purpose, the AST performance model was numerically developed for screw performance optimization in MATLAB 2013a environment. The developed model was validated using experimental data. Different structural parameters were optimized to design an appropriate AST for replacing instead of check drop-1 in the east Aghili canal in Khuzestan province (Iran). The canal was simulated using the ICSS hydrodynamic model. The results of the developed model showed a good agreement with reported experimental data. The highest efficiency was obtained 90.83% for the screw length of 6 m, the inclination angle of 20 , and the flight number of 1 at the design flow rate. Based on the findings, the suggested system can be used instead of the canal structures without considerable change in the hydraulic and performance of the canal. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Archimedes screw turbine Numerical optimization Power generation East Aghili canal
1. Introduction Nowadays, producing sustainable energy is one of the main challenges throughout the world. The fossil fuel resources decreasing, CO2 increasing, environmental pollution and global warming cause researchers to find other resources of energies ([1,2]). Renewable energies such as solar, wind, geothermal and hydropower energies as popular kinds of renewable energy resources can be found throughout the world ([3e6]). Among the mentioned resources, hydropower energies have been used widely as large-scale hydropower plants in large dams. Although almost all of the large-scale hydropower opportunities have already been exhausted, there is a strong potential for small-scale hydropower (micro hydropower) resources to be exploited. Some
* Corresponding author. Department of Water Science Engineering, Bu-Ali Sina University, Hamedan, Iran. E-mail address: [email protected] (K. Shahverdi). https://doi.org/10.1016/j.renene.2019.07.124 0960-1481/© 2019 Elsevier Ltd. All rights reserved.
of these resources are small rivers, irrigation systems, drinking water networks, wastewater networks, cooling systems, etc. In hydropower plants, the hydraulic power of water is converted to mechanical power using a turbine in order to electricity generation. Recently, inverse use of the conventional Archimedes screw pump is considered as a popular technology to be used as a turbine for electricity generation from flowing water, named Archimedes Screw Turbine (AST). Traditionally, the Archimedes screw was used for pumping water from a lower to a higher level or conveying liquid or solid materials in a horizontal or inclined plane [7]. There are different types of turbine for electricity generation including Kaplan, Pelton, etc. Comparing the relative costs of an AST and the more common Kaplan turbine for a small-scale hydropower site showed that for an energy output of about 15% more, the AST cost is about 10% less, and its annual capital cost 22% cheaper [8]. In addition, the AST is an environmental and fish friendly structure which needs low civil works for installation in even existing structures [9]. Previous researches showed screw
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efficiency decreases when rotation speed increases at higher speed because the friction forces become unexpectedly large [10]. Numeric researches on the real performance of ASTs are limited. Rorres [11] derived relationships using analytical and numerical analysis for the water levels, flow rates and flow leakages based on actual Archimedes screw pump geometry with modern computing techniques. Due to the importance of flow leakage of hydraulic machinery on their performance, flow leakage of hydraulic machinery was investigated experimentally and numerically in Refs. [12,13], and [14]. The design and optimization of hydraulic machinery were investigated in Ref. [15] based on the flow rate, head and rotational speed, and in Ref. [16] based on experimental and numerical analysis. Müller and Senior [17] presented a simple two-dimensional theory of the Archimedes screw. They developed a model based on the geometry parameters of the Archimedes screw. They assumed the hydrostatic pressure creates torque and causes the screw rotation. Questionnaire investigation on about 400 installed ASTs in Europe showed that outer diameter is equal to pitch, and the inner diameter is half the outer diameter in most of the installed screws. Also, the mean and max electrical efficiencies of ASTs were calculated as 69% and 80%, respectively [18]. The effect of the upstream canal water level on the screw diameter was considerable, and for the screw inclination angle of 34.8ᵒ, the AST electrical efficiency has reported 84% [19] which is a high efficiency. C Zafirah and Nurul Suraya [20] investigated the helix turns and a number of flights to optimize the AST performance using CFD (Computational Fluid Dynamic) method. The results showed that the highest performance of 81% could be obtained for a screw with flights number of 3 and the helix turns of 3. Also, the screw with flights number of 2 has higher performance than flights number of 3 for any helix turns. Stergiopoulos et al. [21] studied screw performance with horizontal, vertical and inclined axes using CFD and explained the methodology, but they did not present any results about screw performance. Lashofer et al. [22] tested both screws with rotating trough meaning the trough is fixed to the flights and screw with the fixed trough. They found that the screw with fixed trough has higher efficiency than that of for rotating trough. They investigated screw efficiency for a wide range of geometry parameters and reported the efficiency of up to 90%. Also, the Ritz-Atro company in Germany reported the screw efficiency of up to 90% (www.ritz-atro. de). However, increasing AST efficiency is being studied. Dellinger et al. [23] developed a theoretical model in which screw performance was investigated as a function of screw geometry and flow condition. The flow leakage, friction, and outlet submersion losses were all included and the fill factor was variable. They installed an experimental device in the laboratory and conducted some experiments on the screw used in the theoretical model investigation. The results of the theoretical and experimental models showed good agreements for the calculated torque and efficiency with those of in the experiment. Since flow motion in ASTs are three-dimensional and occurred phenomena are complex, Dellinger et al. investigated screw performance using CFD method, OpenFOAM software, in different flow conditions and rotation speeds of the screw. The validation data for the OpenFOAM simulations were collected using a laboratory set up. The screw computational domain grids were defined about 5 million meshes used for the calculations. Initial and boundary conditions were defined and simulations were then performed. They resulted in that a three-dimensional simulation is a powerful tool in order to investigate the ASTs performance. However, they suggested more studies for the different inclination angle of the screw and various flow condition [24]. A more complete performance model of ASTs was described in
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Refs. [25,26]. In the first work, the ideal model of an AST was numerically developed. Also, the screw performance was investigated experimentally. The numeric developed model was validated using experimental data. The validated model was used for screw efficiency prediction. The predicted mechanical power and efficiency showed good agreements with associated experimental results. Moreover, the maximum efficiency was approximately 80%. Kozyn and Lubitz [26] developed a complete power losses model to real screw efficiency prediction. The complete model was implemented in MATLAB. In that research, the ideal power and efficiency were predicted using Lubitz et al. [25] ideal model, and then real mechanical power and efficiency experimentally estimated. Using ideal and real mechanical power and efficiency difference, all power losses were calculated. Finally, each power loss was estimated using the developed power losses model. This model validated using an installed AST in Waterfored, Ontario, Canada. Most of the studies until now, on the screw performance, are experimentally, and in some cases both numerically and experimentally, but they are not in a real case study and in micro hydropower resources like irrigation canals. Irrigation canals are one of the best micro hydropower resources because they have many energy dissipater structures to reduce the hydraulic energy of flowing water. Some of these structures are drops, chutes, settling basin, etc. which dissipate excess energy of water as usually heat losses. The excess energy of flowing water in such structures can be converted to electricity. Considering ASTs are an efficient, fish friendly, environmentally friendly device, and have low civil works for substituting in existing structures, they could be a good candidate for this purpose. East Aghili canal in Khuzestan province (Iran) is a good case for studying and optimizing an AST performance because it has many check structures which may be substituted with appropriate ASTs. Also, its hydraulic and physical data exist due to previous studies [27,28]. Although, the use of the AST to generate electricity is growing, there are no references dealing with their optimum design and application in irrigation canals throughout the world. It is necessary to exploit these energy sources by designing and applying an appropriate AST instead of irrigation canal structures. The main objectives of this paper are to recognize places which have potential hydraulic energy in the east Aghili canal by ICSS (Irrigation Canal System Simulation) hydrodynamic simulation, and to develop a numerical model of ASTs. Finally, an optimum AST instead of the first check structure (check drop-1) in east Aghili canal was designed using developed model. 2. Modeling and methodology 2.1. General modeling description In this research, a numerical model of an AST system was developed for the estimation of power generation in irrigation canals. This research was conducted for the optimization of the AST for the east Aghili canal as a case study. For this goal, in the first stage, ICSS hydrodynamic model was used for simulating the east Aghili canal and then available head and hydraulic power of water flow in the canal were calculated. In this software, experimental data of the east Aghili canal were used. In the next stage, an advance hydraulic model was developed using hydraulic relationships in the AST systems. All of the codes were written in the MATLAB 2013a. It should be mentioned that all of the hydraulic losses were assumed in the developed model and the results of the modeling were validated using the reported experimental data. Finally, the optimum structural parameters of the AST including the flight numbers, screw length, and screw inclination angle, as well as the performance parameters including water depth and flow were
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optimized for the east Aghili canal. A summary of the investigated methodology in the current study is presented in Fig. 1.
2.2. AST components An AST exploits the kinetic and potential energies of a liquid in places with very low head or nearly zero head. The kinetic and the potential energy of a liquid are transformed into mechanical work for rotating the screw and generating a torque. A coupled generator to the screw converts the mechanical energy into the electrical one. The potential sites for AST installing like rivers, irrigation systems such as canals and conduits, stormwater systems and water distribution systems, drinking water networks, wastewater networks, cooling systems and even a desalination plant, etc. with nearly zero to 6.5 m head and flow rate of fewer than 6.5 m3/s are the most common places. The schematic of AST components is shown in Fig. 2. Based on Fig. 2, an AST system consists of different parts including screw, trough, upstream canal and downstream canal. Water inflows from upstream canal to the screw inlet and causes the screw to rotate and a torque is generated. As the water reaches to the screw end, it inters to the downstream canal which has a constant water level. In the AST system, water is supplied by an upper resource to the inlet of the inclined AST. Water moving down from upstream of the screw to the downstream is entrapped between two adjacent screw flights. Water level difference between the upstream and downstream elevation of either side of the flights creates pressure force acting on the flights and creating a torque that causes mechanical rotation of the screw. Finally, flow is entered into the lower reservoir. The hydraulic and mechanical parameters can be used for computing the mechanical power and efficiency. It should be mentioned, a bucket is a volume of water trapped between two successive flights. There is a gap between the flights and the fixed trough, named as Gap width (Gw ). The gap width allows the screw to rotate freely within the trough, and it causes a gap leakages. The geometrical parameters of an AST are shown in Fig. 3. They are outer diameter (Do ), inner diameter (Di ), the pitch of the screw (S), total length (L), number of flights (N), and screw inclination angle (b). These parameters should be optimized for any values of the net water head (H) and the total volume flow rate flowing through the system (Qt ).
Fig. 1. A summary of the investigated methodology in the current study.
Fig. 2. Schematic of AST components.
Fig. 3. Geometrical parameters of an AST.
2.3. AST model developing As shown in Fig. 4, consider an AST with an inclination angle of b (related to the horizontal axis and in a cylindrical coordinate system) in which w is aligned with screw centerline, r is the radial position of the considered element from the centerline and q is the angular position of the element from the centerline in the w axis. Steady-state flow condition (constant rotation speed u and volume flow rate Qt ) was assumed for hydraulic modeling. An individual bucket was considered to calculate its torque (Tb ) and volume (Vb ) using numerical integration. All buckets were assumed to have the same behavior; therefore, total torque and volume flow rate can be calculated using single bucket torque and volume. The flow chart of the mechanical power and efficiency calculation is shown in Fig. 5 described as follow.
Fig. 4. Coordinate system of a rotating screw.
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2.3.1. Geometric parameters calculation According to the geometry of the screw, geometric parameters are defined as below [26]:
wðrÞ ¼ r
qðwÞ ¼ 2p
(1) w S
z1 ¼ r cosðqÞcosðbÞ
(2)
Sq sinðbÞ 2p
z2 ¼ r cosðqÞcosðbÞ ð
Sq S ÞsinðbÞ 2p N
(3)
(4)
in which z1 and z2 are the vertical positions of any point (r q) on the downstream and upstream surfaces of the flights, respectively. Also, the minimum (zmin ) and maximum (zmax ) value of vertical point occur at the downstream and upstream surfaces of the flights, respectively (Fig. 6). For a bucket, q ranges between 0 and 2p, and r ranges between Di =2 andDo =2; therefore, by substituting q ¼ p , r ¼ Do = 2 in Equation (3), and q ¼ 2p, r ¼ Di =2 in Equation (4), zmin and zmax can be calculated as following Equations:
Do S cosðbÞ sinðbÞ zmin ¼ 2 2
zmax ¼
Do S cosðbÞ sinðbÞ 2 2
(5)
(6)
Introducing fill factor f as relative depth in the screw section, the actual water level can be defined as follows:
zwl ¼ zmin þ f ðzmax zmin Þ
(7)
If f ¼ 0 then z ¼ zmin and the bucket is empty. Whenf ¼ 1, water level reaches to the top point of the central shaft of the screw and z ¼ zmax . The volume of water in a bucket (Vb ) can be calculated by numerical integration of dV, Equation (8), for q between 0 and 2p, and r between Di =2 andDo =2.
Fig. 6. Position of the minimum (zmin ) and maximum (zmax ) value of the vertical point.
z2 > zwl ; z1 > zwl
0 z z1 S ð wl Þ rdrdq dV ¼ f z2 z1 N S rdrdq N
z2 > zwl ; z1
(8)
z2 < zwl ; z1 > zwl
2.3.2. Ideal power calculation The geometric parameters are used for calculating ideal power (no flow leakages or power losses) generated within an AST. The hydrostatic pressure created at points z1 and z2 due to the weight of water within a bucket are calculated using Equations (9) and (10), respectively, as follow:
0
z1 > zwl z1 < zwl
(9)
0
z2 > zwl z2 < zwl
(10)
p1 ¼ f
rgðzwl z1 Þ
p2 ¼ f
rgðzwl z2 Þ
in which p1 and p2 are the hydrostatic pressure downstream and upstream surfaces of the flights, respectively. The bucket torque (Tb ) and total generated torque (T) due to the hydrostatic pressure are calculated using Equations (11) and (12), respectively: r¼Do=2 ðp ð q¼2
Tb ¼
ðp1 p2 Þ r¼Di=2 q¼0
T ¼ Tb ð
NL Þ S
S rdrdq 2p
(11)
(12)
Given a constant rotation speed (u), ideal power (Pideal ) in which there are no flow leakages or power losses is calculated by Equation (13):
Pideal ¼ u:T
(13)
When water enters the AST, some flow leakages and some power losses are occurred reducing ideal power. The flow leakages are gap leakage and overflow leakage, and the power losses are bearing power loss, outlet expansion power loss, hydraulic friction power loss and outlet submersion power loss.
Fig. 5. Flow chart of the mechanical power and efficiency calculation.
2.3.3. Flow leakages calculation The gap leakage (Qgl ) is not contributed to the screw torque
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generation. Nagel (1968) suggested an empirical model as Equation (14) to estimate gap leakage when f ¼ 1. This model has been used widely in previous researches. Note that the optimal performance of the screw occurs when f ¼ 1; therefore, this model is used for screw design. Nagel model was used in this research to estimate gap leakage.
Qgl ¼ 2:5Gw D1:5 o
(14)
When fill factor becomes greater than 1, an overflow leakage (Qo ) will occur. This leakage is estimated based on the relation of Vnotch overflow defined by Equation (15) [10].
Qo ¼
4 pffiffiffiffiffiffi 1 þ tanðbÞÞðzwl zmax Þ2:5 m 2gð 15 tanðbÞ
(15)
in which m is the flow coefficient and is equal to 0.537 according to Nuernbergk and Rorres [10]. 2.3.4. Power losses calculation 2.3.4.1. Bearing friction power loss. The bearing friction power loss occurs due to screw rotation. At this point, it is important to state that higher rotation speed leads to higher bearing power loss. Typically, bearing power loss (Pl;b ) is a function of rotation speed given by bearing manufacture. In this research, the screw material was considered as smooth steel with power loss equation as Equation (16):
Pl;b ¼ 0:0003u þ 0:0082
(16)
2.3.4.2. Outlet expansion power loss. When water flows between two different cross-section areas, a power loss occurs, named outlet expansion power loss. Moving water from trough with a lower cross-section area to the receiving outlet canal with a greater crosssection area faces cross-section expansion power loss. The overall outlet expansion power loss (Pl;OE ) can be calculated using BordaCarnot relation defined as Equation (17).
Pl;OE ¼ rgQt :ðzo
v2t Þ 2g
(17)
in which ris water density, g is gravitational acceleration, zo is the Borda-Carnot coefficient and vt is the transport velocity of the buckets along the screw length defined as Equations (18) and (19), respectively:
A zo ¼ ð1 Q Þ2 Ao vt ¼
Su 2p
(18)
(19)
Where Ao is the cross-section area of the downstream canal, and AQ is the average cross-section area within the AST calculated using Equation (20):
AQ ¼ Vb
N S
(20)
water passing through it. These contacts produce some frictions in the transport direction and rotational direction. In the transport direction, the screw flights produce no torque. The shear stresses of the trough (tt ) and central shaft (tcsh ) due to the fluid viscosity can be calculated using Equations (21) and (22), respectively:
tt ¼ lt
rv2t
(21)
8
tcsh ¼ lcsh
rv2t
Where lt and lcsh are Darcy-Weisbach friction factor for the trough and central shaft, respectively. Note that the relationship between the two mentioned friction factor coefficients can be driven using Darcy-Weisbach and Manning equilibrium easily. Shear forces (F) on the wetted area of the trough (Awt ) and central shaft (Awcsh ) can be calculated by Equation (23):
F ¼ tt BAwt þ tcsh BAwcsh
(23)
In which, Bis number of buckets. Finally, overall head loss (hl;ht ) and power loss (Pl;ht ) due to hydraulic friction in the transport direction are given by Equations (24) and (25), respectively:
hl;ht ¼
rBVb g
(24)
FL
Pl;ht ¼ rgQhl;ht
(25)
Hydraulic friction power loss in the rotational direction has two components including friction between water and central shaft and friction between water and flights. The shaft relative velocity (vshaft ), generated shear stress (tshaft ) and power loss (Pl;hshaft ) can be calculated using Equations (26)e(28), respectively:
vshaft ¼
Di u 2
tshaft ¼ lchs
(26)
rv2shaft
(27)
8
Pl;hshaft ¼ lchst
rv2shaft 8
BAshaft
(28)
in which Ashaft is the shaft wetted area. Determining shear stress between water and flights are rather complex. Relative moving of water has two components; the radial component which is orthogonal to the shaft axis and the component parallel to the shaft which causes no friction loss. The relative velocity between water and flights, related shear stress and power loss depend on the radial position of the considered element; therefore, to calculate the power loss due to flights friction (Pl;hflight ), Equation (29) must be integrated from D2i to D2o and radial position from 0 to 2p. Do 2
ð 2ðp
Pl;hflight ¼ B
lf 1 r 8
Di 2
2.3.4.3. Hydraulic friction power loss. Hydraulic friction power loss (Pl;h ) occurs due to fluid motion and its viscosity when it contacts with the screw and trough. In an AST system, a portion of the trough, central shaft and flights are directly in contact with the
(22)
8
0
Do 2
r 3 u3 dAf 1 þ B
ð 2ðp
lf 2 r 8
Di 2
r 3 u3 dAf 2
(29)
0
in which lf 1 and lf 2 are Darcy-Weisbach friction factor for the upstream surface and downstream surface of the flights, and subscriptions 1 and 2 are corresponding to the upstream surface and downstream surface of the flights, respectively. The values of the
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wetted surfaces area of the flights (dAf 1 and dAf 2 ) are calculated using Equations (30) and (31), respectively:
0 ; z1 > zwl pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 4p r þ S rdrdq; z1 zwl 2pr
(30)
0 ; z2 > zwl pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ f 4p2 r 2 þ S2 rdrdq; z2 zwl 2pr
(31)
dAf 1 ¼ f
dAf 2
The total hydraulic friction power loss is calculated using Equation (32)
Pl;h ¼ Pl;ht þ Pl;hshaft þ Pl;hflight
(32)
2.3.4.4. Submersion power loss. To calculate the submersion power loss (Pl;S ), an empirical equation derived from experimental results by Kozyn and Lubitz [26] was used in this research for our allowed submersion ranges defined by Equation (33).
Pl;S ¼ ð0:01765Qnd 0:1397Qnd þ 0:1989Þ:Pideal
(33)
in which Qnd is the non-dimensional flow calculated using Equation (34)
Qnd ¼
uS ðD2 D2i Þ 2pQt o
(34)
2.3.5. Mechanical power calculation Considering the flow leakages and power losses in the ideal power, mechanical power can be calculated by Equation (35).
Pmech ¼ Pideal :ð1
Qgl þ Qo Pl;b þ Pl;OE þ Pl;h þ Pl;S Þ:ð1 Þ Qt Pideal
(35)
Note that generator power loss is not included in the above equation as well as in this research. Finally, screw mechanical efficiency (hmech ) is calculated using Equation (36):
hmech ¼
Pmech Pideal
(36)
Based on the described Equations above, a mathematical model of AST was implemented in MATLAB 2013a environment to design appropriate AST for any condition. As hydraulic parameters like water depths and volume flow rate are calculated using the ICSS model, the AST mathematical model is started to run. To find the optimum values of the radial element (dr) and angular element (dq) for numerical integration, the angular 2p , and several radial elements element was first assumed to be 360 were then investigated. The model convergence results showed that the volume and torque of a single bucket remain constant for dr 0:0075 ; therefore, dr ¼ 0:0075 was selected to the calculations. About ten dr values larger than the optimum value were investigated. 2.4. East Aghili canal specification and its simulation Irrigation canals are conveying water from places with a higher height to those of with a lower height. Water is transformed due to its potential and kinetic energies. There are some energy dissipater
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structures to lose the extra energy of flowing water in some places. These losses are usually as heat losses. Here, this hydraulic energy is used for electricity generation. The ASTs can be used for this purpose, but the existing conditions of the canal must keep without any change. In an irrigation canal, water depth should be controlled at a dead band in order to deliver a constant volume flow rate to the turnouts. The dead band is a margin around target depth (usually ±10%) within which water level variations are accepted. Therefore, substituting existing structures with an AST, water depth must remain within the dead band as much as possible, and an AST in such a condition must be designed. The east Aghili canal, located in Aghili district in Khuzestan province in southwest Iran (Fig. 7) was used in this study. It has 20 rectangular turnouts and 11 check structures. The canal length is 16.215 km, Manning's roughness coefficient is 0.017 and trapezoidal cross-section side slopes is 1:1. The base width of the canal is 1.5 m from 0 to 9.485 km and 1 m from 9.485 to 16.215 km. The bed slope varies along the canal between 0.0001 and 0.0004. The turnouts are rectangular gates with width and height of 0.6 m and 0.6 m, respectively. Also, the width of all check structures are equal to the canal width and their heights are 0.8 m in the first reaches and 0.6 m in the last reaches. A check structure controls water depth within the dead band at the target depth. At least one turnout is located between two successive check structures in this canal. According to the capacity of the turnouts, a fraction of water exists from canal to each turnout for supplying the farmers need; therefore, the volume flow rate decreases along the canal. The volume of water which passes from each check structure is contributed to a corresponding check structure power generation. In some check structures location, there is a drop from which water falls to the next reach to dissipate extra energy of passing water. A view of the investigated canal is shown in Fig. 8. The main parameters of the structures except turnouts are given in Table 1. To exactly deliver water to the turnouts, water depth at upstream of the check structures must remain within the dead band and as much as possible at the target depth. In this research, the first check structure (check drop-1) is only examined to design an appropriate AST for a better explanation of the methodology. In the design stage, water depth at upstream of the check structure is designed exactly at the target depth (design depth); therefore, the total energy value upstream of the check drop-1 is the sum of water height and water depth at this point. To calculate water depth downstream of the check structures at the specified volume flow rate, the ICSS simulations on the canal are needed. The net head H is the difference between the energy at upstream and downstream of the check structure.
2.5. ICSS hydrodynamic model The ICSS 4 (ICSS version 4) software was used in this research as an irrigation canal simulation model for simulating the east Aghili canal. Using the ICSS outputs, available head and hydraulic power can be calculated. This model is a fully hydrodynamic model [29]. It solves partial differential Saint-Venant Equations and simulates an open canal water conveyance system with various structures. Various hydraulic and hydrologic conditions are the model inputs as boundary and initial conditions. This model was widely used in many studies. The inputs to the ICSS model are physical and hydraulic parameters, described in the second paragraph of the previous section as well as Table 1. The ICSS outputs are water depth profile along the canal and volume flow rate of the structures.
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Fig. 7. Location of the east Aghili canal in Aghili district [27].
2.6. Validation To validate the developed Archimedes screw model, Lubitz et al. [25] experimental data was used. The screw specification used in Lubitz et al. [25] model is given in Table 2. The results of the Lubitz et al. [25] experimental model and the developed model in this research are illustrated in Fig. 9. As shown, the model results have good agreement with the experimental data, and could accurately Fig. 8. A view of the east Aghili canal, a) downstream and b) upstream.
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Table 1 The main parameters of the east Aghili canal structures except turnouts. Structure name
Water height at upstream of the structure (m)
Water height at downstream of the structure (m)
Target depth (m)
Passing flow
inlet (reservoir) Check Drop-1 Check-1 Check-2 Check-3 Check Drop-2 Check-4 Check-5 Check-6 Check-7 Check Drop-3 Check-8
195.642 192.304 188.945 188.205 187.263 185.804 183.164 182.404 181.714 180.992 179.646 178.184
195.642 191.194 188.937 188.25 187.22 183.844 182.964 182.254 181.604 180.904 179.244 178.024
1.25 1.25 1.15 1.15 1.05 1.05 1.05 0.95 0.85 0.75 0.75
1.47 1.22 1.07 0.94 0.79 0.67 0.61 0.55 0.48 0.36 0.25 0.15
predict the screw power specifically around optimum point, i.e. for rotation speeds of 7e14 rad/s.
Table 2 Lubitz et al. (2014) experimental screw specification used for validation. Parameter
variable
unit
value
Outer diameter Inner diameter Screw length Pitch Flights Number Rotation speed Volume flow rate head Inclination angle Gap width
Do Di L S N
cm cm cm cm rad/s l/s cm ᵒ cm
14.6 8.03 0.584 0.146 3 10 1.13 25 24.9 0.0762
u Qt H
b Gw
3. Results and discussion In this section, the results of the ICSS hydrodynamic model for prediction of the depth and hydropower potential are first presented. In the next step, the results of the screw performance under variation of screw length, flight number and inclination angle are presented. Finally, the effect of canal volume flow rate and depth are investigated on the screw efficiency. 3.1. ICSS hydrodynamic results
Fig. 9. Model validation using Lubitz et al. (2014) experimental data.
In this section, the results of the ICSS hydrodynamic simulation are presented. As mentioned, when the existing structures are replaced with the desired AST, it must be tried to do this without any considerable changes in the existing conditions of the canal as well as with low civil works. Designed water depths upstream of the check structures were target depths. Water depth downstream of the check structures was simulated for the inlet volume flow rate of 1.47 m3/s which is the design flow of the canal inlet. The design volume flow rate for the check drop-1 is 1.22 m3/s. Available head and hydraulic power in different locations of the east Aghili canal were calculated (Table 3). As seen in Table 3, the overall hydraulic power can be produced in the east Aghili canal is 65.9 kW. In this research, only the check drop-1 have been considered to design an optimum AST using the developed model. The accumulative hydraulic power in the first five reaches of the east Aghili canal is about 77.8% of the total hydraulic power due to large volume flow rates passing the corresponding check structures.
Table 3 Water depths at upstream and downstream of each check structure, available head and hydraulic power. Structure name
Water depth at upstream of the structures (m)
Water depth at downstream of the structures (m)
Available head (m)
Hydraulic power (kW)
inlet (reservoir) Check Drop-1 Check-1 Check-2 Check-3 Check Drop-2 Check-4 Check-5 Check-6 Check-7 Check Drop-3 Check-8 Sum
0.584 1.25 1.25 1.15 1.15 1.05 1.05 1.05 0.95 0.85 0.75 0.75
0.584 0.529 0.717 0.82 0.528 0.588 0.622 0.59 0.529 0.388 0.295 0.249
1.831 0.541 0.285 0.665 2.422 0.628 0.61 0.531 0.550 0.857 0.661
21.9 5.7 2.6 5.2 15.9 3.8 3.3 2.5 1.9 2.1 1.0 65.9
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Fig. 10. Volume flow rate and water depth variations in check drop-1 during the third month of the winter season.
Table 4 The screw specifications for the check drop-1 in the east Aghili canal. Parameter
variable
unit
value
Outer diameter Inner diameter Pitch Gap width Fill factor Volume flow rate Head Water density Gravitational constant
Do Di S Gw f Qt H
m m m mm m2/s m kg/m3 m/s2
1.5 0.75 1.5 0.762 1 1.22 1.831 1000 9.81
r g
Volume flow rate changes during the cultivation season because of different water requests of the farmers. According to the Author investigation and simulations by ICSS, these variations are important in the third month of the winter season, 2011 (Fig. 10), in which crop water requirement and consequently flow variations in the check drop-1 is high. As shown, water depth is always within the dead band by regulating check drop-1 while flow is varying. 3.2. Design criteria To design an appropriate AST for substituting instead of the check drop-1, some considerations were made. Since the canal geometry changes must remain minimum, the outer diameter of the canal was set to be equal to the base width of the canal, i.e. Do ¼ 1.5 m. Based on [18] questionnaire survey on almost 400 installed commercial screws in Europe, the pitch and the outer diameter of the investigated screws were nearly equal, and the inner diameters were half the outer diameters. So, this accepted values for the commercial structures were used for the pitch and inner diameter values. The last ratios, i.e. S ¼ 1.5 m and Di ¼ 0.75 m, were taken in this research. Also, the optimum performance of the ASTs in term of fill factor reported f ¼ 1 was used [25]. The screw parameters for the check drop-1 in the east Aghili canal are presented in Table 4. Several simulations were performed based on the various inclination angles, flights number, and screw lengths to obtain the optimum structure of an AST for using instead of the check drop-1 in the east Aghili canal. The same methodology can be used for designing the optimum structure of an AST for generating with the highest mechanical power in the other structures of the canal. All power losses existed in an AST system were taken into account in the modeling.
Fig. 11. The screw performance for variation of screw length, and inclination angle at N ¼ 1.
3.3. Structural parameters In this section, the AST performance under variation of different structural parameters including screw length, flights number and inclination angle was considered and optimized. Fig. 11 shows the screw efficiency variation under the screw length and inclination angle variations with the flight number of 1. As shown, with an increase of the inclination angle, the screw efficiency increases for all lengths until it reaches the peak point and then it decreases quickly. Since the volume flow rate is constant, the screw rotation speed must increase with the increase of inclination angle and consequently mechanical power will be increased as well as efficiency. After peak point, both hydrostatic pressure and therefore generated torque decrease and friction power losses increase which cause efficiency decreases quickly. Since upstream and downstream water depths are constant, the minimum value of the inclination angle differs for each screw length. The minimum value of inclination angle for the shorter screw is higher than that of for larger screw; therefore, curves move to the left hand with a screw length increase. In case of peak point on the curves, peak point for screw length of 4 m is 44.3%. As screw length increases, bucket numbers and consequently torque, mechanical power and efficiency all increase as well as friction power losses. In screw length of 6 m produced
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mechanical power is highest and friction power losses are not yet dominant in the system. Increasing screw length to the 7 m, mechanical power is still increasing but the values of the friction power losses are very high (friction power loss in the rotational direction is a function of rotation speed with the order of 3), and therefore peak point falls down. As seen in Fig. 11, the highest efficiency was obtained 90.83% for the screw length of 6 m, inclination angle of 20 and flight number of 1. This is the best performance compared to the other investigated screw lengths. Such a high efficiency in the AST system was reported in Ref. [22] and by Ritz-atro company in Germany (www.ritz-atro.de). Since screw length and net head are constant during each modeling, therefore minimum value of the inclination angle for each length is different. For the optimum screw length, efficiency variation under the screw inclination angle and flights number variations were shown in Fig. 12. Inclination angle ranges between 17O and 45O, and flight numbers change from 1 to 5. The Archimedes screw with the flight number of 1 resulted in the best performance of 90.83% atb ¼ 20+ . When flights number increases at a specific screw length, friction losses increase and cause the efficiency to be decreased. Fig. 13 depicts a variation of the mechanical power under variation of flight numbers and inclination angles at the screw length of 6 m. The mechanical power of the point with peak efficiency is 19.9 kW for N ¼ 1 and b ¼ 20+ as efficiency diagram (Fig. 12). Since the hydraulic power is constant and is equal to 21.9 kW, values of the efficiency and mechanical power have the same behavior. Fig. 14 shows the variation of power losses, mechanical power, rotational speed, and torque under variation of inclination angle at L ¼ 6 m and N ¼ 1. It could be seen in Fig. 14 that as the inclination angle increases the screw rotation speed also increases in order to stay a constant volume flow rate passing under the check drop-1 at the design value of 1.22 m3/s. Also, as the inclination angle increases, the screw end is submerged within the outlet receiving canal because screw length and water levels at the upstream canal and downstream receiving canal are all constant. Increasing screw rotation and screw submersion cause bearing power loss, friction power loss and submersion power loss increase and to be dominant in the system. Therefore, efficiency decreases after inclination angle ofb ¼ 20+ . While power losses are increasing, the mechanical power is decreasing. At b ¼ 25:5+ , the mechanical power and sum of all power losses are equal and then power losses are become greater than mechanical power, meaning all powers converted to the power losses.
Fig. 12. Efficiency variation as a function of screw inclination and flights number for screw length of 6 m.
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Fig. 13. Variation of the mechanical power under variation of flight numbers, and inclination angles at screw length of 6 m.
Fig. 15a, b, and c show variation of efficiency investigated under variation of inclination angles, flight numbers for screw length of 4 m, screw length of 5 m, and screw length of 7 m, respectively. Also, Fig. 16a, b, and c show those of for the mechanical power. These behaviors are the same as those of for screw length 6 m, and the same discussion and reasons may be presented. It may only be noticed that for screw lengths of 4 and 5 m, efficiency corresponded to the flight number of 3 are higher. For screw lengths 7 m, this occurred at N ¼ 2. 3.4. Performance parameters Effect of volume flow rate on the AST performance was considered in this section. As said, analysis of the volume flow rate of the canal and the ICSS simulations showed that the water flow ranges between 1.06 and 1.35 m3/s at the check drop-1. Considering the target depth and the dead band values, water depth deviation is between 1.125 and 1.375 m (±10% of the target depth) which are upper and lower limit of the dead band, respectively. In Fig. 17, efficiency and mechanical power of the AST were considered under volume flow rate variations. The optimized AST have the flight number of 1, screw length of 6 m, and the inclination angle of 20, the rotation speed of 9.54 rad/s, upstream water depth of 1.25 m and design flow of 1.22 m3/s. The effect of the flow variations was investigated for the optimized AST (Fig. 17). There are some important points in Fig. 17 as volume flow rate was changed between its maximum (1.35 m3/s) and minimum (1.06 m3/s) values. As an AST is substituted in the canal, water depth upstream of the AST is controlled by AST mechanism. Water depth at the downstream canal is always constant because there is a weir at the end of the downstream canal. As volume flow rate to the check drop-1 is increasing from the lower flow and since rotation speed is constant, the resultant pressure and torque values increase. This fact increases produced mechanical power. Also, the volume flow rate increase causes the hydraulic power to be increased. In this condition, efficiency decreases because the volume flow rate has more impact on the mechanical power than hydraulic power. For lower volume flow rate, the efficiency is higher, but the mechanical power is 17.24 kW. The mechanical power at the optimum point is 19.90 kW and corresponding efficiency is 90.83%. As the maximum point is reached, optimum efficiency and maximum produced mechanical power are reached. Also, the water level is reached to the highest point of the inner cylindrical shaft means fill factor is 1. After this point, the hydraulic power increase will
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Fig. 14. Variation of power losses, mechanical power, rotational speed, and torque under variation of inclination angle at L ¼ 6 m and N ¼ 1.
Fig. 15. Efficiency of the screw under variation of inclination angles, flight numbers, at a) L ¼ 4 m, b) L ¼ 5 m, and c) L ¼ 7 m.
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Fig. 16. Variation mechanical power under variation of inclination angles, flight numbers, at a) L ¼ 4 m, b) L ¼ 5 m, and c) L ¼ 7 m.
Fig. 17. The screw performance for a range of volume flow rate variations.
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Fig. 18. Water depth variation after the optimum designed AST installing.
Table 5 Optimum values of the screw for various flights number.
N¼1 N¼2 N¼3 N¼4 N¼5
Inclination angle (ᵒ)
Screw length (m)
Mechanical power (kW)
Efficiency (%)
20 26 22 26 26
6 6 7 6 6
19.9 19.23 18.06 15.8 13.76
90.83 87.8 82.41 71.2 62.8
continue because volume flow rate increases and contributed water depth in hydraulic power generation is fixed; therefore, overflow leakage will occur and mechanical power is reducing. Design volume flow rate and design head are equal to 1.22 m3/s and 1.25 m respectively. The maximum efficiency is expected to be occurred at the design flow rate and design head. The maximum mechanical power occurred at the design flow rate, but efficiency was not maximum at this point. The reason for this phenomena is that a dead band must be defined in irrigation canals. This causes water depth is not fixed at the target depth exactly, but it is established within the dead band. This causes water height contributed to hydraulic power to be variable and between upper and lower dead band. Depending on the water depth position within the dead band, the hydraulic power and consequently efficiency are variable. Therefore, maximum efficiency does not occur at design flow rate necessarily. The water depth variations in Fig. 17 confirm this claim. Water depth in the presence of the AST was added to Fig. 10 and illustrated in Fig. 18 to have a comparison between flow and water depth variation before and after the AST application. As seen, when volume flow rate variation is significantly higher than design flow, for example, 1.35 m3/s, water depth at upstream of the dead band exceeded upper dead band limit; however, it does not have considerable deviation. Also, water depth decreases for less volume flow rate than design flow and vice versa regardless of the initially established water depth. In could be concluded that mechanical power for the designed AST is between 17.24 kW and 19.90 kW and the canal mechanism remain almost constant for most of the volume flow rate occurred in the canal. There was only a small impact on the water depth for high volume flow rate. Now, ASTs can be suggested to be applied in the irrigation canals guarantying high efficiency. Although N ¼ 1 was investigated as an optimum choice,
efficiency and mechanical power for other values of the flight number were acceptable (Table 5). For example, for N ¼ 3 which is a typical value for the flight number, the mechanical power was obtained 18.06 kW and corresponding efficiency was 82.41%. For real plants, financial efficiency is more important than mechanical efficiency, and these two do not usually occur simultaneously. In a study like this, it is difficult to estimate financial efficiency, because the cost of parts and construction is difficult to estimate. This work only was investigated mechanical power, but not electrical power or financial efficiency. 4. Conclusions In the current study, a numerical model of screw system was developed in MATLAB 2013a to the optimal design of an appropriate AST for substituting instead of irrigation canal structures. This optimization was conducted for a case study in east Aghili canal, Khuzestan province, Iran. The first check structure (check drop-1) was considered for this purpose, and an optimum AST was designed to be substituted instead of check drop-1. The ICSS hydrodynamic model was used for simulating the canal condition including water depth and flow in the structures. To design an optimum AST, different structural parameters of the screw turbine were considered including screw inclination angle, number of flights, and volume flow rate of water. Available head and hydraulic power in different locations of the canal were calculated using ICSS. The overall hydraulic power that can be produced in the canal was obtained 65.9 kW. Hydraulic power existing in check drop-1 was 21.9 kW. Due to existing conditions of the canal and for low civil works, the outer diameter of the screw was chosen equal to the canal width (1.5 m). Also, the inner diameter and pitch of the screw were selected 0.75 m and 1.5 m, respectively.
K. Shahverdi et al. / Renewable Energy 145 (2020) 2130e2143
The best screw, with the highest efficiency, which can be substituted instead of check drop-1 was a screw with the length of 6 m, inclination angle of 20 , flight number of 1, and the rotation speed of 9.54 rad/s. The highest efficiency was obtained 90.83% for the optimum screw, and corresponding mechanical power was obtained 19.90 kW. The mechanical power for a wide range of the volume flow rate around design flow (1.22 m3/s) occurred in the canal in the third month of the winter season, in 2011, was ranged between 17.24 kW and 19.90 kW. The results showed that the optimum screw designed in this research have no considerable effect in the canal condition and can be substituted successfully instead of the check drop-1. Substituting irrigation canals check structures with an optimum AST which can be designed using this research methodology is recommended for future works. Acknowledgement Reyhaneh Loni, B. Ghobadian, and G. Najafi are grateful to the Tarbiat Modares University (http://www.modares.ac.ir) for financial supports given under IG/39705 grant for renewable Energies of Modares research group. References [1] K. Kusakana, J. Munda, A. Jimoh, Economic and environmental analysis of micro hydropower system for rural power supply, in: Power and Energy Conference, 2008. PECon 2008, IEEE 2nd International, 2008, pp. 441e444. IEEE. [2] S. Khurana, A. Kumar, Small hydro powerda review, Int. J. Tumor Ther. 1 (2011) 107e110. [3] J. Du, H. Yang, Z. Shen, J. Chen, Micro hydro power generation from water supply system in high rise buildings using pump as turbines, Energy 137 (2017) 431e440. [4] M.R.B. Khan, R. Jidin, J. Pasupuleti, S.A. Shaaya, Optimal combination of solar, wind, micro-hydro and diesel systems based on actual seasonal load profiles for a resort island in the South China Sea, Energy 82 (2015) 80e97. [5] H. Lavri c, A. Rihar, R. Fiser, Simulation of electrical energy production in Archimedes screw-based ultra-low head small hydropower plant considering environment protection conditions and technical limitations, Energy 164 (2018) 87e98. [6] E. Tasdemiroglu, Development of small hydropower in Türkiye, Energy 18 (1993) 699e702. [7] A. Kozyn, S. Ash, W. Lubitz, Assessment of archimedes screw power generation potential in Ontario CCTC 2015 paper number 1570095585, in: Climate Change Technology Conference, 2015. Montreal. [8] REN21, Renewables 2013: Global Status Report, Renewable Energy Policy Network for the 21st Century, 2013. [9] L. Lisdiyanti, Y. Hizhar, B. Yulistiyanto, Effect of Flow Discharge and Shaft Slope
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