Design and analysis of a hydro-powered water turbine pump: a sustainable irrigation infrastructure

0

At the eye of the impeller

1

At the inlet of runner or impeller

2

At the outlet of runner or impeller

m

In meridional direction

u

In the tangential direction

x

In the axial direction

C

Absolute velocity

U

Blade speed

W

Relative speed

D

Diameter

R

Radius

H

Design head for turbine

Q

Design flow rate for turbine

h

Delivery head of the pump

q

Delivery flow rate for turbine

η

Efficiency

h_∞

Theoretical head for pump

N_max

Max possible speed for turbine

N

Rotation speed of turbine

C_p

Pfleiderer correction factor

LE

Leading edge

TE

Trailing edge

Nepal has 65% of its population engaged in agriculture, while this sector contributes only 27% of the GDP of the nation (Government of Nepal 2021). It clearly shows the lack of commercialization in the agricultural sector of Nepal which is due to a massive share of smallholder farms. Here, 2.7 million smallholder farms account for 70% of the food produced with an average smallholder farm size of only 0.52 ha (Raj & Hall 2020). Among many other problems leading to the low productivity of the smallholder farms, lack of irrigation facilities and poor distribution of irrigation networks are major (JICA 2013).

In Nepal, only 54% of cultivated land is facilitated with irrigation out of which only one-third gets irrigated all year round (WECS 2017). Even in the lower plains, where clusters of irrigation projects have been launched, the problem persists equally due to the lack of on-farm irrigation facilities and insufficient tertiary canals (JICA 2013). A large number of smallholdings certainly pose great difficulty in expanding tertiary networks. So, plot to plot irrigation is practiced in most cases resulting in heavy loss of water (JICA 2013). An alternative to this practice would be the deployment of on-farm pumping systems.

Pumped irrigation is ruled by fuel-based and electrical pumps worldwide and the case of Nepal is no different. However, these pumps turn out to be expensive for smallholders farmers in a long run because of the high operation and maintenance costs associated with each. They are also not an environment-friendly option, considering the emissions from fuels and the high energy intensity of electrical pumping. In addition, the problems related to the distribution of power and fluctuating voltages in Nepal add to the ineffectiveness of the electrical pumping system (Pande et al. 2016). So, as a better alternative for environment-friendly and inexpensive irrigation infrastructure, this paper proposes the design methodology of a community-operated hydro-powered pump called water turbine pump (WTP). The WTP system requires much less civil works than expanding tertiary canal networks and can also work as an infrastructure for water supply in combination with a water treatment facility. However, this infrastructure may not be economically viable for individual farmers and rather is recommended to be installed and operated by a community or a governing body.

WTP consists of a turbine and a pump linked together in such a way that the rotational speed of the turbine is utilized by the pump to lift the water to a certain head. The combination of turbine and pump may vary according to the head and flow rate available for the turbine and the delivery conditions required for the site. WTPs are advantageous over their RE counterparts such as solar- and wind-powered pumps, as they: (i) can operate 24 hours a day, regardless of weather fluctuation, in a more controlled and predictable manner, (ii) have higher power to size ratio, leading to a compact size, and (iii) are mechanically simpler and more efficient (Zambrano et al. 2019). Moreover, since there is no electromechanical or any other intermediate conversion involved, they are easy to fabricate at a local level, require less skilled manpower for operation and maintenance, and operate at zero cost.

The history of WTPs can be traced back to the 1920s when they were reported to be in use specifically in China where, by 1979, about 60,000 WTPs were irrigating 400,000 ha (Fraenkel 1986). However, more recent documents on this technology are missing. In some documents, they have been classified according to the diameter of the propeller and the ratio of the installation head to the delivery head (head ratio). Series of models have ranged from 10 to 120 cm in rotor diameter and from 4:1 to 6:1 in head ratio. Some products with higher head ratios of 8:1, 10:1, 12:1, 18:1, and 20:1 have also been reported which seems very promising (Tsutsui 1990). However, the available literature and documentation on WTPs are insufficient to support the design decisions. The research and development on this topic seem to have lagged significantly behind due to the takeover of fuel and electricity-based pumping systems. So, the main objective of this paper is to provide technical documentation on WTP technology. This paper is expected to (i) introduce the WTP technology to agriculture practitioners and infrastructure planners, (ii) provide a methodology of the hydraulic design of a WTP to engineers, and (iii) give a head start to the long-stagnant research and development of WTPs.

In this paper, we have presented a detailed methodology for the hydraulic design of WTP and evaluated the performance of each hydraulic component using Computational Fluid Dynamics (CFD). The CFD techniques used in this paper have been verified experimentally by other researchers. Finally, we have predicted the performance of the overall system.

The design methodology of a WTP is highly case-specific. Moreover, the mechanical power generated by the turbine and the power required by the pump require meticulous harmonization. So, a site was defined, and the hydropower resources were assessed. The types of the turbine and the pump were selected based on resource availability, deliverables, and their compatibility with each other. They were designed and their performances were evaluated using CFD. Finally, the system was modeled in SOLIDWORKS, and its characteristics were defined. An overview of the design methodology is depicted in Figure 1.

This paper focuses on the design of WTP for low head and high flow rate application, specifically in the plains (Terai region) of Nepal. The design is in reference to the specification of a canal network situated in Bethani, Thakurdwara VDC, Bardiya. The source stream is originated from the Karnali River and is one of the canals within the network of the Surya Patuwa irrigation plant. A fairly stable average annual flow of 1.5 m³/s flows through the canal. A total head of 3.3 m and a flow rate of 0.15 m³/s can be made available after simple civil construction. A basic layout of the installation site is presented in Figure 2.

Considering that the efficiency of the canal lies in the range of 90–95% (Harvey et al. 1993), the system was designed for (i) design head (H) = 3 m and (ii) flow rate (Q) = 0.15 m³/s.

The selection of a turbine requires careful consideration of the head and flow rate available at the site. Propeller turbine is selected for this case, as (i) it is suitable for the low head (as low as 1 m) and high flowrate applications, (ii) it has a high specific speed that can run a centrifugal pump, and (iii) it is easier and cheaper to fabricate locally compared to its other counterparts (Williamson et al. 2014). The selection of the pump, on the other hand, depends on its application. Here, a centrifugal pump was selected, as it provides a high flow rate (Dixon & Hall 2013) as desired for flood irrigation purposes at the site.

In this case, the propeller turbine can be directly coupled with a centrifugal pump and can be installed directly into a canal drop or a weir on a canalized river where the head of 1 – 5 m is available. The resulting system leads to a compact configuration. However, in the case of the high head requirements, a reciprocating pump may be chosen.

Figure 3 shows the schematic diagram of the WTP installed in a canal drop.

Considering a reasonable efficiency of 85% (JICA 2011), the theoretical power output of the propeller turbine was calculated to be 3,750 W. The head ratio of WTP was targeted in the range of 5:1–6:1 (Tsutsui 1990). A design head (h) of 17 m and a delivery flow rate (q) of 16.4 lps were selected after iterations with several combinations, considering two criteria: (i) the value of head coefficient and flow coefficient shall be within the acceptable range of 0.7–1.3 and 0.05–0.2, respectively (Tuzson 2000), and (ii) the theoretical power required to drive the pump shall be less than the theoretical power output from the propeller turbine.

Considering reasonable efficiency (η) of 85% (Tuzson 2000), the pump was designed for the theoretical head ⁠. Since the propeller turbine and the pump are directly connected by a shaft, the rotational speed of both components is equal.

The propeller turbine design process involves the design of a runner, a guide ring, and a draft tube. The spiral casing could be omitted in this case because the value of H is less than 6 m (Pai 2017). Alternatively, the turbine was designed to be installed into a rectangular channel or an open volute (Susanto & Stamp 2012).

The design of the propeller turbine, presented in this paper, is mostly based on the design methodology for a low head propeller turbine (2–10 m) with output less than 5 KW, provided by Simpson & Williams (2011). The methodology involves the following steps: (i) choosing the right rotational speed (N), (ii) sizing of the runner (diameter and hub-tip ratio), (iii) deciding the number of blades and pitch, (iv) calculating the blade parameters such as flow velocities and angles, and (v) designing the guide vanes and draft tube.

A value of N, less than N_max, was selected such that the specific speed based on power ranged within 255–860 rpm (Hothersall 2004).

The runner diameters were calculated using the statistical relationship provided by Siervo & Leva (1977). A smaller hub-to-tip ratio (less than 0.5) would result in more twisted blades. Thus, for simplicity of manufacturing, a slightly larger than calculated hub-to-tip ratio was used (Simpson & Williams 2011). Although the number of blades suggested was four (Simpson & Williams 2011), the performances of the runners with four, five, and six blades were analyzed. The main parameters of the propeller turbine are summarized in Table 1.

After calculating the sizing parameters, blades were designed. As long as the camber and twist of the blades are preserved, the performance of the propeller turbine does not vary significantly by using a constant thickness profile instead of an airfoil profile (Demetriades et al. 1996). So, to simplify the manufacturing process, blades were designed with circular arcs and a constant thickness. The velocity components and blade parameters, shown in Figure 4, were calculated for five spans distributed equally along the radius. The solidity (i.e. chord length of blade/blade pitch) at the hub of the runner was confined near 1 for minimum profile losses (Chen & Engeda 2019). To incorporate the effect of the flow deviation, the angle of deviation was subtracted from the blade stagger angle. The angle of deviation was calculated using Carter's parameter for the circular arc camber line (Hothersall 2004). The summary of spanwise values and other blade parameters is provided in the Supplementary Material.

For guide vanes, the radial configuration was chosen over axial, as it is more robust. The number of guide vanes was selected to fulfill two criteria: (i) the number of guide vanes shall be greater than the number of runner blades and (ii) their ratio shall not be an integer, to avoid stalling of the runner blades (Kim 2015). Other basic dimensions of the guide vane were calculated as suggested by Nechleba (1957) and Zu-yan (2018). They are summarized in Table 2.

A simple conical draft tube with a divergence angle of 4° was designed. The length of the draft tube was selected to be 2.02 m such that: (i) the length is smaller than the maximum allowed suction head and (ii) the total head available to the runner would be maintained at 3 m. Care should be given to select the length of the draft tube because a length greater than the suction head leads to a destructive phenomenon called cavitation. The cavitation is caused by the loss in pressure that occurs downstream due to the conversion of pressurized flow to the free surface. Aerator tubes can also be employed to control this phenomenon (Yamini et al. 2021). The detailed procedure of draft tube design can be found in Pai (2017).

The design of the centrifugal pump is mostly based on the methodology given by Srinivasan (2008) and Gülich (2010). The design process involves the following steps: (i) determining the inlet conditions (eye diameter, inlet diameter, inlet width, and velocities), (ii) determining the outlet conditions (outlet diameter and velocities), (iii) selecting the number of blades and the blade thickness, (iv) developing blade profile and flow passage, and (v) design of volute.

The rotational speed of the pump is equal to that of the turbine, i.e., 1,450 rpm. The specific speed of 19.63 rpm was obtained which led to the selection of radial configuration of the pump (Girdhar & Moniz 2005). As the pump had low specific speed, the eye velocity (C₀) of 3 m/s was deemed suitable, as they provide good cavitation characteristics (Srinivasan 2008). Using this eye velocity, the diameter of the eye (D₀) was calculated. The iterative procedure suggested by Srinivasan (2008) was then used to calculate the inlet blade angle (β₁) and meridional velocity at the blade inlet (C_m1). An angle of attack of 5° was added to β₁ for having shock-less entry at the blade (Srinivasan 2008). For the determination of outlet conditions, first, the diameter of impeller (D₂) was to be selected. It was assumed in such a way that the flow coefficient obtained was within the acceptable range of 0.05–0.2 (Tuzson 2000). Thus, the impeller diameter of 240 mm was selected, as it satisfied the flow coefficient criteria. It also resulted in a practical blade width at the outlet hence, making the manufacturing process easy. All the necessary calculations for the determination of inlet and outlet parameters were done using the Euler equation of turbomachinery and the velocity triangles. The velocity triangles at the impeller are shown in Figure 5.

Impeller blades with blade outlet angle (β₂) of less than 90° produce backward curved vanes. These types of blades are mostly preferred in centrifugal pumps, as they provide higher efficiency with less secondary loss. According to Srinivasan (2008), for a specific speed of less than 30 rpm, outlet blade angle must be less than 30° to obtain higher efficiency. Since the β₂ of 28° was obtained, therefore, the blades were backward-curved under the required criteria.

For a cast iron impeller, mechanical strength requirements are generally met when the thickness of the blade is 0.016–0.022 times the diameter of the impeller (Gülich 2010). Since thicker blades can withstand high stresses and can be cast or welded easily, the blade thickness of 5 mm was considered to be appropriate. The leading edges (LEs) were filleted, and the trailing edges (TEs) were made as thin as possible. The main impeller parameters obtained are shown in Table 3.

The radial and axial velocities, from the LE of the blade to the TE of the blade, were assumed to vary linearly. The differential equation (4) was then integrated to obtain the streamline. MATLAB code was generated to develop the blade camber line, meridional streamline, and the varying blade width. The data generated were then used for the CAD modeling of the impeller in SOLIDWORKS.

Finally, the volute was designed using the constant velocity method, as it is easier to cast, economical to produce, and efficient in practice (Srinivasan 2008). Assuming a constant flow velocity, the maximum throat area of volute at 360° was first calculated. The throat areas at different wrap angles were then calculated considering a directly proportional relationship between the throat area and the angle. A certain fillet was provided at the cutwater section, and the volute pipe area was increased with a 5° of angle of divergence after the volute made a full 360° wrap angle (Gülich 2010).

All the design data along with codes are provided in the Supplementary Material.

After obtaining all the design points, CFD tools were used to verify the performance of WTP. A single CFD setup for the entire system would be computationally complex. Thus, two different setups, one for the propeller turbine and another for the centrifugal pump, were generated. This paper uses the CFD methods that have been experimentally validated by other researchers for propeller turbines (Vu et al. 2018) and centrifugal pumps (Ding et al. 2019). The analysis was expected to verify the power delivered by the turbine, power requirement of the pump, and the head delivered by the pump.

The propeller turbine domain consisted of three subdomains namely: guide vane domain (S1), rotor domain (R1), and draft tube domain (S2). S1 and R1 were taken as a unit periodic segment of the guide vane and the rotor, respectively, to reduce the computational cost. The structured mesh was generated using Turbo-Grid software for S1 and R1, while the S2 subdomain was meshed using ANSYS Auto-mesh. The meshes generated for the domains are shown in Figure 7. The number of elements in S1, R1, and S2 was obtained as 362,740, 2,308,278, and 93,060, respectively, after a grid-independent test. The boundary layer resolution around the guide vane and rotor blade had a y+ value in the range of 1–2.

The centrifugal pump domain consisted of two subdomains, namely: impeller domain (r1) and volute domain (s1). A unit periodic element of the impeller was used as the r1 subdomain, and a structured mesh was generated in Turbo-Grid. The subdomain s1 had unstructured mesh created in ANSYS Auto-mesh. The meshes generated for the domains are shown in Figure 8. The number of elements in s1 and r1 was obtained as 653,058 and 1,737,491, respectively, after the grid independence test. The boundary layer resolution around the impeller blade had a y+ value in the range of 1 – 2.

ANSYS CFX solver was used for the analysis of both domains. In the case of the propeller turbine, a total pressure boundary condition of 29,341 Pa was applied at the inlet of S1, while an opening boundary condition with static pressure 0 Pa was applied at the outlet of S2 as shown in Figure 9. Frozen rotor configuration was selected on the interface between S1 and R1, and R1 and S2, with specified pitch angles of 40 and 72°, and 72 and 360°, respectively. The advection scheme was set to a blend factor of 0.5, and the turbulence numeric was set to ‘High resolution’ with a physical time step of 2e-4. The RMS residual target was set to 1e-4. The models were solved for steady-state with the K−ω SST turbulence model.

For the centrifugal pump, a total pressure of 0 Pa was specified at the inlet of r1, while a mass flow rate of 16.4 kg/s was specified at the outlet of s1 as shown in Figure 10. Frozen rotor configuration was selected on the interface with a specified pitch angle of 45 and 360°. The advection scheme was set to a blend factor of 0.5, and turbulence numeric was set to ‘Higher Order’ with a physical time step of 4.5e-5. The RMS residual target was set to 1e-5.

Runners with four, five, and six blades were evaluated using CFD. Table 4 summarizes the results obtained by varying the number of blades from four to six.

Under the constant total head of 3 m, the flow rate in the turbine decreased with the increase in the number of blades due to the decrease in the annulus area of the runner. The power generated by the runner and the overall efficiency was observed to increase with the increase in the number of blades. However, the rotor efficiency was found to decrease because of increased losses due to blade friction.

Although four blades were considered optimal from the analytical calculation, the simulation results showed that the five-bladed turbine has matched the design point more accurately. The turbine with four blades would require a flow rate higher than available to achieve the full load condition, which means it will operate at partial load condition under the flow rate of 150 lps. Since the efficiency of the propeller turbine decreases at partial load conditions, five blades were chosen for the final design. Nevertheless, a runner with six blades could also be used, but the addition in the power would not be significant compared to the complication in fabrication it would add.

For an axial turbine, the meridional velocity (C_m) is equal to the axial velocity (C_x) and is supposed to be constant throughout the rotor. The value of C_m obtained from CFD was plotted against meridional distance as well as radial span as shown in Figure 11(a). The theoretically obtained value of meridional velocity was also plotted on the same chart. From the figure, it is clear that axial velocity computed from the simulation was almost constant throughout the runner and near about the analytical value (C_m = C_x = 5.03 m/s). The average value of computed streamwise and spanwise C_m was obtained to be 5.24 and 5.08 m/s, respectively, with standard deviations of 0.16 and 0.4, respectively. The value of C_m was obtained larger than calculated analytically at inner spans and smaller than expected at the hub and tip regions. It is because the boundary layer formed at the hub and tip constricts the area of flow increasing the axial velocity.

The free vortex theory applied for the runner design assumes that the angular momentum at the LE and the TE along the span is constant. Also, for the maximum efficiency of the rotor, it was expected that the tangential fluid velocity (C_u) at the TE be near about zero. Figure 11(b) shows the distribution of C_u.r in the spanwise direction at LE and TE. Theoretically, C_u.r was calculated to be 0.23 at LE and 0.02 at TE, whereas the average value of C_u.r obtained from CFD was 0.32 and 0.16 at LE and TE with 0.078 and 0.076 standard deviations, respectively. The possible explanation for this difference is that since the fluid must overcome some frictional forces while flowing from LE to TE, the flow deviates less than the angle of the blade. It results in the value of C_u being higher than assumed at TE. Similarly, due to the constant angle of attack at all spans of inlet because of flat blade guide vanes, spanwise distribution of C_u.r could not be achieved as steady as assumed during calculation.

For the simplicity of manufacturing, flat guide vanes and twisted runner blades with constant thickness were used instead of an airfoil, which is subjected to certain losses. Figure 12(a) shows the contour of total pressure around 50% of the radial span of the guide vane. The LE of the guide vane is observed to have resulted in a total pressure loss. The profile of the pressure contour suggests that the use of an airfoil cross-section could reduce the loss. Similarly, it can be observed in Figure 12(b) that the LE and TE of the propeller blade has undergone abrupt pressure change (rise at LE and fall at TE) in the direction of flow because of thinner LE and thicker TE. Furthermore, a small region of flow separation can be visualized at the immediate vicinity of the LE due to the use of circular arc camber (Bian et al. 2018). The results also suggest that flow separation is likely to occur in blades with a slight change in an angle of attack of the fluid, i.e., at the off-design conditions. Thus, the off-design performance of the rotor is suspected to be poor.

Figure 13 shows the blade loading characteristics of the circular arc blade. The maximum pressure difference on the blade was observed to be around the maximum camber position at the mid-span. The abrupt changes in pressure at the LE and the TE were observed due to separation at LE and TE.

Figure 14(a) and 14(b) show the pressure and velocity distribution in the pump. The total pressure rose when the water flowed from the LE to the TE. This is due to the energy imparted by the rotor to the water which causes the increase in the velocity as well as the static pressure of the water. In the case of the volute, the total pressure is mostly constant. However, due to the increasing cross-section area, the velocity decreases, as the velocity head is converted into the pressure head. A region of flow separation was also observed from the cutwater towards the outlet.

The characteristics of the impeller were observed under different flow rates of 8, 12, 14, 16.4, and 19 lps by using CFD. Flow separation zones were observed in the suction side of the impeller blades at the flow rate of 8 lps. It is because, at the flow rate much lower than the design flow rate, the flow angle at the inlet is small to cause the flow to separate toward the suction side. As a result, the efficiency also decreases significantly. However, the separation was not detected for flow rates of greater than 8 lps. Figure 15(a) and 15(b) show velocity vectors at 8 and 16.4 lps, respectively.

The effect of change in flow rate at the volute cutwater region was also studied using CFD. Figure 16 shows the velocity vectors in the cutwater region of the volute under different flow rates. It was observed that the flow separation starting from the cutwater toward the discharge side became prominent, as the flow rate increased. As the flow rate increases, the flow accelerates downstream. This leads to a decrease in the static pressure which causes backflow of fluid. Furthermore, the increase in velocity at the outlet causes the flow angle to decrease and deviate from the cutwater toward the discharge, resulting in the separation of flow from the cutwater toward the throat region (Gülich 2010).

At the design point, the pump could deliver a flow of 16.4 lps to a total head of 14.4 m and a static head of 13.5 m with an efficiency of 79%. At this condition, the pump required an input power of 2.92 KW. However, the power output from the turbine was insufficient to drive the pump at that point. To evaluate feasible operation range, the characteristic curves of the centrifugal pump were obtained by varying flow rates at the inlet of the pump. The characteristic curves of the centrifugal pump are shown in Figure 17(a) and 17(b). Theoretically, the head provided by the pump should increase with the decrease in flow rate. After a certain point, the head must decrease even with the decrease in flow rate. The CFD results were observed to be less than the analytically calculated values with a maximum error of 7.5% between the two calculation methods. This deviation is due to the profile losses and the separation losses unaccounted by the analytical method.

Although a 16.4 lps flow rate was selected as the design point, it could be observed from the CFD simulation results that the flow rate of 14 lps could be delivered at the best efficiency point. The efficiency at 14 lps was observed to be 81%, whereas at 16.4 lps, the efficiency was 79%. The increase in efficiency at a lower flow rate is because of the low magnitude of frictional losses subsequently due to the lower flow rates. At 14 lps, the input power required to operate the pump was found to be 2.62 kW which is less than the power output of the turbine. The total head of 15.5 m and the static head of 14.9 m were obtained at this discharge rate.

The section view of WTP assembly is shown in Figure 18. The pump, at the design point, required input power of 2.92 KW, but the turbine could only generate an output power of 2.77 KW, which was insufficient to run the pump. However, at the best efficiency point of 14 lps, the pump only required an input power of 2.62 KW. Thus, a WTP working under the head of 3 m and the flow rate of 150 lps, which could pump 14 lps of water to the height of 14.9 m at its best efficiency point, was obtained. The individual efficiencies of the turbine and the pump were obtained as 63 and 81%, respectively, with an overall efficiency of 50.5% assuming 1% mechanical losses at bearing. The head ratio of 1:5 could be obtained from the design.

In conclusion, this paper presented a methodology that could be used to design a WTP for low head and high flow rate applications, in the case of an irrigation canal network at Bardiya, Nepal. This technology is expected to be a reliable, economic, and environment-friendly alternative for irrigation infrastructure, over fuel, electricity, and other RE-based pumping systems.

To sum up, a WTP was designed using the methodology presented in this paper, and the design was verified using experimentally validated CFD methods. It could utilize the head of 3 m and the flow rate of 150 lps to deliver 14 lps of water to a height of 14.9 m, yielding a head ratio of 1:5 at its best efficiency point. The individual efficiencies of the turbine system and the pump system were obtained as 63 and 81%, respectively, with an overall efficiency of 50.5%, considering 1% mechanical losses at bearing.

The scope of this paper was limited to the hydraulic design of WTP components for given site specifications. This topic has wide prospects to be deployed in irrigation systems and/or water supply systems. Further research and development are required to strengthen its potential, all of which could not be covered in this project due to time and resource constraints. To the researchers willing to investigate this topic further, off-design characteristics of WTP can be analyzed with experimental validation. Furthermore, combinations of various kinds of pumps and turbines can be tested.

All relevant data are included in the paper or its Supplementary Information.