Remote river energy system: an open-source low-maintenance turbine design for remote areas Open Access

Globally, countries are attempting to increase energy supply capacity while ensuring that any energy solution is reliable and affordable for all people (The World Bank Group, 2009). This paper describes a contribution to that effort: the design of a product capable of harnessing energy from a river to be implemented in remote access locations, a remote river energy system (RRES). The concept generates electricity using a water current turbine that drives a dual-action piston pump, pumping water to an on-shore hydro-electric generator. Emphasis is placed on the installation and repair facilities that would likely be present in developing communities, and how these communities would have to interface with the turbine without any external aid, such as with self-repair.

Sustainability is defined as meeting the world's present needs without compromising future generations and includes the key concept that the essential needs of the world's poor must be met with all priority (UN, 1987). The UN Sustainable Development Goals also include access to affordable and clean energy for all, and making cities and human settlements sustainable (Griggs et al., 2013). Therefore there is a definite need for an inexpensive device capable of generating electricity off-grid for poor communities that minimises the time and resources required over the device's operational life.

High costs hinder the progress and deployment of remote river turbines (Kirke, 2019). Minimising the number of components, manufacturing processes and business costs are key considerations throughout this paper in order to mitigate these high costs. As such, it is proposed that the turbine drawings will be published open source. The use of an open-source license will mean the turbine can be made anywhere, by anybody; enabling the potential for rapid deployment of the turbine all over the world. Remote communities and people groups could then build their own turbine and generate decentralised electricity, in an inexpensive manner. The designs will be distributed in a format that conforms to the standards for redistribution outlined in the Open Source Hardware Association definition (OSHWA, 2020).

Floating river and canal turbines are emerging technology. One well-distributed and published example is the ‘Smart Monofloat’ from Smart Hydro Power (Smart Hydro Power, 2015). The same company has also developed a turbine system which can be positioned on the river bed (Smart Hydro Power, 2016). The Smart Monofloat is a very similar design concept to the design proposed here; however, it is very heavily engineered. This means that it requires complete manufacture in a factory, followed by deployment to the required location.

The Ocean Renewable Power Company (ORPC) (ORPC, 2020a) has designed generation systems that are fixed to the river bed. The ORPC systems are larger than the proposed RRES design, and are designed to fulfil a different electrical demand, such as a relatively large settlement in Alaska (ORPC, 2020b), rather than to smaller and off-grid communities. Designs have also been developed for small communities that harness wave power, for example (Castro and Chiang, 2020).

Alternatives suitable for use in remote locations include solar power and small-scale wind power (Razmjoo et al., 2019). Solar power is most useful nearer the equator (Boddapati and Daniel, 2020). Wind power offers a good method for larger open spaces (Al-Bahadly, 2009). However, if the proposed location is heavily forested or in a valley, it may not get enough wind or clear enough access to the sun, which are required to provide continual power (Anyi et al., 2010; Bansal et al., 2005; Tong, 2010), and multiple renewable sources could provide a solution. Additionally, river or tidal systems could be used in high-latitude locations as there is very limited exposure to sunlight for solar power during winter.

While there are pre-existing river turbines with similar designs and purpose to the proposed design, they require complex and specialist manufacturing techniques (ORPC, 2020a; Smart Hydro Power, 2015). The blades and specialist components of the RRES could be purchased from a supply company, but the rest of the design can be manufactured in an inexpensive way, reducing overall capital cost. Designing the turbine for a minimal number of moving parts (Orme and Masters, 2005) should reduce the need for expensive installation and maintenance.

The goal of an easy-to-repair, robust system was formalised into the design specification shown in Table 1. Offshore, the RRES is a stationary floating platform which suspends a two-blade turbine in the flow of the river. The platform is held in situ by two submerged cables which can be used to angle the turbine directly into the flow. The platform comprises a chassis constructed from C and L beams, which can be coated in a corrosion-resistant paint, and decommissioned barrels; as shown in Figure 1. The bow at the front aids buoyancy, especially in higher-flow-rate scenarios. The power output of the generator and other parameters across the operational river velocities can be seen in Figure 2. A series of iterations of rotor diameter and rated power was made, using the overall maximum lifting weight as a constraint, resulting in a 3.6 m dia. rotor producing 3 kW electrical output (after losses) at a rated river speed of 1.76 m/s. This is a compromise between capturing energy efficiently at a range of flow speeds without the excess structural costs that would be required to continue generating at higher, infrequently occurring, flow speeds.

The blades are made using a fibreglass shell to create the profile and a central steel spar for stiffness. The blades, hub and shaft are filled with closed-cell foam to ensure neutral buoyancy when in the river, as per the specification in Table 1. They harness energy in the river by turning a gear system to actuate the power take off (PTO) system, comprising a dual-action piston pump and one-way valves. The use of a gear system avoids the need for a chain or belt drive, which would be more susceptible to damage and wear.

The PTO pumps water to the onshore 3 kW hydro-electric generator through a closed-loop system (Figure 1). The use of a closed-loop water system allows all of the electronics to be kept onshore, in accordance with the design specification, avoiding expensive submerged electrical cables. A closed-loop control system is used to operate a throttling valve which regulates the flow of water. This keeps the pump flow within operating conditions of the generator and stops the blades if the river flow exceeds 4 m/s.

The turbine is installed by lifting it into the river using a truck-mounted crane, then towing it into position with a boat and fixing the two mooring lines. The device is designed to be sited up to 200 m from the shore. An in situ inspection and wet service would be required every 6 months. As all offshore components are mechanical, with all electrical components being on shore, the servicing process is simplified and safer to carry out. During this service, the turbine blades would be stopped using the on-shore control system. More thorough inspections of components would be done onshore during dry services every 2.5 years.

All components have been designed with minimal complexity so that they can be manufactured from readily available components and generic materials using basic manufacturing techniques. While there are specialist components used in this design, many could be purchased off-the-shelf or constructed and supplied separately.

The turbine was developed through an iterative system design process. From concept drawings, initial design calculations were formalised into a specification, designs of component parts revised in parallel and then tested with a design review. After this, designs were iterated and calculations undertaken, then tested with failure modes and effects analysis (FMEA) (Masters et al., 2020) and a final design loop conducted. The last stage was refinement of connections between subsystems, assembly design and drawings. Two notable stages in the design led to significant design alterations in order to improve the functionality of the turbine. These were the completion of the FMEA and the results of a 1/50th scale model test, carried out in a flume.

The initial design iteration began by modelling the blade dynamics for a simple two-bladed rotor in the Matlab software program (detailed in Section 4.1). This gave initial blade dimensions and preliminary power, torque and thrust values to be used in the remaining component designs. During later design iterations, the PTO and control system model was developed in the Simulink software program (Section 4.2), giving the complete operating characteristics of the RRES to validate the components against. The values from the turbine loading and PTO models provided vital information for simulation and analysis of the overall design. Nodal analysis, finite-element analysis (FEA) and computational fluid dynamics (CFD) were utilised during the component design stage. These simulations were used to refine the design of individual components, and the stability of the device as a whole was tested experimentally using a flume and 1/50th scale model.

The FMEA focused on each individual component, examining how any given component could hinder the performance of the turbine or render the component or turbine inactive. Examples of changes resulting from this analysis included the introduction of a closed-loop pump system (to prevent grit from entering the piping) and the identification of quality assurance measures to be applied during manufacture, such as checking the bearings to ensure concentricity. Further details of this process and its results can be found in the report by Masters et al. (2020).

The loading characteristics for a turbine 3.6 m in diameter, with a 0.5 m dia. hub, were generated using blade element momentum theory (BEMT) (Chapman et al., 2013). The hub and rotor diameter were chosen to comply with the specification in Table 1. The turbine blade geometry and corresponding coefficients of power and thrust were taken from Mycek et al. (2014), and the lift and drag coefficients for the aerofoil section used in the design were taken from Togneri et al. (2020) and Zhuang et al. (2012), respectively.

Figure 3 shows the initial turbine design performance, with a tip speed ratio (TSR) at the optimal point for this rotor, TSR = 3 (Edmunds et al., 2020; Mycek et al., 2014). The power, torque and thrust generated by the turbine at higher flow rates are far greater than required (Table 1). To mitigate this and reduce overall loads to a more easily managed level, a braking control system (Section 4.2) uses back pressure from the pump and generator system to maintain a constant rotational speed of 30 r/min, which is derived from the optimal TSR (Mycek et al., 2014). The characteristics of the turbine with this closed-loop control system applied are shown in Figure 4, which shows the variation in power and torque coefficients, $CP$ and $CT$⁠, with river flow speed $U$⁠. The plot shows the turbine operating at optimal TSR between approximately 1.3 and 1.7 m/s, with the TSR reduced by the control system until the cut-off speed of 4 m/s is reached and the rotor is braked.

The PTO system is shown in Figure 5 and includes the pump, its mechanical links to the axle, the hydro-electric generator, valves and pipework. The aim of the PTO system is to convert the mechanical power of the turbine into water flow, by way of a pump, and then into electricity using a hydro-electric generator.

Simulink was used to model the turbine system in detail, allowing the behaviour of the system at different river velocities to be fully quantified. An overview of the Simulink model is shown in Figure 6. The coloured regions of the model correspond to different components of the RRES design, and are discussed below.

Equation 1 balances the torque generated by the turbine with the torque required by the pump and allows the rotational velocity, $ωr$⁠, of the turbine to be modelled at different river speeds by rearranging in terms of the angular acceleration, $d2θr/dt2$⁠, and integrating (Equation 2).

The mechanical torque, $Tm$⁠, generated by the turbine is a function of the river velocity, rotor speed and the rotor design as discussed in Section 4.1.

The gear ratio and rotor angular velocity, $ωr$⁠, determine the pump volume flow, $V˙$⁠, which allows losses in the system to be calculated. The minor losses are given by the Darcy–Weisbach equation (Massey and Ward-Smith, 1998) (taking into account pipe, joint and valve losses) and the generator losses are modelled as a nozzle with the same characteristics. The pressure losses combined with the area of the piston and the crank geometry then allow the pump drive torque, $Tp$⁠, to be calculated.

A proportional-derivative (PD) controller was used to keep the flow rate from exceeding the maximum limit by increasing the resistance to the flow using a throttling valve. This valve is part of the brake system highlighted in yellow. As flow rate is proportional to both the electrical output of the generator and the pressure loss across it, either value could be used for system control depending on the available sensors. The control system also closes the valve completely if flow rate and pressure show the river velocity is at or above 4 m/s.

The throttling valve used by the control system can also be closed manually to stop the rotor spinning. This could be done either in anticipation of storm water or flooding events, or to stop the turbine for maintenance.

Running the Simulink model using the values for system components described below generates the full system characteristics shown in Figure 2. The generator will output 2 kW at $U=1.308m/s$ and 3 kW from $U=1.76m/s$⁠. The maximum internal pressure of the generator is 296.5 kPa at $U=4m/s$⁠. The river turbine blades are subject to a maximum thrust of 20.34 kN at $U=4m/s$⁠.

The design presented here could incorporate any suitable hydroelectric generator available in a particular region; however, a single example turbine was selected in order to illustrate the capabilities of the design. The turbine used in the modelling presented here was a 3 kW dual-nozzle generator from Suneco, based on the wide operating range and low minimum power requirement as detailed on their website (Suneco Hydro, 2020). Figure 7 provides a visual summary of the operational ranges of turbines from this manufacturer.

Polyethylene water pipe will be used for the turbine as it is flexible and commonly used for water. This pipe has a roughness value (ε) of $3×10−6$ m. For the simulation, 400 m of pipe was assumed and the diameter of generator input (150 mm) was specified as the pipe diameter.

A dual-stroke piston system achieves consistent flow while minimising components. Section 4.1 showed the optimal $CP$ of the river turbine at rated current flow occurs at 30 r/min. Pump volumes calculated from the r/min range of the river turbine were considered to account for the gearing of the system. The pump volume of 17.73 l was chosen to minimise the size of the pump while maintaining a practical gear ratio and minimising the maximum force exerted on the system. Evaluating the velocity of the piston throughout each revolution of the turbine, the average flow rate was calculated as 32.58 l/s and the maximum flow rate as 54.33 l/s.

By increasing the gear ratio between the turbine and the pump the ratio of the corresponding torques, $Tm:Tp$⁠, can be adjusted. Simulation showed (Figure 8) that as the gear ratio is increased the operating torque coefficient, $CT$⁠, of the system can be kept closer to the peak value. This ensures the hydrodynamic performance peaks then decreases as the brake is applied at higher river speeds, minimising the peak torque required as the control system engages. If the gear ratio is too high, however, the mechanical torque, $Tm$⁠, required to drive the pump is too high and the turbine does not spin. The optimal gear ratio was found to be around 3.6 so the pump volume was adjusted to fit a practically achievable gear ratio of 3.5.

To minimise the pressure losses across the pump, and also given the large internal diameter of the pipe, a one-way valve was designed to be assembled using a minimal number of specialist components. To ease the replacement of the components susceptible to wear, a flange is welded to the pipe that can then be bolted to the outlet (Figure 9).

Simulations were conducted to ensure sufficient flow through the valve with an acceptable drop of pressure across the component. A large pressure drop would reduce the efficiency of the pump system, and could risk additional wear due to cavitation (Plesset, 1949). The CFD simulation used the maximum flow rate expected through the valve, 54.33 l/s, and an inlet pressure of 400 kPa. This includes a safety factor (SF) of 1.5. A $k−ε$ turbulence model was used, as this offers an acceptable compromise between computational expense and complexity required for turbulent flows (Kim et al., 2001). The results of this simulation showed that the pressure would reduce by approximately 20 kPa between the valve inlet and outlet. This should not induce cavitation, and means that the valves should be operating at 95% efficiency. Additional simulations of the valve both partially open and fully closed also show that cavitation should not occur.

The crank is located in a sealed chamber on top of the deck and incorporates a sliding cross head to reduce bending forces as shown on the right of Figure 5. A non-linear static FEA including mesh refinement was conducted to ensure the design was structurally sound. The maximum pressure in the system of 296.5 kPa gives a maximum force on the piston head of 5523.4 N. The final simulation (Figure 10) shows the minimum SF for this design is 2.17, above the design requirement.

The PTO system is required to transfer power vertically from the turbine shaft to the pump (bidirectionally) at a gear ratio of 3.5:1. To achieve this a 3.5:1 bevel gear was selected. This was chosen over a 1:1 bevel gear and gearbox combination as the gearbox was significantly more complex, although the weights of the two systems were comparable. Using force analysis and beam strength theory (Bhandari, 2010), a minimum modulus of 17.57 was calculated so the bevel gears were designed with a modulus of 18.

The PTO uses three sets of O-rings designed to ISO 3601-1:2008 (ISO, 2008). A pair of 434 O-rings are used on the piston, three 116 O-rings are used on the piston rod to separate the water and oil sections and a 141 O-ring is used to mitigate ingress into the lower bearing. The top of the pump will use a 0.4 mm gasket and the inspection cover will use a rubber seal.

Material selection was based on the requirements to mitigate corrosion, minimise cost and be easy to machine. Due to the potential surface wear from the seals, a coating could not be used on the piston or piston rod so they will be made from stainless steel. These components will be electrically insulated from the remainder of the PTO system using nylon inserts, gaskets and washers to prevent galvanic corrosion (Bouzid et al., 1995; Zhang, 2011). The designed one-way valves will be made from stainless steel, with a polycarbonate ball, as both offer a long working life and are recyclable (Gordon et al., 2006; Liu et al., 2017; Payet-Gaspard, 2012). The ball needs to move freely within the valve, and the use of polycarbonate gives it a density similar to water – in this case the specific gravity of the polycarbonate ball is 1.2, meaning it is nearly neutrally buoyant (Khurshudov and Kato, 1997; Utracki and Sammut, 1990). The crank casing will be made from cast iron and all remaining components will be made from carbon steel.

To keep the manufacture of the bearing components simple, designs requiring bearing seals were excluded at an early stage. Journal bearings have been designed, rather than ball or roller bearings, which reduces the number of moving parts and allows for larger clearances. The larger clearances reduce the vulnerability of the bearings to interference caused by sedimentation.

A preliminary observation of some lubrication regime graphs showed that for the design envelope of a maximum r/min of around 25–30, hydrodynamic lubrication would not be reached unless an impractically large shaft diameter was used (Welsh, 1983). Hydro-static lubrication was also deemed infeasible, as it required the pump to already be in motion in order to lift the bearing surface enough to create a suitable oil wedge. This requires that the bearings operate in a boundary-lubricated regime. As such, flat-plate thrust bearings and plain journal bearings were designed for the blade shaft. The loads on the main shaft bearings are shown in Figure 11, with the thrust forces created by the blades acting against the relatively large front thrust bearing and a second thrust bearing at the rear of the shaft, providing a contact surface for the rear bevel gear.

The methodology used to obtain the geometry of the thrust bearings is detailed by Wilcock and Booser (1957b). Bearing sizing calculations were carried out using an early estimate of thrust load, with $Wth=23kN$⁠. The outer diameter of a thrust bearing can be calculated using Equation 3, where the meaning and units of each variable are stated in the notation list.

Normal pressure loads for flat plate thrust bearings should be kept to below $75psi$ (⁠$517kPa$⁠), with the maximum loads being less than $150psi$ (Wilcock and Booser, 1957b). Using an SF of 2, a design target $P$ value of $517kPa$ is taken. The pad/circumference ratio, $kg$⁠, is usually given as 0.8. Given that both $D1$ and $D2$ are unknown, an iterative process was used to find suitable values that would satisfy the general criteria given in Equation 4. The final $D1$ value also defines the shaft diameter.

Additional geometries including $b$⁠, $i$⁠, $B$ and $G$ may be calculated using Equations 5–8. The rear thrust bearing was designed using the same dimensions as that of the front, as this avoids assembly errors that could be caused by interchanging the two parts.

The power loss due to each thrust bearing can be estimated by first calculating $Ud$ using Equation 9. A $Ud$ value of $16mm/min$ can be reached for the front thrust bearing (under the greatest load). An estimate for $M$ can then be found by comparing with past data values of $Ud$ (Wilcock and Booser, 1957b), resulting in $M≪0.1$⁠. The actual power loss is found using Equation 10, indicating that the power loss due to the thrust bearings is negligible.

Using the inner diameter determined by the thrust bearings, $Ljo$ can be determined using the standard $L:D$ ratio of $0.5:1.5$⁠. $Pjo$ is given in Equation 11 (Childs, 2013), where $Wjo$ is assumed to be approximately equal to 100 kg (140 kg after applying the partial SF of 1.4). $C$ is subsequently given in Equation 12 (O'Connor et al., 1968).

The bearing thickness is found using Equation 13 (Berard and Waters, 1924). A Stribeck curve can be used to estimate the friction factor of journal bearings based on their lubrication regime, or more accurately by using their Hersey number as calculated using Equation 14 (Williams, 2004). In this case, a Hersey number of 0.009 corresponds to a friction factor of around 0.1 as expected. This is consistent with friction factors of around $0.08−0.1$ for typical boundary-lubricated bearings.

A rough estimate of friction factor for partially lubricated bearings can be calculated using Equation 15, where $V$ is calculated as shown in Equation 16 and $C1$ and $C2$ are constants that depend on the bearing's operating conditions and type, respectively (Vallance, 1938). This results in a friction factor, $f$⁠, of 0.135 under ordinary conditions. A worst-case scenario with major sedimentation interference would increase this to 0.27.

Given that the very low r/min creates a dry rubbing condition at times and considering the relatively low loading conditions of the RRES, a plastic material with low dry friction coefficient was chosen for the bearings. Plastics also have the benefit of being softer than the steel shaft journal material. This is useful when considering particulate interaction with the bearing – there is no filtration in the system so there is potential for particulates to enter the bearing and damage the shaft surface. The softer interface material can be regarded as sacrificial, protecting the more expensive shaft (Williams, 2004). Nylon could be used, which is cheap (Wilcock and Booser, 1957b), tough and easier to machine, while polytetrafluoroethylene (PTFE) has a lower coefficient of friction, better chemical resistance and higher operating temperatures (Freeman, 1962; Wilcock and Booser, 1957a). The most important characteristic for the RRES bearings is the material wear rate, considering the desire for longer design life and the expectation of sedimentation interference. For these reasons, PTFE was selected (Zsidaia et al., 2002).

Development of the blade structure was designed to fulfil the requirements set out in Table 1. The blade dimensions are scaled up from Mycek et al. (2014) with a new radius of 1.8 m, maximum chord length of 0.223 m and a minimum of 0.0590 m using a National Advisory Committee for Aeronautics (NACA) 63418 profile. In line with the requirement that the design must use common materials, simple manufacturing methods and must be easily repaired, an open-mould, wet-layup fibreglass process is proposed.

The design was verified using a static load simulation in the Solidworks software program. The thrust was applied to the face of the blade in the direction of the axis of rotation. To simplify the geometry, a basic blade was modelled with the same thickness and approximate shape as the actual blade. This is shown in Figure 12(a). The internal geometry is shown in Figures 12(b) and 12(c). Under the assumption that the control system fails to bring the rotor under control in storm conditions, the maximum thrust load is 60 000 N (Figure 3), split between the two blades. This was multiplied by an SF of 3.3 as suggested in the small wind turbine design standard IEC61400-2 (IEC, 2013) to include an allowance for fatigue effects, meaning no additional fatigue analysis is required. A mesh refinement was conducted on the final assembly, shown in Figure 13, and results from the FEA showing the stress distribution for the blade and support structure are presented in Figure 14. Figure 15 shows an exploded view of the rotor assembly. To ensure easy replacement of the blades, it is mostly bolted together.

The chassis holds all components together and provides buoyancy, mooring points and shaft housing. As noted in the design specification, this must be designed for reliability, ease of manufacture and repair, and for low cost. The main framework has been designed for manufacture from readily available standard beams using only welding and bolted joints to assemble.

Decommissioned plastic barrels (⁠$210l$⁠) filled with closed-cell expanding foam are used for buoyancy – the foam ensuring that the barrels retain their buoyancy even when damaged. They fully cover the turbine below, so boats can approach the sides. Treating the underside of the RRES chassis as a flat plate allows the boundary layer flow between the chassis and blades to be calculated. Setting the gap between the turbine blade tip and chassis to $250mm$ ensures that as the blade passes this region, the flow into the turbine is no less than $90%$ of the river speed, $U$⁠, up to flow speeds of $2m/s$⁠.

The RRES is suspended in the river flow by two mooring lines for stability and simplicity in one-directional flow; in accordance with DNVGL-OS-E304 offshore mooring standard (Lohne, 1996). Woven steel wire rope and spiral steel strand rope were considered. Spiral strand was selected to ensure longevity for applications across the 10–20 year time frame as the flexibility of the woven steel rope was not necessary for this application (Sefton et al., 1998). The SF of lines and anchors must be at least 3, in the scenario where one fails the other must still function under the entire design load, tethering the RRES until a crew arrives. These mooring lines shall pass through the chocks (mooring line guide-holes) to a turnbuckle wire tension device which in turn is fixed by the deck, which allows the mooring to be adjusted to angle the turbine into the flow. The steel chocks shall have a bolt-in chock liner to protect the lines from wear at this most crucial point (Taylor and Hawkins, 2000).

An open-channel, 300 mm wide, hydraulic flume was used for the test to improve the design of the chassis as shown in Figure 16. A 1/50th scale model of the chassis was made with wire and three-dimensional-printed lugs using polystyrene as buoyancy for flume testing. To replicate the drag loads from the rotor, the actuator disc approach of Myers and Bahaj (2010) was used and a disc with 42% porosity was manufactured.

The flume testing proved to be a crucial development step as it showed that, when moored from a brace as shown in Figure 16(a) in high flow, the structure could invert as shown in Figure 16(b). From the tests it was concluded that the mooring lines should be attached above and forward of the turbine position, resulting in the stable configuration shown in Figure 16(c). This configuration is stable even in adverse conditions, but meant that the bow of the RRES would dive underwater in high flow rates, which was resolved with a bow structure (Figure 16(d)).

The final design with these revisions incorporated is shown in Figure 17.

The structural strength was verified using truss nodal analysis and to determine which size of the C-section beams are used. The thrust load on the turbine, buoyancy and weight of the pump and gear system are shown in the free-body diagram (FBD) in Figure 18(a). Staad Pro nodal analysis is shown in Figure 18(b). Five C-beams were tested. All of these were standard dimensions from the UPE series defined by BS EN 10365 (BSI, 2017): UPE 140, 160, 180, 200 and 220. The UPE 160 option gave the lightest weight and an SF of 2.

This turbine design will provide electrical power for a remote location. The design envelope encompasses water speeds between 1 and 4 m/s and rated power of 3 kW from a river flowing at $1.8m/s$⁠. The design concept has been refined to minimise the use of complex manufacturing techniques, and to use materials that are widely available. There are no electronics off-shore, minimising the complexity of maintenance. The turbine, pump and chassis systems are completely mechanical, pumping water on-shore to power a generator. This can accommodate the use of a throttling system to prevent the turbine entering an overspeed state and exceeding design limits. The publication of the designs under an open license allows for the future development and deployment of the turbine wherever it is needed.

A 1/50th scale model was tested together with a variety of simulation techniques to validate the different component designs, including CFD, nodal analysis and FEA.

Therefore, this paper has shown a new potential direction for the provision of electricity in remote areas. The design encourages local ownership and local engagement with the technology and could be a truly sustainable solution.

This work has been supported in part by two Engineering and Physical Sciences Research Council (EPSRC)-funded Supergen ORE project grants: SURFTEC grand challenge project EP/N02057X/1 and WTIMTS flex fund project EP/S000747/1.

$A$

area (m²)

$Ab$

Bolt nominal diameter (mm)

$Ac$

crank angle (⁠$rad/s$⁠)

$B$

pad length (m)

$b$

pad width (m)

$C$

average diametral clearance (in.; 1 in. = 2.54 cm)

$CD$

coefficient of drag (dimensionless)

$Cf$

coefficient of thrust (dimensionless)

$CL$

coefficient of lift (dimensionless)

$CP$

coefficient of power (dimensionless)

$CT$

coefficient of torque (dimensionless)

$D1$

inner bearing diameter (m)

$D2$

outer bearing diameter (m)

$dpiston$

piston diameter (mm)

$Fb$

tensile bolt force (N)

$FD$

drag force (N)

$FL$

lift force (N)

$FN$

normal force (N)

$Fr$

friction force (N)

$f$

friction factor (dimensionless)

$G$

groove width (m)

$Hjo$

journal bearing power loss (W)

$Hth$

thrust bearing power loss (W)

$i$

number of pads (dimensionless)

$J$

polar moment of inertia (⁠$m4$⁠)

$kg$

pad/circumference ratio (dimensionless)

$Ljo$

journal bearing length (m)

$lc$

crank rod length (mm)

$M$

horsepower per square inch (hp/in.²; 1 in.² = 6.45 cm²)

$Pjo$

radial load capacity (Pa)

$Pth$

pressure bearing capacity (Pa)

$r$

blade radius (m)

$rc$

crank radius (mm)

$Tf$

torque friction (N)

$Tm$

mechanical torque (N m)

$Tp$

pump torque (N m)

$tjo$

bearing thickness (in.)

$U$

river velocity (m/s)

$Ud$

pitch diameter peripheral speed (⁠$m/min$⁠)

$V˙p$

pump volume flow (⁠$m3/s$⁠)

$vpiston$

piston velocity (mm/s)

$Wjo$

maximum vertical (weight) load (N)

$Wth$

maximum thrust load (N)

$xpiston$

piston position (mm)

$η$

lubricant viscosity (⁠$Pas$⁠)

$θr$

river turbine angle (⁠$rad/s$⁠)

$μ$

coefficient of friction (dimensionless)

$ρ$

density of water (⁠$kg/m3$⁠)

$ρpart$

density of part (⁠$kg/m3$⁠)

$σb$

Bolt stress (⁠$Pa$⁠)

$Ψ$

power (W)

$ωr$

river turbine angular velocity (⁠$rad/s$⁠)

$ωrev$

shaft rotational speed (r/min)