STREAM WHEELS FOR APPLICATIONS IN SHALLOW AND DEEP WATER Gerald Müller (1), Sally Denchfield (2), Reinhard Marth (3), Bob Shelmerdine (4) (1)
Department of Civil Engineering, University of Southampton, Highfield, Southampton SO17 1BJ, UK, Tel. +44 23890 592442, email: g.muller:soton.ac.uk (2) Department of Engineering Sciences, University of Southampton, Highfield, Southampton SO17 1BJ, UK, email:
[email protected] (3) Department of Civil Engineering, Technical University of Berlin, Gustav-Meyer Allee 25, Berlin, 13355, Germany, email:
[email protected] (4) Department of Engineering Sciences, University of Southampton, Highfield, Southampton SO17 1BJ, UK, email:
[email protected]
ABSTRACT The interest in renewable energies has initiated a re-consideration of hydropower resources. Currently there is no economical energy converter for the kinetic energy of shallow free surface flows available. Stream wheels or impulse type water wheels were employed in this role until the middle of the last century, and this type of water wheel could again be of interest today. Little engineering or performance information is however available for such machines. Following a literature review, three types of stream wheels were identified and theoretical models for performance evaluation were developed. Model tests were employed to verify theoretical predictions. It was found that both in terms of potential power production and number of possible sites the stream wheel in deep water is the most promising candidate for further development. Keywords: hydropower, low head, stream wheel
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INTRODUCTION The interest in renewable energy has led to a re-evaluation of the possibilities of micro- and pico hydropower applications. The current unused potential in the UK in the area of low head micro-hydropower (P < 100 kW, h < 2m) is estimated as 600 – 1000 MW. There are two main reasons why small hydropower with low head differences is not exploited: 1. Conventional turbines are not economical 2. Turbines are thought to have negative effects on the ecology. Recently, water wheels have been demonstrated to be efficient energy converters for small hydropower with head differences h of more than 1 m, Müller & Wolters (2004). Considerable efforts have also been expended in the search for energy converters for very low head differences (h < 0.8 m) and for the exploitation of fast flowing streams, so far without convincing results. Historically, water wheels were employed to utilise this hydropower bracket. Stream wheels convert the kinetic energy of flowing water into mechanical energy and were already mentioned by the Roman Architect Vitruvius. From the 18th Century onwards, streamwheels were frequently employed in order to generate mechanical energy. They were considered cost effective since little civil engineering work was required for a stream wheel installation. It was quickly realised that the power output from stream wheels in slow flowing situations was small; fast flowing streams were however the exception rather than the rule. The English engineer John Smeaton conducted 1
the first measurements on a scale model of an undershot wheel and determined efficiencies of 30%, Smeaton (1794). Kinetic energy wheels were also employed on floating mills; here the wheels used very narrow boards (t < 0.5m) as blades, resulting in low efficiencies. With the advent of hydraulic engineering as a science, the difference between subcritical and supercritical flows was realised and theories were developed for stream wheels, Morin (1864). Fig. 1 shows typical stream wheels for shallow supercritical flow and deep water. The power output and efficiencies from stream wheels were however considered to be small when compared with other types of water wheels which employed the potential energy of the flow, e.g. Müller (1899).
a. Stream wheel for supercritical flow - D = 5.2m, b = 3.65m, P = 33 kW – Müller, (1899)
b. Floating mill, Ernst (1805)
Fig. 1: Historical stream wheels in shallow and deep water To the authors’ knowledge, stream wheels for energy production have not been built for more than 80 years. This is probably caused by the fact that their efficiencies are low, there was no need for the exploitation of small and very small hydropower sources and since there is very little engineering information about stream wheels available. Today, stream wheels could be of interest for special applications where local fast flows occur in a river or canal, or as energy converters for fast surface flows such as encountered in larger rivers or tidal currents.
2 TYPES OF STREAM WHEEL 2.1 OVERVIEW From theoretical considerations, three different types of stream wheels can be defined, depending on speed of water v0, the critical depth of the flow dcr, the actual depth of water t1 and submerged depth of blade d: 1. Shallow water depth in subcritical flow (d ≈ t1, v0 < vcr ) 2. Shallow water depth in supercritical flow (d ≈ t1, v0 > vcr ) 3. Deep water (d v w =
(1)
g d1
Traditionally, stream wheels were built in shallow artificial channels, whereby the blades extended to the bottom of the channel in order to utilise all available energy. Floating mills were built for deep water situations; here the wheel was located between two barge-like hulls which had vertical side walls and wedge-type bows, the actual flow velocity of the stream was not accelerated, Fig. 1b. 2.2 THE STREAM WHEEL IN SUBCRITICAL, SHALLOW FLOW Stream wheels in subcritical flows were only built occasionally. They were considered costeffective since little work on the stream itself was required, power outputs were however low (often less than 1.7 kW for a 3.6 m diameter wheel with 2.8 m width, Fig. 2).
Fig. 2: Stream wheel in subcritical flow, D = 3.50m, b = 2.80m, P = 1.5 – 1.7 kW (Müller, 1899) Fig. 3 shows the assumptions for the theory of the subritical stream wheel, with the flow being obstructed by a blade of depth d ≈ t:
Fig. 3: Subcritical flow in channel, Morin (1864) The power is generated by the momentum exchange between flow and blade, leading to a higher water level in front and behind of the blade. The power P is then given as:
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(
P = ρ w b d 2 v 2 v1 − v 2
)
2
(2)
The power maximum occurs for v2 = 0.5 v1; with a maximum efficiency of 29.6%. A 1 m deep river channel flowing with a velocity of 1.5 m/s would therefore produce mechanical energy of only 0.5 kW per m width; this indicates the very small amount of energy which can be produced with stream wheels in subcritical flow. The wheel itself in this case acts as a weir, increasing the water level in front and behind of it. This effect should be noted when considering an application of this technology. Experiments on stream wheels led to maximum efficiencies of 30% (taking the efficiency as the ratio of extracted mechanical to available hydraulic energy); here it should be noted that the blades were fully submerged so that the assumptions made for Eq. (1) are not completely valid, Gotoh et al. (2001). 2.3 THE STREAM WHEEL IN SHALLOW WATER – SUPERCRITICAL FLOW In the 19th Century, stream wheels were preferably employed in situations where supercritical flow velocities occurred. A transition to supercritical flow can be generated by small head differences or undershot weirs. The higher velocity of the flow means that smaller water wheels are required and, since upstream conditions in supercritical flow are not affected by an obstacle, higher efficiencies become possible. Fig. 4a shows the – to the authors’ knowledge - only still existing stream wheel, which was built in 1892 and used to power a paper mill in Zug / Switzerland. It had a power rating of P = 26 - 33kW. The theoretical power output of a stream wheel in supercritical flow can be determined by examining the possible differences in the Total Energy Line (TEL), Fig. 4b:
a. Stream wheel, D = 5m, b. Supercritical flow in channel, e.g. Björling (189 (Landesmuseum Mannheim) Fig. 4: Stream wheel in supercritical flow
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P = ρ w g Q ∆h ⎛ v 22 ⎜ ∆h = d1 + − d2 + 2 g ⎜⎝ 2g v1 d1 d2 = v2 v 12
⎞ ⎟ ; ∆h ≥ 0 ⎟ ⎠
(3)
The minimum energy of the downstream flow – or the maximum energy production - will be reached when the depth d2 reaches the critical depth dcr . For a flow volume Q, and a channel width b the critical depth dcr becomes: d cr = 3
Q2 gb2
(4)
The water depth behind the wheel assumes the critical depth dcr , for a ratio of wheel speed to initial velocity of water v1 / v2 = 0.56. The maximum theoretical efficiency becomes a function of v1, and in this case reaches 0.40. Experiments were conducted at the Technical University of Berlin with a 0.50 m diameter stream wheel in order to investigate efficiencies. Fig. 5a shows the results both from theory and experiments with v1 = 1.5 m/s, d1 = 0.047m, b = 0.17 m and Pmax = 4.88 W, giving a maximum efficiency of 36.3 %. The theory cannot as yet model the condition with low wheel speeds, with vwheel / vflow < 0.4, and does not match the point of maximum performance accurately; this will need to be addressed. The theory also neglects some issues: 1. In order to maintain the high flow velocities, a significant gradient of the river bed is required. This will lead to some additional power as well as to an acceleration of the water as inside of the wheel. The ‘wave’- like water level inside of the wheel demonstrates a transformation of kinetic into hydrostatic energy as well as the acceleration of the flow, Fig. 5b. In addition, the efficiency increases with increasing flow which would indicate that for a given head drop even a narrowing of the channel might be advisable. In case of the model tests, this increase in available power was estimated as 4% and could explain the small gap between experimental and theoretical curves. 2. There is a gap between the blades and the straight bed of the channel which on average allows for a leakage of 4%; this could be minimised by employing a curved bed section. In consequence it can be said that a more complex theory as well as an improved geometry of the wheel will be required for an adequate assessment of this type of energy converter. The tests indicated that a 22.5 degree forward inclination of the blades gave the maximum power output. In an actual application, it appears desirable to have a curved section of the river bed in order to minimise gap losses and increase power output, giving an estimated overall efficiency of 38 - 40 %. The model tests were conducted in order to investigate the possibility of hydropower production at a site in Munich/Germany where a flow of 8 m³/s with a depth of 0.47 m and a flow velocity of 5 m/s was available from a head difference (1:10 ramp) of 0.5 m. The results indicate that a mechanical power of 37.8 – 40 kW could be made available.
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a. Theory and experimental results
b. Stream wheel with internal water surface
Fig. 5: Stream wheel in supercritical flow
2.4 THE STREAM WHEEL IN DEEP WATER Recent research at Southampton University has been focussing on the utilisation of stream wheels for fast river or tidal flows where the water depth t is substantially larger than the submerged depth d of the blade. In deep water, increased forces act on the blade resulting from momentum exchange and hydrostatic head differences. The flow separation at the tip of the blade creates a vortex, which in turn leads to a significant drop of the water surface downstream of the blade, increasing the hydrostatic force, Fig. 6. The ratio of head difference ∆h1 / ∆h2 = 3 / 2 was determined from experiments with a fixed blade, and was found to be independent of the flow velocity.
Fig. 6: Single blade in deep water
∆ h1 =
v12 − v22 2g
2 ∆ h 2 ≈ ∆ h1 ( from tests ) 3 b 2 2 P = ρ w g (d + ∆ h ) − ( d − ∆ h ) v2 + ρ w b ( d + ∆ h1 ) v1 − v2 2
[
]
(
(5)
)
2
v2
(6)
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a. Theoretical results
b. Experimental results
Fig. 7: Power output for a model wheel, d = 500mm, b = 1 m, d = 55 mm (1m width) A series of tests with a 500mm diameter model wheel of 180 mm width (internal) was conducted at Southampton University in a water channel of 210 mm depth. The power output was measured with a submerged depths of 55 mm for v1 = 0.40, 0.52 and 0.60 m/s. Contrary to the stream wheels in confined water, the number of blades in contact with the water affects the power output, with power increasing for increasing number of blades. Following the theory of Pelton wheels, the increase in power for the given number of blades (20) and submerged depth was determined as 70%, Becker (1986). In Fig. 7a, the theoretical results for similar parameters are shown. The theoretical values differ slightly from the experimental measurements, Fig. 7b, in particular so for smaller flow velocities. This was attributed to friction in the bearings which was noticeable when spinning the wheel and which was assumed to be a constant breaking force. It should be noted that the theoretical power output is a function of the velocity cube, so that even small changes in velocity measurements will have a substantial effect on the calculated power. Currently, a prototype floating wheel of 2 m diameter and 1.0 m width and a submerged depth d = 0.35m with a mechanical power output of 6 kW for 1.2 m/s free stream velocity is under construction. The floating mill is deigned to accelerate the flow between the two hulls from 1.2 to 2.5 m/s. Assuming 2.5 to 3 blades to be in contact with the water at any moment, the efficiency could be estimated as 56 - 68 %. This type of water wheel could be employed to generate electricity from fast flowing streams or tidal currents. In particular in combination with an arrangement for the increase in flow velocities, the stream wheel in deep water may offer significant power output. Fig. 8 shows the power per m width for a wheel of 10m diameter with a submerged depth d = 1.0, 1.25 and 1.5 m for flow velocities of 1 – 4 m/s. Assuming an average flow velocity of v1 = 2.5 m/s and a flow velocity acceleration factor of 2, a power output of 96 kW/m (or 960 kW for a wheel of 10 m width) appears possible.
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Fig. 8: Maximum power as a function of free stream velocity v0 and submerged depth d
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CONSTRUCTION AND OPERATIONAL ISSUES The diameter of stream wheels was usually chosen as D = 3.5 – 5 m with blade depths of 0.15 – 0.2 D, Müller (1899). The number of blades in a stream wheel is usually determined so that for a given depth, always at least one full blade area is submerged. The blades are curved with a radius which allows for the exit of the blade out of the water with a minimum of energy loss. This is ascertained by keeping the tangent on the blade at its exit point normal to the water surface. Wheels in shallow water were designed with the bearings on a lever, see e.g. Fig. 1s, so that the wheel can be lifted out of the water or the submerged depth be adjusted to the water level. A curved section in the bed of a channel can be expected to improve the power output significantly. The operational speed of the wheel is determined at the centre of the submerged blade, and is a fixed proportion of the velocity of the flowing water. For electricity production this implies that the wheel must be able to operate with variable speed. The comparatively slow speed of the wheel (16 rpm for the 2 m / 6 kW, 5.1 rpm for a 10 m diameter / 960 kW wheel) in combination with high torque will require gear ratios of 37 to 118 for the production of mains electricity.
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DISCUSSION The utilisation of the kinetic energy of flowing water is often suggested, in particular by nonengineers. Stream water wheels appear to constitute a simple and effective technology for the exploitation of this energy resource. To date however, no overview over the types of stream wheels and their theoretical analysis has been published. The authors have tried to compile all available information, from the literature as well as from own experiments, to give a reasonably complete overview over the subject. It was found that stream wheels in subcritical flow, due to their low efficiency and the low energy density of the flow, can only be of interest in special combinations of circumstances, such as where no other power source is available. Stream wheels in supercritical flow conditions can be more efficient and more powerful. Supercritical flow can however only exist in artificial channels since it would otherwise erode the river bed and banks. The authors assume that the number of possible locations for such water wheels is limited. Stream wheels in deep water finally can achieve substantial power outputs if the water depth t is large enough (t > 2 d), and if the flow is fast enough (v0 > 2.5 m/s). Since this type of wheel would be installed on a floating device, the local flow velocity could be accelerated. Experiments
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on a catamaran-type device with a water wheel and a hydrofoil were conducted at Southampton University and showed an acceleration of 50%. The combination of an effective geometry of the floating body with a stream wheel could be an interesting power generator for large rivers or tidal flows with flow velocities of more than 1 m/s. The authors consider the floating stream wheel as the most promising type of stream wheel both in terms of energy production and number of possible locations.
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CONCLUSIONS Stream wheels, or water wheels which employ the kinetic energy of flowing water, can be classified into three different types, depending on flow velocity and water depth: shallow subcritical flow, shallow supercritical flow and deep water wheels. Theoretical models were developed for all three types and validated with experimental results. Stream wheels in subcritical flows have a maximum efficiency of 29.7% and low power output of probably less than 2 kW. Stream wheels in supercritical flow have a theoretical efficiency of 40%; which would probably increase by a more detailed analysis of the complex flow conditions inside the wheel to 45%. Measurements resulted in an efficiency of 36.3 % whereby this value could be improved to 3840 % by small changes in geometry. Power outputs for typical locations can reach up to 40 kW. The efficiencies of stream wheels in deep water can be estimated as 56 – 68%. The power outputs for stream wheels in deep water may reach 100 – 1000 kW. The number of possible locations for shallow water applications appears limited, whereas deep water locations with flow velocities of more than 1.5 m/s are much more numerous. The stream wheel in deep water therefore can be considered the most likely candidate for further development and application.
REFERENCES Becker E., 1986, Techn. Strömungslehre, Teubner Studienbücher Mechanik, B.G. Teubner, Stuttgart. Björling P.R. (1894) Water or hydraulic motors, E. & F. N. Spon, London, New York. Ernst H. (1805) Anleitung zum praktischen Mühlenbau (Guide to practical mill construction, in German), Leipzig. Gotoh M., Kowata H., Okuyama T. & Katayama S. (2001) Characteristics of a current water wheel set in a rectangular channel, Proceedings of FEDSM’01: 2001 ASME Fluids Engineering Division Summer Meeting May 29-June 1, 2001 New Orleans, Louisiana, paper FEDSM2001-18149. Morin, A. (1864) Aide-Mémoire de Mécanique Pratique, 5th Ed., Librarie de L. Hachette et Cie, Boul. St. Germain. Müller W. (1899) Die eisernen Wasserräder- Atlas (The water wheels – technical drawings, in German), Veith & Comp., Leipzig. Müller G. & Kauppert K. (2004) Performance characteristics of water wheels, IAHR Journ. Hydr. Res., Vol. 42, No. 5. Müller G. & Wolter C. (2004) The breast shot water wheel: design and model tests, Proc. ICE Eng. Sustainability, Vol. 157, Issue ES4, 203 – 212. Smeaton J. (1794) An experimental enquiry concerning the natural powers of wind and water to turn mills and other machines etc., 2nd Ed. I. & J. Taylor, London.
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