Performance characteristics of water wheels PDF

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Journal of Hydraulic Research Vol. 42, No. 5 (2004), pp. 451–460 © 2004 International Association of Hydraulic Engineering and Research Performance characteristics of water wheels Caractéristiques d’exécution des roues d’eau GERALD MÜLLER, Lecturer, Civil Engineering Department, Queen’s University B...

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Journal of Hydraulic Research Vol. 42, No. 5 (2004), pp. 451–460 © 2004 International Association of Hydraulic Engineering and Research

Performance characteristics of water wheels Caractéristiques d’exécution des roues d’eau GERALD MÜLLER, Lecturer, Civil Engineering Department, Queen’s University Belfast, Stranmillis Road, David Keir Building, Belfast BT7 5AD, UK. Tel.: +44 2890 274517; fax: +44 2890 663754; e-mail: [email protected] (author for correspondence) KLEMENS KAUPPERT, Managing Director, IFMW Ltd., Nebeniusstr. 34, 76134 Karlsruhe; Tel.: +49 721 3529 200; Fax: +49 721 3592 201; e-mail: [email protected] ABSTRACT During the eighteenth, nineteenth and the first half of the twentieth century, water wheels were important hydraulic energy converters. It is estimated that in England 25,000–30,000 wheels were in operation around 1850; in Germany 33,500 water wheels were recorded as late as 1925. Today, only very few water wheels are still in use. Low head hydropower is seldom exploited, since cost-effective energy converters for these conditions are not available. A small number of companies are currently again manufacturing apparently economically attractive over- and undershot water wheels; the performance characteristics of these wheels are however unclear so that the assessment of the potential of a site as well as their design and efficient operation relies on estimates. A number of engineering textbooks and three detailed experimental studies of water wheel design and performance were published between 1850 and 1935, but nowadays appear to be virtually unknown. A detailed study of these reports was conducted, and the performance characteristics of overshot water wheels were analysed in order to assess the application of such wheels for electricity generation. It was found that water wheels have to be designed for a given flow rate, head difference and intended operating regime. Properly designed overshot wheels have an efficiency of 85%, undershot wheels of approximately 75% for 0.2 < Q/Qmax < 1.0, making this type of energy converter suitable for the exploitation of highly variable flows. Water wheels must, however, be operated within certain parameter ranges in order to be able to perform efficiently; they appear to offer an efficient and cost-effective solution for the exploitation of low head hydropower sources. RÉSUMÉ Pendant le dix-huitième, le dix-neuvième et la première moitié du vingtième siècle, les roues à eau furent d’importants convertisseurs d’énergie hydraulique. On estime qu’en Angleterre 25.000–30.000 roues étaient en fonction autour de 1850; en Allemagne 33.500 roues à eau ont été enregistrées jusqu’en 1925. Aujourd’hui, seulement très peu de roues sont encore en service. Les basses chutes hydro-électriques sont rarement exploitées, car la production rentable d’énergie dans ces conditions est inexploitable. Un nombre restreint de compagnies fabriquent encore actuellement des roues à eau par en dessus et par en dessous, économiquement attrayantes en apparence; les caractéristiques d’exécution de ces roues sont cependant peu claires de sorte que l’évaluation du potentiel d’un emplacement aussi bien que la conception et le fonctionnement efficace ne peuvent être fondés que sur des estimations. Un certain nombre de manuels et trois études détaillées expérimentales de conception et de performance de roues à eau ont été édités entre 1850 et 1935, mais semblent de nos jours être pratiquement inconnus. Une étude détaillée de ces rapports a été entreprise, et les caractéristiques de performance des roues à eau par en dessus ont été analysées afin d’évaluer l’utilisation de telles roues pour la production d’électricité. On a constaté que les roues à eau doivent être conçues pour un débit donné, une chute et un régime de fonctionnement donnés. Les roues par en dessus correctement conçues ont un rendement de 85%, les roues par en dessous approximativement de 75% pour 0.2 < Q/Qmax < 1.0. rendant ce type de convertisseur d’énergie approprié à l’exploitation des écoulements fortement variables. Les roues à eau doivent, cependant, fonctionner dans une certaine gamme de paramètres pour être efficaces; elles semblent offrir une solution efficace et rentable pour l’exploitation des basses chutes hydro-électriques.

Keywords: Low head hydropower, micro-hydropower, water wheels, history of hydraulics. 1 Introduction

wheels were operated in England alone (McGuigan, 1978). In Germany 33,500 water wheels with power outputs ranging from 0.75 to 75 kW were licensed as late as 1925 (Müller, 1939). The design of water wheels was then part of the syllabus of mechanical and civil engineering courses at university level (Albrecht, 1900), and engineering textbooks covering all aspects of the design calculations of water wheels were published until 1939; e.g. Bresse (1876), Bach (1886a,b), Müller (1899a,b), Frizell (1901), and Müller (1939). Water wheels were developed further even after the advent of turbines; the most efficient undershot wheel was

Water wheels are today often considered to be relics from the beginning of the industrial revolution; romantic but inefficient hydraulic machines made of wood and belonging to the past, e.g. Smith (1980) and Reynolds (1983). It is generally believed that turbines evolved from water wheels, that they are much more efficient and subsequently replaced them as hydraulic power converters. A closer look at the statistics however reveals a slightly different picture. In the 1850s, an estimated 25,000–30,000 water

Revision received May 22, 2003 / Open for discussion until February 28, 2005.

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only patented in 1883. Engineers, manufacturers and mill owners clearly regarded water wheels as efficient and commercially interesting power sources. The water wheels were almost exclusively employed as mechanical power sources driving grist-, powder-, and mineral mills as well as textile and other machinery, mostly in small businesses. With the advent of the electric motor as a cheap power source, however, in the 1940s and 1950s, the water wheels disappeared virtually completely. Today, the requirement for the utilization of low head hydropower sources for electricity generation is greater than ever. In the industrialized countries, the demand for renewable energy sources is constantly increasing in order to meet non-fossil fuel targets. The currently unused low head micro-hydro potential is estimated as 500 MW in Germany and around 600–1000 MW in the UK (König and Jehle, 1997; Goring, 2000). In developing countries, the rising demand for electricity in combination with large distances means that decentralized electricity generation has a high priority. Most low head, low flow hydropower sources, however, are not exploited in recent times since standard turbines cannot be employed economically in such conditions. Consequently, there exists a demand for a cost-effective low head hydraulic energy converter, which still could not be met. Water wheels may offer an attractive solution to this problem. A small number of companies in Germany and the USA are again manufacturing water wheels for electricity generation, see Internet references. For an overview of the current water wheel types and their utilization today, see Müller and Kauppert (2002). The performance characteristics of such wheels, however, still appear to be largely unknown, so that the assessment of the available power potential, comparisons with other turbine types such as the Kaplan or the Ossberger (crossflow) turbine and even the determination of optimum operating conditions for water wheels relies on estimates. Most modern hydraulic engineering textbooks do not even mention water wheels any more, and if they do, they provide very little information on the performance and design, e.g. König and Jehle (1997) and Giesecke and Mosónyi (1998). Although a significant amount of information about water wheels still exists, it is often hidden in old textbooks and long forgotten reports. The authors set up a small non-profit research company (IFMW Ltd.) in Karlsruhe, Germany, which specializes in hydraulic engineering research. Within the company, the available engineering literature on water wheels was collected and analysed in order to establish the design and performance characteristics of “modern” water wheels. In this article, the results of this review will be presented. 2 Types of water wheels In order to be able to utilize the head differences from 0.5 to around 12 m, different types of water wheels were developed and perfected during the nineteenth century: 1. Overshot water wheels, Fig. 1(a): the water enters the wheel from above. This wheel type was employed for head differences of 2.5–10 m, and flow rates of 0.1–0.2 m3 /s per metre width.

2. Breast wheels, Fig. 1(b): the level of the upstream water table lies at approximately the level of the wheel’s axis. This wheel type was mostly used for head differences of 1.5–4 m, and flow rates of 0.35–0.65 m3 /s per metre width. 3. Undershot or Zuppinger wheels, Fig. 1(c): the water enters the wheel below its axis. This wheel type can be used for very small head differences of 0.5–2.5 m, and large flow volumes ranging from 0.5–0.95 m3 /s per metre width. Between these wheel types, a large number of intermediate forms existed. What all “modern” wheels have in common is that they employ the potential energy of the water, they operate under atmospheric pressure and that they are built of steel. Impulse type wheels, which use the kinetic energy of flowing water were also built occasionally, although it was well known that their efficiencies were too low to be used economically except in special locations; see, e.g. Müller (1899a). The different wheel types have different characteristics in the way the function, they perform and the way they are designed. In the following, the wheel types and their performance characteristics—as far as they are known—will be described.

3 The overshot wheel 3.1 Principles An overshot water wheel installation consists of three elements: inflow detail, water wheel and tailwater channel. “Modern” overshot water wheels are made of steel and feature a very distinctive geometry of the cells as well as a specially designed inflow detail. Figure 2 shows a typical overshot wheel with a close-up of an inflow detail. The wheel in Fig. 2(a) has a weir type inflow without controlling elements, so that the upstream water level and the velocity of the inflowing water particles are a function of the flow volume. The inflow detail shown in Fig. 2(b) consists of a channel with inflow slots, the area of which can be regulated, at the bottom. The slots are shaped so as to direct the water at the right angle into the cells. Here, the upstream water level (and the velocity of the inflowing water) can be kept constant. A somewhat similar inflow detail, with a sluice gate, can be seen in Fig. 1(a). The cells themselves are formed in a way so that the water jet can enter each cell at its natural angle of fall. The opening of each cell is slightly wider than the jet, so that the air can escape. The cells are however kept as narrow as possible so that the weight of the water can become effective almost immediately. In order to avoid an early loss of water, each cell should only be filled with up to 30–50% of its volume. For a detailed discussion of the optimum cell geometry see Bach (1886a); an English translation of the relevant section is contained in Weidner (1913). The peculiar shape of the cells retains the water inside of the cell until the lowermost position, when it finally empties rapidly. In the overshot wheel, it is thus the potential energy of the water that constitutes the driving force for the wheel. Figure 1(a) also illustrates the in- and outflow condition. The wheel has a regulated inflow with a sluice gate, so that the inflowing water enters the cells as a fast and thin sheet; the outflow only starts at a very

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Figure 1 Types of water wheels: (a) overshot wheel (Müller, 1899a); (b) breast wheel (Fairbairn, 1849); (c) undershot (Zuppinger) wheel (Müller, 1899a). (a)

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Figure 2 Overshot cell wheel (Müller, 1939): (a) cell wheel with free inflow; (b) cells and inflow detail.

low level. No water is carried over the lowermost point. Figure 3 shows an old and a modern overshot water wheel.

3.2 Hydraulic design Water wheels are designed for a given application, head difference and flow volume. For the design of an overshot water wheel, the diameter is determined by the head difference, although it

has to be decided whether the wheel will be operated with free or regulated inflow (i.e. constant or variable speed) since this affects the available head. The wheel speed and the number, depth and shape of the cells then has to be determined as well as the width of the wheel for a given design flow volume and wheel speed. The inflow detail with or without a sluice gate has to be designed so that the design flow volume can be guided into the wheel.

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Figure 3 Overshot wheels: (a) with sluice gate entry detail, USA, ca. 1900; (b) with free inflow, 2.9 m diameter, 4 m width, 26 kW (el.), Hydrowatt Ltd., 2000.

4 Performance characteristics of overshot water wheels 4.1 General The complex in- and outflow conditions in an overshot water wheel have so far prevented the development of a theoretical model of the water wheel and its characteristics. The actual efficiency and performance characteristics of water wheels can therefore only be determined by tests. Although a large number of wheels were in operation in the last century, only three series of such tests appear to have been performed, the key results of which will be presented in the following. Most of the test results were never published in hydraulic engineering textbooks or journals and are only available in not so widely known articles and reports; see Weidner (1913a,b), Staus (1928) and Meerwarth (1935). To the authors’ knowledge, Staus’ results were never published in English, and Meerwarth’s, except in his PhD thesis, not even in German engineering journals. The results from the experiments performed in Germany subsequently remained unknown in the US and vice versa. 4.2 Efficiency curves The efficiency against flow rate curve displays one of the main characteristics of a hydraulic energy converter. Similar to other

turbine types, the efficiency of overshot water wheels is a function of the flow rate. Figure 4 shows the efficiency curves from the three reported tests as a function of the ration of actual flow rate Q and design flow rate Qmax . The results are quite consistent, and it can be seen that the efficiencies reach around 85% even for very small ratios of Q/Qmax of 0.2. The efficiencies remain at this level up to Q = Qmax , so that the water wheel (when well designed) can be regarded as a rather efficient energy converter with the additional advantage of having a broad performance band width, so that power can be generated efficiently even from quite small flow volumes. Standard turbines for low head differences can only approach such wide performance band widths with a sophisticated design and the help of costly active control elements. It should be noted that Meerwarth and Staus measured the power at a drive shaft with a gear ratio of 1 : 25, so that in their measurements gear losses are actually included. Weidner’s results were taken with a gear ratio of 1 : 4; he determined the transmission losses at 3–4.5% at maximum efficiency so that in his experiments a maximum shaft efficiency of 89% was achieved. A fourth efficiency measurement (not shown here) was conducted by Günther (1997), and resulted in maximum efficiencies of 77% and an efficiency versus Q/Qmax curve similar to those shown in Fig. 4. In this test, however, the speed of the wheel was fixed and the inflow not controlled; the

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Figure 4 Measured efficiency curves for overshot water wheels. (a) Efficiency of a 3.054 m wheel (Weidner, 1913a,b); (b) efficiency of a 3.60 m wheel (Staus, 1928); (c) efficiency curve for a 3.60 m wheel at 9.0 rpm (Meerwarth, 1935).

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measurements may therefore not have been taken at the point of maximum efficiency (compare Fig. 6a).

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4.3 Operating conditions

4.4 Variable speed operation Weidner conducted the majority of his tests with an open inflow channel, i.e. with inflow velocities varying with changing flow volumes, whereas Meerwarth employed a sluice gate to keep inflow velocities constant. Figure 6(a) shows some results from Weidner’s investigation (1 feet-second = 0.0278 m3 /s). For

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The efficiency of many hydraulic machines is also a function of the speed at which the machine works with respect to the velocity of the water particles. In order to extract a maximum of power from a given hydro power source, knowledge of the operational characteristics of a hydraulic machine is thus essential. Experiments to establish these characteristics were conducted by Weidner (1913a,b) and Meerwarth (1935). Figure 5 shows typical results for power plotted against wheel speed for a 3.60 m diameter wheel and a constant flows of Q = 0.060–0.149 m3 /s. This figure illustrates that power production is indeed a function of the wheel speed. Although the power output is fairly constant for speeds ranging from 6 to 12 rpm, the power drops steeply for higher speeds. The curve thus indicates that for an effective operation of an overshot water wheel the correct choice of the operational speed is essential. By way of explanation it can be assumed that the efficiency of a water wheel must be a function of the relative speed of the inflowing water and the speed of the cells which are catching the water particles. The inflowing water must move faster than the cells. When the cells move with a very low speed, they fill up completely and water may even be lost. When the cells move too fast, only little water can enter each cell and the weight of the water which drives the wheel becomes small. For both cases the efficiency drops. The point of maximum efficiency should therefore be a function of the ratio of water particle velocity and peripheral speed of the wheel.

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Figure 6 Efficiency as a function of flow volume and wheel speed: (a) varying inflow velocity (Weidner, 1913a,b); (b) constant inflow velocity (Meerwarth, 1935).

comparison, the efficiencies from Meerwarth’s test as shown in Fig. 5 are plotted in Fig. 6(b). In Fig. 6(a), the efficiency of the wheel is a function of the wheel speed and flow volume (i.e. inflow velocity). For a certain combination of flow volume and wheel speed the wheel attains a maximum efficiency which drops off rapidly for slower or faster wheel speeds. For increasing flow volumes, the point of maximum efficiency moves t...