paper hidraulica.docx

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Hydraulic performance of water wheels in channels

ECUADOR 31-JULIO-2014

Miguel ngel Chvez

Gnesis Figueroa

Juan Diego Marazita

Cristhian Ponguillo

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A R T I C L E I N F O A B S T R A C T

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The research upon how an undershot water wheel is affected by varying the width of a particular zone of the channel involved is the main topic analyzed. For achieving this, a controlled environment provided by an artificial hydraulic system in lab is performed while taking into account several restrictions to the system. The kinetic energy involved in the Head will be taken as negligible for the analysis and only the difference between depths at upstream and downstream region will be taken into account. This Head will remain constant through the whole research, while the load exerted over the water wheel and the widths of the channel will be the dominant factors. By having different values of flow Q, it will be obtained respective values of Power input and output, with which a relation being the efficiency is calculated. This results will be organized in graphs so that it can be appreciated from which point up to what limited it will be prudent to minimize the width of the channel and increase the flow Q. It will be evident at the results that clearly defined range for minimum a maximum variations of the width and flow Q provide the peak efficiencies in this hydraulic energy system.

Keywords:

Water Wheel

Channel

Flowing

Efficient

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ESPOL FICT Hydraulic Investigation

1. Introduction

The use of renewable energy has been a priority since the last decades, as with the human progress in technology and other developments, the environment has taken a critical impact. The application of Hydraulic energy has taken a very important role for this matter of clean energy and even since very antique times this system already been used. As time passed, the water wheels were exchanged for more complex systems such as turbines, which would provide greater results but at environmental costs.

Water wheels consist of wheel with blades that vary according the chosen materials of construction. These wheels rotate through their defined axe, while the striking force of the flow of water thrusts the blades of the wheel and by applying a torque in the shafts and thus generating a movement. There are four main types of water wheels, the overshot, undershot, free fall and horizontal water wheel. Each one has its specific applications and respective efficiencies, some of them such as the horizontal wheel, have been discarded as obsolete due to low efficiencies compared to the rest.

The undershot water wheel works for cases in which low difference in head depths are taken into account, having also other limitations such as flow rate. While the overshot has superior results in terms of efficiency, the limitation of this kind is that it is needed great differences between depth heads, or potential energy to be applicable. The use of undershot water wheels is applicable to regions where high potential energies are not accessible due to the topographic and hydrologic factors of that place.

For the undershot water wheel to be able to reach its maximum performance it is needed that a restricted flow of volume of water and width of the channel are taking in consideration. When taking into account the flow through a channel, other aspects such as the gradient %, the depth, length of the channel are a must for a complete analysis but but only the two factors established before. Further aspects will be involved in this study, such as a supercritical state been involved and how a different material would affect the performance of the wheel itself.

2. Theoretical foundations

A water wheel is a mechanism that extract usable power using the water flowing in a river or stream [3] (Anurat, Chainaron, 2011). Invented around two centuries before Christ, it was long one of the most important way to get power in antiquity [4] (Reynolds, 1983).

The Greek and Roman Empire used it to increase the production in mills, also for another way to get power. There are many types of water wheels, the figure 1 shows the main types of them.

Figure 1. Types of water wheel (Anurat T., Chainaron I., 2011).

All those types of water wheels have different performance and they was an important source of energy in the past. However this survey is oriented to analyze the performance of the undershot water wheel.

The main difference between undershot water wheel and breastshot water wheel is that the water enters in the wheel bellow the axle, it was originally used as an impulse wheel, employing the kinetic energy of the flow (Mller, 2011). Poncelet a French engineer noticed that the potential energy of the slow moving water masses in small rivers was appreciably larger than the kinetic energy, and designed the first wheel for very low head differences which employed the potential energy only.

After many years Sagebien another French engineer improved the original design, the basic change was the backward inclination of the blades, this made the water enter in a wheel without impact decreasing energy losses [4], but the most efficient shape for these wheels was finally developed by the Swiss hydraulic engineer Walter Zuppinger. The wheel employs only the potential energy of the flow as the principal driving force, the figure 2 shows the section and geometry required for efficient operation. The water enters the wheel over a weir, so that the cells can be filled rapidly.

Figure 2. Cross-section of undershot water wheel and Work Principle (Mller, 2011)

The blades are arranged in a way so as to avoid losses at the water entry, then to gradually reduce the head of water in each cell and finally to discharge the water, again with a minimum of losses. [5]

In the undershot water wheels the water enters the wheel below its axis. This design configuration it can be used for very small differences range from 0.5 to 2.5 m, and large volumes of flow ranges between 0.5 to 0.95 m / s per m width.

3. Methodology

3.1 Analysis of the efficiency of a vertical water wheel relative to the channel width.

In one of the publications of the Renewable Energy international Journal, called Experimental investigation on the effect of channel width on flexible rubber blade water wheel performance was found an experiment to analyze the efficiency of a water wheel. The analysis been performed by the influence of the channel width in the efficiency of a waterwheel has been established considering some fixed factors as limitations. Been centered solely in a shallow water analysis, when considering the energy generated by this hydraulic tool, the following parameters are to be calculated and later analyzed

To calculate the produced energy from the water wheel, the extractable hydraulic power is:

Where:

: Hydraulic power input to the wheel

Density of water (kg/m3)

9.81 m/s2

Volumetric water flow rate (m3/s)

H: Difference in total energy line upstream and downstream of the wheel (m)

The dynamic head difference between upstream and downstream sides is negligible, so it has not taken into consideration.

To calculate the efficiency of the water wheel, it is necessary to calculate the net energy obtained, and make a comparison with the energy produced.

Where:

The angular velocity, calculate from the number of revolutions N. (rpm)

The shaft torque, this is calculated by the product of the force produced in each of the water wheel blades and the moment arm, which in this case, is the wheel radius.

Finally, the efficient of the water wheel is calculated by:

For the study been made, a maximum flow Qmax will be used and it will be given by a flow passing through the power wheel with no resistance at all from a particular load cell. In other words the water wheel will revolve at maximum capacity.

This equation depends of a constant C that is related with the height at the notch and the respective head at the very same point. The factor that will provide the different results of study will be, depending in how are realized the restrictions of analysis. Using real results been provided by the hydraulic study realized at the university of South Hampton, it will be explained how has the different parameters been affected by the width.

This experiment consisted in a test channel of 2.7m long, 0.74m wide and 0.4m deep, with a variable height at the entrance and the exit of the water in the channel, and a fixed sharp crested weir at the outlet measurement. The water wheel consists of acrylic cylindrical hub of 150 mm diameter and 250mm wide with 12 blades of 100x250mm size. Blades are made of flexible butyl rubber sheet of 1mm thickness.

All tests were done keeping the head constant. The key variables is the channel width

Figure ___: Assembled mechanism for testing

Source: Renewable Energy international Journal- Experimental investigation on the effect of channel width on flexible rubber blade water wheel performance (2013)

The revolutions of the wheel were recorded manually with the use of a stop watch and the numbers of revolution were within the precision of 0.3 rpm. Three different time values for 10 revolutions were recorded for better accuracy and a mean value was taken for the calculations.

Trials with different channel widths were performed experimentally and were compared with the largest channel width that corresponds to 740mm.

The following test set ups were investigated experimentally and compared with the full width set up of 740 mm both on upstream and downstream.

Tests performed were:

Full channel width of 740 mm both on upstream and downstream.

Reduced upstream channel width tests

Upstream 445 mm and downstream 740 mm

Upstream 350 mm and downstream 740 mm

The results of the produced energy with different width of the channel are shown in the graph as a function of the variation of flow rate versus maximum channel flow.

Graph ___: Power output as a function of relative flow rate for changing upstream width.


With the values of the generated energy in the water wheel, with different channel widths, proceeds to calculate the efficiency in each of the cases with the equations shown above.

Graph ___: Efficiency as a function of relative flow rate for changing upstream width.


The results were evident, as it clearly stated that for limited flow rates 3-6 l/s , it was given a maximum efficiency for all the cases been stated before. The second most relevant aspect was that for the smallest width of 350mm at upstream flow, the efficiency reached its peak at 66%. While for the greater widths the efficiency diminished. The reason for this first result to happen, was that at greater widths, the turbulence losses been given at the blades of the wheel would be high.

It is preferred that this turbulence loss is diminished by having minor widths and thus improving the rotational quality of the water wheel as higher flow rates can still be used without efficiency loss. For generating energy it is indeed a certain amount of power input needed but if the flow Q been applied is greater than a certain amount, then the efficiency will gradually drop. Even though a greater power input is generated, the unstable flow will generate splashes that will mean turbulence on the upstream region. Both the shaft torque and the rotational speed of the wheel will increase by having a small width at the upstream region, but the angular speed will be the one that define how much will the performance of the system has improved or not depending on the variation of width.

The second analysis will consider variations of width for the downstream region, while assuming the maximum width at the upstream zone. The following chart presents the results as the graph previously shown. In this case we will have a maximum a constant upstream flow of 740mm and a 320mm downstream flow. The last case is a special diverged channel in the downstream flow with an angle of 12 grad. For this case and simplicity of analysis, it will only be shown the variations of efficiency, since what was previously shown for the power output chart will somehow replicate in this second case.

Graph ___: Efficiency as a function of relative flow rate for changing downstream width.


One more time, it was proven that by having minor widths, the efficiency, power output, torque and angular speed will all improve until a certain point. The only clear difference in this second study was that a diverged channel setup at the downstream region was used, it had an angle of 12 grad. By having this configuration, the efficiency improved up to nearly 65% because of particular action of the flow happening right at the water wheel in the downstream.

Due to this great angle, a hydraulic jump was provoked at that point, meaning that a supercritical flow happened. This means that a great velocity of the flow will occur and thus will provide high rotational speeds for the water wheel. The latter will mean greater power outputs and better efficiency. It is stated based in the results that either by varying the upstream or downstream width of the channel involved in this water wheel, will improve the efficiency if the flow is in a determined interval and the width also is not exceed past a minimum length. The fact of using rubber materials for the edges of the blades indeed also improved the performance of the system as it aids with the flow of sediments and decrease in gap losses.

4. Conclusions and recommendations

Analyzing the hydraulic performance of water wheel has too many parameters to be considered with many possible results depending on the criteria and limitations applied to the case. Thats why the vast pool of possibilities was narrowed to the specific case of an undershot water wheel, which would have its Head H constant at all times, only varying the load applied to the wheel and the width of the channel. Further improvements of the performance were applied, such as changing the material properties of the blades of the wheel, which provided even better results, but the same criteria for an undershot channel was still applied

The results provided by the research study in a controlled environment, gave clear evidence that the efficiency achieved was near 65%, which is the estimate range for undershot water wheels, which is our case of study. The power output, the angular velocity and shaft torque are all directly correlated and gave results of proving that meeting certain conditions of a range of flow Q, while having minor channel widths, efficiency for the water wheel is clearly maximized. The studies showed that further increasing the flow or decreasing the channel width for hoping to achieve greater efficiencies is affected by a steady diminishing value in the efficiency obtained.

The application of a conventional waterwheel and not turbines or any other complex hydraulic system for achieving clear energy is seen as more viable with the increased research in this topic. Complex systems tend to be non-friendly with the environment or either too expensive to be applied in any place or situation. It is highly recommendable to keep researching in all the isolated applications for water wheels, besides the undershot type, there are others such as the overshot, free fall or even horizontal water wheel. These types should be further researched to obtain applications for diverse conditions involving the water wheel at either shallow or deep water.

Even though realizing studies at an enclosed or controlled environment is what its developed with these researches, the study of this application at a non-artificial channel would provide better benefits in general. As a low cost energy alternative, it is important to model this study in a more likely environment given the situation of a rural region where there will not be possible such a high investment in this method applied. Further studies by varying other parameters such as the depth, total Head, gradient would provide even more options for applying in many kinds of conditions. A final recommendation would be to try proving through more theoretical and empirical approach a way to relate this results to a real scale project. This topic been analyzed will indeed be of great use in places where expensive energy sources are not an option or even improving already designed systems that are not working at their maximum capacity.

5. Bibliography

[1] Mler G., Denchfiel S., Marth R., Shelmerdine B. (n.d.). Stream Wheels for applications in shallow and deep water. Retrieved from:

http://hmf.enseeiht.fr/travaux/CD0708/beiere/3/html/bi/3/fichiers/Mullerstreamwheel.pdf

[2] Oleson, J. (1943). Greek and Roman mechanical water-lifting devices. ISBN: 90-277-1693-5, retrieved from http://books.google.es/books?id=ynejM1TATMC&printsec=frontcover&source

=gbs_ge_summary_r&cad=0#v=onepage&q&f=false

[3] Anurat T., Chainaron I. (2011). Energy Procedia, The effect of Paddle number inmersed radius ratio on water wheel perfomance, retrieved from: http://www.sciencedirect.com/science/article/pii/S1876610211017929. DOI:10.1016/j.egypro.2011.09.039

[4] Reynolds, T.S. (1983). Stronger than a hundred men, retrieved from: http://books.google.es/books?hl=en&lr=&id=aZ0runvrq0AC&oi=fnd&pg=PR11&dq=water+wheels+history&ots=mJWM0xXdxm&sig=hcdETg4_hb3ejjWrChc7ooebIXo#v=onepage&q=water%20wheels%20history&f=false. ISBN:0-8018-2554-2554-7.

[5] Mller, D. G. (2011). Water Wheels as a power source. The Queens University of Belfast, Civil Engineering Department Retrieved from: http://hmf.enseeiht.fr/travaux/CD0708/beiere/3/html/bi/3/fichiers/Muller_histo.pdf

[6] Mler G, Wolter C., (2004). The breastshot waterwheel: design and model tests. Retrieved from: http://www.steffenreichel.homepage.t-online.de/Muehlen/Infos/ModernWaterwheels.pdf

[7] Paudel S., Linton N., Uanke, Saenger N., (2013). Experimental investigation on the effect of channel width on flexible rubber blade water wheel performance. Retrieved from: http://www.sciencedirect.com/science/article/pii/S0960148112006519. DOI: 10.1016/j.renene.2012.10.014

[8] Hansen R. (n.d.), Water Wheels. Retrieved from:

http://waterhistory.org/histories/waterwheels/waterwheels.pdf

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