AbstractThe subject of this report is the experimental investigation of the workings of the Francis turbine. This involves the use of a demonstration Francis turbine in order to obtain the performance curves. A brief explanation of the working principle of a reaction turbine is included for better analysis of the data. The efficiency of the Francis turbine is calculated and compared against others who have carried out similar experiments. The results from the experiment largely agree with predictions and literature results. The optimum efficiency was found to be 45.1% with a 4.13W of output shaft power at 865rpm of rotation speed. Efficiencies with higher or lower speeds produced a lower efficiency as to be expected. A significant difference is efficiency was found to be present. This is due to several factors. The fixed position of the guide vanes and friction loses in the pipes contributed to the discrepancies in the data produced. Some of the minor contributions to error involved the difficulty of reading the values of the spring balance the optical tachometer, and the air bubble formed due to the way the apparatus was setup.

Table of ContentsAbstract11.0 Aim32.0 Introduction33.0 Theory44.0 Experimental Investigation64.1 Experimental apparatus64.2 Experimental procedure85.0 Results95.1 Experimental data95.2 Plots of experimental data106.0 Discussion of Results127.0 Comments on Errors148.0 Conclusion15Bibliography16

1.0 AimThe aim of this experiment is to obtain the performance curves of a Francis Turbine setup across a range of rotational speeds. Another aim would be to understand the working principles of a Francis Turbine. 2.0 IntroductionThe Francis turbine was invented by a British-American engineer, James B. Francis. It is an inward flow reaction turbine which has a purely radial flow runner. It operates under medium heads and requires medium flow rate. The Francis Turbine is one of the most common types of turbine used in various forms of applications. The Francis turbine converts the pressure energy of the water into kinetic energy in the control device and in the impeller. The pressure of the working fluid within the housing changes as it goes through the turbine, entering with high pressure and exiting with low pressure. The turbine power is controlled by adjusting the vanes in the control device. (Lab Manual | FRANCIS TURBINE | Engineering Tutorials, 2009)

Figure 1 - Schematic of the Francis Turbine: On the left: guide vane position 0, no water flow, and turbine power at 0; on the right: guide vane position 20, maximum water flow and full turbine power (G.U.N.T., 2014)Operating principle of the Francis turbine:1. Spiral housing 2. Guide vane 3. Impeller with vanes 4. Flow

The speed of the water is control by adjusting the guide vanes. A transparent window is used to view the flow inside the housing (See Figure 3). The turbine torque can is measured by the difference in the readings on the spring balance. A tachometer is used to measure the rotational speed in rounds per minute. (G.U.N.T., 2014)

3.0 TheoryFirst the net force is calculated using;Net Force, F = F1 F2 Equation 1F1 and F2 are the forces from the spring balances on the braking device. The net force is then used to calculate the moment of the shaft using the formula;Moment, M = Equation 2where D is the diameter of the belt pulley.Using the moment calculated, the turbine shaft power is calculated using the following formula;Turbine Shaft Power, Pout = Equation 3where N is the rotational speed in RPM. Using the pressure, P, the density of water, , and the constant of gravity, g, the head is calculated with the formula;Head, H = Equation 4Using this head value, the hydraulic power is calculated using the formula;Hydraulic Power, Phyd = Equation 5where is the volumetric flow rate.Using the value of the turbine shaft power and the hydraulic power we can calculate the efficiency using;Efficiency, = Equation 6

4.0 Experimental Investigation4.1 Experimental apparatus

1. Demonstration Francis turbine with basic hydraulics bench. 2. Optical tachometer

Figure 2 Demonstration Francis turbine with basic hydraulic bench (Front view)

Figure 3 - Demonstration Francis turbine with basic hydraulic bench (Back view)

Figure 4 - Optical Tachometer

4.2 Experimental procedure1. The braking device of the Francis is fully released using the hand wheel. The spring balances are now relaxed and the belt is no longer be pulled against the pulley.

2. The main cock is closed and the pump is switched on. The main cock is then slowly opened to its maximum.

3. The lever for vane adjustment is released by turning it. The air from the draft tube is expelled by slowly opening and closing the vanes.

4. The vane is set to the maximum speed position. 5. The force F on the braking device is increased in stages with the turbine shaft speed N being gradually decreased at intervals of approximately 100rpm. 6. Eighteen readings of the speed are taken with optical tachometer by pointing at the reflector that is fixed to the belt pulley. 7. At each decrement of the speed, the net force F is measured which is the difference between the two values obtained on the spring balances. (F1 F2) The pressure in bar on the pressure gauge is also measured at each decrement of the speed.

2

5.0 Results

5.1 Experimental dataNo.Speed (rpm)Force, F1 (N)Force, F2 (N)F = F1 - F2Torque, M (Nm)Turbine Shaft Power, Pout (W)Pressure, P (bar)Head, H (m)Hydraulic Power, Phyd (W)Efficiency (%)

11977.00.3500.3500000.289582.95188E-0511.004030.00000

21880.50.4000.5500.1500.003750.738470.289582.95188E-0511.004036.71091

31778.50.4500.7750.3250.008121.513230.289582.95188E-0511.0040313.75608

41682.00.5000.9250.4250.010631.871470.289582.95188E-0511.0040317.00775

51583.00.4751.1250.6500.016252.693780.289582.95188E-0511.0040324.47998

61480.50.5001.4250.9250.023123.585240.289582.95188E-0511.0040332.58029

71380.50.5251.5501.0250.025623.704490.289582.95188E-0511.0040333.66458

81270.00.5751.7501.1750.029373.906700.289582.95188E-0511.0040335.49650

91184.50.6251.9001.2750.031873.953790.275792.81132E-0510.4800337.78585

101076.50.6502.1001.4500.036254.086490.275792.81132E-0510.4800339.08813

11986.550.7002.3501.6500.041254.261590.265452.70589E-0510.0870342.68388

12864.750.7252.5501.8250.045624.131640.248212.53019E-059.4320345.07182

13779.00.8002.7001.9000.047503.874890.248212.53019E-059.4320342.24703

14674.00.8252.8502.0250.050623.573170.248212.53019E-059.4320339.04140

15556.50.8753.0002.1250.053123.095940.248212.53019E-059.4320333.59499

16448.30.9253.1002.1750.054372.552680.248212.53019E-059.4320327.61730

17356.70.9503.1752.2250.055622.077500.248212.53019E-059.4320322.42175

18286.01.0003.2002.2000.055901.647240.289582.95188E-0511.0040314.96944

Table 1 Experimental data

5.2 Plots of experimental data

Graph 1 - Curve of torque vs. rotational speed

Graph 2 - Curve of turbine shaft power vs. rotational speed

Graph 3 - Curve of efficiency vs. rotational speed6.0 Discussion of ResultsThe trends obtained for both raw results and calculated results agree well with the predicted outcome of the experiment. In Graph 1, the graph shows that the torque of the output shaft decreases linearly with its rotational velocity. This is an expected relationship since according to Newtons Third Law of equal and opposite reaction, the torque applied by shaft on the belt is equivalent to the resistance torque applied by the belt onto the shaft. The resistance torque from the belt then decreases the rotational speed of the output shaft. A similar pattern was also displayed in St. Gallens book (about designing small hydropower systems) with the title Governor Product Information (Gerhard Fischer, 2014), whose graph in Graph 4 shows how the relative torque of the hydropower system varies with the relative speed of the output shaft. The consistency of the result between the experiment and those from past experiments increases the reliability and credibility of the final conclusion.

Graph 4 - Graph of Relative Torque against Relative Speed from Governor Product Information, St. Gallen, 1990

The results for turbine shaft power and efficiency of Francis turbine experiment also appear to agree well with the theoretical results. In Graph 2 and Graph 3, both turbine shaft power and overall efficiency displayed a similar pattern where they would increase from zero to a peak value of 4.13W shaft power output and 45.1% turbine efficiency, with a rotation speed of 864.75rpm. After the peak, both turbine shaft power and overall efficiency started to fall off with further increase in rotation speed, until they reaches zero at 1977rpm. Since both turbine shaft power and overall turbine efficiency has only one peak at the optimal rotational speed, hence the effect of rotation speed on power output and overall efficiency is best described with a parabolic line of best fit as shown in Graph 2 and Graph 3. The developer of the Francis turbine used for this experiment, G.U.N.T. published an official characteristic performance curve for power output of turbine shaft versus operating speed (G.U.N.T., 2014), and the results were very similar to that obtained from the experiment, as shown in Graph 5. Similarly, the trends demonstrated by these two curves were consistent with the predictions as well. When the torque of the output shaft approaches zero, it is similar to a situation where a generator is disconnected from a turbine, and the rotation speed of the turbine increases to its maximum value. This specific speed where the output torque is zero is known as the Runaway Speed. The experimental runaway speed, however, is usually lesser than its predicted value. There are two ways to explain this situation. The first reason is that at high rotation speed, the frictional energy loss at the shaft is more dominant compared to the kinetic energy loss of the water flowing in the turbines. Besides that, when the turbine runner is rotating at high speed, the relative speed between the runner and water is close to zero. When the relative speed is very low, the pressure difference between the two sides of the blades would be very insignificant, which would in turn hinder the transfer of energy from the flowing water to the turbine. These two factors adds up to cause the drop in overall efficiency and turbine shaft power on the right side of the graphs shown in Graph 2 and Graph 3. On the other hand, at very high output shaft torque, the runner of the turbine can only rotate at a very much lower speed. This caused a disruption of water flow at the runner since there was a huge difference between the speed of water and the runner. This flow disruption in turn affected the efficiency of energy transfer from the flowing water to the rotating turbine, causing the output shaft power and efficiency of the entire Francis turbine to decrease on the left side of the graphs shown in Graph 2 and Graph 3.

Graph 5 - Characteristic performance curve for power output of turbine shaft versus operating speed of G.U.N.T. HM 150.20

Several comparisons were made with industrial-grade Francis turbines by comparing the overall turbine efficiency of their Francis turbines compared to those derived from the experiment. It is found that the maximum efficiency obtained from the experiment was very much lower than that of industrial-grade Francis turbines. Turbogen Engineering, a company in Switzerland that designs and supplies turbines was able to produce a result of more than 90% overall efficiency in its Francis turbines (Sagl, 2014), as compared to the maximum efficiency of 45.1% from the experiment.One of the possible reasons for the significant difference in efficiency is due to the fixed angle position of the guide vanes. The position of the guide vanes was set as a fixed variable, with its angle set to the maximum speed position throughout the experiment. Although the maximum speed position might seem to be the most efficient angle of attack, however experiments comparing different angle of attacks should be carried out to investigate the most suitable angle position for the guide vanes to produce a result of highest efficiency.Besides that, a significant amount of right-angled pipe joints were found throughout the Francis turbine device setup used for the experiment. Frictional loses from these sharp pipe bending would definitely contribute to the low efficiency of the experimental turbine as well, therefore a gentle bend would be much more preferred compared to those used in the setup (Dietzch, 2014).Apart from the above two reasons, lack of maintenance of the Francis turbine setup used in the experiment would contribute to the lack in turbine efficiency as well. The lubrication on the rotating parts of the setup such as the turbines and the rotating shaft might have already worn off after repetitive usage throughout the years. Besides that, due to frequent exposure to air and moisture, there might be corrosion occurring within the turbine. Corrosion on certain important parts such as the rotating shaft or guide vanes would disrupt the motion of the components, hence reducing the efficiency of the turbine. Guide vanes that have served for a long functional period would also tend to be damaged due to cavitation (Pardeep Kumar, 2014).7.0 Comments on ErrorsError analysis is carried out using Equation 7 whereby both the systematic and random errors are taken into account. The elemental systematic error, B is found by analysing the design-stage uncertainty as expressed in Equation 8. Since the number of data collected is N=2, thus the degree of freedom, v is v = N-1 = 1. From this, the t estimator can be found as shown in Equation 9. The elemental random error, P is expressed as in Equation 10 using standard deviation of the means. Following that, the uncertainty of the data with 95% probability can be expressed as in Equation 7.Equation 7Equation 8Equation 9Equation 10Equation 11Most errors that occurred during the experiment concern the apparatus, which caused inaccuracy as well as imprecision in the results. Firstly, the mass balance of the pulley attached to the rotating shaft was not properly tuned, resulting in vibration of the shaft while the turbine is functioning. The vibration of the pulley if then transferred to the belt, causing a fluctuating reading on the spring balance. The vibration and fluctuation effect increases with increasing resistance torque applied by the belt on the pulley. Readings were made by noticing the maximum and minimum values caused by the fluctuations, and then the average of the two values was calculated as the supposed reading for the particular repetition. However, these errors were most likely not sufficient to disagree the trend of the graphs discussed in Graph 1, Graph 2, and Graph 3, but they could have shifted the position of the peak and hence the maximum power and efficiency of the output. The errors contributed by this factor would not cause the shapes of the graphs to change drastically, but it might cause some random errors where the readings are scattered around the true reading by a relatively small margin. Besides that, there were also difficulties in measuring the rotation speed of the shaft. It was difficult to ensure that the optical tachometer was steadily held by the human hand. Human errors were inevitable to vary the height and angle at which the tachometer was held. The variation of the tachometer sensor position and angle with reference to the sticker might lead to inaccurate and imprecise readings of the shaft rotation speed. Adding on to that, optical tachometer functions by detecting the reflection of the light emitted by the LED within it. The area projected by the light source is relatively large, causing the reflection of the light source to scatter across a larger area with a lower intensity. The scattering effect along with the decreased intensity would most likely cause the tachometer reading to further deviate from its true reading. Similar to the first error, the tachometer reading error would not significantly change the trend of the results as well, however it still could shift the position of the peaks. The errors would only cause the readings obtained to deviate from the true reading by a relatively small margin.Another error of which is a concern to the results is the swirling flow observed in the turbine outlet pipe. The flow is decelerating as it exits the runner in the turbine draft tube, resulting in a conversion of excess kinetic energy to static pressure (Sebastian Muntean, 2007). The decelerated swirling flow often results in vortex breakdown, which contributes to error in data acquisition. Although precautionary measures were taken to eliminate the air bubbles by opening and closing the vanes each time before the resistance torque was changed, air bubbles are still continuously forming even when measurements were being made. This situation might have led to minor errors in the results collected. It is speculated that the air bubbles might have been due to water from the turbine outlet splashing vertically downwards onto the tank before being channeled to the pump. Air bubbles might have trapped during the vigorous falling process and therefore leading to this particular error.Even though the errors mentioned above did not significantly affect the expected trend, improvements on these errors are still required for a more reliable result. Firstly, maintenance should be done on the Francis turbine device, especially at the region where the shaft is located. The pulley should be checked for damage to ensure that it does not cause any vibration due to unbalanced mass around the rotating shaft. Regular checkup should also be made on highly stress concentrated components such as the bearing connecting the turbine and the rotating shaft. Components that consistently exposed to stress and humidity are more likely to have a shorter lifespan, hence usually causing errors in the experiments. As for the tachometer, an adjustable stand should be used to hold the optical tachometer so that its position and angle which respect to the reflective sticker remains still. Alternatively, with a higher budget, a more accurate and sensitive laser tachometer can be used instead of optical tachometer, where the scattering effect is less and has a much higher light intensity. Lastly, the turbine outlet platform can be slightly modified so that the water exiting from the turbine would flow down into the channel leading to the pump, instead of allowing it to undergo free fall into the tank below it.8.0 ConclusionIn conclusion, the objective of this experiment was met, in which the performance curves of the demonstration Francis turbine over a range of rotational speed was determined and explained. In this experiment, a water pump was used to channel water into the Francis turbine, which would in turn spin a shaft connected to a friction belt to provide power output. By adjusting the frictional torque applied on the rotating shaft, the overall efficiency and the power output of the Francis turbine was able to be measured at different turbine rotational speed. Based on results obtained, the relationship between the output torque and shaft rotational speed was best described with a linearly decreasing graph; while the output power and overall efficiency versus shaft rotational speed was best described with a parabolic best fit line. The parabolic line showed that the output power and efficiency of Francis turbine will increase with increasing rotating speed, until they arrived at a peak value, then decreases after further increase in shaft rotational speed. The highest overall efficiency recorded was 45.1% with a 4.13W output shaft power at 865rpm rotation speed. This relationship is expected with reference to the balancing of inefficiency in energy transfer within the Francis turbine caused by an overly high and overly low turbine rotation speed as discussed in the context. Conclusively, the overall efficiency will increase as the shaft rotation speed approaches the optimum balanced speed.Although this result was also verified by comparison with other similar experiments, nevertheless there were various errors encountered regarding the measuring methods and devices that affected the accuracy of the raw data. The lack in accuracy of the data did not affect the accuracy of the trend, but would definitely significantly affect the precision of the readings from the true results. As a consequence, future work needs to be focused on reducing the uncertainties in measuring devices and method for more reliable readings. With more accurate readings, optimal shaft rotation speed can be found accurately by interpolating the results to determine the peak shaft power output and overall turbine efficiency.Conclusively, this experiment was successful in producing a reliable relationship or trend involving the overall efficiency and shaft rotational speed that agrees with reasonable explanations. Hence, the relationship between shaft torque output, output power, and overall efficiency, against shaft rotational speed can be applied and related to larger scaled Francis turbines for further designs and developments.BibliographyG.U.N.T. (2014, April). G.U.N.T. - Equipment for engineering education - HM 150.20. Retrieved August 26, 2014 from G.U.N.T. - Equipment for engineering education: www.gunt.de/networks/gunt/sites/s1/mmcontent/.../07015020%202.pdfLab Manual | FRANCIS TURBINE | Engineering Tutorials. (2009, October 2009). Retrieved August 26, 2014 from Engineering Tutorials for all Branches of Engineering | Engineering Tutorials: http://engineering.myindialist.com/2009/lab-manual-francis-turbine/#.U_x9SKNdy3FGerhard Fischer, A. A.-M. (2014, September 2). Governor Product Information: Annex: Technical Notes and Definitions: A3. Dynamics of the turbine/generator/consumer system. From New Zealand Digital Library: http://www.nzdl.org/gsdlmod?e=d-00000-00---off-0hdl--00-0----0-10-0---0---0direct-10---4-------0-0l--11-en-50---20-help---00-0-1-00-0-0-11-1-0utfZz-8-00-0-0-11-10-0utfZz-8-00&a=d&c=hdl&cl=CL1.7&d=HASH019081d439253e9516222689.9.3Dietzch, C. (2014, September 02). Minimizing Pumping-System Friction Loss | Pumps & Systems. From Pumps & Systems: http://www.pump-zone.com/topics/piping/minimizing-pumping-system-friction-lossSagl, T. E. (2014, September 02). Turbogen Engineering - Hydraulic Turbines - Power Technology. From Power Technology: http://www.power-technology.com/contractors/powerplant/turbogenengineering/Pardeep Kumar, R. S. (2014, September 02). Study of cavitation in hydro turbinesA review. From ScienceDirect: http://www.sciencedirect.com/science/article/pii/S1364032109001609Sebastian Muntean, A. R.-R. (2007). Development of a Swirling Flow Apparatus for Analysis and Development of Swirling Flow Control. Turbomachinery Hydrodynamics. Romania: Romanian Government Ministry of Education and Research, National Authority for Scientific Research.