Experiment No. 1 PELTON WHEEL TURBINE Objective To investigate the performance of the Pelton Wheel turbine with different range of flow rates and rotational speeds. Summary of theory Pelton Wheel turbine is an impulse type of hydraulic turbine. The total drop in pressure of the fluid takes place in stationary nozzles. A proportion of the kinetic energy of a high velocity jet is converted into mechanical work delivered to the shaft, the remainder being dissipated by fluid friction and partly retained as kinetic energy of fluid leaving the cups. The fluid transfers its momentum to buckets mounted on the circumference of a wheel. Pelton Wheel or impulse type hydraulic turbine is used in hydroelectric scheme when the head available exceeds about 300m. The turbine is supplied with water under high head through a long conduit called penstock. The water is then accelerated through a nozzle and discharge at high-speed free jet at atmospheric pressure, which then impinges the cascade of impulse buckets. Control Volume Consider Pelton Wheel rotating in an anti-clockwise direction (refer to figure 2) with an angular velocity,, due to the combined action of an incident water jet and a clockwise resisting moment. We take a control volume that is moving at a constant velocity with the bucket on the Pelton Wheel as shown in figure 3. The velocity of the incident jet relative to the bucket is given by: - V r1 = V 1 - U = V 1 - R Where R is the mean radius of the wheel. Since the incident and emergent jets are both exposed to atmospheric pressure, the magnitude of the emergent jet will be only slightly less than the frictional resistance which can be allowed for by introducing a frictional resistance coefficient k 1 so that: - V r2 = K 1 V r1 1
The jet will be deflected so that the emergent jet is at an acute angle to the incident jet. The change in the component of relative velocity in the plane of the wheel (i.e. in the line of the incident jet) will be: - V r = V r1 + V r2 Cos = V r1 (1 + k 1 Cos ) = (V 1 U) (1 + k 1 Cos ) Which can be written as: V r = (V 1 U) (1 + c) Flow Discharge The discharge through the nozzle, Q from an inlet height H at pressure P is given by: H = P/ g Q = A n V 1 Where A n is the nozzle opening area. But, V Hence, 1 C v 2gH Q AnC v 2gH Where C v is the nozzle flow coefficient. Power Output Using the force-momentum equation, the force, F exerted on the bucket by the water jet is given by: F = Q V r The torque acting on the shaft of the Pelton Wheel is then: = FR = Q V r R 2
And the power output, W out is: W out = = Q V r U Substituting for V r gives: Efficiency W out = UQ (V 1 U) (1 + k 1 Cos ) The input hydraulic power, W in to the Pelton Wheel is the product of the inlet pressure and flow rate. W in = PQ = ghq and the efficiency of the Pelton Wheel is = W ou t / W in = U V / gh Procedures In this experiment, we will fix the flow rate and gradually varying the brake load from zero load to a maximum load. The speed is influenced by the coefficient of friction between the band and the shaft pulley, which is influenced by temperature; therefore, it is necessary at each condition to wait for the speed to stabilize before taking readings. The torque produced can be then determined knowing the force applied and the wheel speed. The experiment will be repeated for 3 different flow rates (3 different pressure values). 1. Zero the tension gauge at no load. 2. Prepare the friction band and weight hanger (weighing 350g) of the friction dynamometer. 3. Make sure that the suction valve and volumetric measuring valve are open (in line). 4. Switch on the Hydraulic Bench pump. 5. Fully open the bench flow-regulating valve. 6. Slowly increases the pump speed regulator until maximum (the white-line pointed to the downward direction). 7. Adjust the nozzle spear valve until the inlet pressure reads approximately 0.7 bar. 8. Wait until the condition has stabilized. 9. Record the weight (i.e. 350g) and the reading of the tension gauge. 10. Using the non-contact optical tachometer, measure the speed of rotation of the wheel in rpm. Point the light beam to a position least affected by the water in order to obtain 3
better accuracy. At low speed, the variation in the reading will be quite significant. (call the instructor to use the optical tachometer) 11. Add another 100 grams weight and repeat steps 8 to 10. 12. Repeat 11 in the step of 100 grams until the wheel stall (the wheel stop rotating). 13. Remove all the weight from the hanger. 14. Measure the flow rate. To measure the flow rate, close the volumetric measuring valve and note the time taken for the water to fill a certain volume using the scale (take 10 liters). 15. Open back the volumetric measuring valve. 16. Adjust the nozzle spear valve until the inlet pressure is approximately 0.9 bar and repeat steps 8 to 15. 17. Adjust the nozzle spear valve until the inlet pressure is approximately 1.1 bar and repeat steps 8 to 15. 18. Switch off the hydraulic bench pump. Data, Observation and Results Record the results of the experiment on the results sheet provided. Calculate the inlet head (H), the discharge or flow rate (Q) and the power input (W in ). H 5 (Px10 ) m g Where = 1000 kg/m 3 g = 9.81 m/s 2 Q Vol t x Win ( Px10 5 )( Qx10 3 ) Watt Calculate the measured torque ( m ), the measured power output (W out,m ) and the measured efficiency ( m ). (W S) m x grd 1000 Where W = Applied weight in grams S = Tension gauge reading in grams R d = Radius of dynamometer wheel = 0.03 meter 4
W out, m 2 m Watt m = W out,m / W in Calculate the theoretical values of output torque ( th ), power output (W out,th ) and efficiency ( th ). th Qx10 3 C v (2gH) R2 1 k1cos R Where K 1 = 0.8 = 25 o W out, th th 2 Watt th = W out,th / W in Calculate the velocity ratio U/V 1. U V 1 C v R 2gH 2 x Watt Where R = 0.05m C v = 0.94 Plot the graph of measured power against wheel speed for all conditions. (All three conditions on the same graph Graph 1) Plot the graph of measured efficiency against wheel speed for all conditions. (All three conditions on the same graph Graph 2) Analysis and Discussion Explain the working principle of Pelton Wheel Turbine. Comment on Graph 1 and Graph 2. Discuss the performance of the Pelton Wheel turbine with respect to different range of flow rates and different range of rotational speeds. List the possible sources of errors and safety precaution. 5
Figure 1: Detail of Pelton Wheel Buckets Figure 2: Absolute Velocities Figure 3: Velocities Relative to Bucket 6
Figure 4: General Arrangement of Cussons Pelton Wheel 7
Example of Result Table Inlet pressure P = bar Inlet Head H = m Volume of water collected Vol = liter Time taken t = s Discharge Q = liter/min Power Input W in = Watt Weight W (g) 350 450 550 650 750 850 950 1050 1150 1250 1350 Tension S (g) Speed (rpm) Measured Torque m (Nm) Measured Power Out W out,m (Watt) Measured Efficiency m Theoretical Torque th (Nm) Theoretical Power Out W out,th (Watt) Theoretical Efficiency th U/V 1 8