Investigating The Performance Characteristics Of Pelton Turbine

Objectives

To explore the performance of a Pelton turbine and calculate power at 2 distinct nozzle diameters and varied turbine speeds.

The Pelton Wheel turbine is an impulse-based hydraulic turbine. The overall pressure of fluid is lowered with stationary nozzles. A portion of the kinetic energy of a high-velocity jet is transformed into mechanical work for the shaft, while the rest is squandered as kinetic energy as the fluid get out of the turbine cups. The fluid’s force is conveyed to buckets installed and arrayed on the circular wheel (Gupta and Prasad 2012, pp.364-370; (Perrig et al., 2006, n.p.)). An impulse type hydraulic turbine, such as a Pelton Wheel is preferred for use used in a hydroelectric plant or setup when dealing with a head of over 300 meters. The penstock, a long pipe that delivers water to the turbine, is used. The water is then accelerated through a nozzle and ejected at atmospheric pressure as a high-speed free jet, impinging on the impulse buckets in a cascade.

 

Figure 1: Pelton Turbine Unit

Steam passes through a nozzle and impinges on moving blades in an impulse turbine. Kinetic energy is transferred from the steam to the buckets. The relative velocity and steam pressure are both constant (Dixon and Hall, 2013). The blades of this type of turbine are symmetrical, and there are fewer stages necessary for the same amount of power to be created than with a reaction turbine.

Steam is discharged from the guiding mechanism first, followed by the moving blades. The steam pressure is reduced as it glides over the rotating blades. The relative velocity, on the other hand, is rising. The blades are not symmetrical, as they are with impulse turbines, and the number of stages necessary for the same amount of power is higher (Okot 2013, pp.515-520).

The Pelton Wheel turbine is a hydraulic turbine that works on the principle of impulse. In stationary nozzles, the total pressure decrease of the fluid occurs. Some of the total energy produced as kinetic energy from the high-velocity fluid water jetting from the nozzle is transformed into mechanical work and supplied to the shaft. The rest of the energy that is not transformed into useful mechanical energy is lost through friction due fluids interactions and small portions retained as fluid kinetic energy exiting the cups (Zoppé et al., 2006, n.p.). When the available head in a hydroelectric scheme surpasses roughly 300m, a Pelton wheel is preferred and is useful. Water is delivered to the turbine via a long conduit known as the penstock, which has a high head. The water is then accelerated through a nozzle and discharged at atmospheric pressure as a high-speed free jet, impinging the cascade of impulse buckets.

Impulse Turbines

Euler Turbomachine principle is used, which is expressed as follows;

Where;

r1 = r2 = r: the mean radius of the wheel, and ????: turbine angular velocity,w= 2????n⁄60, (rad/s).

The relative departure speed of the water in the relative frame of reference travelling with the bucket is:

Vj − U = Vj − wr

whereby;Vj : jet speed, m/s, U = wr,

The tangential velocity at turbine inlet, V2, ????:

V2, t = Vj

The tangential velocity at turbine outlet at V1, ???? is given from the below velocity triangle:

sin (β − 90°) = − cos β

V1, t = wr+ (Vj − wr) cosB (3)

Taking an assumption that water makes angle B, and there is no energy lose;

r = 82.5mm

B = 175°

Computation of discharge via nozzle, V can be arrived at using the inlet height H at pressure p3;

p3 = pgH; H = p3⁄pg, V = AjVj, Vj = Cv√2gH

Therefore,

V = AjCv√2gH

 

Figure 2: Need Position Versus CSA of the narrowest point in the nozzle

The submittal of energy due to water transmitted to the turbine, ????hyd2,, is the input hydraulic power supplied to the wheel. The following equation applies to both the turbine and the pump when using the energy equation for incompressible fluids without taking friction into account:

 

As a result, hydraulic power is equal to the sum of all energy changes that the centrifugal pump has added to the water., and it is expressed as follows (White 2008, n.p.);

 

Considering all the assumptions;

 

The following formulas can be used to calculate the Pelton turbine’s efficiency, both empirically and theoretically.:

The theoretical efficiency:

 

The measured efficiency:

 

Where

The Pelton Wheel Turbine refers to an impulse water turbine. In this case, the water head is extremely high. A rotor wheel forms the basis of a Pelton wheel. The rotor of the turbine is a circular disc with a series of double spoon-shaped buckets evenly distributed around the edge. The water is provided by a neighboring reservoir. This Turbine’s nozzle turns the water’s available hydraulic energy into kinetic energy at atmospheric pressure. Each nozzle directs the jet along a tangent to the circle, passing through the centers of the buckets. Each bucket includes a splitter that divides the incoming jet into two equal pieces, and the water exits with a relative velocity roughly opposite to the original jet after traveling around the smooth inside surface of the bucket. As the water jet travels over the buckets, it puts tangential force on the wheel, causing it to spin. The hydraulic energy is transformed to mechanical energy by spinning the shaft.

Reaction Turbines

 

Figure 3: Schematic Layout of Experiment

The flow rate was set at a constant in this lab, while the brake load was steadily increased until the turbine when stalled. The torque will be calculated using the applied force and wheel speed. Three distinct flow rates were used in this experiment. The tension gauge was first set to zero when there was no load. Friction dynamometer’s friction band and weight hanger were ready. The suction valve and volumetric measurement valve remained open. The hydraulic bench pump was switched on when the bench flow-regulating valve was fully opened. The pump speed regulator was gradually raised until it reached its maximum setting. The spear valve nozzle was adjusted until the inlet pressure was around 0.8 bar, then the situation was allowed to stabilize. The weight was then recorded, as well as the reading gauge. After that, a non-contact optical tachometer was used to measure the wheel’s rotation speed. Weights were gradually added after that, with weight, strain, and speed all being recorded until the wheel stall. All weights were removed from the hanger when the wheel halted. The flow rates were calculated by closing the volumetric metering valve and using the scale to record the amount of time it took for the water to fill a certain volume. The volumetric measurement valve was then turned back on. Finally, the nozzle spear valve was adjusted to attain a pressure of around 1.01 bar, then the procedure was repeated until the pressure reached 1.2 bar.

Table 1: Showing Raw Data Collected During Lab Experiment

Pump Speed (), rpm	Flow Rate (), L/min	Needle Position ()	Turbine torque (), N.m	Turbine inlet pressure (), bar	Turbine speed (), rpm
2800	114	4	0	2.97	1648
2800	114	4	0.7	2.97	1426
2800	114	4	1.3	2.97	1142
2800	114	4	2	2.97	840
2800	114	4	2.6	2.97	544
2800	114	4	3.3	2.97	158
2800	114	4	4	2.97	66
2800	114	4	4.6	2.97	16
2800	114	4	5.3	2.97	0

Thus,

 

Table 2: Showing Computed Values of Tangential Velocity at Turbine Outlet and Turbine Mech Power at different Turbine Speeds (*highlighted is sample computed case above)

Turbine speed	Turbine’s Angular Speed,		Tangential velocity at turbine outlet,  (m/s)	Mechanical Shaft Power,  (W)
1648	172.5781565	14.23769791	5.57648026	820.3807883
1426	149.3303708	12.31975559	1.747893979	866.4635886
1142	119.5899604	9.86617173	-3.149937119	854.3318506
840	87.96459431	7.257079031	-8.358194132	753.8903669
544	56.96754679	4.69982261	-13.46297584	567.8857688
158	16.54572131	1.365022008	-20.11988712	195.1056877
66	6.911503839	0.570199067	-21.70650846	84.50341507
16	1.675516082	0.138230077	-22.56880267	20.88140376
0	0	0	-22.84473682	0

Turbine Inlet Hydraulic power

 

Turbine Mech power

 

Turbine Efficiency

Theoretical efficiency;

 

Measured efficiency;

 

Table 3: Showing Turbine Mech power, Turbine hydro power and Turbine Efficiency

Turbine speed	Turbine’s Angular Speed	Mechanical Shaft Power,  (W)	Turbine Mech power (W)	Turbine hydro power	Theoretical efficiency	Measured efficiency
1648	172.5782	820.3808	0	675.8254	1.2139	0.0000
1426	149.3304	866.4636	104.5313	675.8254	1.2821	0.1547
1142	119.5900	854.3319	155.4669	675.8254	1.2641	0.2300
840	87.9646	753.8904	175.9292	675.8254	1.1155	0.2603
544	56.9675	567.8858	148.1156	675.8254	0.8403	0.2192
158	16.5457	195.1057	54.6009	675.8254	0.2887	0.0808
66	6.9115	84.5034	27.6460	675.8254	0.1250	0.0409
16	1.6755	20.8814	7.7074	675.8254	0.0309	0.0114
0	0.0000	0.0000	0.0000	675.8254	0.0000	0.0000

Figure 4: Showing  a graph of Mechanical Power against Turbine Speed

Figure 4 depicts relationship between mechanical power and turbine speed. The power represented here are both theoretical and measured power by mechanical shaft power and turbine mech power, respectively. The turbine mech power (measured power) increases with speed up to a maximum where it declines to zero. The reason where this measured power declines to zero is because the turbine was loaded until it stalled hence the ultimate power obtained is zero as it takes into consideration the turbine speed and turbine torque. On the other hand, mechanical shaft power increases from zero speed to the maximum speed and slightly decline. This speed takes into theoretical parameters such as tangential velocity at turbine outlet, velocity and discharge at the nozzle opening. 

Summary of Theory

Figure 5: Showing Turbine Torque against Turbine Speed

Figure 5 shows the association concerning turbine torque and turbine speed. As the turbine speed increase, the torque is reduced drastically until it is zeroed. The reason for this behavior is attributed the fact the speeds of the turbine was forced to stall, and at this point the torque was at their maximum recorded values.

 

Figure 6: Showing Efficiency against Turbine Speed

Figure 6 depicts relationship between efficiency and the speed of the turbine. The measured efficiency starts from zero and gradually increase with speed and eventually falls at zero. This graphs trace similar path to mechanical shaft power and turbine mech power because they are factors of these parameters. The theoretical efficiency increases gradually with speed, and it goes beyond the ultimate efficiency of 1. This shows that theoretical efficiency is not realistic hence does not practical sense. On the other measured efficiency is quite low below 0.4. This implies most of the power created as hydrologic power is lost and transmitted to mechanical turbine power.

We can examine how Pelton Wheel reacts to various inputs based on the findings. Load input is valued differently at different conditions (Alomar et al., 2022, p.101684). The large the weights added, the slower speed while the turbine torque increases as it tries to counter the load imposed on it. On the contrary, measured efficiency declines with increase on the loading.

Conclusions 

Finally, it can be concluded that the performance of the Pelton wheel turbine is influenced by a variety of turbine speeds and turbine torque as well as the angular rotational speeds. The power or work input is controlled by a combination of flow rate and jet velocity. The larger the nozzle’s diameter, the faster the flow rates, but the lower the jet velocity. As a result, we require the ideal combination of both. In general, an impulse turbine is a device with a high head and low flow rate. As a result, we can conclude that our experiment was a success.

References

White, F.M., 2008. Fluid Mechanics, Sixth edit. ed.

Gupta, V. and Prasad, V., 2012. Numerical investigations for jet flow characteristics on pelton turbine bucket. International Journal of Emerging Technology and Advanced Engineering, 2(7), pp.364-370.

Alomar, O.R., Abd, H.M., Salih, M.M.M. and Ali, F.A., 2022. Performance analysis of Pelton turbine under different operating conditions: An experimental study. Ain Shams Engineering Journal, 13(4), p.101684.

Zoppé, B., Pellone, C., Maître, T. and Leroy, P., 2006. Flow analysis inside a Pelton turbine bucket.

Perrig, A., Avellan, F., Kueny, J.L., Farhat, M. and Parkinson, E., 2006. Flow in a Pelton turbine bucket: numerical and experimental investigations.

Dixon, S.L. and Hall, C., 2013. Fluid mechanics and thermodynamics of turbomachinery. Butterworth-Heinemann.

Okot, D.K., 2013. Review of small hydropower technology. Renewable and Sustainable Energy Reviews, 26, pp.515-520.