thermal lab

ABSTRACT

A pelton wheel is considered as an impulse turbine, a turbine that converts pressure head into velocity head. This lab will use this mechanism along with a prony brake to calculate the input power, output power, and efficiency of the turbine. The team will be provided with measuring devices such as a stroboscope to measure the turbine speed as well as a hydraulic bench to control the flow rate of the liquid flowing through the turbine [1].

The experiment will consist of two separate trials with two different water heads. This experiment will neglect all frictional forces for the theoretical calculations. The hydraulic bench will be calibrated to have a water head of 8m H2O and 12m H2O. The team will record the needed data for the experiment: turbine inlet pressure, flow rate, turbine speed, and the net spring forces. For the first trial, 8m H2O, the Prony brake net spring force will be set to have a net force of 10N and will be adjusted to decrease by 1N until the net force reaches 4N, having 7 data points for the first trial. The experiment will then be repeated for a water head of 12m H2O with the Prony brake net force set to 12N and adjusted to decrease by 2N until the net force reaches 2N, having 6 data points. The volume of the flow will be recorded at every other data point to ensure that flow rate remains constant.

The team concluded that the efficiency of the turbine increases as the angular velocity increases. The percent error between experimental and theoretical calculations were relatively high. Which were expected because the theoretical calculations did not account for any frictional losses.

INTRODUCTION

1. The main objectives of this lab experiment are following

i. Observe flow through a mini Pelton Turbine

ii. Calculate input power, output power, and efficiency for readings taken at a constant nozzle inlet pressure.

iii. Calculate the efficiency of the turbine and compare it to the theoretical efficiency value.

2. The purpose of this lab work is to study Pelton wheel turbine which make us able to understand the working of the turbine, design of the turbine and factors which effect the efficiencies.

3. The experiment will be done to check the effect of angular velocity on the efficiency, it is expected that increase in angular velocity will result in increase in the efficiency

4. List of Equations [1]:

· Gage Pressure:

(1)

Where

= Density of water

g = Gravitational Acceleration

h = Head of water

· Work Input:

(2)

Where

Q = Flow rate of water

= change in pressure

· Work Output:

(3)

Where

F = Force of water

r = distance measured from the axis of rotation to where the force is applied

= Dynamometer Angular velocity

· Work Theoretical:

(4)

Where

= Force of water in x direction

r = distance measured from the axis of rotation to where the force is applied

= Dynamometer Angular velocity

U = Speed of bucket

V = Absolute fluid inlet velocity

· Efficiency:

(5)

Where

Wo = Work out

Wi = Work in

· Theoretical Efficiency:

(6)

· Percent Error:

(7)

METHODS

The experiment is done on a nozzle which eject a jet of constant area. The experiment starts with the tightening up of the tensioning screw on the pulley wheel until the turbine is almost stalled (rotor just turning). Decide on suitable increments in force to give adequate sample points and note the value of the pulley brake. Slacken off the tensioning screw so no force is being applied to the turbine. Tighten the screw to give the first increment in force for the brake. When readings are steady enough, record all the readings again. Repeats above steps for a gradually increasing set of ” values. The data may now be used for analysis and to plot the Pelton turbine characteristic curve. Now change the water head to a new setting by adjusting the reservoir position and at the same time also change the spear valve position to maintain the pressure at 1.0 N/m2

RESULTS

Trial one was conducted at a water head of 8m H20, with a starting force of 10N, this was the largest force that could be applied without the wheel stopping. Readings for were recorded in decreasing increments of 1N. Using equations 2-6 and the recorded speeds the team is able to determine the work input and output as well as the experimental and theoretical efficiencies. Figure 1 shows that as the torque decreases the angular speed of the turbine increases. Since the force applied is gradually decreasing the turbine can rotate more freely. The experimental efficiency followed a parabolic form, reaching a peak efficiency at 126.6 rad/s. At lower speeds the efficiency was lower, but as the speed increased so did the experimental efficiency until hitting its peak then decreased slightly. Table1 shows the values for the theoretical and experimental efficiencies, and the percent error between the two. The theoretical efficiency took a liner path, as the rotational speed increases so did the efficiency (Please see Appendix for more information).

Figure 1: Trial one data for torque and efficiency vs. rotational speed

Table1 shows the values for the theoretical and experimental efficiencies for trial 1, and the percent error between the two. The percent error was relatively low with the highest error having 31%. The theoretical efficiency took a liner path, as the rotational speed increases so did the efficiency.

Table 1: % error between theoretical and experimental efficiency trial 1

For Trial 2 a water head of 12m H20 and a starting force of 12N, largest force that could be applied and the wheel could still rotate. Readings for this trial were recorded at decreasing intervals of 2N. Figure 2 shows that a decrease in torque allows for an increase in rotational speed. The hypothesis is that the peak efficiency should occur at the lowest torque, highest rotational speed, this did not occur.

Figure 2: Trial two data for torque and efficiency vs. rotational speed

Table 2 shows the values of the experimental and theoretical efficiencies for trial 2, the largest percent error was 75.5%. The theoretical efficiency also followed a linear path, as the rotational speed is increased the efficiency also increases. The peak efficiency for the experiment occurred at a speed of 138.8 rad/s which is about 10 rad/s faster than the speed of peak efficiency of trial 1. The efficiencies occur at different rotational speeds due to the differing water heads as well as having a different flowrate between the trials.

Table 2: % error between theoretical and experimental efficiency for trial 2

DISCUSSION

As the rotational speed increases so does the efficiency. The experimental efficiency increased to a peak efficiency then started to decrease for both trials. The assumptions for the theoretical calculations were that the flow is at steady state, the fluid is incompressible, the pressure is at atmospheric pressure, and the exit angle for the flow is 150 degrees. The assumptions made for the experiment was the flow is incompressible and the mass flow rate is constant. The stroboscope readings varied, more at lower rpm’s, so a median value was obtained to use as the rpm for that reading. This led to having a range of error for the theoretical output work, either the rotational speed was higher than the team assumed or the actual speed was lower than assumed. Using a median value had the greatest effect on the values for the theoretical work output. The rotational speed approximations were the greatest source of error, the team took several readings and tried to get a close to an actual value however there was still a range of readings.

CONCLUSIONS

The team hypothesized that the efficiency of the turbine will increase as angular velocity increases. Assuming that all frictional forces are neglected and that the fluid is incompressible the hypothesis should hold up true for the theoretical analysis. However, the experimental efficiencies did not match the same trend as the theoretical efficiencies. The experimental efficiencies peaked while the theoretical efficiencies seemed to increase exponentially. Therefore, the percent error between experimental and theoretical increased for each data point of both trials. This huge difference between the two are also due to the assumption that frictional forces can be neglected for the theoretical calculations. The team recommends purchasing a more precise device to measure the angular velocity of the wheel. As the stroboscope gave the team a wide range of possible values. Which resulted in a mean angular velocity rather than a more precise reading. The team believes that a precise reading of angular velocity would improve the data points. As the data has a direct relationship with , as previously stated in the results and discussion.

REFERENCES

[1]. Ciocanel, C. – FORCE ON VARIOUS SHAPE OBJECTS DUE TO PELTON TURBINE lab handout, Northern Arizona University, pp. 1-4, 2016.

APPENDIX

APPENDIX: Pelton Turbine Spreadsheet