Introduction
Steam power is one of the most common means of power generation, as the heat source can be many different fuels such as fossil or nuclear. The Rankine cycle is a thermal cycle which demonstrates the thermal processes involved in power generation with steam. Although the United Kingdom’s total energy consumption per capita has decreased over the past years more efficient ways to provide energy are sought for [1]. Due to the high demand for more efficient power plants it is vital for engineers to be able to model these thermal cycles and to understand how these idealised results vary from experimental results.
The aims of the experiment were to determine the performance of the steam plant cycle and analyse it in comparison with the idealised Rankine cycle including the specific steam consumption (SSC) and energy distribution. This was achieved by examining a steam motor working in the Rankine cycle. For this the theoretical results based on an ideal Rankine cycle were compared to the results produced in the experiment.
Shaft power is given by the following equation
At the outlet of the calorimeter steam is assumed to be superheated, and as no work is done by the calorimeter . The dryness fraction is determined knowing the boiler temperature and pressure, allowing the entropy of a fluid and the entropy of a fluid-gas mixture to be found on the steam tables.
The energy balance for the experimental rig can easily be determined my splitting the rig into its three sub sections, boiler, engine and condenser. Figure 1 shows the system split into these sections and the relevant energies.
The overall thermal efficiency is given by
Examining the boiler alone the efficiency becomes simply the increase in enthalpy over the heat supplied to the system.
The Rankine cycle is a thermal cycle used to describe steam engines, shown on the temperature-entropy diagram in Figure 2. Between points one and two isentropic compression occurs, increasing the temperature at constant entropy, representing the pump work associated with the pressure of the liquid being increased. This term; however, is very small and was ignored in this investigation. Isobaric heat addition occurs between points two and three, as these lie on a constant pressure line. This is the high-pressure liquid entering the boiler where the liquid is initially heated up to its saturation point . Further heat addition results in the full evaporation of the liquid (3). Isentropic expansion occurs between points three and four. In this stage, the steam is expanded in the engine or turbine, thus allowing the steam to do work, such as rotating the crankshaft in the steam engine. This is followed by isobaric heat rejection between four and one. The steam liquid mixture is condensed at a low temperature, thereby rejecting heat to the surroundings. [3]
Apparatus
The experimental apparatus, shown in Figure 3, is the TecQuipment Ltd’s TD1050 steam motor and energy conversion test set. This contains a reservoir and an electric pump to feed water into the electrically-heated boiler. The steam leaving the boiler passes through a calorimeter and enters the two-cylinder steam engine. There is also a mains water condenser and a waste tank to collect the condensate.
The experimental rig is shown diagrammatically in Figure 4. Water is fed from the reservoir to the boiler with the help of the electric pump. The steam generated by the boiler is fed into the engine. The flow of the steam is controlled with a valve and the enthalpy is measured with the calorimeter. The steam passes through the condenser and is collected in the waste tank.
For this experiment several safety aspects were considered, due to high pressures and temperatures.
Method
The boiler pressure was increased to approximately . The calorimeter was used to measure the dryness fraction and it was assumed to be constant throughout the experiment. The cycle efficiency of an ideal Rankine cycle was calculated with a boiler pressure of and a condenser pressure of ambient (1bar). The experimental procedure for this experiment is outlined in the following steps:
1. Direct the condensate pipe into the waste tank
2. Turn on heaters and open the boiler valve when the pressure has reached approximately 200 until the water inlet pressure reaches 80
3. Turn the motor starting handle to start the motor
4. Switch off one heater to stabilise the boiler pressure at 200
5. Control steam valve to maintain constant motor rpm (2000)
6. Apply torque loads with the dynamometer in increments of 0.05Nm. continue loading until rpm cannot be sustained.
7. Record heater power, boiler pressure, boiler temperature, motor inlet pressure, motor speed, motor power, condenser cooling water temp, flow rate, condensate flow rate
8. Condensate flow rate by directing flex pipe into measuring cylinder and measure volume over 60 sec
9. Shut down rig
Results
The graph on the left axis system shows the steam flow plotted against the motor power for a constant motor speed. There is a clear linear trend in the blue circular data points. The blue dashed line is the line of best fit given by . This line of best fit is known as the Willians line. The black cross indicates the point at which the line of best fit (Willians line) crosses the power axis. Hence the steam flow is equal to zero. This occurs at the point – if the Willians line is extrapolated back to negative power.
On the right y-axis the inlet pressure is plotted against the motor power. There is a linear upwards trend signifying that inlet pressure increases with motor power. This is plotted with the square data points. A line of best fit was plotted to show this linear trend .
The figure to the right shows a plot of specific steam consumption (SSC) against motor power. The red data points decrease with increasing motor power. The blue line is a possible interpolation between these points to demonstrate the downward trend of the data points. Furthermore, the decrease in SSC becomes less with higher motor power. The SSC appears to be converging to a minimum value at large motor powers. Also, the SSC tends to infinity for low motor power.
The energy balance throughout the experimental setup can be examined. The sum of all energies is equal to zero. The work extracted by the motor is small. The losses are significantly bigger that the extracted work. The rejected heat is significantly bigger than the losses incurred in the thermal cycle.
For an ideal Rankine cycle the dryness fraction is assumed to be , such that the steam is fully gaseous. The dryness fraction for the Rankine cycle for the experimental setup and conditions was determined to be .[Appendix 1]
For an ideal Rankine cycle the thermal efficiency was calculated to be . The diagram for this cycle is shown below. As the cycle has no internal inefficiencies all processes associated with heat addition or rejection are isobaric and all processes associated with work are isentropic. The thermal efficiency was also determined for an imperfect cycle. Here the efficiency was determined to be . The Rankine cycle for this is also shown.
Discussion
The Willians line shown in Figure 5 should go through the origin for a system with no mechanical losses, as the motor cannot produce any power if there is no steam flow. However, the line is displaced upward due to the inefficiencies in the motor. If the Willians line is extrapolated to zero flow the intercept with the power axis is at -88W. This suggest that the motor needs to exert 88W to start rotating and to overcome any mechanical losses. These losses include frictional forces, as well as the inertia of moving motor components. [4]
The plot of inlet pressure against motor power is limited by the boiler pressure, as the inlet pressure cannot be bigger than the boiler pressure. Hence when the inlet pressure reaches the boiler pressure the system cannot produce more power, as no more steam flow can occur. Furthermore, the pressure curve is shifted upwards due to the inefficiencies in the system, associated with the mechanical losses in the motor.
There also appear to be more convergence of the data points to the line of best fit for higher motor powers and at lower power the data points have more variability. This suggest that there are greater errors in the measurements at low motor powers. This may be attributed to the slip of the screw, due to vibrations of the system, used to adjust the torque applied to the motor shaft. Constant motor speed was assumed which is not the case [Appendix 1], resulting in data fluctuations.
The SSC vs Power graph shows a clear downward trend with a convergence to a minimum amount of SSC. The SSC tends to infinity for low motor powers, as it needs to overcome the mechanical losses in the motor. This suggests the motor is running more efficiently when it produces higher power. The SSC reaches a minimum as the power required to overcome mechanical losses has a less significant effect for large power outputs.
In the energy balance analysis, the total of all energies is equal to zero. This suggests that the assumption of no pump work is accurate for the level of accuracy of the measuring devices. The energy balance analysis shows that the extracted work is small in comparison to the added heat, which is approximately 2%. This is also equal to the thermal efficiency. The thermal losses are significantly higher than the extracted work. This suggests large inefficiencies in the cycle. In addition, the heat rejected is the largest amount of unused energy. Therefore, in order to increase the cycle efficiency the percentage of rejected heat must be reduced.
An ideal Rankine cycle has the largest possible efficiency for the given conditions in the experiment. Here the entire cycle is reversible. The boiler pressure is equal to the motor inlet pressure as no losses are incurred. Furthermore, the dryness fraction of 1 is assumed. This means the fluid is entirely gaseous.
For the real Rankine cycle examined in the experiment inefficiencies were incurred. Firstly, there are inefficiencies in the pump due to irreversible processes, increasing the entropy. However, for the experiment the work done in this cycle is still assumed negligible and hence ignored. Furthermore, the dryness fraction was calculated to be 0.97, which can be attributed to the radiation from the boiler and leaks in the boiler and valves. Lastly there is an inefficiency in the motor, associated with the irreversibilities, arising from mechanical losses and leaks.
One of the major errors encountered in this experiment was the variation in torque. This occurred as the torque was dictated by tightening a screw, which, in particular for low torque measurements, undid itself, due to the oscillations in the machine arising from the motor. This resulted in the torque measurements being significantly unreliable. However, this shortcoming could be overcome by simply implementing a more resilient system to apply a torque.
Similarly, the motor speed was manually controlled by adjusting a valve by the boiler. This resulted in large fluctuations in motor speed, due to response lag and experimenter accuracy. This particularly impacted results shown on the Willians line as constant rpm was assumed for all data-points. This error could be adjusted with an electronic closed loop control system to stabilise the motor speed at 2000rpm.
An additional error arises from the steam leaking from the valves in the boiler and the motor. This affects the flow to the motor and any consequent measurements. These leaks were observed in particular in the motor, as steam escaped from the cylinders.
Furthermore, the condensate, which was collected in the measuring vessel, was contaminated by lubricants from the motor. This made the condensate cloudy and affected volume measurements. Also, this dirtied the measuring vessel. To reduce this error the condensate would have to be separated from the engine oil. Also, the measurement may have been subject to parallax error, as the measuring vessel was difficult to access.
A closely related error arises from the communication required between the experimenters responsible for timing and measuring. The consequent delay resulted in larger condensate measurements. This can be improved by combining this system into an automatically controlled system.
Another shortcoming of the experiment was that one of the two boilers was not functional; during the experiment. This significantly impacted the pressure the boiler could maintain for high motor powers. Hence the amount of data that could be collected during the experiment was very limited. This means that if any data points were subject to significant random error these would significantly impact the conclusions drawn from the experiment.
Although all measurements were conducted using the same device, there may have been some instrumentation error. This would result in a systematic error. Furthermore, a random instrumentation error may have been in the measuring device. This occurs when noise in the wires is mixed with the signal. To counteract this a filter can be used to limit the range of frequencies observed to those emitted by the signal.
Conclusion
Although the experimental data was subject to several significant errors, the results displayed appropriate qualitative behaviour. The Willians line displays linear behaviour and suggests that energy must be added to the motor to initially overcome the mechanical losses. This is as expected, and is in line with the theory.
It was observed that specific steam consumption decreases with motor power. This suggests that the efficiency increases with motor power. This means less steam is required to run at higher power, as the mechanical losses have a less significant effect on the total amount of work done.
The ideal Rankine cycle efficiency was determined to be 8%, while the true efficiency is 2%. This is in line with the theory, as the inefficiencies in the true cycle mean less work can be extracted. This also means that the cycle is no longer reversible. Additionally, the heat rejected was significantly higher than all losses and was approximately equal to 78% of all added heat. These significant differences suggest vast differences in the cycle diagrams. The inefficiencies in the work extraction of the pump result in irreversibilities that increase the entropy. There are most likely also are inefficiencies in the boiler and condenser due to thermal and pressure losses.
The cycle efficiency can be increased through several different ways. The steam could be superheated to a high temperature. By superheating the stream to a high temperature, the average steam temperature during heat addition can be increased [5]. This is shown in Figure 10.
Also the boiler pressure could be increased. If the operating pressure of the boiler is increased the boiling temperature of the steam automatically increases. For a fixed temperature there is a work loss due to the leftward shift of the turbine conditions, but also an increase I work as the pressure is increased. Also, the moisture content of the steam increases, which is an undesirable side effect, which can be corrected with a reheat cycle [5]. This is shown on Figure 11.
Figure 11:T-s Diagram of Rankine cycle with superheated steam [6]
Bibliography
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[3]
M. Steinhagen and H. M. Gottfried, “RANKINE CYCLE,” [Online]. Available: http://www.thermopedia.com/content/1072/. [Accessed 12 March 2018].
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Appendices
Appendix 1: Experimental Data