RANKINE CYCLER, STEAM TURBINE POWER SYSTEM

Kelsea Hubka, Hunter Cressman, Andrew Braum, & Ramzi Daouk

Mechanical Engineering Department

Loyola Marymount University

Los Angeles, California 90045

February 14, 2008

ABSTRACT

The purpose of this lab was to gain an understanding of the thermodynamic performance of the

Rankine Cycle. By gaining an understanding of the Rankine Cycle, similar analyses can be

applied for application in power generation. Energy analysis was performed on the cycle as a

whole and on the individual components. By using the first law of thermodynamics for open

systems, analysis was performed on the boiler, turbine, and condenser. Key results included an

expected isentropic power of 8261 watts, condenser heat loss was 126 watts, power generated

was 1.61 watts, turbine isentropic efficiency was 0.0195%, Rankine Cycle thermal efficiency

was 0.0186%, and the estimated time to boiling was 26 minutes and 51 seconds. Conclusions

suggest that entropy losses from the boiler to the turbine were due to irreversibilities in the cycle.

Recommendations included rerunning experiment with a more efficient turbine, and also using a

true Rankine Cycle with pump. Note the current setup did not include a pump in the cycle. The

results of this lab were intended to parallel applications in power generation.

Proofread by,

Andrew MacDonell

2

TABLE OF CONTENTS

Section Page:

Introduction 3

Theory and Analysis 4

Experimental Procedure 10

Results and Discussion 13

Conclusion and Recommendations 20

References 21

Appendices 22

Appendix A: Raw Data & Charts 23

Appendix B: Meeting Times & Sample Calculations 32

3

INTRODUCTION

The objective of this experiment is to understand the thermodynamic performance of a Turbine

Technologies Rankine Cycler System and to understand the details of each component which

composes the system. The analysis will include performing an energy balance on the cycle and

each individual constituent. The Rankine Cycler Steam Turbine Power System is composed of

the following parts: the cooling tower, the boiler, the generator, the steam turbine, the steam

admission valve, and the gas valve. In preparation for this experiment, six liters of water are

poured inside of the boiler. Once the water reaches boiling at a high temperature and pressure,

the steam admission valve must be opened to allow for the steam to pass through the turbine.

This produces power which is recorded as current and voltage as a function of time. Readings

are taken for around thirty minutes and are collected in a data acquisition system. From the

cooling tower, a thick cloud of condensed vapor can be observed. The data recorded is plotted

and analyzed to determine the efficiency of the system. Using the first law of thermodynamics,

the turbine power, the turbine efficiency, the heat transfer to the boiler and from the condenser at

steady-state conditions, the Rankine Cycle efficiency, and the time it takes for the water to boil

inside of the boiler can be found. The boiler, before the valve is opened, can be viewed as a

closed system to determine the time it takes for the water to boil inside of the boiler. However,

once the valve is opened, each component under analysis must be viewed as an open system.

The efficiency of the generator is expected to be very low. The efficiency of the turbine is also

expected to be low. The total efficiency of the cycle is expected to be relatively low. These

results will be used to determine the performance of the Rankine Cycler system. These results

will provide the basis for a better understanding of the Rankine Cycle which can be applied to

power generation.

4

THEORY AND ANALYSIS

The Rankine Cycler, or Steam Turbine Power System, is an ideal isentropic thermodynamic

process which generates electrical power by using steam as the working fluid. This cycle does

not involve any internal irreversibilities and consists of the following four processes: constant

pressure heat addition in a boiler, isentropic expansion in a turbine, constant pressure heat

rejection in a condenser, and isentropic compression in a pump (Çengel, 2008). Inside the high-

pressurized boiler, superheated vapor is produced from the heat of burning fuel, in this case

propane gas. Assuming an open system, the high pressure forces the superheated vapor to the

turbine where it expands isentropically and work is produced by the rotation of the turbine shaft

(Çengel, 2008). This rotation spins a generator, transforming this mechanical energy into

electrical power. The water vapor then exits into a condenser where the saturated vapors cool

into a saturated liquid by rejecting heat to a cooling medium such as a lake or the atmosphere

(dry cooling in a large open tower) (Çengel, 2008). The liquid then moves through a pump,

before returning to the boiler as a compressed liquid. This process is cyclical, thus creating a

steady flow. A schematic diagram of this cycle is shown in Figure 1.

5

Figure 1 – Schematic of simple ideal Rankine cycle (Saniei, 2008).

The Carnot vapor cycle is a good model to approximate and compare actual devices; however

the Rankine cycle is more efficient in producing working fluid at completely saturated states,

thus making it a more accurate model (Çengel, 2008). In order to analyze the cycle, the

properties at every inlet and exit of each component must be measured. These properties can be

used compute the accuracy and efficiency of energy transfer throughout a Rankine Cycler. For

this energy analysis the first law of thermodynamics, energy conservation, is used. It is stated as

follows (Saniei, 2008):

6

..

22

)2

()2

(vc

ee

eeii

iit

Uzg

vhmWQzg

vhm

∂∂

⋅⋅++⋅+=+⋅++⋅ &&&& (1)

where, m& = mass flow, kilograms per second, kg/s

h = enthalpy, kilojoules per kilogram, kJ/kg

v = velocity, meters per second, m/s

g =gravity constant, meters per second squared, m/s2

z = height position, meters, m

Q& = heat flow, Joules per second, J/s

W& = power, Watts, W

U = internal energy, kilojoules per kilogram, kJ/kg

t = time, seconds, s

i = inlet

e = exit

c.v. = control volume

Assuming all systems are in a steady state and have steady flow (S.S.S.F.), the first law of

thermodynamics can be reduced to a heat transfer equation to solve for energy exchange in a

boiler or condenser. Potential and kinetic energy changes of the working fluid are insignificant

relative to heat transfer, so the previous equation (1) can be reduced even further to (Saniei,

2008):

)( ie hhmQ −⋅= && (2)

where, Q& = heat flow, Joules per second, J/s

m& = mass flow rate, kilograms per second, kg/s

he = enthalpy at exit, kilojoules per kilogram, kJ/kg

hi = enthalpy at inlet, kilojoules per kilogram, kJ/kg

The first law of thermodynamics can also be reduced to an isentropic work equation. Potential

and kinetic energy changes of the working fluid are also insignificant relative to work. Therefore

to solve for the power produced by a turbine or the power consumed by a pump, equation (1) can

be reduced to (Saniei, 2008):

7

)( ei hhmW −⋅= && (3)

where, W& = power, Watts, W

m& = mass flow rate, kilograms per second, kg/s

hi = enthalpy at inlet, kilojoules per kilogram, kJ/kg

he = enthalpy at exit, kilojoules per kilogram, kJ/kg

It is important to understand how much heat in the boiler is required to superheat the compressed

liquid completely, because this energy promotes the flow of the entire cycle. It is also important

to know the time it takes for this maximum efficiency to first occur. The time it takes to first

meet this efficiency is the moment the cycle reaches a steady state and moves at a steady flow.

After this moment in time, the property values at each inlet and outlet of the entire cycle will be

most accurate. Before this time, temperature and pressure can vary greatly producing imprecise

results. This time is found first by simplifying the first law of thermodynamics for a closed

system. Work, and potential and kinetic energy changes of the working fluid remain

insignificant relative to heat transfer. Therefore the first law can be simplified to the following

equation (Saniei, 2008):

dt

dUQ =&

An integration and simplification of this equation is made:

∫∫ =⋅ dUdtQ&

ie UUtQ −=∆⋅&

The final result is an equation to calculate the time taken for a heat exchanging system (boiler) to

reach a steady state (Saniei, 2008):

8

⋅

−⋅=∆

Q

uumt ie

&

)( (4)

where, t∆ = power, Watts, W

m = mass flow rate, kilograms per second, kg/s

ui = specific internal energy at inlet, kJ/kg

ue = specific internal energy at exit, kJ/kg

Q& = heat flow, Joules per second, J/s

Also, the heat exchanged in the boiler is proportional to the cost of resources (propane gas),

which is accounted for in the total cost of the running system. This total cost is used to

determine the price being charged for consuming the power outputted by the generator. In order

to maximize the efficiency of the power output relative to the inputted energy, the efficiency of

the generator proportional to the turbine is calculated. The following equation is used to find the

efficiency of a generator (Saniei, 2008):

%100×=T

gen

genW

W

&

&

η (5)

where, genη = generator efficiency, percentage, %

genW& = power output recorded, Watts, W

TW& = power input by turbine, Watts, W

In addition, the efficiency of the generated power relative to the entire isentropic cycle is

calculated. The following equation is used to find the thermal efficiency of the cycle (Saniei,

2008):

%100×∆

=Q

Wgen

th

&

η (6)

where, thη = thermal efficiency, percentage, %

genW& = power output recorded, Watts, W

Q∆ = potential energy transfer, Joules per second, J/s

9

The following diagram (Figure 2) shows the thermodynamic process of the Rankine Cycle in

terms of temperature and entropy. It shows that the heat exchangers (boiler and condenser) are

always at steady temperature, verifying its steady state. Yet because this cycle is not Carnot, the

irreversibility of the turbine (useful work) creates a difference in entropy from the inlet to the

exit of the system. This is shown on the right side of the diagram. However, in the experimental

cycle analyzed, the pump does not exist. Instead, the boiler begins with a specified quantity of

working fluid, and is depleted from the system through a dry cooling tower. The system must

shut down before the entire fluid supply disappears. Although there appears to be a major

discrepancy in the cycle, all theory holds true.

Figure 2 – T-s Diagram of Rankine Cycle (Engineers Edge, 2008).

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EXPERIMENTAL PROCEDURE

The following materials were used for the experiment:

• Turbine Technologies Rankine Cycler System (Figure 3)

The subsequent procedure was followed in order to obtain data to determine several parameters

of the Rankine Cycler system. These parameters included, but were not limited to, the

following: turbine efficiency, Rankine Cycle efficiency, and the time it took for water to boil

inside of the boiler. The following step by step procedure was used:

1. Supplied power to the computer and Rankine Cycler. Turned on the computer.

2. Locked the caster wheels, opened the steam admission valve, and verified the load and

burner switches were in the off position.

3. Filled the boiler with 6 liters of water.

4. Closed the steam admission valve.

5. Turned the load rheostat knob to the fully counter clockwise position (minimum load)

6. Opened the valve on the LP gas cylinder. Turned the gas valve knob CCW to the ON

position

7. Turned the master switch ON.

8. Turned the burner switch ON.

9. Observed the voltmeter and opened the steam admission valve. Regulated the turbine

speed to indicate 7-10 volts. This pre-heated the turbine components and pipes. Closed

the valve for 20 seconds and waited for boiler pressure to rise. Leaks were visible due to

11

condensation and cold turbine bearing clearances. This was normal and stopped after

operating temperatures were attained.

10. Opened the steam admission valve to read a nearly maximum voltage.

11. Verified the upper water level was set to ¾ boiler door height.

12. Began recording the data using the data acquisition system.

13. When the boiler water level dropped to the lower level on the site glass, stopped

recording the data stream and turned the steam admission valve OFF.

14. Moved the burner switch to the OFF position. Turned the gas valve to the OFF position.

Turned the LP gas cylinder valve to the OFF position.

15. Held a heat resistant measuring beaker under the condenser for draining purposes.

Drained the condenser by squeezing the hose. Measured the condensate.

16. Waited until the boiler cooled and the pressure was below 10 PSIG, then opened the

steam admission valve. When the boiler pressure was equal to atmospheric pressure,

filled a measuring beaker with distilled water and re-filled the boiler through the drain/fill

port to the exact upper water level.

17. Nine readings of the sensor were obtained from the data acquisition system.

18. Shut off the master switch. Removed power from the entire system. Removed all water

from the system.

12

Figure 3. Picture of Turbine Technologies RankineCycler Steam Turbine Power System

(Hubka, 2008).

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RESULTS AND DISCUSSION

All raw data was placed in Appendix A along with sample calculations in Appendix B. All raw

data gathered during the experiment was tabulated in the following table.

With the final and initial volumes in the boiler measured, the volume of water moved through the

cycle was calculated from the difference between the two. The ambient enthalpy was referenced

from the ambient temperature at atmospheric pressure from tables found in a thermodynamics

book (Cengel & Boles, 2008). The start of the mass flow was depicted as a red line in the graph

below.

Table 1. Raw Data, 1/31/08, 1:30 pm

Vol Initial (L) Vol Final (L) Vol Condenser (L)

6.00 2.30 0.550

Ambient Temperature (°C) Ambient Enthalpy

(kJ/kg) Q Boiler (BTU/ft^3)

25.0 419.17 2600

Mass Water (L or kg) ∆Time (hr:min:s) Mass Flow (kg/s)

3.70 0:16:49 0.00367

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With this data, the difference between the ending time and starting time was used to determine

the overall mass flow (total mass divided by total time).

Graph 1. Graph of turbine RPM vs. the Time with red line denoting when the water was

denoted as not flowing (left of line) and flowing (right of line).

15

Next, the steady state was identified on the turbine temperature graph above (Graph 2). Note the

temperature was nearly constant which ensured the water cycling through was not changing

state.

For the steady state time identified on the data, the averages of the boiler, turbine, and condenser

pressures and temperatures were taken. The temperature and pressures were each used to

identify the entropy for each of the components. The following table summarizes the results.

Graph 2. Steady state identification on turbine temperature graph.

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Table 2 Boiler Pressure (kPa) Boiler Temp (°C) Entropy (kJ/kg-K)

Steady State 852 176 6.69

Averages from Turbine Pressure In (kPa) Turbine Temp In (°C) Entropy (kJ/kg-K)

3:55:00 to 188 119 7.15

3:58:42 Turbine Pressure Out (kPa) Turbine Temp Out (°C) Entropy (kJ/kg-K)

129 106 1.49

Condenser Pressure Out (kPa) Condenser Temp Out

(°C) Entropy (kJ/kg-K)

101 25.0 1.31

With the different entropy values recorded, a plot of the cycle was made on a T-s diagram. It

should be noted that the condenser out was considered to be atmospheric pressure and

temperature. This cycle, was in fact, not a closed cycle. Therefore, to create a closed cycle,

before the boiler, a constant temperature line was drawn across to where the pump entropy would

have been. A connecting line was also drawn from the turbine out to connect to the constant

entropy line ended. Results were plotted and displayed below.

Graph 3. Graph of T-s diagram assuming a closed cycle (Cengel & Boles, 2008)

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Note on the T-s diagram, there was a large slant from the boiler to the turbine (top right to

bottom right). This change in entropy might be accounted for by the irreversibilities of the

turbine and the overall inefficiency of the cycle deviating from the ideal cycle.

Next the turbine pressures and temperatures were tabulated to fix the state again. This time, the

goal was to identify the enthalpies (Table 3). Using the enthalpies and equation 3, the isentropic

turbine power was calculated (Table 4). After referencing the ambient temperature and ambient

pressure as the condenser pressure and temperature, the condenser heat flow was calculated

using equation 2. Note that the results were negative due to heat flow leaving the control

volume. Results were tabulated below.

The turbine average current and voltage were taken for steady state conditions. With these

values, the turbine power generated was calculated by multiplying the voltage by the current.

Then by using equations 5 and 6, the turbine isentropic efficiency and Rankine Cycle thermal

efficiency was calculated, respectively. Calculations were tabulated along with the percent

differences of the efficiencies.

Table. 3

Steady State Turbine Pressure In (kPa) Turbine Temp In (°C) Enthalpy In (kJ/kg)

Averages from 187.95 118.64 2706

3:55:00 to Turbine Pressure Out (kPa) Turbine Temp Out (°C) Enthalpy Out (kJ/kg)

3:58:42 129.392 106.22 453

Table 4.

Isentropic Turbine Power (W) 8261

Condenser Heat Flow (J/s) -126

Table 5.

Turbine Power Generated (W) 1.61

Turbine Isentropic Efficiency (%) 0.0195

Thermal Efficiency (%) 0.0186

Efficiency Differences (%) 4.79

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Lastly, using the starting time of the experiment to the start time of the mass flow, the boiler

pressures and temperatures were averaged. With the averages, the internal energies were

referenced (Cengel and Boles, 2008) and used in equation 4 to calculate the time to boiling.

Furthermore, graphs of boiler pressure, turbine in/out pressure (plotted together), boiler

temperature, turbine in/out temperature (plotted together), generator current, generator voltage,

fuel flow, and turbine RPM were all plotted with respect to time. Graphs were placed in

Appendix A along with the raw data.

Analysis resulted in extremely low efficiencies (<1%) which confirms expectations. Such a

small plant was not engineered to maximize efficiency, therefore yielding results discussed

above. Both the isentropic efficiency and thermal efficiency were close (5% difference), thus

solidifying confidence in the turbine analysis results. However, the estimated time to boiling

was about 27 minutes, which should have been around half that time (16 minutes based on data).

Table 6.

Time Boiler Pressure (kPa) Boiler Temp (°C) Internal Energy

(kJ/kg)

3:40:48 99 34 419

3:52:50 861.673 174 2579

Table 7.

Estimated Time (min) 26.85338 26 min and 51 sec

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In terms of accuracy, the time was correct on the magnitude scale (time was not estimated as

seconds or hours).

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CONCLUSIONS & RECOMMENDATIONS

The follow conclusions were made for the experiment:

• The entropies for each component were plotted on a T-s diagram which resembled

reference data for Rankine Cycles.

o The entropy loss from the boiler to the turbine was due to turbine irreversibilities.

• The turbine was expected to produce 8,261 watts of isentropic power.

• The condenser lost heat at a rate of 126 joules per second.

• The power generated was calculated to be 1.61 watts.

• The Isentropic efficiency was 0.0195% (extremely inefficient).

• The Rankine Cycle thermal efficiency was 0.0186% (extremely inefficient).

• Efficiency difference of <5% confirmed accurate inefficiencies.

• Estimated time to boiling was 27 minutes which was correct in magnitude to the actual

boiling time (around 16 minutes).

The following recommendations were made for the experiment:

• Rerun Rankine Cycle with new turbine to test for changes in efficiencies.

• Experiment with a true Rankin Cycle with the condensed water pumped back into the

boiler. Compare differences.

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REFERENCES

Cengel, Y.A., & Boles, M.A. (2008). Thermodynamics, An Engineering Approach, Sixth

Edition. McGraw-Hill Companies Inc., New York, NY.

Engineers Edge (2008). “Heat Rejection – Thermodynamics.” [Online]

http://www.engineersedge.com/thermodynamics/heat_rejection.htm

Hubka, K. (2008). Pictures. Los Angeles, CA: Loyola Marymount University.

Saniei, N. (2008). Personal communication (lecture notes). Los Angeles, CA: Loyola

Marymount University.

Saniei, N., & Es-Said, O. (2007). Laboratory Manual, MECH 342 Mechanical Engineering Lab

II. Department of Mechanical Engineering. Los Angles, CA: Loyola Marymount

University.

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APPENDICES