Table of ContentsTable of Contents

PrinciplePrinciple 33

ObjectiveObjective 33

BackgroundBackground 44

Rankine cycle analysis Rankine cycle analysis 55

I)I) Mass Flow Rate of the Rankine Cycle.Mass Flow Rate of the Rankine Cycle. 66

II)II) Work And Heat Transfer.Work And Heat Transfer. 66

III)III) Thermal Efficiency of CycleThermal Efficiency of Cycle 99

IV)IV) Air -Fuel ratio and Air ExcessAir -Fuel ratio and Air Excess 99

V)V) Mass flow rate in the turbineMass flow rate in the turbine 1111

VI)VI) Boiler analysisBoiler analysis 1111

VII)VII) Cost of Generating Steam and Energy.Cost of Generating Steam and Energy. 1414

Experimental SetupExperimental Setup 1515

ProcedureProcedure 1818

Example#1:Example#1: Rankine cycle analysisRankine cycle analysis 1818

Example#2Example#2: : Combustion analysis of the boilerCombustion analysis of the boiler 2222

DiscussionDiscussion 2424

ReferencesReferences 2424

University of Puerto RicoUniversity of Puerto RicoMayagüez CampusMayagüez Campus

Department of Mechanical EngineeringDepartment of Mechanical EngineeringINME 4032 - LABORATORY IIINME 4032 - LABORATORY II

Spring 2004Spring 2004 Instructor: Guillermo ArayaInstructor: Guillermo Araya

Experiment 4: Powerplant analysis with a Rankine cycleExperiment 4: Powerplant analysis with a Rankine cycle

PrinciplePrinciple

This experiment is designed to acquire experience on the operation of aThis experiment is designed to acquire experience on the operation of a

functional steam turbine power plant. A comparison of a real worldfunctional steam turbine power plant. A comparison of a real world

operating characteristics to that of the ideal Rankine power cycle will beoperating characteristics to that of the ideal Rankine power cycle will be

made. made.

ObjectiveObjective

The objective of this lab is to acquire experience on the basic Rankine cycleThe objective of this lab is to acquire experience on the basic Rankine cycle

and to understand the factors and parameters affecting the efficiency andand to understand the factors and parameters affecting the efficiency and

cost of generating energy. In this lab, we will determine:cost of generating energy. In this lab, we will determine:

a)a) Mass Flow Rate of a Rankine Cycle.Mass Flow Rate of a Rankine Cycle.

b)b) Thermodynamics properties (entropies, enthalpies, quality, etc).Thermodynamics properties (entropies, enthalpies, quality, etc).

Draw a schematic of the cycle in a T-S diagram.Draw a schematic of the cycle in a T-S diagram.

c)c) Work and heat transfer in the different stages of the cycle.Work and heat transfer in the different stages of the cycle.

d)d) Thermal efficiency of the cycle.Thermal efficiency of the cycle.

e)e) Mass flow rate in the turbine.Mass flow rate in the turbine.

f)f) Boiler efficiencyBoiler efficiency

g)g) Air-Fuel ratio and air excess.Air-Fuel ratio and air excess.

h)h) Cost of generating steam and energy.Cost of generating steam and energy.

BackgroundBackground

The Rankine cycle is the most common of all power generation cycles and isThe Rankine cycle is the most common of all power generation cycles and is

diagrammatically depicted via Figures 1 and 2. The Rankine cycle wasdiagrammatically depicted via Figures 1 and 2. The Rankine cycle was

devised to make use of the characteristics of water as the working fluid. Thedevised to make use of the characteristics of water as the working fluid. The

cycle begins in a boiler (State 4 in figure 1), where the water is heated untilcycle begins in a boiler (State 4 in figure 1), where the water is heated until

it reaches saturation- in a constant-pressure process. Once saturation isit reaches saturation- in a constant-pressure process. Once saturation is

reached, further heat transfer takes place at a constant temperature, untilreached, further heat transfer takes place at a constant temperature, until

the working fluid reaches a quality of 100% (State 1). At this point, the high-the working fluid reaches a quality of 100% (State 1). At this point, the high-

quality vapor is expanded isoentropically through an axially bladed turbinequality vapor is expanded isoentropically through an axially bladed turbine

stage to produce shaft work. The steam then exits the turbine at State 2.stage to produce shaft work. The steam then exits the turbine at State 2.

The working fluid, at State 2, is at a low-pressure, but has a fairly highThe working fluid, at State 2, is at a low-pressure, but has a fairly high

quality, so it is routed through a condenser, where the steam is condensedquality, so it is routed through a condenser, where the steam is condensed

into liquid (State 3). Finally, the cycle is completed via the return of theinto liquid (State 3). Finally, the cycle is completed via the return of the

liquid to the boiler, which is normally accomplished by a mechanical pump.liquid to the boiler, which is normally accomplished by a mechanical pump.

Figure 2 shows a schematic of a power plant under a Rankine cycle.Figure 2 shows a schematic of a power plant under a Rankine cycle.

Figure Figure 11: Diagrams for a simple ideal Rankine cycle:: Diagrams for a simple ideal Rankine cycle:

a) P-V diagram, b) T-S diagrama) P-V diagram, b) T-S diagram

Figure Figure 22: Schematic of a simple ideal Rankine cycle: Schematic of a simple ideal Rankine cycle

Rankine cycle analysis Rankine cycle analysis

This experiment has an important difference with the cycle shown in FigureThis experiment has an important difference with the cycle shown in Figure

2. The difference is that there is not a pump to complete the cycle. This is2. The difference is that there is not a pump to complete the cycle. This is

not exactly a cycle. Instead, it is an open system. The water crossing thenot exactly a cycle. Instead, it is an open system. The water crossing the

condenser is stored in a tank as show in Figure 3, but the principle ofcondenser is stored in a tank as show in Figure 3, but the principle of

Rankine cycle studied in Thermodynamic is still valid.Rankine cycle studied in Thermodynamic is still valid.

The boiler will be filled with water before the experiment and the experimentThe boiler will be filled with water before the experiment and the experiment

will be ended when the water is reaches the minimum level of correctwill be ended when the water is reaches the minimum level of correct

operation, given by the manufacturer.operation, given by the manufacturer.

Another important difference is that between the boiler and turbine there is aAnother important difference is that between the boiler and turbine there is a

valve that generates a throttling effect. The throttling process is analyzed asvalve that generates a throttling effect. The throttling process is analyzed as

an isenthalpic process. This phenomenon will be analyzed more in detail.an isenthalpic process. This phenomenon will be analyzed more in detail.

Also, the boiler generates a superheated vapor.Also, the boiler generates a superheated vapor.

Figure Figure 33: Schematic of Rankine cycle steam turbine apparatus: Schematic of Rankine cycle steam turbine apparatus

I.I. Mass Flow Rate of the Rankine Cycle.

Evaluating the time of operation and volume of consumed water, the mass

flow rate can be measured as:

Here, time is measured with a chronometer for a known volume of water

in the boiler.

Figure 4: Real Rankine cycle

II.II. Work and Heat Transfer

For this analysis, it is assumed that the process is ideal and there are not

pressure losses occurring in the piping, but as has been said previously the

boiler generates superheated vapor and there is a throttling process in the

valve. Figure 4 shows the modified cycle of the plant.

The evaporator, in this case a fire-tube boiler, produces a superheated vapor

(Stage ). Taking a control volume enclosing the boiler tubes and drums, the

energy rate balance gives:

neglecting kinetic and potential energy, the energy equation reduce to:

Then, vapors pass through the valve, states1’-1”. For a control volume

enclosing the valve, the mass and energy rate balance reduces under steady

state to:

Since there is not work done in the valve and heat transfer can be

neglected, last equation reduces to:

which means that there is an isenthalpic expansion in the valve.

Making a similar analysis for the pump and condenser, the work and heat

transfer are:

and

The energy balance for a control volume around the turbine under steady

state condition is:

Neglecting heat transfer to the surrounding, the process in the turbine is

assumed adiabatic and reversible, so isentropic ( ) and the energy

equation reduces to:

Then, knowing that and also and which could be estimated with

the pressure and temperature at outlet of the turbine, the quality of the

vapor can be calculated as:

with , the enthalpy is calculated as:

where and are calculated with the outlet temperature. It is important to

emphasize that the valve generates entropy from state to the state .

Without the expansion valve the cycle would be close to an isentropic

expansion in the turbine. All parameters , , , , , and

can be determined from temperatures and pressures at each stage.

III.III. Thermal Efficiency of Cycle

The net work of the cycle is defined by the difference between the turbine

work and the pump work:

If the pump work is neglected, the net work of the cycle reduces to:

Then the thermal efficiency of this system is defined by the rate between the

net work and heat transfer from the boiler:

IV.IV. Air -Fuel ratio and Air Excess.

The chemical composition of the gases at the outlet of boiler is:

at the inlet, there are dry air and fuel (butane):

Then, making a balance between inlet and outlet:

so,

Where the coefficients (A, B, C, D, F, G and Mi) are the molar mass necessary

to balance the equation. Then the air excess is:

the is the molar mass of air when the chemical reaction is

complete, and there is not formation of water and intermediate compounds:

Balancing this equation: , , and , which

is:

Then, the Air-Fuel ratio is defined by:

Where and are the atomic weight of air and combustible,

respectively. The kg/Kmol and the kg/Kmol.

V.V. Mass flow rate in the turbine

From the generated amperage and voltage:

so, the mass flow rate in the turbine is:

Where is the efficiency of the turbine. Here, we will assume this efficiency

equal to one.

VI.VI. Boiler analysis

From the chemical equation of combustion, balanced in term of moles:

the first law of thermodynamics for a volume enclosing the boiler is:

where and are the sum for each reactants and products of

combustion. Remember that , where is mass, is number of

moles and is the molar mass of the i-th component. Last equation is

written in the form:

Here, is the enthalpy of reactants and products at the temperature of inlet

and outlet of the boiler. They could be found in the table of enthalpies of

formation.

Figure 5: Enthalpy of formation

Another form to write the first law is:Another form to write the first law is:

where where is the enthalpy of reactants and products, respectively, at the is the enthalpy of reactants and products, respectively, at the

standard temperature and pressure. Rearranging:standard temperature and pressure. Rearranging:

The first two terms are the enthalpy of combustion (The first two terms are the enthalpy of combustion ( ) at standard ) at standard

temperature and pressure.temperature and pressure.

Table 1: Enthalpy of formation, HHV and LHVTable 1: Enthalpy of formation, HHV and LHV

The enthalpy of combustion also is called The enthalpy of combustion also is called heating valueheating value (HV), and this is (HV), and this is

number indicative to the useful energy content of different fuels. There arenumber indicative to the useful energy content of different fuels. There are

two types of heating value: two types of heating value: higher heating valuehigher heating value (HHV) and the lo (HHV) and the lower heatingwer heating

value value (LHV). The HHV is obtained when all the water formed by combustion(LHV). The HHV is obtained when all the water formed by combustion

is a liquid. The LHV is obtained when all the water formed by the combustionis a liquid. The LHV is obtained when all the water formed by the combustion

is a vapor. For that HHV is more than LHV (see Table 1). For calculations, weis a vapor. For that HHV is more than LHV (see Table 1). For calculations, we

will assume that water formed is in the liquid state and the HHV will be usedwill assume that water formed is in the liquid state and the HHV will be used

for for . Now, we can calculate the efficiency of the boiler as:. Now, we can calculate the efficiency of the boiler as:

VII.VII. Cost of Generating Steam and Energy.

The mass flow of fuel is the product between the density and fuel flow mass The mass flow of fuel is the product between the density and fuel flow mass

and the time of operation:and the time of operation:

where where is the density of butane gas at atmospheric pressure. Then the is the density of butane gas at atmospheric pressure. Then the

cost of generating steam per unit mass of steam is:cost of generating steam per unit mass of steam is:

where where is the price of the fuel. Also it is possible to determine the cost is the price of the fuel. Also it is possible to determine the cost

of generating energy by:of generating energy by:

Experimental SetupExperimental Setup

The equipment has a data acquisition system to collect the information. Also,The equipment has a data acquisition system to collect the information. Also,

it will be necessary a chronometer for estimating the time operation. A viewit will be necessary a chronometer for estimating the time operation. A view

of the real equipment and data acquisition system is shown in Figure 6.of the real equipment and data acquisition system is shown in Figure 6.

Figure Figure 66: The mini-power plant : The mini-power plant

The mini-power plant has a boiler (see Figure 7), which is a dual-pass, flameThe mini-power plant has a boiler (see Figure 7), which is a dual-pass, flame

through tube type unit. A burner fan speed is electronically adjustable tothrough tube type unit. A burner fan speed is electronically adjustable to

operate whit a minimum of excess of air. A vortex disc, located downstreamoperate whit a minimum of excess of air. A vortex disc, located downstream

of the boiler unit, mixes fuel and air and sets up a rotary gas flow thatof the boiler unit, mixes fuel and air and sets up a rotary gas flow that

results in efficient heat transfer from the flame tube to the boilers water,results in efficient heat transfer from the flame tube to the boilers water,

(see Figure 8).(see Figure 8).

Figure Figure 77: Boiler: Boiler

Electromechanical and electronic burner and boiler controls are locatedElectromechanical and electronic burner and boiler controls are located

within the front operator panel enclosure. An A.G.A. certified electronicwithin the front operator panel enclosure. An A.G.A. certified electronic

ignition gas valve and microprocessor based gas ignition module automateignition gas valve and microprocessor based gas ignition module automate

and supervise flame control. A transducer assists in regulating boilerand supervise flame control. A transducer assists in regulating boiler

pressure by cycling the burner on and off. A poppet valve, located on top ofpressure by cycling the burner on and off. A poppet valve, located on top of

the boiler, serves as a safety valve. In the event of control malfunction, thethe boiler, serves as a safety valve. In the event of control malfunction, the

poppet valve will open and relieve boiler pressure.poppet valve will open and relieve boiler pressure.

Figure Figure 88: Forced air gas burned : Forced air gas burned

The other component is the turbine and generator, (see Figure 9). The The other component is the turbine and generator, (see Figure 9). The

turbine consists of the following major components:turbine consists of the following major components:

1.1. A precision machined, stainless steel front and rear housing.A precision machined, stainless steel front and rear housing.

2.2. A nozzle ring and a single stage shrouded impulse turbine wheelA nozzle ring and a single stage shrouded impulse turbine wheel

Figure Figure 99: Turbine and Generator: Turbine and Generator

The generator is a 4-pole, permanent magnet, brushless unit. The rotor isThe generator is a 4-pole, permanent magnet, brushless unit. The rotor is

supported by pre-loaded precision ball bearings. The generator includes asupported by pre-loaded precision ball bearings. The generator includes a

full wave, integral rectifier bridge that delivers direct current to thefull wave, integral rectifier bridge that delivers direct current to the

generators D.C. terminals. The generator terminal board also carries a set ofgenerators D.C. terminals. The generator terminal board also carries a set of

AC output terminals for experimental procedures that may entail the use ofAC output terminals for experimental procedures that may entail the use of

a transformer, or deal with frequency related topics, rpm measurement anda transformer, or deal with frequency related topics, rpm measurement and

other AC related experiments.other AC related experiments.

Figure Figure 1010: Cooling tower: Cooling tower

Finally, the condenser towers outer mantle is formed from a single piece ofFinally, the condenser towers outer mantle is formed from a single piece of

aluminum, (see Figure 10). The towers large surface area affects heataluminum, (see Figure 10). The towers large surface area affects heat

transfer to ambient air and provides a realistic appearance. Turbine exhausttransfer to ambient air and provides a realistic appearance. Turbine exhaust

steam is piped into the bottom of the tower. The steam is kept in closesteam is piped into the bottom of the tower. The steam is kept in close

contact with the outside mantle by means of 4 baffles.contact with the outside mantle by means of 4 baffles.

ProcedureProcedure

1.1. At the moment of making the experiment, the steam turbine will beAt the moment of making the experiment, the steam turbine will be

operational in the no load condition. So, the first step is to set the ¼ ofoperational in the no load condition. So, the first step is to set the ¼ of

the maximum load applied on the turbine by the generator.the maximum load applied on the turbine by the generator.

2.2. Allow the system to reach steady state, and take readings. They are:Allow the system to reach steady state, and take readings. They are:

a)a) Boiler temperature.Boiler temperature.

b)b) Boiler pressure.Boiler pressure.

c)c) Turbine inlet temperature.Turbine inlet temperature.

d)d) Turbine exit temperature.Turbine exit temperature.

e)e) Turbine inlet pressure.Turbine inlet pressure.

f)f) Turbine exit pressure.Turbine exit pressure.

g)g) Water flow.Water flow.

h)h) Generator amperage.Generator amperage.

i)i) Generator voltage.Generator voltage.

j)j) Time operation.Time operation.

k)k) Repeat the step 2) for ½ and ¾ of the maximum load applied.Repeat the step 2) for ½ and ¾ of the maximum load applied.

Example #1: Rankine cycle analysisExample #1: Rankine cycle analysis

PProblem:roblem:

Steam is the working fluid in an ideal Rankine cycle. Saturated vapor entersSteam is the working fluid in an ideal Rankine cycle. Saturated vapor enters

the turbine at 8.0MPa and saturated liquid exits the condenser at a pressurethe turbine at 8.0MPa and saturated liquid exits the condenser at a pressure

of 0.008MPa (see Figure 11). The net power of cycle is 100MW. Determineof 0.008MPa (see Figure 11). The net power of cycle is 100MW. Determine

for the cyclefor the cycle::

a)a) The thermal efficiency.The thermal efficiency.

b)b) The mass flow rate of steam.The mass flow rate of steam.

c)c) The rate of heat transfer, into the working fluid as it passes throughThe rate of heat transfer, into the working fluid as it passes through

the boiler.the boiler.

d)d) The rate of heat transfer, from the condensing steam as it passesThe rate of heat transfer, from the condensing steam as it passes

through the condenser.through the condenser.

e)e) The mass flow rate of condenser cooling water, if cooling waterThe mass flow rate of condenser cooling water, if cooling water

enters the condenser at 15°C and exits at 35°C.enters the condenser at 15°C and exits at 35°C.

Figure Figure 1111: Schematic of the Rankine cycle : Schematic of the Rankine cycle

SolutionSolution

Assumption:Assumption:

1.1. Each component of the cycle is analyzed as a control volume at steadyEach component of the cycle is analyzed as a control volume at steady

state. state.

2.2. All processes of the working fluid are internally reversible.All processes of the working fluid are internally reversible.

3.3. The turbine and pump operate adiabatically.The turbine and pump operate adiabatically.

4.4. Kinetic and potential energy effects are negligible.Kinetic and potential energy effects are negligible.

5.5. Saturated vapor enters the turbine. Condensate exits the condenserSaturated vapor enters the turbine. Condensate exits the condenser

as saturated liquid.as saturated liquid.

Analysis:Analysis:

To begin the analysis, let us fix each of the principal states located on theTo begin the analysis, let us fix each of the principal states located on the

accompanying schematic and accompanying schematic and T-sT-s diagram. Starting at the inlet to the diagram. Starting at the inlet to the

turbine, the pressure is 8.0MPa and the steam is a saturated vapor, so fromturbine, the pressure is 8.0MPa and the steam is a saturated vapor, so from

Table A-3 of Moran and Shapiro, Table A-3 of Moran and Shapiro, and and

Stage 2 is fixed by Stage 2 is fixed by and the fact that specific entropy is constantand the fact that specific entropy is constant

for the adiabatic, internally reversible expansion through the turbine. Usingfor the adiabatic, internally reversible expansion through the turbine. Using

liquid and saturated vapor data from Table A-3 of Moran and Shapiro, we findliquid and saturated vapor data from Table A-3 of Moran and Shapiro, we find

that the quality at stage 2 is:that the quality at stage 2 is:

The enthalpy is thenThe enthalpy is then

Stage 3 is saturated liquid at 0.008MPa, so Stage 3 is saturated liquid at 0.008MPa, so . Stage 4 is fixed. Stage 4 is fixed

by the boiler pressureby the boiler pressure and the specific entropy and the specific entropy . The specific. The specific

enthalpy enthalpy can be found by interpolation in the compressed liquid tables. can be found by interpolation in the compressed liquid tables.

However, because liquid data are relatively sparse, it is more convenient toHowever, because liquid data are relatively sparse, it is more convenient to

solve solve for for , using , using to approximate the pump work. to approximate the pump work.

With this approach:With this approach:

Substituting property values from Table A-3 of Moran and Shapiro:Substituting property values from Table A-3 of Moran and Shapiro:

a)a) The net power developed by the cycle is:The net power developed by the cycle is:

Energy balance for a control volume around the turbine and pump gives, Energy balance for a control volume around the turbine and pump gives,

respectivelyrespectively

and and

where where is the mass flow rate of the steam. The rate of heat transfer tois the mass flow rate of the steam. The rate of heat transfer to

the working fluid as it passes through the boiler is determined using anthe working fluid as it passes through the boiler is determined using an

energy rate balance as:energy rate balance as:

the thermal efficiency is then:the thermal efficiency is then:

b)b) The mass flow rate of steam can be obtained from the expression for theThe mass flow rate of steam can be obtained from the expression for the

net power given in part a). Thus:net power given in part a). Thus:

c)c) With the expression for With the expression for from part a) and previously determined from part a) and previously determined

specific enthalpy values:specific enthalpy values:

d)d) Mass and energy rate balances applied to a control volume enclosing theMass and energy rate balances applied to a control volume enclosing the

steam side side of the condenser give:steam side side of the condenser give:

Alternatively, Alternatively, can be determined from an energy rate balance on the can be determined from an energy rate balance on the

overall vapor power plant. At steady state, the net power developedoverall vapor power plant. At steady state, the net power developed

equals the net rate of heat transfer to the plant:equals the net rate of heat transfer to the plant:

then,then,

e)e) Taking a control volume around the condenser, the energy rate balanceTaking a control volume around the condenser, the energy rate balance

gives at steady state:gives at steady state:

where where is the mass flow rate of the cooling water. Solving for is the mass flow rate of the cooling water. Solving for ::

the numerator in this expression is evaluated in part d). For the coolingthe numerator in this expression is evaluated in part d). For the cooling

water, water, , so with saturated liquid enthalpy value from Table A-2, so with saturated liquid enthalpy value from Table A-2

Moran and Shapiro at the entering and exiting temperatures of theMoran and Shapiro at the entering and exiting temperatures of the

cooling water:cooling water:

Example #2: Combustion analysis of the boiler Example #2: Combustion analysis of the boiler

Problem:Problem:

Find the useful heat generated by the combustion of Find the useful heat generated by the combustion of of ethane in aof ethane in a

furnace in a 20 percent deficient air if the reactants are at furnace in a 20 percent deficient air if the reactants are at and the and the

products at 1500K. Assume that hydrogen, being more reactive than carbon,products at 1500K. Assume that hydrogen, being more reactive than carbon,

satisfies itself first with the oxygen it needs and burns completely to satisfies itself first with the oxygen it needs and burns completely to ..

Five percent of the heat of combustion is lost to the furnace exterior.Five percent of the heat of combustion is lost to the furnace exterior.

SolutionSolution

The stoichiometric equation for ethane in air is:The stoichiometric equation for ethane in air is:

(where there are 3.76 mol(where there are 3.76 mol in atmospheric air, thus 13.16=3.5x3.76).in atmospheric air, thus 13.16=3.5x3.76).

With 20 percent deficient air multiply the With 20 percent deficient air multiply the and and by 0.8. by 0.8. will burnwill burn

completely to completely to and and will burn partially to will burn partially to and partially and partially ::

carbon balance:carbon balance:

oxygen balance:oxygen balance:

thus thus , , and the combustion equation is:and the combustion equation is:

As here is no work done in a furnace, the first law of thermodynamics for As here is no work done in a furnace, the first law of thermodynamics for

steady states written as:steady states written as:

thus,thus,

The useful heat generated by the combustion is:The useful heat generated by the combustion is:

Discussion Discussion

ReferencesReferences

Moran, M. J. and Shapiro, H. N., 1995, Fundamental of EngineeringMoran, M. J. and Shapiro, H. N., 1995, Fundamental of Engineering

Thermodynamics, 3rd edition, John Wiley & Sons, Inc., New York.Thermodynamics, 3rd edition, John Wiley & Sons, Inc., New York.

El-Wakil, M.M., 1984, Powerplant Technology, McGraw-Hill, Inc., New York.El-Wakil, M.M., 1984, Powerplant Technology, McGraw-Hill, Inc., New York.