Analysis Of A Vapor Power Plant

Analysis of A Vapor Power Plant

8/20/96

ME1361 T

hermo II

3.0 Abstract

The objective of this study is to construct a computer model of a water vapor

power plant. This model will be used to calculate the state properties at all

points within the cycle. Included is an analysis of the ideal extraction

pressures based on the calculated values of net work, energy input, thermal

efficiency, moisture content, and effectiveness.

4.0 Body 4.1 Introduction System to be Analyzed Steam enters the

first turbine stage at 120 bar, 520 Â°C and expands in three stages to the

condenser pressure of .06 bar. Between the first and second stage, some steam is

diverted to a closed feedwater heater at P1, with saturated liquid condensate

being pumped ahead into the boiler feedwater line. The Terminal Temperature

Difference of the feedwater heater is 5Â°C. The rest of the steam is reheated to

Analysis of A Vapor Power Plant

8/20/96

ME1361 T

hermo II

3.0 Abstract

The objective of this study is to construct a computer model of a water vapor

power plant. This model will be used to calculate the state properties at all

points within the cycle. Included is an analysis of the ideal extraction

pressures based on the calculated values of net work, energy input, thermal

efficiency, moisture content, and effectiveness.

4.0 Body 4.1 Introduction System to be Analyzed Steam enters the

first turbine stage at 120 bar, 520 Â°C and expands in three stages to the

condenser pressure of .06 bar. Between the first and second stage, some steam is

diverted to a closed feedwater heater at P1, with saturated liquid condensate

being pumped ahead into the boiler feedwater line. The Terminal Temperature

Difference of the feedwater heater is 5Â°C. The rest of the steam is reheated to

500Â°C, and then enters the second stage of expansion. Part of the steam is

extracted between the second and third stages at P2 and fed into an open

feedwater heater operating at that pressure. Saturated liquid at P2 leaves the

open feedwater heater. The efficiencies of all pumps are 80%, and the

efficiencies of all turbines are 85%.

Throughout this report the states will be referenced as depicted above with the

numbers 1-13. The analysis of the system will involve the use of the Energy Rate

Balance to isolate the specific enthalpies and associated values of temperature,

pressure, specific volume, and steam quality. The Entropy balance equation will

be used to calculate the specific entropy at all the above noted states. Energy

Rate Balance (assume KE&PE=0) dEcv/dt = Qcv-Wcv Smi(hi) - Sme(he)

Entropy Rate Balance dScv/dt = SQj/Tj Smi(si) - Sme(se) scv

For simplicity, it is assumed in all calculations that kinetic and potential

energy have a negligible effect. It is also assumed that each component in the

cycle is analyzed as a control volume at steady state; and that each control

volume suffers from no stray heat transfer from any component to its

surroundings. The steam quality at the turbine exits will also be constrained

to values greater than or equal to 90% (Moran, 337). 4.2 Code Development

The C program "finalproject.cÂ² was developed to calculate the state values given

the constraints listed in section 4.1. The program structure consists of three

extracted between the second and third stages at P2 and fed into an open

feedwater heater operating at that pressure. Saturated liquid at P2 leaves the

open feedwater heater. The efficiencies of all pumps are 80%, and the

efficiencies of all turbines are 85%.

Throughout this report the states will be referenced as depicted above with the

numbers 1-13. The analysis of the system will involve the use of the Energy Rate

Balance to isolate the specific enthalpies and associated values of temperature,

pressure, specific volume, and steam quality. The Entropy balance equation will

be used to calculate the specific entropy at all the above noted states. Energy

Rate Balance (assume KE&PE=0) dEcv/dt = Qcv-Wcv Smi(hi) - Sme(he)

Entropy Rate Balance dScv/dt = SQj/Tj Smi(si) - Sme(se) scv

For simplicity, it is assumed in all calculations that kinetic and potential

energy have a negligible effect. It is also assumed that each component in the

cycle is analyzed as a control volume at steady state; and that each control

volume suffers from no stray heat transfer from any component to its

surroundings. The steam quality at the turbine exits will also be constrained

to values greater than or equal to 90% (Moran, 337). 4.2 Code Development

The C program "finalproject.cÂ² was developed to calculate the state values given

the constraints listed in section 4.1. The program structure consists of three

parts: Header/variable declaration Calculation section Data Report section The

Header section includes all the variable declarations, functions to include and

system definitions. To obtain accurate data values, this program uses floating

point values. The Calculation section is the function that is used to calculate

all the state values. In essence this section consists of two nested while()

loops that are used to vary the extraction pressures from 12000 kPa to 300 kPa.

The while loops are set to terminate when the steam quality becomes less than

90% as defined in the constraints in 4.1. The Data Reporting section is found

within the nested while() loops and are used to report the values found in the

preceding Calculation section. 4.3 Results and Discussion T-s diagram

The T-s diagram above shows how specific entropy changes related to temperature.

At State 1 the water vapor has just left the boiler and is superheated. It then

undergoes an expansion through the turbine. Since the efficiency of the turbine

is not 100% the entropy increases and is denoted by the point labeled Å’2Â¹.

During the reheat the pressure remains constant but the entropy increases to

point Å’3Â¹. Then another two expansions occurs and the fluid reaches state 4 and

5 respectively. The fluid then condenses at constant pressure to a saturated

liquid at state 6. The working fluid then enters a pump of efficiency 80% to

state 7. The fluid is then heated in an open feedwater heater at constant

pressure until it is a saturated liquid at state 8. The fluid is then sent

through a pump to a pressure equal to that at state 1 at point Å’9Â¹. The closed

Header section includes all the variable declarations, functions to include and

system definitions. To obtain accurate data values, this program uses floating

point values. The Calculation section is the function that is used to calculate

all the state values. In essence this section consists of two nested while()

loops that are used to vary the extraction pressures from 12000 kPa to 300 kPa.

The while loops are set to terminate when the steam quality becomes less than

90% as defined in the constraints in 4.1. The Data Reporting section is found

within the nested while() loops and are used to report the values found in the

preceding Calculation section. 4.3 Results and Discussion T-s diagram

The T-s diagram above shows how specific entropy changes related to temperature.

At State 1 the water vapor has just left the boiler and is superheated. It then

undergoes an expansion through the turbine. Since the efficiency of the turbine

is not 100% the entropy increases and is denoted by the point labeled Å’2Â¹.

During the reheat the pressure remains constant but the entropy increases to

point Å’3Â¹. Then another two expansions occurs and the fluid reaches state 4 and

5 respectively. The fluid then condenses at constant pressure to a saturated

liquid at state 6. The working fluid then enters a pump of efficiency 80% to

state 7. The fluid is then heated in an open feedwater heater at constant

pressure until it is a saturated liquid at state 8. The fluid is then sent

through a pump to a pressure equal to that at state 1 at point Å’9Â¹. The closed

feedwater heater, heats the fluid at constant pressure to state 10; and then is

heated again by the mixing with the feedwater at state 13. The fluid is then

heated back to point Å’1Â¹ in the boiler. To find the optimum extraction pressure

it is necessary to analyze the net work, energy input, thermal efficiency and

moisture content at various extraction pressures. These results can be found in

the appendix and graphed on the following pages. In "Plot of Net Work as a

Function of Extraction Pressure P2,P4"" it is evident that net work is maximized

when extraction pressure, P2 is 300 kPa and pressure P4 is 100 kPa. The

corresponding minimum value occurs when P2 is 3100 kPa, and P4 is 100 kPa. In

the following graph the total energy input to the system is plotted as a

function of extraction pressure. The minimum value is obtained when P4 is 100

kPa and P2 is 3100 kPa. However, it is noteworthy to observe that for all

values of P2 the energy input is minimized when P4 is 100 kPa. In "Plot of

Thermal Efficiency as a Function of Extraction Pressure P2,P4", the thermal

efficiency is maximized when P4 is 100 kPa and P2 is 300 kPa. This corresponds

directly to the results obtained for the net work of the cycle. The moisture

content at the exit of the third stage turbine can then be analyzed to see which

extraction pressure combination will be less damaging to the system. The graph

shows that the value of steam quality is maximized when P4 is 100 kPa and P2 is

300 kPa. From this it can be concluded that an extraction pressure of P4 equal

to 100 kPa and P2 equal to 300 kPa would be optimal for cycle performance. Not

only is net work maximized, but damage to system components is minimized by

heated again by the mixing with the feedwater at state 13. The fluid is then

heated back to point Å’1Â¹ in the boiler. To find the optimum extraction pressure

it is necessary to analyze the net work, energy input, thermal efficiency and

moisture content at various extraction pressures. These results can be found in

the appendix and graphed on the following pages. In "Plot of Net Work as a

Function of Extraction Pressure P2,P4"" it is evident that net work is maximized

when extraction pressure, P2 is 300 kPa and pressure P4 is 100 kPa. The

corresponding minimum value occurs when P2 is 3100 kPa, and P4 is 100 kPa. In

the following graph the total energy input to the system is plotted as a

function of extraction pressure. The minimum value is obtained when P4 is 100

kPa and P2 is 3100 kPa. However, it is noteworthy to observe that for all

values of P2 the energy input is minimized when P4 is 100 kPa. In "Plot of

Thermal Efficiency as a Function of Extraction Pressure P2,P4", the thermal

efficiency is maximized when P4 is 100 kPa and P2 is 300 kPa. This corresponds

directly to the results obtained for the net work of the cycle. The moisture

content at the exit of the third stage turbine can then be analyzed to see which

extraction pressure combination will be less damaging to the system. The graph

shows that the value of steam quality is maximized when P4 is 100 kPa and P2 is

300 kPa. From this it can be concluded that an extraction pressure of P4 equal

to 100 kPa and P2 equal to 300 kPa would be optimal for cycle performance. Not

only is net work maximized, but damage to system components is minimized by

having a high steam quality in the turbine. For this, energy input to the

system is sacrificed, however the net result is a more efficient and maintenance

free power plant.

5.0 Conclusion The computer model of the vapor power plant was used to

construct a table of data corresponding to every state of the system cycle.

Using this data, an optimal Å’solutionÂ¹ could be found for a combination of

extraction pressures that optimizes the performance of the power plant. In

particular a solution was found that maximized net work and efficiency while

minimizing the need for equipment replacement. The graphs of net work, thermal

efficiency and moisture content versus extraction pressure, depict this contrast

in values.

#include "h2osuperc.c" #include "h2osaturc.c" #include #include

#include #include

#define P1 12000 /* kPa */ #define T1 793.15 /* degrees

Kelvin */ #define T3 773.15 /* degrees Kelvin */ #define P5 6

/* kPa */ #define EFF_TURB .85 /* Isentropic

Turbine Efficiency */ #define EFF_PUMP .8 /* Isentropic Pump

Efficiency */ #define MIN_QUALITY .9 /* Lowest allowable Turbine Exit

Quality */ #define INCREMENT 100 /* kPa */ #define TTD

5.0 /* degrees Celsius */ #define C 4.179

system is sacrificed, however the net result is a more efficient and maintenance

free power plant.

5.0 Conclusion The computer model of the vapor power plant was used to

construct a table of data corresponding to every state of the system cycle.

Using this data, an optimal Å’solutionÂ¹ could be found for a combination of

extraction pressures that optimizes the performance of the power plant. In

particular a solution was found that maximized net work and efficiency while

minimizing the need for equipment replacement. The graphs of net work, thermal

efficiency and moisture content versus extraction pressure, depict this contrast

in values.

#include "h2osuperc.c" #include "h2osaturc.c" #include #include

#include #include

#define P1 12000 /* kPa */ #define T1 793.15 /* degrees

Kelvin */ #define T3 773.15 /* degrees Kelvin */ #define P5 6

/* kPa */ #define EFF_TURB .85 /* Isentropic

Turbine Efficiency */ #define EFF_PUMP .8 /* Isentropic Pump

Efficiency */ #define MIN_QUALITY .9 /* Lowest allowable Turbine Exit

Quality */ #define INCREMENT 100 /* kPa */ #define TTD

5.0 /* degrees Celsius */ #define C 4.179

/* specific heat */ #define T_ENV 293.15 /* Environment temp,

deg. Kelvin */ #define T_BOUND 1123.15 /* Boundary temp, deg. Kelvin

*/

void main()

/*** FUNCTION DECLARATION ***/

float h2osuper(int,float,float,int);

float h2osatur(int,float,int);

/*** VARIABLE DECLARATION ***/

float h1, s1, v1, t1, p1;

float p2, t2, s2, h2, h2s, x2, hg2, hf2, s2s, sf2, sg2, vf2, vg2, v2;

float p3, s3, h3, v3, t3;

float p4, t4, s4, h4, h4s, x4, s4s, sf4, sg4, hf4, hg4, vf4, vg4, v4;

float t5, s5, h5, h5s, s5s, sf5, sg5, x5, hf5, hg5, p5, vf5, vg5, v5;

float p6, t6, s6, h6, h6s, v6;

float p7, t7, s7, h7, h7s, v7;

float p8, t8, s8, h8, h8s, v8;

float p9, t9, s9, h9, h9s, v9;

float p10, t10, s10, h10, h10s, hf10, vf10, v10;

float p11, t11, s11, h11, h11s, v11;

float p12, h12, t12, v12, s12;

deg. Kelvin */ #define T_BOUND 1123.15 /* Boundary temp, deg. Kelvin

*/

void main()

/*** FUNCTION DECLARATION ***/

float h2osuper(int,float,float,int);

float h2osatur(int,float,int);

/*** VARIABLE DECLARATION ***/

float h1, s1, v1, t1, p1;

float p2, t2, s2, h2, h2s, x2, hg2, hf2, s2s, sf2, sg2, vf2, vg2, v2;

float p3, s3, h3, v3, t3;

float p4, t4, s4, h4, h4s, x4, s4s, sf4, sg4, hf4, hg4, vf4, vg4, v4;

float t5, s5, h5, h5s, s5s, sf5, sg5, x5, hf5, hg5, p5, vf5, vg5, v5;

float p6, t6, s6, h6, h6s, v6;

float p7, t7, s7, h7, h7s, v7;

float p8, t8, s8, h8, h8s, v8;

float p9, t9, s9, h9, h9s, v9;

float p10, t10, s10, h10, h10s, hf10, vf10, v10;

float p11, t11, s11, h11, h11s, v11;

float p12, h12, t12, v12, s12;

float p13, h13, t13, v13, s13;

float y2, y1, psat, w_turb_1, w_turb_2, w_turb_3;

float w_pump_1, w_pump_2, w_pump_3, w_turb_total, w_pump_total;

float w_net, q_boiler, q_reheat, thermal_eff, irrev;

/* OPEN A FILE FOR DATA */

FILE *fp;

fp=fopen("/bitbucket/ashoemak/proj.out","w");

fprintf(fp, "|______________________STATE_1______________________");

fprintf(fp, "|________________________STATE_2____________________________

");

fprintf(fp, "|______________________STATE_3______________________|");

fprintf(fp, "|________________________STATE_4____________________________

");

fprintf(fp, "|________________________STATE_5____________________________

");

fprintf(fp, "|______________________STATE_6______________________|");

fprintf(fp, "|______________________STATE_7______________________|");

fprintf(fp, "|______________________STATE_8______________________|");

fprintf(fp, "|______________________STATE_9______________________|");

fprintf(fp, "|______________________STATE_10_____________________|");

fprintf(fp, "|______________________STATE_11_____________________|");

float y2, y1, psat, w_turb_1, w_turb_2, w_turb_3;

float w_pump_1, w_pump_2, w_pump_3, w_turb_total, w_pump_total;

float w_net, q_boiler, q_reheat, thermal_eff, irrev;

/* OPEN A FILE FOR DATA */

FILE *fp;

fp=fopen("/bitbucket/ashoemak/proj.out","w");

fprintf(fp, "|______________________STATE_1______________________");

fprintf(fp, "|________________________STATE_2____________________________

");

fprintf(fp, "|______________________STATE_3______________________|");

fprintf(fp, "|________________________STATE_4____________________________

");

fprintf(fp, "|________________________STATE_5____________________________

");

fprintf(fp, "|______________________STATE_6______________________|");

fprintf(fp, "|______________________STATE_7______________________|");

fprintf(fp, "|______________________STATE_8______________________|");

fprintf(fp, "|______________________STATE_9______________________|");

fprintf(fp, "|______________________STATE_10_____________________|");

fprintf(fp, "|______________________STATE_11_____________________|");

fprintf(fp, "|______________________STATE_12_____________________|");

fprintf(fp, "|______________________STATE_13_____________________|");

fprintf(fp, "|______________________Misc_Data____________________|n");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) ");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) | x

");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) ");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) | x

");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) | x

");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) ");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) ");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) ");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) ");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) ");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) ");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) ");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) ");

fprintf(fp, "| W_T1 | W_T2 | W_T3 | W_P1 | W_P2 | W_P3 | WTT | WPT |

Wnet | q_b | q_r | T_eff | Irrev. |n");

fclose(fp);

fprintf(fp, "|______________________STATE_13_____________________|");

fprintf(fp, "|______________________Misc_Data____________________|n");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) ");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) | x

");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) ");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) | x

");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) | x

");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) ");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) ");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) ");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) ");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) ");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) ");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) ");

fprintf(fp, "| T(C) | P(kPa) | v(m^3/kg) | h(kj/kg) | s(kj/kg-K) ");

fprintf(fp, "| W_T1 | W_T2 | W_T3 | W_P1 | W_P2 | W_P3 | WTT | WPT |

Wnet | q_b | q_r | T_eff | Irrev. |n");

fclose(fp);

p2 = P1;

x2 = 1;

x4 = 1;

x5 = 1;

s2 = 0;

s4 = 0;

while( x2 >= MIN_QUALITY )

/*** TURBINE INLET ***/

p1=P1;

h1 = h2osuper(12,T1,P1,4);

s1 = h2osuper(12,T1,P1,5);

v1 = h2osuper(12,T1,P1,3);

t1 = T1-273.15;

h2s = h2osuper(25,p2,s1,4);

if (h2s == 0)

s2s = s1;

sf2 = h2osatur(2,p2,7);

sg2 = h2osatur(2,p2,8);

x2 = (s2s-sf2)/(sg2-sf2);

if(x2 < MIN_QUALITY || p2 = MIN_QUALITY )

h4s = h2osuper(25,p4,s3,4);

if (h4s == 0)

s4s = s3;

sf4 = h2osatur(2,p4,7);

sg4 = h2osatur(2,p4,8);

x4 = (s4s-sf4)/(sg4-sf4);

if(x4 < MIN_QUALITY || p4

sg2 = h2osatur(2,p2,8);

x2 = (s2s-sf2)/(sg2-sf2);

if(x2 < MIN_QUALITY || p2 = MIN_QUALITY )

h4s = h2osuper(25,p4,s3,4);

if (h4s == 0)

s4s = s3;

sf4 = h2osatur(2,p4,7);

sg4 = h2osatur(2,p4,8);

x4 = (s4s-sf4)/(sg4-sf4);

if(x4 < MIN_QUALITY || p4