Prof. Dr. enol BAKAYA STUDENT NAME :

NUMBER :

GAZI UNIVERSITY

FACULTY OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING

Q1 Q2 Q3 Q4 TOTAL

/25 /25 /25 /25 /100

MM416E ENERGY ENGINEERING 1st HOMEWORK

Due on Monday 6th, April 2015 1. A steam power plant operates on an ideal reheat-regenerative Rankine cycle with one reheater and two

feed-water heaters, one open and one closed. The problem is specified for each student according to the last two digits of the student number. For this purpose, steam enters the high pressure turbine at a pressure and temperature given in Table 1 according to the last digit and the digit before the last one, respectively. Steam enters the low-pressure turbine at 1 MPa and 500C. The condenser pressure is 5 kPa. Steam is extracted from the turbine at 0.6 MPa for the closed feedwater heater and at 0.2 MPa for the open feedwater heater. In the closed feedwater heater, the feedwater is heated to the condensation temperature of the extracted steam. The extracted steam leaves the closed feedwater heater as a saturated liquid, which is subsequently throttled to the open feedwater heater. Show the cycle on a T-s diagram with respect to saturation lines. Determine (a) the fraction of steam extracted from the turbine for the open feedwater heater, (b) the thermal efficiency of the cycle, and (c) the net power output for mass flow rate of 45 kg/s through the boiler.

Note: Prepare a table indicating state properties of the system before solving the problem. Table 1. High pressure inlet pressure and temperature according to student number.

Last two digits of the student number 0, 1, 2, 3 4, 5, 6 7, 8, 9

(Last digit) High pressure turbine inlet

pressure

14 MPa 15 MPa 16 MPa

(The digit before the last one)

High pressure turbine inlet temperature

580 C 590 C 600 C

2. Consider a regenerative vapor power cycle with one open feedwater heater. The problem is specified for each student according to the last two digits of the student number. For this purpose, steam enters the turbine at a pressure and temperature given in Table 2 according to the last digit and the digit before the last one, respectively, and expands to 0.7 MPa, where some of the steam is extracted and diverted to the open feedwater heater. The remaining steam expands through the second-stage turbine to the condenser pressure of 0.008 MPa. Saturated liquid exits the open feedwater heater. The isentropic efficiency of each turbine stage is given in Table 2 according to the last digit of the student number. Each pump operates isentropically. If the net power output of the cycle is 120 MW, determine (a) the thermal efficiency and (b) the mass flow rate of the steam entering the first turbine stage, in kg/h.

Note: Prepare a table indicating state properties of the system before solving the problem. Table 2. Turbine inlet pressure, temperature and isentropic efficiency.

Last two digits of the student number 0, 1, 2, 3 4, 5, 6 7, 8, 9

(Last digit) Turbine inlet

pressure 7 8 9

(The digit before the last one) Turbine inlet temperature

480 490 500

(Last digit) Isentropic

efficiency of each stage of turbine

%85 %87 %89

3. A boiler delivers steam at 10 MPa, 550 C, to a two-stage turbine, as shown in the figure below. After the first stage, an amount of the steam is extracted for a process application and returned at 1 MPa, 90C, to the feedwater line. The extracted amount of steam and pressure are given in Table 3 according to the last digit and the digit before the last one, respectively. The remainder of the steam continues through the low-pressure turbine stage, which exhausts to the condenser at 10 kPa. One pump brings the feedwater to 1 MPa, and a second pump brings it to 10 MPa. Assume all components are ideal. If the process application requires 7 MW of power, how much power can then be cogenerated by the turbine?

Note: Prepare a table indicating state properties of the system before solving the problem. Table 3. Extracted steam amount and pressure

Last two digits of the student number 0, 1, 2, 3 4, 5, 6 7, 8, 9

(Last digit) Extracted steam

amount %20 %25 %30

(The digit before the last one)

Extracted steam pressure

1.4 MPa 1.5 MPa 1.6 MPa

4. A power plant produces 25 kg/s steam at the conditions given in Table 4 according to the last two digits of the student number, in the boiler. It cools the condenser to an exit of 45C, and the cycle is shown in the figure below. An extraction is done at 500 kPa to an open feedwater heater; in addition, a steam supply of 5 kg/s is taken out and not returned. The missing 5 kg/s water is added to the feedwater heater from a 20C, 400 kPa source. Find the needed extraction flow rate to cover both the feedwater heater and the steam supply. Find the total turbine power output.

Note: Prepare a table indicating state properties of the system before solving the problem. Table 4. Produced steam properties

Last two digits of the student number 0, 1, 2, 3 4, 5, 6 7, 8, 9

(Last digit) Pressure of the

boiler 3 MPa 3.5 MPa 4 MPa

(The digit before the last one)

Temperature of the produced steam in

the boiler

600 C 630 C 660 C