Aškerčeva 6 SI-1000 Ljubljana, Slovenia tel.: +386 1 4771200 fax: +386 1 2518567 http://www.fs.uni-lj.si e-mail: [email protected]
University of Ljubljana
Fakulty of mechanical engineering
Department of Energy Engineering
Laboratory for Heat and Power
Energy Systems
Theoretical practice
Program: Erasmus
Authors: Mitja Mori
Mihael Sekavčnik
Ljubljana, 20. august 2010
University in Ljubljana
Faculty of mechanical engineering Askerceva 6, Ljubljana
THERMAL TURBOMACHINERY
Theoretical exercises 2
CONTENTS
1. ENERGY, MASS BALANCES AND REGENERATIVE HEATING OF FEED WATER 3
2. ENERGETIC SYSTEM 5
3. NUCLEAR POWER PLANT 6
4. GAS TURBINE POWER PLANT 8
5. STEAM SUPERHEATING 9
6. NUMERICAL MODELING OF STEAM SUPERHEATING SYSTEM IN IPSEPRO CODE 12
University in Ljubljana
Faculty of mechanical engineering Askerceva 6, Ljubljana
THERMAL TURBOMACHINERY
Theoretical exercises 3
1. Energy, mass balances and regenerative heating of feed
water
On the basis of power plant scheme, given below, determine:
Saving in boiler when regenerative heating is in use, compared to a plant with regenerative
heating disabled;
Difference in power plant efficiency for both cases.
Note: When calculating saving, consider cases with constant turbine power.
Assumptions:
1. Pressure drop in boiler is 10 % of pressure
at inflow.
2. Pressure drops in heat exchangers (feed
water side) are approximately 3 % of
pressure at inflow (0,1 bar).
3. Feed water temperature at regenerative
heater outflow is 1,, TTT isofw , where
T1 = 5 K.
condensationcondensate cooling
feedwater heating
distance
tem
per
ature
Tfw,i
Tc,o
Ts,i
Tfw,o
4. Temperature of condensate from LPRH is 2,, TTT ifwoc , where T2 = 6 K.
7
1
5
2
4
3
12
6 11
LPRH 1LPRH 2
10
8
9
closed
Figure: Schematical image of steam power plant with 2 low pressure regenerative heaters
University in Ljubljana
Faculty of mechanical engineering Askerceva 6, Ljubljana
THERMAL TURBOMACHINERY
Theoretical exercises 4
p T m x h
point bar °C kg/s – kJ/kg
1 200 550 1
2 0,05 2160
3
4 3 33
5
6
7 132
8 3 0,943
9 0,6 0,897
10
11
12
University in Ljubljana
Faculty of mechanical engineering Askerceva 6, Ljubljana
THERMAL TURBOMACHINERY
Theoretical exercises 5
2. Energetic system
Discussing: Energy- and mass-balances, power at the turbine shaft, fuel mass flow, internal
pump power.
On the picture the high pressure and middle pressure part of energetic system is shown. On the
basis of data, shown on the schema calculate following:
a) Calculate steam mass flow and
b) turbine power on the turbine shaft, if internal efficiency of the middle turbine part is
known (0,85).
c) On the basis of boiler heat power calculate fuel mass flow, if boiler efficiency is known
( 9.0K ) and the caloric value of the fuel also known ( MJ/kg 10B ).
d) Additionally calculate the steam mass flow for degasification (point 5) and
e) internal feed water pump power.
8
1
6
5
2
10
7
9
3
4
60500
20350
1.390
80175
310
1.25
82107
20200
University in Ljubljana
Faculty of mechanical engineering Askerceva 6, Ljubljana
THERMAL TURBOMACHINERY
Theoretical exercises 6
3. Nuclear power plant
Given below is a simplified diagram of the Krško nuclear power plant.
1) Draw the upper part of the process in a h-s diagram;
2) Determine steam quality before moisture separator reheater using three different methods;
3) Calculate high pressure turbine and low pressure turbine efficiency, if steam quality before
water drain is x22 = 0,94;
4) Calculate thermal efficiency and estimate complete efficiency of the secondary circuit;
5) Estimate heating surfaces in a two-stage steam reheater, if the overall heat transfer
coefficient is k = 2,5 kW/m2K.
10
1 2
43
6
5
22odv
13
11
20
7
8
21
12
16 17 18 19
1514
9
Schematic view of nuclear power plant
University in Ljubljana
Faculty of mechanical engineering Askerceva 6, Ljubljana
THERMAL TURBOMACHINERY
Theoretical exercises 7
Table: Properties of water/steam in specific points on the scheme
p T x m h
točka bar °C - kg/s kJ/kg
1 65,4 281,3 1 1030 2778,4
2 62,1 277,8 983 2778,4
3 61,5 277,2 47 2778,4
4 8,7 260,5 677,7 2970,7
5 0,053 33,9 561 2405,3
6 17,4 32,9 139,5
7 15,3 171,3 725,3
8 15,3 171,1 724,3
9 77,7 172,2 732,5
10 77,6 220,2 946,0
11 26,9 227,9 104 2665,0
12 9 175,4 64 2509,1
13 60,9 0 47 1218,8
14 8,2 0 101,3 742,7
15 26,8 0 36 979,4
16 3 156 34 2774,1
17 1,2 29 2632,0
18 0,474 14 2528,0
19 0,275 67 2493,0
20 0,268 39,4 165,1
21 15,3 170,7 722,4
22 0,162 0,94 10 232,6
University in Ljubljana
Faculty of mechanical engineering Askerceva 6, Ljubljana
THERMAL TURBOMACHINERY
Theoretical exercises 8
4. Gas turbine power plant
Calculate electrical power and efficiency for the following 5 power plants:
a. Pressure at turbine entry is 5 bar and temperature at turbine entry is 750 °C.
b. Pressure at turbine entry is 5 bar and temperature at turbine entry is 1200 °C.
c. Pressure at turbine entry is 12 bar and temperature at turbine entry is 1200 °C.
d. Pressure at turbine entry is 12 bar and temperature at turbine entry is 1200 °C. Degree of
regeneration is 0,8.
e. Pressure at turbine entry is 12 bar and temperature at turbine entry is 1200 °C. Thermal
efficiency of steam power plant, attached to gas turbine exhaust, is 0,35. Flue gases are
cooled in heat recovery steam generator (HRSG) to a temperature of 120 °C.
Ambient pressure is 1 bar and ambient temperature is 20 °C, compressor efficiency is 0,85, gas
turbine efficiency is 0,87, mechanical efficiency of compressor is 0,97, mechanical efficiency of
gas turbine is 0,98, mechanical efficiency of steam turbine is 0,99 and generator efficiency is
0,98. Pressure drops are: 0,2 bar at compressor entry, 1 bar in combustion chamber, 0,1 bar at
gas turbine exhaust to ambient, 0,2 bar in regenerative air heater (flue gas side and air side) and
0,3 bar in HRSG. Fuel mass flow can be neglected. For determination of air and flue gas
enthalpies use h-s or T-s diagram for dry air.
5
1 14 4
332 2
6
Power plant a, b in c Power plant d
7
14
32
Power plant e
University in Ljubljana
Faculty of mechanical engineering Askerceva 6, Ljubljana
THERMAL TURBOMACHINERY
Theoretical exercises 9
5. Steam superheating
Calculate the efficiency of thermodynamic cycle in optimum working conditions for:
a) the system without repeated steam superheating;
b) the system with one degree repeated steam superheating.
Processes should be represented in T – s diagram. For case b) calculate the optimal temperature
before repeated superheating (T2). The expansion thru turbine is assumed to be isentropic. The
pressure drop in the boiler with superheater is 30 bar and 2 bar in next superheater.
2
77 88
3
11
6b6a
Picture 1: Scheme of the thermodynamic cycle without repeated superheating and the system
with one degree repeated steam superheating.
p T m h
point bar °C kg/s kJ/kg
1 190 540
2
3 540
6a 0,05
6b 0,05
7
8 34
With repeated steam superheating we achieve increase in the thermodynamic efficiency of the
cycle. With regenerative heating of feeding water we increase the average temperature level of
the fluid during heat addition in the region of low temperatures, with repeated superheating we
increase the average temperature level of the fluid during heat addition in the region of high
temperatures.
University in Ljubljana
Faculty of mechanical engineering Askerceva 6, Ljubljana
THERMAL TURBOMACHINERY
Theoretical exercises 10
The connection between the average temperature level of the fluid during heat addition and
efficiency of steam thermodynamic cycle goes out from the steam cycle carnotization.
Carnotization: To the steam cycle the Carnot cycle is ascribed with the same work potential.
That means (picture 2) that shaded surface inside steam cycle (7-8-1-6) that represents the
difference between added and taken heat (gain work) is the same like by the ascribed Carnot
cycle (7-8c-1c-6).
T
s
1
678
8c1c
T
T
m,do
od
Picture 2: Carnotization of the steam cycle.
If the surfaces are the same it means that the average temperature level of the fluid during heat
addition in the case of Carnot cycle is the same value like in the case of steam cycle (Tm,do). The
average temperature level of the fluid during heat addition (Picture 2) is calculated with
81
81,
ss
hhT dom
It is well known that the Carnot efficiency is:
do
odC
T
T 1
So the efficiency of Carnot cycle can be inceased with increasing of the average temperature
level of the fluid during heat addition. From comparison with steam cycle it follows that the
efficiency of steam cycle can be increased also with increasing the average temperature level of
the fluid during heat addition.
Both processes can be shown in T – s diagram. The point 2 is not known that’s why the cycle
with one degree repeated steam superheating in this point cannot be sketched.
University in Ljubljana
Faculty of mechanical engineering Askerceva 6, Ljubljana
THERMAL TURBOMACHINERY
Theoretical exercises 11
0
100
200
300
400
500
0 1 2 3 4 5 6 7 8 9
T
[°C]
7
8
1
2
3
6a 6b
Picture 3: T – s diagram for the cycle without one degree repeated steam superheating
(7-8-1-6a) and the cycle with one degree repeated steam superheating (7-8-1-2-3-6b).
University in Ljubljana
Faculty of mechanical engineering Askerceva 6, Ljubljana
THERMAL TURBOMACHINERY
Theoretical exercises 12
6. Numerical Modeling of steam superheating system in
IPSEPro code
PREPARATIONS
1. Check if IPSE is installed on the computer and elements library (App lib) is updated and
connection with MS Excel is assured.
2. Before you start you should have hardware license key (LPT port).
3. In MS windows you should set dot instead comma (Control Panel -> Regional and
Language Options).
EXCERCISE:
o Start the IPSEpro-PSE program.
o In menu Options -> Set Page set format to A5, landscape.
o In menu Options -> Set Scale set the Scaling Factor to 1.5.
The template could be prepared, where these settings are already set to appropriate values.
Setting of the working fluid
In menu Objects -> New Global Object set the working fluid. There are 3 possibilities:
ambient (for defining the environment)
composition (for defining the structure of the working fluid)
fuel composition (for defining the structure of the fuel)
o Chose composition and write water in the box.
o The structure of fluid is defined in Objects -> Edit Global Object.
o We chose water (composition).
o The basic compounds are given. We define working fluid with prescribing mass ratios for all
compounds. In our case we are dealing with water, so by WATER we chose estimate and set
the value to 1, at all other compounds we chose set and set value to 0. If we chose set by the
water is the system of equations over defined.
The demonstration of the graphical interface
o In library chose source and place it on the right side on the sheet for modeling. On the right
side of the source place sink. With source and sink we define inflow and outflow of the
working fluid. Empty green square represents the outflow connector, full green square
represents the inflow connector.
o Connect source and sink with click from one in other green square. The connection (stream)
represents the fluid path.
o Double-click the connection and under composition chose water.
University in Ljubljana
Faculty of mechanical engineering Askerceva 6, Ljubljana
THERMAL TURBOMACHINERY
Theoretical exercises 13
o Thermodynamical state is defined with two independent variables (pressure, temperature) and
the flow is defined with mass flow.
o Data that we chose to define should be set to set and the values should be inserted, all other
data will be calculated from others terms (mass and energy balance). In our trivial case set the
pressure to 1 bar, temperature to 20 °C and mass flow to 1 kg/s.
o Click the button for calculating and we get the results in the form of crosses.
o In menu Objects chose Add Reference Cross in order to get the legend.
With right-click on the elements we get the calculated parameters.
Making of the scheme and modeling (Appendix 1)
o At the left side we add boiler.
o Delete the existing connection and connect the boiler between source and sink and define
water as composition.
o Regarding to the exercise, define the pressure after boiler 190 bar and temperature 540 °C.
Before boiler the temperature is 34 °C. Mass flow should be set to 100 kg/s.
o The efficiency of the boiler is 1 and pressure losses thru boiler 30 bar.
o Click the button for calculation.
o Add the first turbine and set the mechanical efficiency to 1 and internal efficiency to 1.
o Click the button for calculation.
o We get error. We can see in the protocol that we have 40 equations and 41 parameters. The
system is not well defined. We forgot to define state after turbine. For the moment we set that
missing state to 100 bar.
o Click the button for calculation.
o We proceed by adding another boiler and turbine.
o Settings:
pressure drop in superheater 2 bar,
temperature after superheater 540 °C,
pressure after turbine 0,05 bar,
mechanical and internal turbine efficiency 1.
o Add the generator and connect it with turbines.
o Click the button for calculation.
o We proceed with the condensator: undercooling 0.001, both pressure drops 0.0001.
o Click the button for calculation.
o Add the pump and numerical connector. The pump mechanical efficiency is 1, internal
efficiency is 0.8.
o Click the button for calculation.
o We can find out that we have 1 equation too many. If we analyze the state around the pump,
we can find out that the temperature after the pump should be let loose (with internal
efficiency, defined state before pump and pressure after pump, the temperature after pump is
University in Ljubljana
Faculty of mechanical engineering Askerceva 6, Ljubljana
THERMAL TURBOMACHINERY
Theoretical exercises 14
well defined). If we like to have 34 °C after the pump, we should change the internal
efficiency of the pump. Instead 0.8 we set it to 0.9.
o Because the troubles with convergence occurs, we use option Import Estimates in menu
Calculation.
o The scheme is now finished; we should just define state before superheating with temperature
instead with pressure.
The connection with the Excel
o For simplification the particular stream in the program should have the same number as in
the scheme in Appendix 1.
o We run Excel and open template PSEExcel. If the template is not shown, we usually find it in
"C:\Program Files\Microsoft Office\Templates\PSExcel.xlt".
o We set font to 16pt.
o In Excel we create the simple table. In the first column the state is marked in second the
enthalpy will be written.
o With the button Insert Item the enthalpies are inserted.
o In specific cell the equation for cycle efficiency is written:
2381
786321,
hhhh
hhhhhh
Q
PP b
do
čtbkp
o In specific cell the temperature T2 is written and is set as initial value with Add Item to
Sendlist. Insert value and click Calculate button and observe how cycle efficiency is changed.
The automatical variation of the parameter
o In menu DDE chose Create Variation.
o Set to one-parameter variation and T2 as parameter.
o Initial value should be 200, end 500. The step 10 and max. steps 100.
o As required results we set all enthalpies and entropies, that we can calculate the middle
temperature of the heat transfer to the water.
o In IPSE should be done the calculation 200 °C, that we don’t have any problems with
convergence.
o By the column where variation is, add one column for the middle temperature of heat transfer
to the water defined with: 2381
2381,
ssss
hhhhT dom
and one column for cycle efficiency.
o Search the maximum of the middle temperature of heat transfer to the water and we can find
out that it coincide with maximum value of the cycle efficiency.
Draw the diagram Tm (T2).
University in Ljubljana
Faculty of mechanical engineering Askerceva 6, Ljubljana
THERMAL TURBOMACHINERY
Theoretical exercises 15
APPENDIX 1: The scheme that should be modeled
2
77 88
3
11
6b6a