CHAPTER 2 POWER PLANT THERMODYNAMICS 2.1. Thermodynamic Prciples... 2 2.2. Steady Flow Engeerg Devices and Processes... 4 2.3. Heat Enge and Cycles... 8 2.4. Carnot Cycle... 10 2.5. Ranke Cycle... 10 Chapter 2 1
In a thermal power plant, all processes are based on the fundamentals of thermodynamics, heat transfer, and fluid mechanics. Fossil-fuel fired power plants, nuclear power plants, and diesel enges are thermal heat enges. 2.1. Thermodynamic Prciples The first and second laws of thermodynamics provide the fundamentals relationships for a power plant cycle analysis. In the thermodynamics, there are two types of system: closed system, and open system. Before discussg the systems, we need to talk on system. A system is the object that we want to analyze it. In the closed system, there is no mass transfer to the system and from the system. In an open system there is mass transfer. Let s consider an open system (i.e. control volume). The first law is the energy balance equation and is given by Heat (Q) Mass Control Volume Mass Work (W) Figure 2.1. Open System E E = ΔE (kj) (2.1) system or terms of rate this equation will be E E & Δ system E & = Δt (kj/s) or (kw). (2.2) Energy can transfer to an open system three ways: heat transfer, work teraction, and carryg by mass. Energy (E) has components of enthalpy, ketic energy, and potential Chapter 2 2
energy. If the ketic and potential energies are omitted from this equation, for an open system this equation can be written as Δ(Mu) Q& cv Q& + W& W& + m & h m & h = (2.3) Δt where Q & = heat transferred to control volume (kj/s) Q & = heat transferred from control volume (kj/s) W & = work done on the control volume (kj/s) W & = work done by the control volume (kj/s) m& = total enthalpy entered to control volume by mass flow (kj/s) h m& = total enthalpy entered from control volume by mass flow (kj/s) h Δ(Mu) cv = ternal energy change control volume (kj) Similarly, the mass balance equation for control volume will be ( ΔM ) cv & (2.4) t m m& = Δ For steady-state and steady-flow process, there is no mass and energy accumulation the control volume. Then the energy and mass balance equations will be Q& Q& + W& W& + m & h m & h 0 (2.5) = and m & = & 0 (2.6) m Chapter 2 3
2.2. Steady Flow Engeerg Devices and Processes Turbe Process (Expansion Process) Turbe is a device that converts heat energy of workg fluid (e.g. steam) to mechanical energy. If it is assumed that the process is adiabatic (i.e. no heat transfer), and there are no ketic energy and potential energy changes, and under steady-state condition, the energy equation becomes Superheated Steam m P1 h 1 1 1 W Figure 2.2. Turbe system 2 m P2 h 2 2 W & = m& h m& h (2.7) Sce the steady-state condition m& = m& m& then, w t = ΔW m& cv = h h (kj/kg) (2.8) The turbe work (w t ) by unit mass of workg fluid equals the difference between let enthalpy and exit enthalpy of the turbe. The steam temperature and pressure at the turbe let (h i ) determe the let enthalpy. To determe the exit enthalpy (h e ), the turbe ternal efficiency is used. The turbe ternal efficiency is defed as Chapter 2 4
h h w i e a η t = = (2.9) hi hes ws It is the ratio of the actual enthalpy drop to the enthalpy drop that would occur the correspondg adiabatic and reversible process. Figure 2.3 Turbe Expansion Process Pump Process (Compression Process) Pump is a device that creases the pressure of liquid fluid, for example water. The pump process can be considered as a reversed turbe process. Then, the pump efficiency is defed by w h h s i es η p = = (2.10) wa hi he and the actual pump work for unit mass is w p = h h (2.11) i e Isentropic pump process can be written as w p = v P P ) (2.12) i ( e i Chapter 2 5
Figure 2.4. Compression process. Mixg Process a Mixg Chamber For the mixg chamber, mass balance and energy balance equations are m & i = m& e and h im& i = hem& e m1 P1 1 h1 Cold m P2 h 2 2 2 Hot Mixg Chamber P =cons. Figure 2.5. Mixg chamber system 3 m P3 h 3 3 Heat Exchange Process a Heat Exchanger Heat exchanger is a device that transfers heat energy from hot fluid to cold fluid. Heat exchangers have to have at least two fluids: hot fluid and cold fluid. The fluids do not mixed, thus, fluids can be different pressure, can also be different fluids. Heat exchangers can be classified terms of flow direction of the fluids as follows: Parallel flow (hot fluid and cold fluid flow same direction) Counter flow (hot fluid and cold fluid flow opposite direction) Chapter 2 6
Cross flow (hot fluid and cold fluid flow perpendicular each other). For example, car radiator is a cross flow heat exchanger which hot fluid is water and cold fluid is air. Sce heat exchangers are steady-flow engeerg devices, they can be analyzed by the steady-flow energy balance equation. T h, m h m c Hot Fluid Q T h, T c, Cold Fluid T c, Figure 2.6. Turbe system Energy Balance Equation: For Hot Fluid (Hot side): Q = m& h h ) (2.13a) h ( h, h, Q = m& h c p, h ( Th, Th, ) (2.13b) For Cold Fluid (Cold side): Q = m& h h ) (2.14a) c ( c, c, Q = m& c c p, c ( Tc, Tc, ) (2.14b) If heat exchanger is ideally sulated (i.e. nor heat losses), the energy changes for hot fluid and cold fluid must be equal. Namely, m& h h ) = m& ( h h ) (2.15) h ( h, h, c c, c, The temperature distribution of the hot fluid and cold fluid is shown the followg figures. If there is phase changg process like condenser and evaporator, there are no temperature changes the phase changg side. In that case, the energy equations must be written terms of enthalpy, because there is not sensible heat change. Chapter 2 7
T h, Parallel Flow T h, Counter Flow T h, T c, ou t T h, T c, T c, T c, Condenser T h, Evaporator T h, T h, T h, T c, ou t T c, T c, T c, Figure 2.7. Temperature distribution hot and cold fluid Throttlg Process In the throttlg process, pressure will decrease, and the exit enthalpy is equal to the let enthalpy. In another word, the enthalpy of the fluid durg this process does not change, namely h i = h e 2.3. Heat Enge and Cycles Heat enge is a device that takes thermal energy from the hot reservoir, and converts part of this energy to work, and dumps the rest of it to the cold reservoir. Accordg to the 2 nd Law of thermodynamics, with two reservoirs, a heat enge cannot be designed. For example, car enge is a heat enge. The car enge is ternal combustion enge which has Chapter 2 8
maly two thermodynamics cycles: Diesel Cycle (compression cycle), and Otto Cycle (spark ignition cycle). In a car enge, as a result of fuel combustion, a great amount of thermal Heat Source (T ) H Q H Heat Enge Work Q L Sk (T ) L Figure 2.8. Heat Enge energy is released which will be as Hot Reservoir of enge. In this case, hot reservoir is side the heat enge that s why called ternal combustion enge. Brayton Cycle is the thermodynamic cycle for gas-turbe cycle enges, and Ranke Cycle is the thermodynamics cycle for steam-turbe cycle enges. The energy balance for the heat enges can be written as Q = W + H Q L (2.16) The ma purpose of heat enges is generatg mechanical work. This mechanical energy drives generator, and then electrical energy generated. Generator is a device that converts mechanical energy to electrical energy. In the fossil fuel-fired heat enges the fuel is coal, oil, or natural gas; while nuclear power plants the fuel is uranium. Chapter 2 9
2.4. Carnot Cycle The Carnot cycle is the most efficient cycle that can operate between two constant temperature reservoirs. One of them is high temperature reservoir, which is called source, and the other is low temperature reservoir, which is called sk. The Carnot cycle consists of four ternally reversible processes. Thus, it can be called a reversible cycle. Process 1-2 : Process 2-3 : Process 3-4 : Process 4-1 : reversible, isothermal heat addition reversible, adiabatic reversible, isothermal heat rejection reversible, adiabatic Sce the processes are reversible, the Carnot cycle offers maximum thermal efficiency attaable between two constant temperature reservoirs. The cycle thermal efficiency is generally defed as η th = work produced by the cycle heat supplied to the cycle (2.17) For the Carnot cycle the thermal efficiency becomes W Q Q Q H L L η th = = = 1 (2.18) QH QH QH or T = T T η th H L H T = T L 1 (Note that all temperature must be Kelv.) (2.19) H 2.5. Ranke Cycle Simple Ideal Ranke Cycle The Ranke cycle is similar to the Carnot cycle with one exception the condensation process. In the Ranke cycle the condensation process termates at the saturated liquid state. The processes of a Ranke cycle are followg: Chapter 2 10
Process 1-2 : Process 2-3 : Process 3-4 : Process 4-1 : Isentropic compression process pump Constant pressure heat addition boiler Isentropic expansion process turbe Constant pressure heat rejection condenser. Superheated Steam Boiler Turbe Steam W t, Q Compressed Liquid Pump Condenser Saturated Liquid Figure 2.9. Simple ideal Ranke cycle Coolg Water Q It is evident that the T-s diagram that the Ranke cycle is less efficient than a Carnot cycle for the same maximum and mimum temperatures. T Q 3 Boiler P=P 2 3Pressure W t, W p, 2 1 4 P=P 1 4 Condenser Pressure Q S Chapter 2 11
Figure 2.10. T-s Diagram of Simple ideal Ranke cycle. The thermal efficiency of the cycle can written as W net, η th = and W net, Wt, W p, Q = or Wnet, = Q Q As it is given above, there are four steady state processes: Process 1-2: Pump Process, = h2 h1 or w p ( P ) w p, v1 2 P1 = for isentropic pump Process 2-3: Boiler Process q = h 3 h2 Process 3-4: Turbe Process, = h3 h4 w t Process 4-1: Condenser Process q = h 4 h1 Now we can ask why we have to use condenser. Accordg to the 2 nd Law of Thermodynamics, with two reservoirs we cannot design a heat enge, so condenser needed cycle to damp some heat to sk. Another reason is that we use condenser is that the work needed for compressg liquid is much less than that of vapor. Thus, always at the let of pumps we need saturated liquid. The Figure 2.11 shows the deviation of the actually Ranke cycle form the ideal one. The efficiency of the Ranke cycle can be creased by lowerg the condenser pressure creasg turbe let temperature creasg boiler pressure creasg boiler let temperature. Chapter 2 12
Figure 2.11 (a) Deviation of actual vapor power cycle from the ideal Ranke cycle. (b) The effect of pump and turbe irreversibilities on the ideal Ranke cycle. Lowerg the Condenser Pressure: The work produces the Ranke cycle can be creased by lowerg the condenser pressure. However, it does not mean the condenser pressure should be reduced fitely. Lowerg the condenser pressure can cause an crease the moisture content the turbe exhaust end. These will affect adversely the turbe ternal efficiency, and erosion of turbe blades. Also, a low condenser pressure will result an crease condenser size and coolg water flow rate. Increasg Turbe Inlet Temperature: Increasg the steam temperature also result an crease of heat supplied the boiler. Increasg the steam temperature not only improves the cycle efficiency, but also reduces the moisture content at the turbe exhaust end. Increasg Boiler Pressure: The maximum steam temperature and the condenser pressure are held constant. It is seen that the steam pressure creases, the net work tends to rema unchanged. Increasg Boiler Inlet Temperature: Chapter 2 13
If the boiler let temperature is creased, the amount of heat supplied the boiler will decrease. Figure 2.12. The effect of lowerg the condenser pressure on the ideal Ranke cycle. Figure 2.13. The effect of superheatg the steam to higher temperatures on the ideal Ranke cycle. Chapter 2 14
Figure 2.14. The effect of creasg the boiler pressure on the ideal Ranke cycle. The Ideal Reheat Ranke Cycle In this design, the idea is to crease turbe let temperature. The use of reheatg is very common steam power plants. Reheatg process may not improve the cycle efficiency, but it does reduce the moisture content the steam leavg the turbe. This may improve the turbe ternal efficiency and thus crease the cycle performance. Chapter 2 15
Figure 2.15 The ideal reheat Ranke cycle. In this cycle, Q + W = W + W = Qboiler Qreheater and t, HPT LPT so W W W net, = t, p, In the analysis of the system given Figure 2.15, we can write The Ideal Regenerative Ranke Cycle The ma idea this process is to crease boiler let temperature, namely to preheat the feedwater before enterg to the boiler usg the waste energy of the turbe. The average temperature for heat addition the Ranke cycle us usually lower than maximum temperature. It is only due to the liquid heatg the boiler. If this liquid heatg could be elimated from the boiler, the average temperature for heat addition would be greatly creased and equal to the maximum cycle temperature the liquid case. Analysis: Boiler Process q = h 5 h4 Condenser Process = ( 1 y)( h h ) q Turbe Process = ( h h ) + ( y)( h ) 7 w t, 5 6 1 6 h7 w, = 1 y w + w, Pump Process p ( ) p1, p2 1 Chapter 2 16
Figure 2.16. The ideal regenerative Ranke cycle with an open feedwater heater. Figure 2.17. The ideal regenerative Ranke cycle with a closed feedwater heater. Feedwater Heaters As it is mentioned above, there are two types of feed water heaters: Open feed water heater (OFWH), and closed feed water heater (CFWH). Open Feedwater Heater (Direct-Contact Heater): Chapter 2 17
Open Feedwater Heaters (OFH) are called Direct-Contact Feedwater Heaters as well. They are mixg chamber. In OFH the extraction steam is mixed directly with the comg sucooled feedwater to produce saturated water at the extraction steam pressure. Every Ranke cycle power plant has at least one OFWH to remove non-condensable gases from the system. The condensate water (saturated water) leaves the condenser is pumped to a pressure equal to that of the extraction steam pressure from the turbe. The subcooled water after pumpg process and wet steam, which comes from the turbe, mix the OFH to produce saturated water. Thus the amount of bled steam (from the turbe) is essentially equal to that would saturate the subcooled feedwater. Closed Feedwater Heater (Surface Heater): Closed Feedwater Heaters (CFH) are heat exchanger. This type of feedwater heater, though it results a greater loss of availability than the open type, is the simples and most commonly used type power plants. The closed feed water heaters are a shell-and-tube type heat exchanger. In a closed feedwater heater, the feedwater (i.e. cold fluid) flows the tubes, and the bled steam (i.e. hot fluid), which is superheated steam or saturated steam, flows the shell side, and it passes its energy to the feedwater, and it condenses. Thus, they are small condensers. Because the feedwater goes through the tubes successive closed feedwater heaters, it does not mix with the bled steam and therefore can be pressurized only once by the first condensate pump, which then doubles as a boiler feed pump. Another boiler feed water pump is required and placed after the open feedwater heater (i.e. deaeratg) if one used the power plant. Steam (superheated or saturated) 1 T sat 4 T y 3 Feedwater (cold) T x 2 T dra In the design of closed feed water heaters, there are two approaches: Chapter 2 18
Termal Temperature Difference (TTD) Dra Cooler Temperature Difference (DCTD) TTD = T sat T DCTD = T dra T y x The value of TTD varies with heater pressure. In the case of low-pressure heaters, which receive wet or at most saturated bled steam, the TTD is positive and often of order of 5 C. This difference is obtaed by proper heat-transfer design of the heater. Too small a value, although good for plant efficiency, would require a larger heater than can be justified economically. Too large a value would effect cycle efficiency. In the dra cooler, the dra (i.e. condensate) is slightly sobcooled. The low-pressure feedwater heater receives saturated or wet steam can have a dra cooler and thus physically composed of a condensg section and a dra cooler section. The high-pressure feedwater heater receives superheated steam bled form the turbe has desuperheatg section and condensg section. Thus, there are four physical possibilities of closed feedwater heaters composed of the followg section: 1. Condenser 2. Condenser, dra cooler 3. Desuperheater, condenser, dra cooler 4. Desuperheater, condenser. T C T DC C TTD TTD DCTD L L T DC C DS T C DS TTD TTD DCTD L L Chapter 2 19
Figure 2.20. Temperature distribution of (a) Condenser, (b) Condenser and dra cooler, (c) Desuperheater, condenser, and dra cooler, (d) Desuperheater and condenser. There are two types of connection of closed feedwater heaters: forward connection, backward connection. For the forward connection a pump is needed to crease pressure. For the backward connection, a throttlg valve is needed to decrease pressure. Steam (hot) Steam (hot) Feedwater (cold) Feedwater (cold) Forward Pump Backward Throttlg Valve Chapter 2 20