Lecture No.1. Vapour Power Cycles

Transcription

1 Lecture No INTRODUCTION Thermodynamic cycles can be primarily classified based on their utility such as for power generation, refrigeration etc. Based on this thermodynamic cycles can be categorized as; (i) Power cycles, (ii) Refrigeration and heat pump cycles. (i) Power cycles: Thermodynamic cycles which are used in devices producing power are called power cycles. Power production can be had by using working fluid either in vapour form or in gaseous form. When vapour is the working fluid then they are called vapour power cycles, whereas in case of working fluid being gas these are called gas power cycles. Thus, power cycles shall be of two types, (a) Vapour power cycle, (b) Gas power cycle. Vapour power cycles can be further classified as, 1. Carnot vapour power cycle 2. Rankine cycle 3. Reheat cycle 4. Regenerative cycle. Gas power cycles can be classified as, 1. Carnot gas power cycle 2. Otto cycle 3. Diesel cycle 4. Dual cycle 5. Stirling cycle 6. Ericsson cycle 1

2 7. Brayton cycle Here in the present text Carnot, Rankine, reheat and regenerative cycles are discussed. (ii) Refrigeration and heat pump cycles: Thermodynamic cycles used for refrigeration and heat pump are under this category. Similar to power cycles, here also these cycles can be classified as air cycles and vapour cycles based on type of working fluid used. 1.2 PERFORMANCE PARAMETERS Some of commonly used performance parameters in cycle analysis are described here. Thermal efficiency: Thermal efficiency is the parameter which gauges the extent to which the energy input to the device is converted to net work output from it. Back work ratio: Back work ratio is defined as the ratio of pump work input ( ve work) to the work produced (+ve work) by turbine. Generally, back work ratio is less than one and as a designer one may be interested in developing a cycle which has smallest possible back-work ratio. Small back-work ratio indicates smaller pump work ( ve work) and larger turbine work (+ve work). Work ratio: It refers to the ratio of net work to the positive work. Specific steam consumption: It indicates the steam requirement per unit power output. It is generally given in kg/kw. h and has numerical value lying from 3 to 5 kg/kw. h 2

3 1.3 CARNOT VAPOUR POWER CYCLE Carnot cycle has already been defined earlier as an ideal cycle having highest thermodynamic efficiency. Let us use Carnot cycle for getting positive work with steam as working fluid. Arrangement proposed for using Carnot vapour power cycle is as follows. 1 2 = Reversible isothermal heat addition in the boiler 2 3 = Reversible adiabatic expansion in steam turbine 3 4 = Reversible isothermal heat rejection in the condenser 4 1 = Reversible adiabatic compression or pumping in feed water pump Fig. 1.1 Fig. 1.2 Assuming steady flow processes in the cycle and neglecting changes in kinetic and potential energies, thermodynamic analysis may be carried out. 3

4 Also, heat added and rejected may be given as function of temperature and entropy as follows: Let us critically evaluate the processes in Carnot cycle and see why it is not practically possible. 1 2: Reversible Isothermal Heat Addition Isothermal heat addition can be easily realised in boiler within wet region as isothermal and isobaric lines coincide in wet region. But the superheating of steam can t be undertaken in case of Carnot cycle as beyond saturated steam point isothermal heat addition can t be had inside boiler. This fact may also be understood from T S diagram as beyond 2 the constant pressure line and constant temperature 4

5 lines start diverging. It may be noted that boiler is a device which generates steam at constant pressure. 2 3: Reversible Adiabatic Expansion Saturated steam generated in boiler at state 2 is sent for adiabatic expansion in steam turbine upto state 3. During this expansion process positive work is produced by steam turbine and a portion of this work available is used for driving the pump. 3 4: Reversible Isothermal Heat Rejection Heat release process is carried out from state 3 to 4 in the condenser. Condenser is a device in which constant pressure heat rejection can be realized. Since expanded steam from steam turbine is available in wet region at state 3. Therefore, constant temperature heat rejection can be had as constant temperature and constant pressure lines coincide in wet region. Heat rejection process is to be limited at state 4 which should be vertically below state 1. Practically it is very difficult to have such kind of control. 4 1: Reversible Adiabatic Compression (Pumping) Carnot cycle has reversible adiabatic compression process occurring between 4 and 1, which could be considered for pumping of water into boiler. In fact it is very difficult for a pump to handle wet mixture which undergoes simultaneous change in its phase as its pressure increases. Above discussion indicates that Carnot vapour power cycle is merely theoretical cycle and cannot be used for a practical working arrangement. Also the maximum efficiency of Carnot cycle is limited by maximum and minimum temperatures in the cycle. Highest temperature attainable depends upon metallurgical limits of boiler material. EXAMPLE 1.1. A Carnot cycle works on steam between the pressure limits of 7 MPa and 7 kpa. Determine thermal efficiency, turbine work and compression work per kg of steam. 5

6 Solution: T-s representation for the Carnot cycle operating between pressure of 7 MPa and 7 kpa is shown in Fig. 1.3 Fig

7 Thermal efficiency = 44.21% Turbine work = kj/kg (+ve) Compression work = kj/kg ( ve) Ans. H.W. 1.1 A steady-flow Carnot cycle uses water as the working fluid. Water changes from saturated liquid to saturated vapor as heat is transferred to it from a source at 250 C. Heat rejection takes place at a pressure of 20 kpa. Show the cycle on a T-s diagram relative to the saturation lines, and determine (a) the thermal efficiency, (b) the amount of heat rejected, in kj/kg, and (c) the net work output. ANS. (a) 36.3%. (b) kJ/kg. (c) 632 kj/kg. 7

8 1.4 RANKINE CYCLE Many of the impracticalities associated with the Carnot cycle can be eliminated by superheating the steam in the boiler and condensing it completely in the condenser, as shown schematically on a T-s diagram in Fig The cycle that results is the Rankine cycle, which is the ideal cycle for vapor power plants. The ideal Rankine cycle does not involve any internal irreversibilities and consists of the following four processes: 1-2 Isentropic compression in a pump 2-3 Constant pressure heat addition in a boiler 3-4 Isentropic expansion in a turbine 4-1 Constant pressure heat rejection in a condenser FIGURE 1 4 The simple ideal Rankine cycle. Water enters the pump at state 1 as saturated liquid and is compressed isentropically to the operating pressure of the boiler. The water temperature increases somewhat during this isentropic compression process due to a slight decrease in the specific volume of water. The vertical distance between states 1 and 2 on the T-s 8

9 diagram is greatly exaggerated for clarity. Water enters the boiler as a compressed liquid at state 2 and leaves as a superheated vapor at state 3. The boiler is basically a large heat exchanger where the heat originating from combustion gases, nuclear reactors, or other sources is transferred to the water essentially at constant pressure. The boiler, together with the section where the steam is superheated (the superheater), is often called the steam generator. The superheated vapor at state 3 enters the turbine, where it expands isentropically and produces work by rotating the shaft connected to an electric generator. The pressure and the temperature of steam drop during this process to the values at state 4, where steam enters the condenser. At this state, steam is usually a saturated liquid vapor mixture with a high quality. Steam is condensed at constant pressure in the condenser, which is basically a large heat exchanger, by rejecting heat to a cooling medium such as a lake, a river, or the atmosphere. Steam leaves the condenser as saturated liquid and enters the pump, completing the cycle. In areas where water is precious, the power plants are cooled by air instead of water. This method of cooling, which is also used in car engines, is called dry cooling. Several power plants in the world, including some in the United States, use dry cooling to conserve water. Remembering that the area under the process curve on a T-s diagram represents the heat transfer for internally reversible processes, we see that the area under process curve 2-3 represents the heat transferred to the water in the boiler and the area under the process curve 4-1 represents the heat rejected in the condenser. The difference between these two (the area enclosed by the cycle curve) is the net work produced during the cycle. Energy Analysis of the Ideal Rankine Cycle All four components associated with the Rankine cycle (the pump, boiler, turbine, and condenser) are steady-flow devices, and thus all four processes that make up the Rankine cycle can be analyzed as steady-flow processes. 9

10 The kinetic and potential energy changes of the steam are usually small relative to the work and heat transfer terms and are therefore usually neglected. Then the steady-flow energy equation per unit mass of steam reduces to The boiler and the condenser do not involve any work, and the pump and the turbine are assumed to be isentropic. Then the conservation of energy relation for each device can be expressed as follows: The thermal efficiency of the Rankine cycle is determined from Where 11

11 EXAMPLE 1.2 Consider a steam power plant operating on the simple ideal Rankine cycle. Steam enters the turbine at 3 MPa and 350 C and is condensed in the condenser at a pressure of 75 kpa. Determine the thermal efficiency of this cycle. 11

12 EXAMPLE 1.3 Steam is the working fluid in an ideal Rankine cycle. Saturated vapor enters the turbine at 8.0 MPa and saturated liquid exits the condenser at a pressure of MPa. The net power output of the cycle is 100 MW. Determine for the cycle (a) the thermal efficiency, (b) the back work ratio, (c) the mass flow rate of the steam, in kg/h, (f ) the mass flow rate of the condenser cooling water, in kg/h, if cooling water enters the condenser at 15 o C and exits at 35 o C. SOLUTION 12

13 Analysis: To begin the analysis, we fix each of the principal states located on the accompanying schematic and T s diagrams. Starting at the inlet to the turbine, the pressure is 8.0 MPa and the steam is a saturated vapor, so from Table, h 1 = kj/kg and s 1 = kj/kg. K. State 2 is fixed by p 2 = MPa and the fact that the specific entropy is constant for the adiabatic, internally reversible expansion through the turbine. Using saturated liquid and saturated vapor data from Table, we find that the quality at state 2 is State 3 is saturated liquid at MPa, so h 3 = kj/kg. State 4 is fixed by the boiler pressure p 4 and the specific entropy s 4 = s 3. The specific enthalpy h 4 can be found by interpolation in the compressed liquid tables. However, because compressed liquid data are relatively sparse, 13

14 (a) Mass and energy rate balances for control volumes around the turbine and pump give, respectively, where m is 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 mass and energy rate balances as The thermal efficiency is then (b) The back work ratio is (c) The mass flow rate of the steam can be obtained from the expression for the net power given in part (a). Thus 14

15 Lecture No.1 (f) ( ) ( ) H.W 1.2 A steam turbine plant operates on Rankine cycle with steam entering turbine at 40 bar, 350ºC and leaving at 0.05 bar. Steam leaving turbine condenses to saturated liquid inside condenser. Feed pump pumps saturated liquid into boiler. Determine the net work per kg of steam and the cycle efficiency assuming all processes to be ideal. Also show cycle on T-s diagram. Also determine pump work per kg of steam considering linear variation of specific volume. ANS. Cycle efficiency =36.67%. H.W 1.3 A steam power plant operates on a simple ideal Rankine cycle between the pressure limits of 3 MPa and 50 kpa. The temperature of the steam at the turbine inlet is 300 C, and the mass flow rate of steam through the cycle is 35 kg/s. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the thermal efficiency of the cycle and (b) the net power output of the power plant. Ans. (a) 27.1%. (b) 25.2MW. 15

16 References: 1- Thermal Engineering by R.K.Rajput 2- Power Plant Technology by El-Wakil M.M. 3- Power Plant Engineering and Economy by Dr. Rahim K. Jassim 4- Thermodynamic Fundamentals by Eistop 5- Thermodynamics by Yunus A. Cengel ENGELا 16