Problem 4.4 - Solar Pond Hybrid Hy brid Steam Power Plant We wish to evaluate the proposed SolarSolar-Pond Pond Steam Power Plant shown in the following diagram. A solar pond is a large body of water having a varying salinity gradient (halocline) which traps the sun's energy such that the storage layer at the bottom of of the pond can reach temperatures temperatures of greater greater than 100°. 100°. !he !he diagram following shows the initial design of a low pressure solar"pond steam power plant# using the storage layer as the boiler heat source# and the upper layer as the heat sin$. %otice the wood"fired superheater in which the steam at the outlet of the boiler is heated heated from 100° to &0°.
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1) %eatly s$etch the complete cycle on the pressure"enthalpy P-h diagram P-h diagram below# below# indicating indicating clearly all all stations stations on the the diagram. diagram. &) sing steam tables# and assuming that the turbine is adiabatic# determine the power output of the turbine *+,$W *+,$W-. -. ) Assuming that the feedwater pump is adiabatic# and that the compressed li/uid eperiences no change in temperature while passing through the pump# determine determine the the power re/uired re/uired to drive the pump 0.&$W 0.&$W-. -. ) sing steam tables# determine the heat transferred to the boiler ,&10$W ,&10$W-as well as the heat transferred to the superheater ++$W ++$W-. -.
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) 2etermine the overall thermal efficiency 3 th of this power plant 14 14-. -. (!hermal efficiency is defined as the net wor$ done by the system (turbine and feedwater pump) divided by the total heat supplied eternally). ,) 2iscuss the proposed system with respect to its environmental impact and feasibility. 5s this a well designed system6 What do you consider to be the ma7or advantages and disadvantages of this system6 8our discussion should include a comparison of the eternal fuel used and the turbine power# as well as the practical aspects of maintaining a system with a low pressure of 10$9a.
Justify all Justify all values used and derive all derive all e/uations used starting from the basic energy e/uation for a flow system.
Problem 4.5 - A Cogeneration Steam Power Plant
What is Cogeneration? " We li$e the definition presented by the Midwest Cogeneration Association as follows: Cogneration is the tili!ation o" # "orms o" energy "rom $ sorce i.e.% hot water&heat and electricity "rom one gen-set.
According to Cogeneration 'echnologies# the world's first commercial power plant " 'homas (dison)s Pearl Street Station built in 1;;& " was a cogeneration plant as it made and and distributed distributed both both electricity electricity and thermal energy energy## thus thus the concept has been around for many years# With the recent interest in greener energy technologies it is currently becoming more popular. !his brings us to the current problem ststement: 5n an effort to decentralise the power grid grid and utili
Justify all Justify all values used and derive all derive all e/uations used starting from the basic energy e/uation for a flow system# the basic definition of thermal efficiency 3 th# and the enthalpy change of incompressible li/uid water Bh.
Problem 4., - An pen eedwater Heater added to the Cogeneration Steam Power Plant !his problem is an etension of Problem 4.5 in which the Athenai 9ower onsulting Croup proposed a uni/ue ogeneration system for ='>leness ?ospital to provide both 00$W electric power and hot water at ,0°. =n analysis we determined that the thermal efficiency 3 th of the proposed power plant was &4#
which is etremely low. 5n an attempt to improve the plant thermal efficiency Athenai proposed a new design as shown in the following schematic diagram:
!he condenser hot water heating system is retained as in the previous design with the hot water storage tan$ immersed in the hotwell of the condenser. !he turbine outlet pressure has been reduced from the original 100 $9a to &0 $9a# and the steam condenses to a subcooled hotwell temperature of ,0°# A condensate pump increases the pressure to &00 $9a# allowing the air to separate and escape in the =pen Deedwater ?eater2e"aerator. A mass fraction y of saturated vapor steam at &00 $9a is tapped from the turbine and mied with the condensate as shown# and the resulting saturated li/uid miture is then pumped to E9a by the feedwater pump before before being supplied supplied to the boiler. boiler. As a young young engineer engineer at Athenai Athenai your purpose is to evaluate evaluate this new design design and compare compare its performance to the previously proposed system. •
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1) %eatly 9lot the complete cycle on the P-h *pressre-enthalpy+ diagram provided# provided# indicating indicating clearly clearly stations stations (1)# (&)# ()# ()# ()# ()# (,)# (,)# and (+) on on the 'ables bles to determine the diagram. =nce this is done then use the Steam 'a following: &) 2etermine the mass fraction y of the bled steam at station (+) in order to provide a saturated saturated li/uid condition condition at station station (). y F 0.100.10 -
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) 2etermine the mass flow rate of the steam through the cycle re/uired in order to provide the re/uired turbine output power of 00$W. 0. $gs) 2etermine the overall thermal efficiency 3 th of this power plant. (@ecall that thermal efficiency is defined as the net wor$ done divided by the total heat supplied eternally to the boiler. 8ou may ignore the feedwater and condensate pump power in this evaluation. &4) ompare the performance of the above system with that of the previously proposed system (Problem 4.5)# and discuss its advantages and disadvantages.
Justify all values used and derive all e/uations used starting from the basic energy e/uation for a flow system# and the basic definition of thermal efficiency 3 th.
Problem 4./ - A 0eothermal Hybrid Steam Power Plant A small community of about 00 households have discovered an underground geothermal brine source that can be used to boil water at 100° and would li$e to use this to generate power. !he following diagram shows the initial design of a low pressure geothermal plant in which the water is boiled by the geothermal source to 100° and subse/uently superheated to &00° by a wood"fired superheater. %otice that the high pressure of the system is at 100$9a allowing a convenient de"aerator to be placed at the pump outlet.
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1) %eatly s$etch the complete cycle on the pressure"enthalpy P-h diagram below# indicating clearly all stations on the diagram. &) sing steam tables# and assuming that the turbine is adiabatic# determine the power output of the turbine +&*$W-. ) Assuming that the feedwater pump is adiabatic# and that the compressed li/uid eperiences no change in temperature while passing through the pump# determine the power re/uired to drive the pump 0.&$W-. ) sing steam tables# determine the heat transferred to the boiler ,&+1$Was well as the heat transferred to the superheater 00$W-. ) 2etermine the overall thermal efficiency 3 th of this power plant 114-. (!hermal efficiency is defined as the net wor$ done by the system (turbine and feedwater pump) divided by the total heat supplied eternally). ,) 2iscuss the proposed system with respect to its environmental impact and feasibility. 5s this a well designed system6 What do you consider to be the ma7or advantages and disadvantages of this system6 8our discussion should include a comparison of the eternal fuel used and the turbine power.
Justify all values used and derive all e/uations used starting from the basic energy e/uation for a flow system.
Problem 4.1 - A Home Heat Pmp "or Space Heating We wish to do a preliminary thermodynamic evaluation of a 1$W input power home heat pump system for space heating using refrigerant @1a. onsider the following system flow diagram
!hus the heat pump system absorbs heat from the evaporator placed outside in order to pump heat into the air flowing through the insulated duct over the condenser section. !he fan provides an air flow of ; m minute# which is enough to cool the refrigerant in the condenser to 0°# 5n this analysis we will neglect the power provided to the fan. We also assume that the duct is adiabatic# and that all the heat re7ected by the condenser is absorbed by the air flowing in the duct. 9lot the four processes on the P-h diagram provided below and use the @1a refrigerant property tables in order to determine the following: •
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2etermine the mass flow rate of the refrigerant @1a 0.01;$gs2etermine the mass flow rate of the air flowing in the insulated duct 0.1,1$gs-. 2etermine the heat re7ected by the condenser ".+$W-. Assuming that all this heat is absorbed by the air# determine the eit temperature of the air at station (,) +.*°-. 5s this value reasonable6 Why6 ( Note: This problem involves heat being transferred from the refrigerant in the condenser to the air flowing through the condenser, and is solved as shown below )
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2etermine the heat absorbed by the evaporator &.+$W-. 2etermine the oefficient of 9erformance of the heat pump (=9 ?9) (defined as the heat re7ected by the condenser divided by the wor$ done on the compressor) .+-.
Problem 4.2 - A Home Air Conditioner 3 Hot Water Heater We wish to do a preliminary thermodynamic evaluation of a 00W input power home heat pump system as applied to summertime use for both hot water heating to 0°# and space cooling (air conditioning)# and thus maintain the inside home temperature at a comfortable &0°..
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!his uni/ue combined air conditioning hot water heating system is designed to absorb heat from the air flowing through the insulated duct in order to pump heat into the hot water heating tan$. !he fan provides enough air flow over the evaporator to cool the air by 10° as it passes through the duct# and the hot water is heated to a maimum of 0°. 5n this analysis we neglect the power provided to the fan. We also assume that both the duct and the hot water tan$ are eternally adiabatic. arefully draw the complete cycle above on the pressure"enthalpy P-h- diagram provided below# showing clearly all five processes (1) " (&) " () "() " () "(1). sing the conditions shown on the diagram above and values obtained from the @1a tables: •
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2etermine the enthalpy values at all five stations $G$g-# and indicate these values on the P-h diagram. 2etermine the mass flow rate of the refrigerant @1a 0.01 $gs2etermine the heat re7ected by the condenser "&.0* $W-. Assuming that all this heat is absorbed by the water in the hot water tan$# determine the time ta$en for 10 liters of water at 0° to reach the re/uired temperature of 0° 1 hr 0 min-. ( Note: The hot water heater is not a flow system, thus we need to first evaluate the energy required to heat the water [!"#$ %J&' This section is solved as shown below )
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2etermine the heat power absorbed by the refrigerant in the evaporator &.0 $W-. Assuming that all this heat is absorbed from the air in the duct and neglecting the fan power# determine the re/uired mass flow rate of the in order reduce the air temperature by 10° while passing through the duct 0.&0 $gs-. 2etermine the oefficient of 9erformance of the hot water heater (=9 ?W) (defined as the heat re7ected by the condenser divided by the wor$ done on the compressor) =9?W F .1+-. 2etermine the oefficient of 9erformance of the air conditioner (=9 A) (defined as the heat absorbed by the evaporator divided by the wor$ done on the compressor) =9A F .0+-. 5f we bypass the outside subcooler (Htate () becomes saturated li/uid as in Htate ()) determine the change in oefficient of 9erformance of the air conditioner evaluated above. 5ndicate this change on the P-h diagram and discuss the relevance of the outside subcooling section in this system. =9A reduced to .1+-
Problem 4.$ " A %ovel WaterHteam Air onditioner We wish to do an initial evaluation of an air"conditioner proposed for an etremely warm and humid environment# in which an evaporative (swamp) cooler would be ineffective because of the high humidity. A novel suggestion is to use an etremely low"pressure watersteam vapor"compression air conditioning system# as s$etched in the figure below. %otice the de"aerator pump and accumulator# in which the saturated li/uid water at station () (10 $9a) is pumped to a pressure of 100 $9a at station () before entering the throttle.
arefully draw the complete air conditioning cycle above on the P-h diagram provided# showing clearly all five processes (1) " (&) " () " () " () " (1). sing the conditions shown on the diagram above and values obtained from the steam tables# evaluate the oefficient of 9erformance (=9 A) of the air conditioning system. 5n this case we define the =9 A as the heat transferred to the evaporator divided by the wor$ done on the compressor plus the wor$ done on the de"aerator pump. =9A F .1-
Justify all values used and derive all e/uations used starting from the basic steady flow energy e/uation.
Problem 4.$$ - A Home 0eothermal Heat-Pmp ntrodction and 6escription With the global /uest for energy efficiency# there is renewed interest in geothermal heat pumps which have been in limited use for more than +0 years. Issentially this technology relies on the fact that a few meters below the surface of the earth the temperature remains relatively constant throughout the year# warmer than the air above it during winter# and cooler during summer. According to the Hpring &00* newsletter from 6a7id White# in Houtheast =hio this temperature is around °D (1°). !his means that we can design a heat pump which can combine hot water and space heating in winter in which the earth is used as a heat source (rather than the outside air) at a considerable increase in coefficient of performance =9. Himilarly# with suitable valving# we can use the same system in summer for hot water heating and air conditioning in which the earth is used as a heat sin$# rather than the outside air. !his is achieved by using a 0rond 8oop in order to enable
heat transfer with the earth# as described in the 9opular Eechanics website: 'he 0ide to Home 0eothermal (nergy .
Problem 4.$$ - We wish to do a preliminary thermodynamic analysis of the following home geothermal heat pump system designed for wintertime hot water and space heating. %otice that with suitable valving this system can be used both in winter for space heating and in smmer for air conditioning# with hot water heating throughout the year.
%otice that the condenser section includes both the hot water and space heater and station () is specified as being in the Juality region. Assume that 0° is a reasonable maimum hot water temperature for home usage# thus at a high pressure of 1., E9a# the maimum power available for hot water heating will occur when the refrigerant at station () reaches the saturated li/uid state. ( 9ic:
9i!% 7ustify this statement). Assume also that the refrigerant at station () reaches a subcooled li/uid temperature of &0° while heating the air.
sing the conditions shown on the diagram and assuming that station () is at the saturated li/uid state •
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=n the P-h diagram provided below carefully plot the five processes of the heat pump together with the following constant temperature lines: 0° (hot water)# 1° (ground loop)# and "10° (outside air temperature) sing the @1a property tables determine the enthalpies at all five stations and verify and indicate their values on the P-h diagram. 2etermine the mass flow rate of the refrigerant @1a. 0.01&+ $gs2etermine the power absorbed by the hot water heater &.0 $W- and that absorbed by the space heater 0.+& $W-. 2etermine the time ta$en for 100 liters of water at an initial temperature of &0° to reach the re/uired hot water temperature of 0° 10 minutes-. 2etermine the oefficient of 9erformance of the hot water heater =9?W F .0- (defined as the heat absorbed by the hot water divided by the wor$ done on the compressor) 2etermine the oefficient of 9erformance of the heat pump =9?9 F .(defined as the total heat re7ected by the refrigerant in the hot water and space heaters divided by the wor$ done on the compressor) What changes would be re/uired of the system parameters if no geothermal water loop was used# and the evaporator was re/uired to absorb its heat from the outside air at "10°. 2iscuss the advantages of the geothermal heat pump system over other means of space and water heating.
Problem 4.$# - Home Air Conditioner and Hot Water System with an nternal Heat (;changer We wish to do a preliminary thermodynamic evaluation of the following proposed heat pump system designed for summertime hot water heating and space cooling.
%otice that this system uses a heat echanger to subcool the refrigerant at the outlet of the hot water heater while heating the refrigerant at the outlet of the evaporator. !his is intended to serve the dual purpose of increasing the both the hot water heating and air cooling capacity of the system .sing the conditions shown on the diagram •
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a) %eatly s$etch the complete air conditioning cycle above on the P-h diagram provided# showing clearly all si processes (1) " (&) " () " () " () " (,) " (1). b) sing the @1a property tables determine the enthalpies at all si stations and verify and indicate their values on the P-h diagram. %ote that in order to determine the enthalpy at stations () and () you will need to consider the heat transferred in the heat echanger as well as the energy e/uation applied to an adiabatic throttle. h F h F 10+. $G$gc) 2etermine the mass flow rate of the refrigerant @1a. 0.0& $gsd) 2etermine the power absorbed by the hot water heater .1 $W- and the oefficient of 9erformance of the hot water heater =9?W F .1- (defined as the heat absorbed by the hot water divided by the wor$ done on the compressor). 2etermine the time ta$en for 1&0 liters of water at 0° to reach the re/uired temperature of 0°. ; minutese) 2etermine the heat transferred from the air blowing through the insulated cooling duct to the evaporator .1 $W-# and the oefficient of 9erformance =9A F .1- of the air conditioning system.
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f) onsider the air passing through the insulated duct of the evaporator section. %otice that the temperature of the air passing through the duct is decreased by 10°. %eglecting the wor$ done by the fan determine the mass flow rate of the air through the duct &0. $gmin-. g) 2iscuss the advantages of the above heat pump system over other means of space cooling and water heating.
Problem 4.$/ - 'he
temperature remains relatively constant throughout the year# warmer than the air above it during winter# and cooler during summer. According to the Hpring &00* newsletter from 6a7id White# in Houtheast =hio this temperature is around °D (1°). !his means that we can design a heat pump which can combine hot water and space heating in winter in which the earth is used as a heat source (rather than the outside air) at a considerable increase in coefficient of performance =9. Himilarly# with suitable valving# we can use the same system in summer for hot water heating and air conditioning in which the earth is used as a heat sin$# rather than the outside air. !his is achieved by using a 0rond 8oop in order to enable heat transfer with the earth# as described in the 9opular Eechanics website: 'he 0ide to Home 0eothermal (nergy # and of course the ubi/uitous Wi:ipedia . Another relevant website is that by Eortgage alculator titled 0eothermal >esorces "or Homeowners (!han$s to Aaron Earch of Gericho# K!# for ma$ing us aware of this interesting website " %ov &1# &011.)
Problem 4.$/ - =n Driday Hept &# &010 professor Gohn Kann from
H's switch from coal powered heat to geothermal heat. !his impressive pro7ect will ta$e years to complete# and is one of the nation's largest closed geothermal energy systems. !he tal$ did not include many technical details# however he did describe the o7erall
We were intrigued by the concept and would li$e to evaluate the thermodynamic feasibility and performance of a geothermal heat pump system. !he following system diagram represents a possible system for summertime usage# in order to provide hot water at ,°# and space cooling using chilled water at around 1°. %ote that this system was devised by us for purposes of this concept feasibility chec$ only# and no data about the system was obtained from >H. We have used the >e"rigerant >$/4a# since this is the only refrigerant for which we have tables available. 5n fact we had to add new data to our tables# since with a limit of 1., E9a we could not reach the re/uired temperature of ,°. %ote that the mass flow and actual power re/uired is not specified# thus this model will represent a system suitable for any si
sing the conditions shown on the diagram do the following •
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1) =n the P-h diagram provided below carefully plot the five processes of the heat pump together with the following constant temperature lines: ,° (hot water)# 1° (ground loop). &) sing the >$/4a property tables determine the enthalpies at all five stations and verify and indicate their values on the P-h diagram. ) 2etermine the energy absorbed by the hot water flow 10 $G$g- and that etracted from the chilled water 1+. $G$g-.
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) 2etermine the energy re/uired to drive the compressor .; $G$g) 2etermine the oefficient of 9erformance of the hot water heating system (=9?W) (defined as the heat absorbed by the hot water divided by the wor$ done on the compressor) =9?W F .,) 2etermine the oefficient of 9erformance of the chilled water system (=9@ ) (defined as the heat absorbed by the chilled water divided by the wor$ done on the compressor). =9@ F .0+) 2etermine the change in performance of the system assuming that no geothermal water loop is used# and plot the changes in the processes on the P-h diagram. 2iscuss the advantages of the geothermal heat pump system for summertime usage.
Problem 4.$4 - 'he
@ecall Problem 4%$/ in which we evaluated the summertime operation of a geothermal heat pump system modeled after the system currently under construction at
%ote again that this system was devised by us for purposes of this eercise only# and no data about the system was obtained from >H. We have used the >e"rigerant >$/4a# since this is the only refrigerant for which we have tables available. 5n fact we had to add new data to our tables# since with a limit of 1., E9a we could not reach the re/uired temperature of ,°. %ote that the mass flow and actual power re/uired is not specified# thus this model will represent a system suitable for any si
sing the conditions shown on the diagram do the following •
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1) =n the P-h diagram provided below carefully plot the five processes of the heat pump together with the following constant temperature lines: ,° (hot water)# 1° (ground loop)# and "10° (outside air). &) sing the >$/4a property tables determine the enthalpies at all five stations and verify and indicate their values on the P-h diagram. ) 2etermine the specific wor$ done to drive the compressor ".; $G$g-. ) 2etermine the oefficient of 9erformance of the hot water heating system (=9?W) (defined as the heat absorbed by the hot water divided by the specific wor$ done to drive the compressor) =9?W F .) 2etermine the oefficient of 9erformance of the space heating water system (=9?9) (defined as the heat absorbed by the space heating water in subcooling the refrigerant to &0° divided by the specific wor$ done to drive the compressor).=9?9 F 1.,,) 5n the event that no geothermal ground loop is used to evaporate the refrigerant then the system would need to be redesigned# reducing inlet to the compressor (1) from ,0 $9a to 10$9a# saturated vapor# and the compressor outlet (&) to &.0 E9a# *0°. arefully plot this new cycle on the P-h diagram. +) sing the >$/4a property tables determine the specific wor$ done to drive the compressor under the new conditions presented in ,) above "+1 $G$g-. ;) sing the new conditions presented in ,) above determine the oefficients of 9erformance of both the hot water and space heating systems and discuss the advantages of using a geothermal ground loop for wintertime operation.=9?W F &.# =9?9 F 0.*,-
Chapter 4% 'he irst 8aw o" 'hermodynamics "or Control olmes c+ >e"rigerators and Heat Pmps ntrodction and 6iscssion 5n the early days of refrigeration the two refrigerants in common use were ammonia and carbon dioide. >oth were problematic " ammonia is toic and carbon dioide re/uires etremely high presures (from around 0 to &00 atmospheresL) to operate in a refrigeration cycle# and since it operates on a transcritical cycle the compressor outlet temperature is etremely high (around 1,0°). When reon $# *dichloro-di"loro-methane ) was discovered it totally too$ over as the refrigerant of choice. 5t is an etremely stable# non toic fluid# which does not interact with the compressor lubricant# and operates at pressures always somewhat higher than atmospheric# so that if any lea$age occured# air would not lea$ into the system# thus one could recharge without having to apply vacuum.
nfortunately when the refrigerant does ultimately lea$ and ma$e its way up to the o$/4a *tetra"loro-ethane+ " not as stable as Dreon 1 however it does not have o@44.com). !he previous two ma7or problems of high pressure and high compressor temperature are found in fact to be advantageous. !he very high cycle pressure results in a high fluid density throughout the cycle# allowing minituri
A $/4a apor-Compression >e"rigeration System nli$e the situation with steam power plants it is common practice to begin the design and analysis of refrigeration and heat pump systems by first plotting the cycle on the P-h diagram. !he following schematic shows a basic refrigeration or heat pump system with typical property values. Hince no mass flow rate of the refrigerant has been provided# the entire analysis is done in terms of specific energy values. %otice that the same system can be used either for a refrigerator or air conditioner# in which the heat absorbed in the evaporator (/ evap) is the desired output# or for a heat pump# in which the heat re7ected in the condenser (/ cond) is the desired output.
5n this eample we wish to evaluate the following: •
?eat absorbed by the evaporator (/ evap) $G$g-
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?eat re7ected by the condenser (/ cond) $G$g-
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Wor$ done to drive the compressor (w comp) $G$g-
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oefficient of 9erformance (=9) of the system# either as a refrigerator or as a heat pump.
As with the Hteam 9ower 9lant# we find that we can solve each component of this system separately and independently of all the other components# always using the same approach and the same basic e/uations. We first use the information given in the above schematic to plot the four processes (1)"(&)"()"()"(1) on the P-h diagram. %otice that the fluid entering and eiting the condenser (Htate (&) to Htate ()) is at the high pressure 1 E9a. !he fluid enters the evaporator at Htate () as a saturated miture at "&0° and eits the evaporator at Htate (1) as a saturated vapor. Htate (&) is given by the intersection of 1 E9a and +0° in the superheated region. Htate () is seen to be in the subcooled li/uid region at 0°# since the saturation temperature at 1 E9a is about 0°. !he process ()"() is a vertical line (h F h) as is discussed below. 5n the following section we develop the methods of evaluating the solution of this eample using the >$/4a re"rigerant tables. %otice that the refrigerant tables do not include the subcooled region# however since the constant temperature line in this region is essentially vertical# we use the saturated li/uid value of enthalpy at that temperature.
%otice from the P-h diagram plot how we can get an instant visual appreciation of the system performance# in particular the oefficient of 9erformance of the system by comparing the enthalpy difference of the compressor (1)"(&) to that of the evaporator ()"(1) in the case of a refrigerator# or to that of the condenser (&)"() in the case of a heat pump. We now consider each component as a separate control volume and apply the energy e/uation# starting with the compressor. %otice that we have assumed that the $inetic and potential energy change of the fluid is negligeable# and that the compressor is adiabatic. !he re/uired values of enthalpy for the inlet and outlet ports are determined from the >$/4a re"rigerant tables.
!he high pressure superheated refrigerant at port (&) is now directed to a condenser in which heat is etracted from the refrigerant# allowing it to reach the subcooled li/uid region at port (). !his is shown on the following diagram of the condenser:
!he throttle is simply an epansion valve which is adiabatic and does no wor$# however enables a significant reduction in temperature of the refrigerant as shown in the following diagram:
!he final component is the evaporator# which etracts heat from the surroundings at the low temperature allowing the refrigerant li/uid and vapor miture to reach the saturated vapor state at station (1).
5n determining the oefficient of 9erformance " for a refrigerator or air"conditioner the desired output is the evaporator heat absorbed# and for a heat pump the desired output is the heat re7ected by the condenser which is used to heat the home. !he re/uired input in both cases is the wor$ done on the compressor (ie the electricity bill). !hus =9@ F /evap wcomp F 1 ,. F &.& =9?9 F /cond wcomp F &10 ,. F .& %otice that for the same system we always find that =9 ?9 F =9@ M 1. %otice also that the =9 values are usually greater than 1# which is the reason why they are never referred to as NIfficiencyN values# which always have a maimum of 1004. !hus the P-h diagram is a widely used and very useful tool for doing an approimate evaluation of a refrigerator or heat pump system. 5n fact# in the official @eference ?andboo$ supplied by the C((S to be used in the Dundamentals of Ingineering eam# only the P-h diagram is presented for @1a. 8ou are epected to answer all the /uestions on this sub7ect based on plotting the cycle on this diagram as shown above.
Chapter 4% 'he irst 8aw o" 'hermodynamics "or Control olmes b+ Steam Power Plants A basic steam power plant consists of four interconnected components# typically as shown in the figure below. !hese include a steam turbine to produce mechanical shaft power# a condenser which uses eternal cooling water to condense the steam to li/uid water# a feedwater pump to pump the li/uid to a high pressure# and a boiler which is eternally heated to boil the water to superheated steam. nless
otherwise specified we assume that the turbine and the pump (as well as all the interconnecting tubing) are adiabatic# and that the condenser echanges all of its heat with the cooling water.
A Simple Steam Power Plant (;ample - 5n this eample we wish to determine the performance of this basic steam power plant under the conditions shown in the diagram# including the power of the turbine and feedwater pump# heat transfer rates of the boiler and condenser# and thermal efficiency of the system.
5n this eample we wish to evaluate the following: •
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!urbine output power and the power re/uired to drive the feedwater pump ?eat power supplied to the boiler and that re7ected in the condenser to the cooling water !he thermal efficiency of the power plant (3 th)# defined as the net wor$ done by the system divided by the heat supplied to the boiler. !he minimum mass flow rate of the cooling water in the condenser re/uired for a specific temperature rise
2o not be intimidated by the compleity of this system. We will find that we can solve each component of this system separately and independently of all the other components# always using the same approach and the same basic e/uations. We first use the information given in the above schematic to plot the four processes (1)"(&)"()"()"(1) on the P-h diagram. %otice that the fluid entering and eiting the boiler is at the high pressure 10 E9a# and similarly that entering and eiting the condenser is at the low pressure &0 $9a. Htate (1) is given by the intersection of 10
E9a and 00°# and state (&) is given as &0 $9a at *04 /uality# Htate () is given by the intersection of &0 $9a and 0°# and the feedwater pumping process ()"() follows the constant temperature line# since ! F ! F 0°# .
%otice from the P-h diagram plot how we can get an instant visual appreciation of the system performance# in particular the thermal efficiency of the system by comparing the enthalpy difference of the turbine (1)"(&) to that of the boiler ()"(1). We also notice that the power re/uired by the feedwater pump ()"() is negligible compared to any other component in the system. ( Note: We find it strange that the only thermodynamics tet that we $now of that even considered the use of the P-h diagram for steam power plants is (ngineering 'hermodynamics - Bones and 6gan (1**). 5t is widely used for refrigeration systems# however not for steam power plants.) We now consider each component as a separate control volume and apply the energy e/uation# starting with the steam turbine. !he steam turbine uses the high" pressure " high"temperature steam at the inlet port (1) to produce shaft power by epanding the steam through the turbine blades# and the resulting low"pressure " low"temperature steam is re7ected to the condenser at port (&). %otice that we have
assumed that the $inetic and potential energy change of the fluid is negligible# and that the turbine is adiabatic. 5n fact any heat loss to the surroundings or $inetic energy increase would be at the epense of output power# thus practical systems are designed to minimise these loss effects. !he re/uired values of enthalpy for the inlet and outlet ports are determined from the steam tables.
!hus we see that under the conditions shown the steam turbine will produce ;EW of power. !he very low"pressure steam at port (&) is now directed to a condenser in which heat is etracted by cooling water from a nearby river (or a cooling tower) and the steam is condensed into the subcooled li/uid region. !he analysis of the condenser may re/ure determining the mass flow rate of the cooling water needed to limit the temperature rise to a certain amount " in this eample to 10°. !his is shown on the following diagram of the condenser:
%otice that our steam tables do not include the subcooled (or compressed) li/uid region that we find at the outlet of the condenser at port (). 5n this region we notice from the P-h diagram that over an etremely high pressure range the
enthalpy of the li/uid is e/ual to the saturated li/uid enthalpy at the same temperature# thus to a close approimation h F hfO0° # independent of the pressure. !hus we see that under the conditions shown# 1+., EW of heat is etracted from the steam in the condenser. 5 have often been /ueried by students as to why we have to re7ect such a large amount of heat in the condenser causing such a large decrease in thermal efficiency of the power plant. Without going into the philosophical aspects of the Hecond Paw (which we cover later in Chapter 5# my best reply was provided to me by @andy Hheidler# a senior engineer at the 0a7in Power Plant. ?e stated that the orth 8aw o" 'hermodynamics states: Do can)t pmp steamE# so until we condense all the steam into li/uid water by etracting 1+., EW of heat# we cannot pump it to the high pressure to complete the cycle. (@andy could not give me a reference to the source of this ama
Drom the steam tables we find that the specific heat capacity for li/uid water ?&= F .1; $G$g°. sing this analysis we found on the condenser diagram above that the re/uired mass flow rate of the cooling water is &1 $gs. 5f this flow rate cannot be supported by a nearby river then a cooling tower must be included in the power plant design. We now consider the feedwater pump as follows:
!hus as we suspected from the above P-h diagram plot# the pump power re/uired is etremely low compared to any other component in the system# being only 14 that of the turbine output power produced. !he final component that we consider is the boiler# as follows:
!hus we see that under the conditions shown the heat power re/uired by the boiler is &.+ EW. !his is normally supplied by combustion (or nuclear power). We now have all the information needed to determine the thermal efficiency of the steam power plant as follows:
%ote that the feedwater pump wor$ can normally be neglected.
Sol7ed Problem 4.$ - Spercritical Steam Power Plant with >eheat "or AthensG hio
5n an effort to decentralioilerN with a NHteam CeneratorN# since at supercritical pressures the concept of boiling water is undefined. Durthermore we have specifically split the turbine into a ?igh 9ressure (?9) turbine and a Pow 9ressure (P9) turbine since we will find that having a single turbine to epand from &E9a to 10$9a is totally impractical. !hus for eample the Cavin 9ower 9lant has a turbine set consisting of , turbines " a ?igh 9ressure !urbine# an 5ntermediate 9ressure (@eheat) turbine# and large 8ow Pressre trbines operating in parallel.
%ote that prior to doing any analysis we always first s$etch the complete cycle on a P-h diagram based on the pressure# temperature# and /uality data presented. !his leads to the following diagram:
=n eamining the P-h diagram plot we notice that the system suffers from two ma7or flaws: •
•
!he outlet pressure of the P9 turbine at port () is 10 $9a# which is well below atmospheric pressure. !he etremely low pressure in the condenser will allow air to lea$ into the system and ultimately lead to a deteriorated performance. !he /uality of the steam at port () is ;04. !his is unacceptable. !he condensed water will cause erosion of the turbine blades# and we should always try to maintain a /uality of above *04. =ne eample of the effects of this erosion can be seen on the blade tips of the final stage of the 0a7in 8P trbine. 2uring &000# all four P9 turbines needed to be replaced because of the reduced performance resulting from this erosion. (@efer: 'or o" the 0a7in Power Plant - eb. # )
!he following revised system diagram corrects both flaws. !he steam at the outlet of the ?9 turbine (port (&)) is reheated to 0 before entering the P9 turbine at port (). Also the low pressure li/uid condensate at port () is pumped to a pressure of ;00 $9a and passed through a de"aerator prior to being pumped by the feedwater pump to the high pressure of & E9a.
!his system is referred to as a >eheat cycle# and based on the data above is plotted on the P-h diagram as follows:
!hus we see that in spite of the compleity of the system# the P-h diagram plot enables an intuitive and /ualitative initial understanding of the system. sing the
methods described in Chapter 4b for analysis of each component# as well as the steam tables# determine the following: •
•
•
1) Assuming that both turbines are adiabatic and neglecting $inetic energy effects determine the combined output power of both turbines 10., EW-.
&) Assuming that both the condensate pump and the feedwater pump are adiabatic# determine the power re/uired to drive the two pumps "&0 $W-.
) 2etermine the total heat transfer to the steam generator# including the reheat system &,.1 EW-.
•
•
•
) 2etermine the overall thermal efficiency of this power plant. (!hermal efficiency ( th) is defined as the net wor$ done (turbines# pumps) divided by the total heat supplied eternally to the steam generator and reheat system) 0 4-.
) 2etermine the heat re7ected to the cooling water in the condenser "1.+ EW-. ,) Assume that all the heat re7ected in the condenser is absorbed by cooling water from the ?oc$ing @iver. !o prevent thermal pollution the cooling water is not allowed to eperience a temperature rise above 10°. 5f the steam leaves the condenser as saturated li/uid at 0°# determine the re/uired minimum volumetric flow rate of the cooling water &&., cubic metersminute-.
•
+) 2iscuss whether you thin$ that the proposed system can be cooled by the ?oc$ing river. 8ou will need to do some research to determine the minimal seasonal flow in the river in order to validate your decision. ( (int- 0oogle: ?oc$ing @iver Dlow)
Sol7ed Problem 4.# *Alternate+ - An pen eedwater Heater added to the Spercritical Steam Power Plant "or AthensG hio !han$s to ris 6ambrin: from mtech.nl (currently inactive)# for ma$ing me aware of this alternative approach to adapting an =pen Deedwater ?eater to a steam power plant ( Deb &010) !his Holved 9roblem is an alternative etension of Sol7ed Problem 4.$ in which we etend the deaerator by tapping steam from the outlet of the ?igh 9ressure turbine and reduce the pressure to ;00 $9a by means of a 'hrottling Control al7e before feeding it into the deaerator. !his allows one to conveniently convert the deaerator into an pen eedwater Heater without re/uiring a bleed tap from the Pow 9ressure turbine at eactly the dearator pressure# as shown in the following diagram:
%ote that prior to doing any analysis we always first s$etch the complete cycle on a P-h diagram based on the pressure# temperature# and /uality data presented on the system diagram. !his leads to the following diagram:
=n eamining the P-h diagram plot we notice the following:
•
•
A mass fraction of the steam y is tapped from the outlet of the ?9 turbine (&) and passed through the throttle such that its pressure is reduced to that of the deaerator (*). 5t is then mied with a mass fraction (1"y) of the li/uid water at station (,). !he mass fraction y is chosen to enable the fluid to reach a saturated li/uid state at station (+). !he feedwater pump then pumps the li/uid to station (;)# thus saving a significant amount of heat from the steam generator in heating the fluid from station (;) to the turbine inlet at station (1). 5t is true that with a mass fraction of (1"y) there is less power output due to a reduced mass flow rate in the P9 turbine# however the net result is normally an increase in thermal efficiency.
!hus once more we see that in spite of the compleity of the system# the P-h diagram plot enables an intuitive and /ualitative initial understanding of the system. sing the methods described in Chapter 4b for analysis of each component# as well as the steam tables for evaluating the enthalpy at the various stations (shown in red)# and neglecting $inetic and potential energy effects# determine the following: •
1) Assuming that the open feedwater heater is adiabatic# determine the mass fraction of steam y re/uired to be bled off the outlet of the ?9 turbine which will bring the fluid from station (,) to a saturated li/uid state in the deaerator. y F 0.&0We first need to evaluate the enthalpy of the fluid at station (*) after passing through the throttling control valve:
!hus we find that for an ideal throttle the enthalpy h* F h& independent of the pressure drop# allowing us to conveniently draw the throttling process as a vertical line on the P-h diagram. We now determine the mass fraction y by considering the miing process in the open feedwater heater as follows:
%otice that we can estimate this value of y directly from the P-h diagram by simply measuring the enthalpy differences (h+ " h,) and (h* " h,) with a ruler. •
•
&) Assuming that both the condensate pump and the feedwater pump are adiabatic# determine the power re/uired to drive the two pumps & $W-. =n eamining the system diagram above we noticed something very strange about the feedwater pump. ntil now we considered li/uid water to be incompressible# thus pumping it to a higher pressure did not result in an increase of its temperature. ?owever on a recent visit to the Cavin 9ower 9lant we discovered that at &E9a pressure and more than 100° water is no longer incompressible# and compression will always result in a temperature increase. We cannot use the simple incompressible li/uid formula to determine pump wor$# however need to evaluate the difference in enthalpy from the Compressed 8iFid Water tables# leading to the following results:
) Assuming that both turbines are adiabatic# determine the new (reduced) combined power output of both turbines. @ecall from Sol7ed Problem 4.$
that the power output of the turbines was found to be 10., EW if no steam is bled from the P9 turbine ;.*; EW-
!hus as epected we find that the net power output is slightly less than the previous system without the turbine tap. ?owever power control is normally done by changing the feedwater pump speed# and we normally find a li/uid water storage tan$ associated with the de"aerator in order to accomodate the changes in the water mass flow rate. 5n our case we simply need to increase the water mass flow rate from + $gs to ;.& $gs in order to regain our original power output. •
•
) 2etermine the total heat transfer to the steam generator# including the reheat system &1. EW-.
) 2etermine the overall thermal efficiency of this power plant. (!hermal efficiency (3 th) is defined as the net wor$ done (turbines# pumps) divided by the total heat supplied eternally to the steam generator and reheat system) 1 4-.
•
•
,) 2etermine the heat re7ected to the cooling water in the condenser "1&., EW-. +) Assume that all the heat re7ected in the condenser is absorbed by cooling water from the ?oc$ing @iver. !o prevent thermal pollution the cooling water is not allowed to eperience a temperature rise above 10°. 5f the steam leaves the condenser as saturated li/uid at 0°# determine the re/uired minimum volumetric flow rate of the cooling water 1;.1 cubic metersminute-.
%ote that it is always a good idea to validate ones calculations by evaluating the thermal efficiency using only the heat supplied to the steam generator and that re7ected by the condenser.
6iscssion% !hus we find that the open feedwater heater did in fact raise the efficiency from 04 to 14. !his may not seem li$e a significant amount# however all the basic components were already in place# since without a de"aerator the steam power plant will deteriorate and become non"functional within a very short time due to lea$age of air into the system. Durthermore# if the reduction in power output is not acceptable# then it can be easily remedied by increasing the mass flow rate in the system design. %ote that this is a contrived eample in order to demonstrate that no matter how comple the system is# we can easily plot the entire system on a P-h diagram and obtain an immediate intuitive understanding and evaluation of the system performance. 5t is helpful to chec$ each value of
enthalpy read or evaluated from the steam tables and compare them to the values on the enthalpy ais of the P-h diagram.
Sol7ed Problem 4.# - An pen eedwater Heater added to the Spercritical Steam Power Plant "or AthensG hio !his Holved 9roblem is an etension of Sol7ed Problem 4.$ in which we etend the deaerator by tapping steam from the Pow 9ressure turbine at ;00 $9a and feeding it into the deaerator at the same pressure# thus converting it into an pen eedwater Heater# as shown in the following diagram:
!his system is referred to as a >egenerati7e >eheat cycle# and we will find that this simple etension of our previous sytem will result in an increase in thermal efficiency of the power plant. %ote that prior to doing any analysis we always first s$etch the complete cycle on a P-h diagram based on the pressure# temperature# and /uality data presented on the system diagram. !his leads to the following diagram:
=n eamining the P-h diagram plot we notice the following: •
•
A mass fraction of the steam y is tapped from the P9 turbine at the turbine tap (t) such that miing it with (1"y) of the li/uid water at station (,) will result in the fluid reaching a saturated li/uid state at staion (+). !he feedwater pump then pumps the li/uid to station (;)# thus saving a significant amount of heat from the steam generator in heating the fluid from station (;) to the turbine inlet at station (1). 5t is true that with a mass fraction of (1"y) there is less power output due to a reduced mass flow rate in part of the P9 turbine from the tap (t) to station ()# however the following analysis shows that the net result is an increase in thermal efficiency.
!hus once more we see that in spite of the compleity of the system# the P-h diagram plot enables an intuitive and /ualitative initial understanding of the system. sing the methods described in Chapter 4b for analysis of each component# as well as the steam tables for evaluating the enthalpy at the various stations (shown in red)# and neglecting $inetic and potential energy effects# determine the following:
•
•
1) Assuming that the open feedwater heater is adiabatic# determine the mass fraction of steam y re/uired to be bled off the P9 turbine which will bring the fluid from station (,) to a saturated li/uid state in the de"aerator. y F 0.1;-
&) Assuming that both the condensate pump and the feedwater pump are adiabatic# determine the power re/uired to drive the two pumps &, $W-. =n eamining the system diagram above we noticed something very strange about the feedwater pump. ntil now we considered li/uid water to be incompressible# thus pumping it to a higher pressure did not result in an increase of its temperature. ?owever on a recent visit to the Cavin 9ower 9lant we discovered that at &E9a pressure and more than 100° water is no longer incompressible# and compression will always result in a temperature increase. We cannot use the simple incompressible li/uid formula to determine pump wor$# however need to evaluate the difference in enthalpy from the Compressed 8iFid Water tables# leading to the following results:
•
) Assuming that both turbines are adiabatic# determine the new (reduced) combined power output of both turbines. @ecall from Sol7ed Problem 4.$ that the power output of the turbines was found to be 10., EW if no steam is bled from the P9 turbine *., EW-
!hus as epected we find that the net power output is slightly less than the previous system without the turbine tap. ?owever power control is normally done by changing the feedwater pump speed# and we normally find a li/uid water storage tan$ associated with the de"aerator in order to accomodate the changes in the water mass flow rate. 5n our case we simply need to increase the water mass flow rate from + $gs to ; $gs in order to regain our original power output. •
) 2etermine the total heat transfer to the steam generator# including the reheat system &&.& EW-.
•
•
•
) 2etermine the overall thermal efficiency of this power plant. (!hermal efficiency (3 th) is defined as the net wor$ done (turbines# pumps) divided by the total heat supplied eternally to the steam generator and reheat system) & 4-.
,) 2etermine the heat re7ected to the cooling water in the condenser "1&.* EW-. +) Assume that all the heat re7ected in the condenser is absorbed by cooling water from the ?oc$ing @iver. !o prevent thermal pollution the cooling water is not allowed to eperience a temperature rise above 10°. 5f the steam leaves the condenser as saturated li/uid at 0°# determine the re/uired minimum volumetric flow rate of the cooling water 1;. cubic metersminute-.
%ote that it is always a good idea to validate ones calculations by evaluating the thermal efficiency using only the heat supplied to the steam generator and that re7ected by the condenser.
6iscssion% !hus we find that the open feedwater heater did in fact raise the efficiency from 04 to &4. !his may not seem li$e a significant amount# however all the basic components were already in place# since without a de"aerator the steam power plant will deteriorate and become non"functional within a very short time due to lea$age of air into the system. Durthermore# if the reduction in