5 10-2 Rankine Cycle: The Ideal Cycle for Vapor Power Cycles Operating principlesVapor power plantsThe ideal Rankine vapor power cycleEfficiencyImproved efficiency - superheat
6 The conventional vapor power plant QINQOUTWTURBINEWPUMP
7 The conventional vapor power plant QINQOUTWTURBINEWPUMPHigh temperature heat addition.Low temperature heat rejectionWork input to compress working fluidTurbine to obtain work by expansion of working fluid.
14 Ideal Turbine Work s h (4) Isentropic process, s = constant s1 = s2 p1 All accessible states lieto the right of the process (1 2).(4)
15 Ideal turbine work Steady state. Constant mass flow Isentropic Expansion (s = Constant)Adiabatic and reversibleNo entropy productionNo changes in KE and PEUsual assumption is to neglect KE and PE effects at inlet and outlet of turbine.
37 Example - 1: A Carnot cycle To begin our analysis of Rankine cycle operations, consider asteady Carnot cycle (a-b-c-d-a) with water as the working fluidoperating between to given temperature limits as shown. Thegiven data are that the boiler pressure is 500 psi (pa = 500 psi) andthe condenser temperature is 70o F (Tc = 70o F). Determine thework output, thermal efficiency, irreversibility, and work ratio.TsabcdT1T2p1p2bcdaT1T2
40 Example 1 - Process quantities DHBTU/lbmdWQSBTU/lbm-RQ/TBTU/lbm-Rsa-b7550.8147b-c-430430c-d-432d-a107-107Net323To get the above process quantities, the First Law for open systemshas been used assuming KE and PE effects are negligible. Theentropy production was obtained from an entropy balance for anopen system. Note that the cyclic heat equals the cyclic work asrequired by the First Law and that entropy production is zero asrequired by the Clausius Equality.
41 Example 1 - Thermal efficiency and back work ratio
43 Example 2 - A Rankine cycle without superheat A Rankine cycle with water as the working fluid operates betweenthe same limits as in Example l, pa = 500 psi and a condensingtemperature of 70o F. Assuming all processes to be internallyreversible, determine the work output, efficiency, entropyproduction, work ratio.TsabcdT1T2papd
47 Example 3 - Effect of irreversibility in the turbine and pump A Rankine cycle operates between the same limits as above and has pump and turbine efficiencies of 80%. Determine the workoutput, efficiency, work ratio, and entropy production. Assume the condensing and ambient temperatures to be the same.T1T2sabcdpapdc’a’T
48 Example 3 - Computed data The states at a’ and c’ are determined via the First Law for anopen system and the definition of isentropic efficiency for turbinesand pumps as appropriate.
49 Example 3 - Process quantities Isentropic processes are determined prior to actual processes whereirreversibility is involved.Work output = 342 BTU/lbm Thermal efficiency = 29.4%Work ratio = Entropy production =BTU/lbm-R
52 Example 4 - SuperheatAn internally reversible Rankine cycle is determined by specifyinga maximum temperature of 800o F, a quality at the turbinedischarge of 0.9, and a minimum condensing temperature of 70oF.Compare the thermal efficiency with that of a Carnot cycleoperating between the same temperature limits.bacdpdpaTs
57 Example 5 - Given and computed data The state at “c” has the same as the pressure specified in Example 4.This determines state “b”. State “a” is determined via the usualapproximation for an incompressible liquid under going processf-a.
58 Example 5 - Process quantities Work output = 701 BTU/lbmThermal efficiency = 701/( ) = 0.424Carnot efficiency = 1-(530/1260) = 0.579
62 The variation of cycle efficiency of a Rankine cycle with one stage of reheat as a function of the pressure at which reheat isdone. Pup is the pressure of high temperature heat addition.
63 Rankine cycle with reheat Rankine cycle with regeneration Key terms and conceptsCycle efficiencyRankine cycle with reheatRankine cycle with regenerationWork ratio
64 10-6 The Ideal Regenerative Rankine cycle Another technique to raise the average temperature of the heat addition process.
65 Review - The reheat cylce The Rankine Cycle with regeneration Example OverviewReview - The reheat cylceThe Rankine Cycle with regenerationOpen and closed feedwater heatersExample
66 The Reheat CycleReheating the expanding fluid with primary heat source is made at inter-mediate points in the expansion process.Net effect is to raise the average expansion temperature of the turbine without raising the temperature of the heat source.
67 The Reheat Cycle s p1 The extra expansion allows a greater enthapy to be released betweenstates 3 to 4.Here one additionalreheat process hasbeen added.Ts123564p2p1The Objective of Reheating: Increase work outputThe reheat process takes place form State 5 to 6. The expansion from States 6 to 4 takes place with no moisture in the turbine as shown here. The second stage of expansion is entirely in the superheat region. Without the reheat process, a single exzpansion would have produced a two-pahse (x < 1) mixture when the temperture dropped blow the saturation temperature at State 5.With reheat, the total work output of the cycle is larger than it would have been with a single expansion process.If State 4 yet lies in the vapor-liquid region (x < 1), at least additional work was extracted and the existense of the two-phase mixture at presumably a high quality (x near unity) would not be too detrimental to the low pressure turbine.As discussedin your text (Moran and Shapiro, pp ), the condsensing process is designed to operate at the lowest possible temeperature, usually the ambinetn. A lower condenser pressure allows the cycle to produce work with the largest possible pressure range and, hence, extract more work. In such systems, the condenser is sealed, and the entire system operates (ideally) in a closed loop.
71 Principle of the regenerative cycle bfWOUTWINQHQCA higher feed water inlettemperature as a result ofheating from States a - b.ed
72 Impacted processesHeating of some of the compressed liquid is done to raise the average temperature of heat addition.Heat is supplied after the liquid is compressed to a high pressure at State a.
73 The T-s diagram for the regenerative cycle bcsInternal heat transfer to feed water heater.eda
74 Practical considerations... Turbines cannot be designed economically with internal heat exchangers.Condensation could occur in the turbine.Not practical!
75 The practical regenerative cycle 5Q2-3 = 0123W2,outWIN,1QH6WIN,27QC4W1,outFeedwater heaterThe Practical Regnerative Cycle ConfigurationA feedwazter heater is inserted between the stages of expansion. The expansion in each turbine is carried out isentropically. Note that after a fraction of mass flow is drawn off at State 6 for the feewater heater, the reminaing fraction passes through states 7 to 2. A unit mass of the working fluid is returned to the high tempeaure source at State 4 for heat addition.The net work of the cycle is obtained in the two stages of expansion less the work input to the two feewater pumps.The feedwater heater (Stated 2 - 3) as depicted here is “closed” feedwater heater. No additional liquid is provided, i.e., makup water is not used. Thus mass conservation is easily determined when a mass balance is made for the device. Idally, the feedwater heater accomplished its purpose adiabatically, i.e., Q2-3 = 0.
76 The h-s diagram for the regenerative cycle 1342WOUT,1QHQCWIN,1567WOUT,2WIN,2(1 kg)(y kg)(1-y kg)
77 Energy balances and thermal efficiency 1342WOUT,1QHQCWIN,1567WOUT,2WIN,2(1 kg)(y kg)(1-y kg)
86 Example - Regeneration with a single extraction and an open feedwater heater
87 Example A regenerative Rankine cycle with a single extraction provides saturated steam at 500 psi a the turbine inlet.Condensation takes place at 70o F. One open regenerativefeedwater heater is included, using extracted steam at atemperature midway between the limits of the cycle.All processes are assumed to be internally reversibleexcept that in the regenerative heater. Neglect KE andPE effects, and determine the thermal efficiency,the internal irreversibility, and the extraction pressure.Assume steady operation.
88 Example - Plant diagram WOUTQCadecbQHy1-yWIN,1WIN,2gf
90 Example - Mass fraction at State “c” The mass fraction of fluid extracted at State c is obtainedfrom the energy balance for an open system applied tothe feedwater heater. Assume adiabatic mixing.abcdefgy1-y1Ts
91 Example - Entropy balance for the feedwater heater Apply the entropy balance for an open system to thefeedwater heater.
95 Example - Process quantities Note the positive entropy production in the feedwater heater.
96 Example - Thermal efficiency Note that regeneration has increased thermalefficiency above that of the previous example atthe expense of some work output per lbm of steam.
97 Commercial steam-power plants Reheat (multiple stages)Regeneration (multiple extractions)Nearly ideal heat additionConstant temperature boiling for water
98 Commercial steam-power plants Heat transfer characteristics of steam and water permit external combustion systemsCompression of condensed liquid produces a favorable work ratio.
99 Commercial steam-power plants The Rankine cycle with reheat and regeneration is advantageous for large plants.Small plants do not have economies of scaleInternal combustion for heat addition.A different thermodynamic cycle
100 10-7 Second-Law Analysis of Vapor Power Cycles