The exergy of asystemis the maximum useful work possible during a process that brings the system into equilibrium with aheat reservoir. (4.

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1 Energy Equation Entropy equation in Chapter 4: control mass approach The second law of thermodynamics Availability (exergy) The exergy of asystemis the maximum useful work possible during a process that brings the system into equilibrium with aheat reservoir. (4.27) The availability function is a characteristic of the state of the system and the environment which acts as a reservoir at constant pressure (p 0 ) and constant temperature (T 0 ).

2 Energy Equation Entropy equation in Chapter 4: control mass approach Availability/exergy Carnot cycle efficiency,,,

3 Energy Equation Entropy equation in Chapter 4: control mass approach The second law of thermodynamics From state 1 to 2 Maximum useful work Maximum useful work obtainable from the specified change

4 Energy and entropy equation in Chapter 4: control mass approach The second law of thermodynamics (4.27) Energy Equation

5 Energy and entropy equation in Chapter 4: control mass approach The second law of thermodynamics (4.27) Energy Equation the second T ds relation

6 Energy and entropy equation in Chapter 4: control mass approach The second law of thermodynamics (4.27) Energy Equation

7 Energy and entropy equation in Chapter 4: control mass approach Entropy change of ideal gas Energy Equation From the first T ds relation From the second T ds relation

8 Energy Equation Energy equation in Chapter 4: control volume approach The first law of thermodynamics In the control volume approach, there are flow in and out. The first law

9 Energy Equation Energy equation in Chapter 4: control volume approach Heat addition term Work term Work done by the mass in the control volume + work associated with mass flow W W normal normal P A x P V P V m P mpv Body force I d m D mgz d mgz D m Dt dt i 1 m i Dt dt I i 1 m i gz

10 Energy Equation Energy equation in Chapter 4: control volume approach Control mass Control volume (4.38) For stationary control volume dw dt normal P dv dt

11 Energy Equation Energy equation in Chapter 4: control volume approach Control volume

12 Energy Equation Entropy equation in Chapter 4: control volume approach Entropy equation For a stationary control volume

13 Energy Equation Entropy equation in Chapter 4: control volume approach Actual work Maximum useful work Actual work Useful work Useful work (useful part of the actual work) Maximum useful work

14 Energy Equation Entropy equation in Chapter 4: control volume approach Energy equation Useful work (useful part of the actual work) Useful work (or useful actual work) Partial derivative? Stationary!

15 Energy Equation Entropy equation in Chapter 4: control volume approach Multiplying, then subtracting from (4.44) Express the actual useful work with entropy

16 Energy Equation Entropy equation in Chapter 4: control volume approach Maximum useful work =0 Irreversibility

17 Energy Equation Entropy equation in Chapter 4: control volume approach Irreversibility

18 Energy Equation Entropy equation in Chapter 4: control volume approach Example

19 Energy Equation Entropy equation in Chapter 4: control volume approach Example (4.27) Maximum useful work

20 Energy Equation Entropy equation in Chapter 4: control volume approach Example Useful work Actual work Useful work

21 Energy Equation Entropy equation in Chapter 4: control volume approach Example Irreversibility Maximum useful work Useful work

22 Energy Equation Entropy equation in Chapter 4: control volume approach Example Irreversibility

23 1. Introduction 2. Nonflow Process 3. Thermodynamic Analysis of Nuclear Power Plants 4. Thermodynamic Analysis of A Simplified PWR System Contents 5. More Complex Rankine Cycles: Superheat, Reheat, Regeneration, and Moisture Separation 6. Simple Brayton Cycle 7. More Complex Brayton Cycles 8. Supercritical Carbon Dioxide Brayton Cycles

24 Introduction Summary of the working forms of the first and second laws First law for control volume Second law Working forms

25 1. Introduction 2. Nonflow Process 3. Thermodynamic Analysis of Nuclear Power Plants 4. Thermodynamic Analysis of A Simplified PWR System Contents 5. More Complex Rankine Cycles: Superheat, Reheat, Regeneration, and Moisture Separation 6. Simple Brayton Cycle 7. More Complex Brayton Cycles 8. Supercritical Carbon Dioxide Brayton Cycles

26 Thermodynamic Analysis of Nuclear Power Plants Analysis of NPPs Provides the relation between the mixed mean outlet coolant temperatures (or enthalpy for BWR) of the core through the primary and secondary systems to the generation of electricity at the turbine. Cycles used for the various reactor types and the methods of thermodynamic analysis of these cycles are described. Rankine cycle for steam driven electric turbines(pwr, BWR) Brayton cycle can be considered for gas cooled reactor systems Both cycles are constant pressure heat addition and rejection cycles for steady flow operation

27 Thermodynamic Analysis of Nuclear Power Plants Analysis of NPPs Simple Brayton cycle Maximum temperature of the Brayton cycle (T 3 ) is set by turbine blade and gas cooled reactor core material limits far higher than those for the Rankine cycle, which is set by liquid-cooled reactor core materials limits.

28 Thermodynamic Analysis of Nuclear Power Plants Efficiency to assess the thermodynamic performance of components and cycles Thermodynamic efficiency (or effectiveness): The ratio between the actual useful work and the maximum useful work Isentropic efficiency: Special case of thermodynamics efficiency Adiabatic case Important for devices such as pump, turbine, compressor Thermal efficiency: The fraction of the heat input that is converted to net work output The cycle efficiency that we are interested in.

29 Thermodynamic efficiency (or effectiveness): Thermodynamic Analysis of Nuclear Power Plants Maximum useful work No entropy generation Fixed, non deformable control volume with zero shear work Negligible kinetic and potential energy differences

30 Thermodynamic Analysis of Nuclear Power Plants Isentropic efficiency: Maximum useful work For steady state condition

31 Thermodynamic Analysis of Nuclear Power Plants Isentropic efficiency: Useful actual work for an adiabatic control volume with zero shear and negligible kinetic and potential energy differences For steady state

32 Thermodynamic Analysis of Nuclear Power Plants Thermal efficiency: Cycle efficiency For adiabatic systems, it is not useful.

33 Thermodynamic Analysis of Nuclear Power Plants Example problem (a) Thermal efficiency: % (a) (b) Thermodynamic efficiency (or effectiveness): % % , ,

34 Thermodynamic Analysis of Nuclear Power Plants Example problem (b) Maximum useful work no entropy generation Entropy in = entropy out Entropy decrease in hot reservoirs = entropy increase in cold reservoir

35 Thermodynamic Analysis of Nuclear Power Plants Example problem (b) %, 35.2, %

36 1. Introduction 2. Nonflow Process 3. Thermodynamic Analysis of Nuclear Power Plants 4. Thermodynamic Analysis of A Simplified PWR System Contents 5. More Complex Rankine Cycles: Superheat, Reheat, Regeneration, and Moisture Separation 6. Simple Brayton Cycle 7. More Complex Brayton Cycles 8. Supercritical Carbon Dioxide Brayton Cycles

37 Thermodynamic Analysis of A Simplified PWR System First Law Analysis of a Simplified PWR System One component with multiple inlet and outlet flow streams operating at steady state and surround it with a non deformable, stationary control volume Energy equation Negligible kinetic energy Steady Negligible Non deformable No shear

38 Thermodynamic Analysis of A Simplified PWR System First Law Analysis of a Simplified PWR System One component with multiple inlet and outlet flow streams operating at steady state and surround it with a non deformable, stationary control volume Energy equation Turbine 0, 0 Left side > 0 Condenser 0, 0 Left side > 0 Mass conservation equation Pump 0, 0 Left side < 0 Steam generator 0, 0 Left side < 0

39 Thermodynamic Analysis of A Simplified PWR System First Law Analysis of a Simplified PWR System Turbine Shaft work, no heat addition adiabatic turbine Actual turbine work is related to the ideal work by the component isentropic efficiency. Isentropic efficiency Pump Shaft work, no heat addition adiabatic pump,

40 Thermodynamic Analysis of A Simplified PWR System First Law Analysis of a Simplified PWR System Steam generator Heat transfer between the primary and the secondary Pinch point temperature Minimum temperature difference between the primary and the secondary Inversely related to the heat transfer area Small temperature difference: large heat transfer area Large temperature difference: small heat transfer area Directly related to the irreversibility of the SG Large temperature difference: large irreversibility Important design choice based on tradeoff between cost and irreversibility Recirculating steam generator

41 Thermodynamic Analysis of A Simplified PWR System First Law Analysis of a Simplified PWR System Steam generator Reactor plant Actual work Positive or negative?

42 Thermodynamic Analysis of A Simplified PWR System First Law Analysis of a Simplified PWR System Reactor plant Maximum useful work In section Maximum useful work expressed with the secondary side properties Thermodynamic efficiency or effectiveness: Single turbine case

43 Review First law analysis in a simplified PWR system Stationary, non deformable control volume operating at steady state =0 Turbine and pump Steam generator and condenser

44 Review First law analysis in a simplified PWR system Stationary, non deformable control volume operating at steady state Thermodynamic efficiency and cycle thermal efficiency

45 Thermodynamic Analysis of A Simplified PWR System First Law Analysis of a Simplified PWR System Assume that the turbine and pump have isentropic efficiencies of 85%.

46 Thermodynamic Analysis of A Simplified PWR System First Law Analysis of a Simplified PWR System Example 6.4: Thermodynamic Analysis of a Simplified PWR Plant Draw the temperature entropy (T s) diagram for this cycle MPa 7.75 MPa 6.89 kpa

47 Thermodynamic Analysis of A Simplified PWR System First Law Analysis of a Simplified PWR System Example 6.4: Thermodynamic Analysis of a Simplified PWR Plant Compute the ratio of the primary to secondary flow rates.

48 Thermodynamic Analysis of A Simplified PWR System First Law Analysis of a Simplified PWR System Example 6.4: Thermodynamic Analysis of a Simplified PWR Plant Compute the nuclear plant thermodynamic efficiency. Calculate the enthalpies of each state! State 1

49 Thermodynamic Analysis of A Simplified PWR System First Law Analysis of a Simplified PWR System Example 6.4: Thermodynamic Analysis of a Simplified PWR Plant State 2 Isentropic efficiencies of 85%. Isentropic process,

50 Thermodynamic Analysis of A Simplified PWR System First Law Analysis of a Simplified PWR System Example 6.4: Thermodynamic Analysis of a Simplified PWR Plant State 3 State 4 Isentropic efficiency Isentropic process 1 1

51 Thermodynamic Analysis of A Simplified PWR System First Law Analysis of a Simplified PWR System Example 6.4: Thermodynamic Analysis of a Simplified PWR Plant Compute the nuclear plant thermodynamic efficiency.

52 Thermodynamic Analysis of A Simplified PWR System First Law Analysis of a Simplified PWR System Example 6.4: Thermodynamic Analysis of a Simplified PWR Plant Compute the cycle thermal efficiency., Thermal efficiency (cycle thermal efficiency) = plant thermodynamic efficiency

53 Thermodynamic Analysis of A Simplified PWR System First Law Analysis of a Simplified PWR System Improvements in thermal efficiency for this simple saturated cycle Pressure Increase the pump outlet pressure/decrease turbine outlet pressure

54 Thermodynamic Analysis of A Simplified PWR System First Law Analysis of a Simplified PWR System Improvements in thermal efficiency for this simple saturated cycle Pressure Increase the pump outlet pressure/decrease turbine outlet pressure Added heat Rejected heat Net work Efficiency

55 Thermodynamic Analysis of A Simplified PWR System First Law Analysis of a Simplified PWR System Improvements in thermal efficiency for this simple saturated cycle Pressure Increase the pump outlet pressure/decrease turbine outlet pressure Added heat Rejected heat Net work Efficiency

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