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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 a system is the maximum useful work possible during a process that brings the system  into equilibrium with a heat reservoir.

The availability function is a characteristic of the state of the system and the environment which acts as a  reservoir at constant pressure (p0) and constant temperature (T).

(4.27)

(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 Equation

 Energy and entropy equation in Chapter 4: control mass approach

 The second law of thermodynamics (4.27)

(5)

Energy Equation

 Energy and entropy equation in Chapter 4: control mass approach

 The second law of thermodynamics (4.27)

the second T‐ds relation

(6)

Energy Equation

 Energy and entropy equation in Chapter 4: control mass approach

 The second law of thermodynamics (4.27)

(7)

Energy Equation

 Energy and entropy equation in Chapter 4: control mass approach

 Entropy change of ideal gas

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

 Body force

Pv m m

P V P W

V P x A P W

normal normal

         

I

i

i I

i

i m gz

dt mgz d

Dt mgz m D

dt m d Dt

m D

1 1

(10)

Energy Equation

 Energy equation in Chapter 4: control volume approach

 Control mass

 Control volume

For stationary control volume

(4.38)

dt P dV dt

dW

normal

(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

 Useful work (useful part of the actual work)

 Maximum useful work

Maximum useful work Actual work

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

 Irreversibility

=0

(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

Actual work Useful 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)

Contents

1. Introduction

2. Nonflow Process

3. Thermodynamic Analysis of Nuclear Power Plants 4. Thermodynamic Analysis of A Simplified PWR System

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)

Contents

1. Introduction

2. Nonflow Process

3. Thermodynamic Analysis of Nuclear Power Plants 4. Thermodynamic Analysis of A Simplified PWR System

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 (T3) 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 Analysis of Nuclear Power Plants

 Thermodynamic efficiency (or effectiveness): 

 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: 

 Thermodynamic efficiency (or effectiveness):  100

70 30 30

100 30%

, 1 1 300

600 · 100 50

(a) (b)

, 1 1 300

1000 · 100 70 30

50 60% 30

70 42.9%

(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)

12

75 16%

, 35.2

, 39.8

12

39.8 30.2 %

(36)

Contents

1. Introduction

2. Nonflow Process

3. Thermodynamic Analysis of Nuclear Power Plants 4. Thermodynamic Analysis of A Simplified PWR System

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

Steady Negligible Non‐deformable No shear

Negligible kinetic energy

(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

 Mass conservation equation

Turbine

0, 0

 Left side > 0

Condenser

0, 0

 Left side > 0

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)

Recirculating steam generator

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

(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 6.4.2.3

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

Turbine and pump 

Steam generator and condenser

=0

(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.

7.75 MPa

6.89 kPa 15.5 MPa

(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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