NUCLEAR SYSTEMS ENGINEERING
Cho, Hyoung Kyu
Department of Nuclear Engineering Seoul National University
Cho, Hyoung Kyu
Department of Nuclear Engineering
Seoul National University
Contents
1. Introduction
2. Nonflow Process
3. Thermodynamic Analysis of Nuclear Power Plants 4. Thermodynamic Analysis of A Simplified PWR System
6.4.1 First Law Analysis of a Simplified PWR System
6.4.2 Combined First and Second Law or Availability 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
The engine cycle is named after George Brayton (1830–
1892), the American engineer who developed it, although it was originally proposed and patented by Englishman John Barber in 1791. It is also sometimes known as
the Joule cycle. The Ericsson cycle is similar to the Brayton
cycle but uses external heat and incorporates the use of a
regenerator. There are two types of Brayton cycles, open to
the atmosphere and using internal combustion chamber or
closed and using a heat exchanger.
Simple Brayton Cycle
Brayton Cycle
Reactor systems that employs gas coolants offer the potential for operating as direct Brayton cycle by passing the heated gas directly into a turbine.
Ideal for single‐phase, steady‐flow cycles with heat exchange and therefore is the basic cycle for modern gas turbine plants as well as proposed nuclear gas‐cooled reactor plants.
The ideal cycle is composed of two reversible constant‐pressure heat‐exchange processes and two reversible, adiabatic work processes
The compressor work, or “backwork," is a larger fraction of the turbine work than is the pump work in a Rankine cycle.
Simple Brayton Cycle
Brayton Cycle
Simple Brayton Cycle
Simple Brayton Cycle
Brayton Cycle Analysis
Pressure or compression ratio of the cycle
For isentropic processes with a perfect gas, constant
For a perfect gas, because enthalpy is a function of temperature only
and the specific heats are constant.
) 1 (
2 1 /
) 1 (
1 2 1
2
v v p
p T
T
s
v
p c
c / ,
c
Tv1 Tp c
1
Simple Brayton Cycle
Brayton Cycle Analysis
Entropy change of ideal gas
From the first T ds relation From the second T ds relation
Y. A. Cengel
Simple Brayton Cycle
Brayton Cycle Analysis
Isentropic Processes of Ideal Gases
cv
R
v
v v
v v
v c
R T
T v
R v T
c T
/
2 1 1
2 1
2 1
2 1
2
ln ln ln ln
ln
0
1 /
, /
,
cp cv
cp cv R cv
R1
2 1 1
2
v v T
T For isentropic process, ideal gas
1)/ (
1 2 1
2 1
2 1
2 1
2 1
2
ln ln ln ln ln
ln 0
PP P
P P
P c
R T
T P
R P T
c T p
c R
p p
/ , / 1 1 1
,
cp cv cp cv R cp R
1)/ (
1 2 1
2
P P T
T For isentropic process, ideal gas
Simple Brayton Cycle
Brayton Cycle Analysis
Isentropic Processes of Ideal Gases
1
2 1 1
2
v v T
T ( 1)/
1 2 1
2
P P T
T
2 1 1
2
v v P
P
Valid for
‐ Ideal gas
‐ Isentropic process
‐ Constant specific heats
Simple Brayton Cycle
Brayton Cycle Analysis
Turbine work
Compressor work
1)/ (
3 4 3
4
P P T
T
1)/ (
1 2 1
2
P P T
T
Simple Brayton Cycle
Brayton Cycle Analysis
The heat input from the reactor
The heat rejected by the heat exchanger
1)/ (
1 2 1
2
P P T
T
1)/ (
3 4 3
4
P P T
T
Simple Brayton Cycle
Brayton Cycle Analysis
Maximum useful work
Thermodynamic efficiency
Optimum pressure ratio for maximum net work
′ 0
Simple Brayton Cycle
Example 6.7
Simple Brayton Cycle
Example 6.7
4 1.658 278 972
Simple Brayton Cycle
Example 6.7
Simple Brayton Cycle
Example 6.7
Simple Brayton Cycle
Example 6.7
The highest temperature in the cycle occurs at the end of the combustion process (state 3), and it is limited by the maximum temperature that the turbine blades can
withstand. This also limits the pressure ratios that can be used in the cycle.
For a fixed turbine inlet temperature T3, the net work
output per cycle increases with the pressure ratio, reaches a maximum, and then starts to decrease. Therefore, there should be a compromise between the pressure ratio (thus the thermal efficiency) and the net work output.
With less work output per cycle, a larger mass flow rate
(thus a larger system) is needed to maintain the same power output, which may not be economical.
In most common designs, the pressure ratio of gas turbines ranges from about 11 to 16.
Contents
1. Introduction
2. Nonflow Process
3. Thermodynamic Analysis of Nuclear Power Plants 4. Thermodynamic Analysis of A Simplified PWR System
6.4.1 First Law Analysis of a Simplified PWR System
6.4.2 Combined First and Second Law or Availability 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
More Complex Brayton Cycles
1)/ (
3 4 3
4
P P T
T
More Complex Brayton Cycles
1)/ (
1 2 1
2
P P T
T
More Complex Brayton Cycles
1)/ (
1 2 1
2
P P T
T s
More Complex Brayton Cycles
More Complex Brayton Cycles
1)/ (
3 4 3
4
P P T
T
More Complex Brayton Cycles
More Complex Brayton Cycles
More Complex Brayton Cycles
More Complex Brayton Cycles
1)/ (
3 4 3
4
P P T
T ( 1)/
1 2 1
2
P P T
T
More Complex Brayton Cycles
Without regeneration With regeneration
More Complex Brayton Cycles
Without regeneration With regeneration
= 38.3 % = 30.7 %
With regeneration, = 4
With regeneration, = 8
= 35.5 %
Without regeneration = 8
= 56.2 % Not desired!
0.993 2.800
More Complex Brayton Cycles
More Complex Brayton Cycles
Reheating by just fuel spraying
High concentration
oxygen
Constant pressure
Constant pressure
A gas-turbine engine with two-stage compression with intercooling, two-stage expansion with reheating, and regeneration and its T-s diagram.
More Complex Brayton Cycles
- Net work of gas turbine = (turbine work output) – (compressor work input) - Efficiency enhancement by
-> Decreasing the compressor work input
-> Increasing the turbine work output Steady flow compression or expansion work is proportional to the specific
volume of fluid.
1. As the number of stages increases, the compression becomes nearly
isothermal at the inlet temperature.
-> compression work decrease.
2. Similarly, turbine work between the two pressure levels can be increases by
expanding the gas in stages and reheating it -> multistage expansion with reheating.
Intercooling
Reheating
More Complex Brayton Cycles
4
More Complex Brayton Cycles
More Complex Brayton Cycles
4
More Complex Brayton Cycles
4
More Complex Brayton Cycles
More Complex Brayton Cycles
HW#5
More Complex Brayton Cycles
More Complex Brayton Cycles
Simple Brayton Cycle
Brayton Cycle
Simple Brayton Cycle
Brayton Cycle
Contents of Lecture
Contents of lecture
Chapter 1 Principal Characteristics of Power Reactors
Will be replaced by the lecture note
Introduction to Nuclear Systems
Chapter 4 Transport Equations for Single‐Phase Flow (up to energy equation)
Chapter 6 Thermodynamics of Nuclear Energy Conversion Systems:
Nonflow and Steady Flow : First‐ and Second‐Law Applications
Chapter 7 Thermodynamics of Nuclear Energy Conversion Systems : Nonsteady Flow First Law Analysis
Chapter 3 Reactor Energy Distribution
Chapter 8 Thermal Analysis of Fuel Elements
Thermodynamics
Heat transport Conduction heat transfer Nuclear system
