NUCLEAR SYSTEMS ENGINEERING
Cho, Hyoung Kyu
Department of Nuclear Engineering Seoul National University Contents
1. Introduction 2. Nonflow Process 3. ThermodynamicThe engine Analysis cycle isof named Nuclear Powerafter GeorgePlants Brayton (1830– 1892), the American engineer who developed it, although it 4. Thermodynamic Analysis of A Simplified PWR System was originally proposed and patented by Englishman John 6.4.1 First Law Analysis of a Simplified PWR System Barber in 1791. It is also sometimes known as 6.4.2 Combined First and Second Law or Availability Analysis of a Simplified PWR System the Joule cycle. The Ericsson cycle is similar to the Brayton 5. Morecycle Complex but Rankineuses external Cycles: Superheat, heat and Reheat, incorporates Regeneration, the use and of Moisture a Separation regenerator. There are two types of Brayton cycles, open to 6. Simplethe Brayton atmosphere Cycle and using internal combustion chamber or 7. Moreclosed Complex and Brayton using Cycles a heat exchanger. 8. Supercritical Carbon Dioxide Brayton Cycles 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
( 1)/ ( 1) T p v 2 2 1 , c / c p v T1 s p1 v2
1 Tv 1 c Tp c
For a perfect gas, because enthalpy is a function of temperature only and the specific heats are constant. 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
R cp cv , cp / cv , R / cv 1
R /c T v T R v v v 2 2 2 2 1 0 cv ln Rln ln ln ln T1 v1 T1 cv v1 v2
1 T2 v1 For isentropic process, ideal gas T1 v2
1 1 R c c , c / c , R / c 1 p v p v p
R ( 1)/ T P T R P P c p P 2 2 2 2 2 2 0 cp ln R ln ln ln ln ln T1 P1 T1 cp P1 P1 P1 ( 1)/ T2 P2 For isentropic process, ideal gas T1 P1 Simple Brayton Cycle Brayton Cycle Analysis Isentropic Processes of Ideal Gases 1 ( 1)/ T v T P P v 2 1 2 2 2 1 T v T P 1 2 1 1 P1 v2
Valid for ‐ Ideal gas ‐ Isentropic process ‐ Constant specific heats Simple Brayton Cycle Brayton Cycle Analysis Turbine work
( 1)/ T4 P4 T3 P3
Compressor work
( 1)/ T2 P2 T1 P1 Simple Brayton Cycle Brayton Cycle Analysis The heat input from the reactor
( 1)/ T2 P2 T1 P1
The heat rejected by the heat exchanger
( 1)/ T4 P4 T3 P3 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)/ T4 P4 T3 P3 More Complex Brayton Cycles
( 1)/ T2 P2 T1 P1 More Complex Brayton Cycles
( 1)/ T2s P2 T1 P1 More Complex Brayton Cycles More Complex Brayton Cycles
( 1)/ T4 P4 T3 P3 More Complex Brayton Cycles More Complex Brayton Cycles More Complex Brayton Cycles More Complex Brayton Cycles
( 1)/ ( 1)/ T4 P4 T2 P2 T3 P3 T1 P1 More Complex Brayton Cycles
With regeneration Without regeneration More Complex Brayton Cycles
= 38.3 % = 30.7 %
With regeneration Without regeneration
0.993 = 35.5 % 2.800
= 4 With regeneration, = 8 With regeneration,
= 56.2 %
Not desired! Without regeneration = 8 More Complex Brayton Cycles More Complex Brayton Cycles
Constant pressure
Reheating by Constant just fuel spraying High pressure concentration oxygen
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 Steady flow compression or expansion -> Increasing the turbine work output 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. Intercooling
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. Reheating More Complex Brayton Cycles
4 More Complex Brayton Cycles More Complex Brayton Cycles
4 More Complex Brayton Cycles
4 More Complex Brayton Cycles HW#5 More Complex Brayton Cycles 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 1Principal Characteristics of Power Reactors Nuclear system . Will be replaced by the lecture note . Introduction to Nuclear Systems
Chapter 4 Transport Equations for Single‐Phase Flow (up to energy equation) Chapter 6Thermodynamics 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 Thermodynamics
Chapter 3 Reactor Energy Distribution Heat transport Conduction Chapter 8 Thermal Analysis of Fuel Elements heat transfer