pdf 5.2 a taste of reactor physics-part 2
TRANSCRIPT
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
1/23
1
A Look at Nuclear Scienceand Technology
Larry Foulke
Module 5.2
A Taste of Reactor Physics Part 2
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
2/23
NuclearEngineeringProgram
Finite System Neutron Balance
Production vs Absorption + Leakage
f = a + Leakage
Note: kkeff (To accommodate leakage)
keff = k =Production
Absorption + Leakage
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
3/23
NuclearEngineeringProgram
Neutron Leakage Effect
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
4/23
NuclearEngineeringProgram
States of criticalitykeff = 1 Critical
keff > 1 Supercritical
keff < 1 Subcritical
No reactor can be constantly critical: Fuel depletion Fission product buildup (absorb neutrons) Temperature changes (changes cross section)
Criticality
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
5/23
NuclearEngineeringProgram
In order to keep an operating nuclear reactor criticalwe will need to adjust terms in the neutron balance
Neutron balance controlled by: ProductionAbsorption Leakage
Criticality Control
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
6/23
NuclearEngineeringProgram
Criticality Control
n Let us consider how we could adjust these parametersto achieve a target keff for two different applications
n Nuclear Power PlantnTarget keff:
nkeff= 1 for steady-state operationnkeff> 1 for start-up, keff< 1 for shutdown
n Nuclear Fuel Processing FacilitynTarget keff:
nkeff< 1 under all possible conditions (including accidents)
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
7/23NuclearEngineeringProgram
Criticality Control (Reactor)
Nuclear ReactorProduction
Determined by the total fissile content of the core Initial fuel loading Conversion of fertile nuclides (breeding) Refueling
On-line
ShutdownAbsorptionLeakage
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
8/23NuclearEngineeringProgram
Criticality Control (Reactor)
Nuclear ReactorProductionAbsorption Fission-Product Absorbers
Cladding, Structure, Coolant Control Rods Soluble Absorbers (poisons) Burnable Absorbers
Leakage
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
9/23NuclearEngineeringProgram
Criticality Control (Reactor)
n Nuclear ReactornProductionnAbsorption (Modern reactor designs):
nMoveable control rods (CR) to change power level and maintainsteady state operation.
nMovable safety rods (SR) to quickly shut down reactor andensure keff< 1.
Soluble boron in reactor coolant (PWR only) toshim
keff(liketrim control in an airplane) and fixed burnable poisons (boron or
gadolinium) that deplete during operation to accommodate fuel
burnup.
nLeakage
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
10/23NuclearEngineeringProgram
Criticality Control (Reactor)
Nuclear ReactorProduction
Absorption
Leakage Core size and shape Reflection of neutrons back into the core Density of core material(s)
(temperature-dependent)
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
11/23
NuclearEngineeringProgram
Water-Reflector
Effect onMinimumCore Size
11
Image Source: See Note 1
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
12/23
NuclearEngineeringProgram
Criticality Control (Reactor)
Nuclear ReactorProduction
Absorption
LeakageModeration
Controls how effectively neutrons can slow downto thermal energies.
Determined by selection of moderator materialand pin dimensions (diameter and pitch).
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
13/23
NuclearEngineeringProgram
Criticality Control (Reactor)
Reactor Criticality Requirements Operation Modes
Power Reactors (Startup / Steady-State / Shutdown) Some Research Reactors (Pulse Mode) All reactors have emergency shutdown (SCRAM) capability
Routine adjustments to reactor criticality are required Account for power fluctuations and feedback effects
Fuel depletion, density changes of moderator Small frequent adjustments: control rods (in PWR) Larger, planned, adjustments: soluble boron (in PWR) BWR reactors use control rods and coolant flow feedback to
adjust criticality.
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
14/23
NuclearEngineeringProgram
nFuel Facility:Always Subcritical!nDesigned subcritical
nVerify that current configuration is subcriticalnConfirm that proposed changes will be subcritical
nkeff< 1 under all conditions; must accountfor:
nUncertainties in Experimental Data and CalculationsnNormal, Anticipated Abnormal & Credible Accident
Scenarios
Criticality Control (Fuel Facility)
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
15/23
NuclearEngineeringProgram
Beyond keff
When designing critical systems (reactors) weneed to know the spatial distribution of neutrons in
the core, in addition to the multiplication factor.
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
16/23
NuclearEngineeringProgram
The Exact Way (Hard)
Write down a neutron balance equation over somedifferential volume element and then solve the resultingintegro-differential equation:
Terms: 1)Time Variance, 2) Leakage, 3) Total Interaction Loss,
4) Fission Source, 5) In-Scattering Source
TR
UTH!
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
17/23
NuclearEngineeringProgram
Typical Core DesignFuel Assemblies
Zoom In on
these 4 assemblies
Core SymmetryImage Source: See Note 2
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
18/23
NuclearEngineeringProgram
Typical Assembly Design
Fuel Pins
Control Rods
Assembly
Symmetry
Zoom In onQuarter Assembly
Image Source: See Note 2
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
19/23
NuclearEngineeringProgram
Typical, Simplified Assembly Model
Simplified 2-D model of anAP600 quarter assembly.
Contains UO2 fuel, boroncontrol rods, and B4Cburnable absorber rods.
Reflecting boundaryconditions on all sides.
Image Source: See Note 2
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
20/23
NuclearEngineeringProgram0 2 4 6 8
0
2
4
6
8
Quarter-Assembly, Control Rods Withdrawn
0 2 4 6 8
0
2
4
6
8
k
= 1.1630
Image Source: See Note 2
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
21/23
NuclearEngineeringProgram0 2 4 6 8
0
2
4
6
8
Quarter-Assembly, Control Rods Inserted
0 2 4 6 8
0
2
4
6
8
k
= 0.93287
Image Source: See Note 2
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
22/23
NuclearEngineeringProgram
A More Approximate Way (Easier)
Write down a neutron balance equation using DiffusionTheory with one energy group
Time Variance, Fission Source, Absorption Loss, Leakage
AL
MOSTTRU
TH!
1
v
(
r,t)
t=
f(
r,t) a(
r,t)+D2(
r,t)
-
7/28/2019 PDF 5.2 a Taste of Reactor Physics-Part 2
23/23
1. Reprinted with permission from the American Nuclear Society.Nuclear Engineering Theory and Technology of Commercial
Nuclear Powerby Ronald Allen Knief, 2nd Edition. Copyright
2008 by the American Nuclear Society, La Grange Park, Illinois.
2. Reprinted with permission from David Griesheimer. FunctionalExpansion Tallies for Monte Carlo Simulations, PhD
Dissertation, Nuclear Engineering and Radiological Sciences,
University of Michigan (2005). ProQuest/UMI, AAT 3163808.
Image Source Notes