pdf 5.4 reactor kinetics-part 2

7/28/2019 PDF 5.4 Reactor Kinetics-Part 2

1/21

A Look at Nuclear Scienceand Technology

Larry Foulke

Module 5.4

Reactor Kinetics Part 2


2/21

Positive Reactivity Feedback Effect

PowerTemperature

ReactivityPositive

Feedback

Enhances the Effect That Produced It & Is Destabilizing


3/21

FEEDBACK MECHANISMS

POSITIVE FEEDBACK

Self-Perpetuating

Drawback

If Unchecked, Causes DivergentPower Increase

Enhances Effect

That Produced It

Power & Temperature Increase

Reactivity Increase

Power & Temperature Increase. . .


4/21

Negative Reactivity Feedback Effect

Power

Temperature

Reactivity

Negative

Feedback

Resists the Effect That Produced It & Is Stabilizing


5/21

FEEDBACK MECHANISMS NEGATIVE FEEDBACK

Power & Temperature Increase

Self-Controlling Drawbacks

Causes Reactivity Loss in Power Escalation

Role in "Cold Water" Accidents

Resists Effect That

Produced It

Reactivity Decrease

Power & Temperature Decrease Reactivity Increase

. . .


6/21

FEEDBACK EFFECTS

COEFFICIENTS OF REACTIVITY

(xi ) =

xi

xi = Tf Fuel Temperature Coefficient [FTC]

Tm Moderator Temperature Coefficient [MTC]

fv Moderator Void Coefficient [MVC]

dm

Moderator Density Coefficient [MDC]

=i

xi

xi=

i xi


7/21

IntegralControl

RodWorthCurve

BOTTOM X1 X2 TOP

ROD WITHDRAWAL, X

INTEGRALRODW

ORTH,

SLOPE OFCURVE FOR

SMALLINCREMENTS X

=

Image Source: See Note 2


8/21

Differential Control-Rod Worth Curve

DIFFE

RENTIALRODWO

RTH,/X

ROD WITHDRAWAL, X

BOTTOM TOP



9/21

CONTROL APPLICATIONS

REACTIVITY CONTROL ROD FEATURES

Routine Control Rod Adjustment for Critical

Full Safety/Control Rod Insertion [Scram/Trip]

Overpower Excessively short Period

Other Parameters Out of Range

Limited Rod Speed/Individual

Partial Insertion [Bite]

Maintain Rods in Position of Neutron Importance

Assures Immediate System Response to Rod Motion

Adjust soluble boron to keep rods in desired position


10/21

SUPERCRITICAL EXCURSION

PULSE REACTOR BEHAVIOR

Sandia National Laboratories Annular

Core Research Reactor [ACRR]

Phases

Initiation

Prompt Supercritical

Pulse

Parameters


11/21

NEUTRON MULTIPLICATION

"STEP" REACTIVITY INSERTION

Prompt Critical

=

= $

Prompt Supercritical

>

eff

eff

eff


12/21


TRANSIENT -- ANNULAR CORE RESEARCHREACTOR [ACRR]

Prompt Fuel-Temperature-Based Feedback

Sequence

Withdraw Pulse Rod Worth 3.5$

Rapid power increase

TfRise Fall

Power Continues Increase, But less rapid

High Tf < 0

"Shutdown" (Temporary, If Rod Stays Out)


13/21


ACRR Pulse

Initial Period ~1 millisecond

Peak Power 35,000 MWth

Duration 7 milliseconds

Power Tail [see LogarithmicPlot]


14/21

Initial Period ~1ms

Maximum Power

35,000 MWth

Pulse Width 7ms

Fuel TemperatureRises

Reactivity(Multiplication) Falls

7 ms

1 ms

+3.5$



15/21

Reactor Energy Removal

In order for the reactor to remain at steady state energymust be removed at the same rate that it is produced.

In all modern reactor designs heat energy, produced byfission in the fuel regions, is transferred to a workingfluid flowing through the core.

W=flow rate

Cp=heat capacity

Tout= outlet temperature

Tin = inlet temperature

Power= (W)(cp )(Tout Tin )

Watts = (kg

sec)(watt sec

kg oC)(oC)


16/21


For thermodynamic efficiency we want to keepthe temperature rise in the core, and therefore,outlet coolant temperature as high as possible,but

without melting any fuel in the core.

Melting fuel:

Changes geometry reactivity effect

Ruins fuel integrity contamination

If melting occurs at even a single spot on a single element, theassembly is destroyed.


17/21


During operation, there is no way to measure the localpower at every location within the core; we typically onlyknow total core power. (and how do we know that?)

How can operators know that they are not melting fuel atsteady state or during transients (or accidentconditions)?

We use calculations to determine engineering factors thatrelate the maximum fuel temperature in the core to theaverage core power under different conditions.


18/21

Steady State Operation (Balancing Act)

Maintain Criticality

Maintain Desired Fission Rate/Power Level

Compensate for Nuclear Temperature Feedbacks

Ensure Thermal-Energy Removal

Ensure no Thermal Limits Violated



19/21

Contrast to Conventional Systems High to Very High Power Density

Fuel Integrity Must Be Maintained

Radiation Effects Limit Material Choices Expensive & Non-Conventional Materials

Example: Zirconium Cladding Tubes

Fission-Product Decay Heat Source Present

7.5% at Shutdown

1.3% at 1 hr

0.4% at 1 day



20/21

Power Density (kW/liter)---------------------------------------------------

System Core Ave Fuel Ave Fuel Max------------------------------------------------------------------

Fossil Fuel Plant 10Aircraft turbine 45Rocket 20,000PTGR 4.0 54 104HTGR 8.4 44 125CANDU 12 110 190BWR 56 56 180PWR 95-105 95-105 190-210LMFBR 280 280 420

Power Density Comparisons



21/21

1. Reprinted with permission from the AmericanNuclear Society. Nuclear Engineering Theory andTechnology of Commercial Nuclear Powerby

Ronald Allen Knief, 2nd Edition. Copyright 2008 bythe American Nuclear Society, La Grange Park,Illinois.

2. DOE Fundamentals Handbook: Nuclear Physics andReactor Theory, Volume 2. (1993). Washington DC:U. S. Department of Energy. Figures 9 (slide 7) and10 (slide 8).http://www.hss.doe.gov/nuclearsafety/techstds/docs/handbook/h1019v2.pdf

Image Source Notes
http://www.hss.doe.gov/nuclearsafety/techstds/docs/handbook/h1019v2.pdfhttp://www.hss.doe.gov/nuclearsafety/techstds/docs/handbook/h1019v2.pdfhttp://www.hss.doe.gov/nuclearsafety/techstds/docs/handbook/h1019v2.pdfhttp://www.hss.doe.gov/nuclearsafety/techstds/docs/handbook/h1019v2.pdf

pdf 5.4 reactor kinetics-part 2

Documents