bechtel bettis, inc. bettis atomic power laboratory p.o. box 79 west mifflin, pa 15122-0079 2008...

Bechtel Bettis, Inc.Bettis Atomic Power Laboratory

P.O. Box 79West Mifflin, PA 15122-0079

2008 International RELAP5 User’s Seminar

Assessing the RELAP5-3D Conduction Enclosure Model

L. D. McCann


Outline

• Introduction• Heat Conduction Enclosure Model Overview• Comparison to Three Exact Heat Conduction Equation

Solutions– Two-Dimensional Steady-State– One-Dimensional Transient– Two-Dimensional Transient

• Conclusions


Heat Conduction Enclosure Model Overview

• RELAP5-3D Heat Structures are One-Dimensional• Heat Conduction Enclosure Allows Directly Connecting

Heat Conductors at Either Surface• User Input Required Includes Conductance Between

the Conductors and View Factors for Each Conductor– Conductance is the Actual Equivalent Heat Transfer

Coefficient– View Factor is the Ratio of Desired Heat Transfer Area to the

Conductor Surface Area


Heat Conduction Enclosure Model Overview

• There Are Three Significant Limitations to the Heat Conduction Enclosure Model

– Axial Conduction Can Only Be Modeled At One of the Two Radial Faces– The Conductance is Time Invariant– The Calculated Heat Flux Is Advanced Explicitly In Time Making

Calculational Stability a Concern

• As a Result of these Limitations– Axial Conduction May be Adequate only to Show Whether Axial

Conduction is Important– Conductance Should Be Based On Average Properties Over the Transient– For Calculational Stability Choose Conductance (h) such that:

))(15.0

(2

x

k

t

xh


Comparison to Exact Heat Conduction Equation Solutions

• Three Exact Solutions to the Heat Conduction Equation Are Compared to RELAP5-3D Using the Heat Conduction Enclosure Model– Two-Dimensional Steady-State– One-Dimensional Transient– Two-Dimensional Transient

• Simplifications Typical of Exact Solutions Tend to be Consistent with the Shortcomings in the RELAP5-3D Heat Conduction Enclosure Model– Time Invariant Conductance– Uniform Radial Temperature

• Thus, Real Problems May not be Predicted as Accurately as Those Analyzed in this Presentation


Two-Dimensional Steady-State

• Rectangle (a x b dimensions) with Three Sides at a Low Temperature and One at a Higher Temperature

• The Exact Solution is [Carslaw, 1959]:

a

bn

a

nyb

a

xn

n n

TTTyxT

)12(csch

)12)((sinh

)12(sin

0 )12(

1)0(4),(

• RELAP5-3D Model Uses 25 Heat Conductors with 25 Axial Structures in Each

• Conduction Enclosure Represents Both Axial and Radial Conduction– Radial Conductance Large Enough to Keep Contacting Conductors

within 1K– Axial Conductance is Thermal Conductivity Divided by Axial

Structure Height


Two-Dimensional Steady-State

• Without Conduction Enclosure Temperature Is Linear in the Y-Coordinate Between the End Values

• With Only 5 Axial and Radial Structures the Error at the Center Was Nearly 100%

• With 25 Axial and Radial Structures Agreement is Excellent As Shown

RELAP5-3D Compared to Exact Solution At the X-Coordinate Center


One-Dimensional Transient

• Thin 3 Meter Long Cylindrical Steel Rod With Convection To T (300K) and the Rod Ends (at x = + l, l = 1.5 m) Fixed At T0 (500K)

• The Exact Solution Is:

• RELAP5-3D Model Uses Cylindrical Coordinates with Two Radial Mesh Points and 60 Axial Structures

• Axial Conduction is Represented With the Heat Conduction Enclosure Model– Conductance is Thermal Conductivity Divided by Structure Height

– View Factor is Axial Rod Cross Sectional Area Divided by Outer Surface Area of One Structure

0

222

]4/)12([0

2/1

2/1

0 )}])12/((4{1)[12(

)2/)12cos(()1()(4

))/(cosh(

))/(cosh()(),(

222

n

ltntn

nln

lxneTT

l

xTTTtxT


One-Dimensional Transient

• Excellent Agreement with the Exact Solution as Typified Here

• This Case Identified an Error in the Cylindrical and Spherical Conduction Calculations in RELAP5-3D– Results Shown Are After the

Error was Corrected

– The Error is Smaller With More Radial Mesh Points

– The Error will be Corrected in a Future RELAP5-3D Version

RELAP5-3D Compared to Exact Solution At 32.5 cm from the End


Two-Dimensional Transient

• Rectangle (2l x 2b dimensions) Initially at a High Temperature T0 (500K) with Four Sides at a Low Temperature T (300K)

• The Exact Solution is:

0

]4/)12([

0

]4/)12([

20 )12(

)2/)12cos(()1(

)12(

)2/)12cos(()1(16

)(

),(222222

n

btnn

n

ltnn

n

byne

n

lxne

TT

TtxT

• Same RELAP5-3D Model as Two-Dimensional Steady-State


Two-Dimensional Transient

• Excellent Agreement with the Exact Solution• Transient Response at Two Axial Locations Are Shown,

Which are Typical

RELAP5-3D Compared to Exact Solution At 46 cm from the End

RELAP5-3D Compared to Exact Solution At 2 cm from the End


Conclusions

• A Correction Was Identified As A Result of this Heat Conduction Model Exercise in RELAP5-3D

• When the Corrections Is Incorporated, the RELAP5-3D Heat Conduction Enclosure Model Matches Exact Solutions to the Heat Conduction Equations Closely

• There are Limitations to the Conduction Enclosure Model, but it Can at Least Identify Whether Multidimensional Heat Conduction is an Important Consideration

bechtel bettis, inc. bettis atomic power laboratory p.o. box 79 west mifflin, pa 15122-0079 2008...

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