1. Bechtel Bettis, Inc. Bettis Atomic Power Laboratory P.O. Box 79 West Mifflin, PA 15122-0079 2008 International RELAP5 User’s Seminar Assessing the RELAP5-3D Conduction Enclosure Model L. D. McCann

2. 2008 International RELAP5 User’s Seminar 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

3. 2008 International RELAP5 User’s Seminar 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

4. 2008 International RELAP5 User’s Seminar 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:

5. 2008 International RELAP5 User’s Seminar 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

6. 2008 International RELAP5 User’s Seminar 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]: 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

7. 2008 International RELAP5 User’s Seminar 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

8. 2008 International RELAP5 User’s Seminar 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 T 0 (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

9. 2008 International RELAP5 User’s Seminar 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

10. 2008 International RELAP5 User’s Seminar Two-Dimensional Transient Rectangle (2 l x 2b dimensions) Initially at a High Temperature T 0 (500K) with Four Sides at a Low Temperature T (300K) The Exact Solution is: Same RELAP5-3D Model as Two-Dimensional Steady- State

11. 2008 International RELAP5 User’s Seminar 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

12. 2008 International RELAP5 User’s Seminar 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