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Assessing the RELAP5-3D Conduction Enclosure Model

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.

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Assessing the RELAP5-3D Conduction Enclosure Model

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  1. Assessing the RELAP5-3D Conduction Enclosure Model L. D. McCann

  2. 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. 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. 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. 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. 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. 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. 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

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

  11. 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 2 cm from the End RELAP5-3D Compared to Exact Solution At 46 cm from the End

  12. 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

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