1. www.inl.gov Multipliers for Single-Phase Heat Transfer Coefficients in RELAP5-3D 2011 IRUG Meeting Cliff Davis

2. 2 Introduction RELAP5-3D calculates the wall heat transfer coefficient for single- phase flow as – H = max (H forced, H laminar, H free ) based on a recommendation by Raithby and Hollands* – Nu = max(Nu forced, Nu free ) The recommendation applies to external flows and is said to provide a rough (often within 25%) estimate of Nu _______ *W. M. Rohsenow, H. P. Hartnett, and E. N. Ganic (ed.), Handbook of Heat Transfer Fundamentals, Second Edition, New York: McGraw-Hill Book Co., 1985.

3. 3 Introduction (cont’d) The code uses the maximum value of all three correlations to ensure a smooth transition between heat transfer regimes – Early code versions applied the free convection correlation based on a comparison of the Grashoff and Reynolds numbers, but this resulted in discontinuities An ANL user questioned the theoretical basis for using the maximum value for internal flows The code manual and literature were reviewed to assess the accuracy of the maximum value for internal flows RELAP5-3D calculations of mixed laminar and free convection in a vertical tube were performed to address the issue

4. 4 The manual states that the code does not account for mixed convection From Volume 4: – “The transition to natural (i.e., free) convection flow occurs over a range of conditions as a function of Re and Gr. The h is also a function of the forced and natural (free) convection component directions (same or opposite) and entrance length effects. Currently, RELAP5-3D © does not account for these factors.” – “There are other situations besides cooling that are not accounted for. These include entrance effects, laminar-turbulent transition and mixed forced, and free convection.” – “The effects of combined free and forced convection are different for opposing flow and result in significant changes in the value of the heat transfer coefficient.”

5. 5 Mixed convection for an external plate From W. M. Rohsenow, H. P. Hartnett, and E. N. Ganic (ed.), Handbook of Heat Transfer Fundamentals, Second Edition, New York: McGraw-Hill Book Co., 1985.

6. 6 Mixed convection inside a vertical tube From S. Kakac, R. K. Shah, W. Aung (ed.), Handbook of Single-Phase Convective Heat Transfer, New York, John Wiley & Sons, 1987.

7. 7 The code currently has multipliers on the wall heat transfer coefficients in various regimes Contained as Words 12 through 19 in the 20-word option of the 1CCCG801 and 1CCCG901 cards Multipliers can be input for forced convection, nucleate boiling, CHF, transition boiling, film boiling, condensation, free convection, and laminar convection regimes – However, the input multipliers are currently used only for the CHF, transition boiling, and film boiling regimes As part of this work, updates to use the input multipliers for the forced convection, free convection, and laminar convection regimes have been submitted

8. 8 Verification calculations were performed The original and revised codes gave identical results when all the heat transfer multipliers were set to 1.0 – The new multipliers did not affect results when they were not supposed to Calculations demonstrated that each multiplier had the appropriate effect on the heat transfer coefficient and heat flux – Transient calculations could not be used because the multiplier affects the fluid temperature – Steady-state calculations could not be used because the free convection heat transfer coefficient is affected by wall temperature, which is affected by the multiplier – Verification calculations were based on t = 0 s results with the steady-state heat transfer flag turned off The heat transfer coefficient and wall heat flux were proportional to the multiplier when the input (fixed) wall and fluid temperatures were used

9. 9 The heat transfer multipliers can be used for Sensitivity calculations Quantification of code uncertainty Representing alternate geometries or boundary conditions – The laminar convection correlation is Nu = 4.36, which is appropriate for fully developed flow in a tube with constant heat flux Nu = 3.66 for constant wall temperature Nu = 8.24 for a thin annulus Representing phenomena more accurately – Mixed convection

10. 10 The capability of RELAP5-3D to represent mixed convection in a vertical tube was evaluated Laminar flow in a uniformly heated vertical tube The assumed conditions were: – Liquid water (P = 1.0 MPa, T = 400 K) – Re = 1000 – D h = 0.01 m – L = 1.0 m – A range of heat fluxes (17.5 < q” < 17,500 W/m 2 ) 10 < Ra*/16 < 10,000 Ra* = [ρ 2 gβC P D h 4 /(μk)](dT w /dx)

11. 11 Results with the original code for a vertical tube The calculated results do not depend on the flow direction The calculated Nu is too large at Ra*/16 ≤ 100 because Nu forced > Nu laminar at Re = 1000 The calculation has the correct trend with Ra* for upflow The RELAP5 free convection correlation for external flow past a flat plate provides a reasonable prediction for upflow in a tube The calculation does not have the correct trend for downflow

12. 12 Results with the revised code for a vertical tube Improved upflow results were obtained at Ra*/16 ≤ 100 by using the Gnielinski correlation (heat transfer package 160), which has a more accurate transition between laminar and turbulent flow than when Dittus- Boelter is used Multiplying H free by 1.e-6 and H laminar by 0.72 results in better agreement for downflow, but the trends are still not correct

13. 13 Conclusions Heat transfer multipliers for single-phase convection have been implemented in RELAP5-3D – These multipliers enhance the code’s capability to model different geometries, boundary conditions, and phenomena Verification calculations demonstrated that the multipliers were implemented correctly Mixed convection is a complicated phenomenon that is not accounted for in RELAP5-3D – However, improved results can be obtained using heat transfer multipliers if the user has sufficient information available