An Investigation into the use of FEA methods for the prediction of Thermal Stress Ratcheting Huse, Stephen

Abstract Calculate heat transfer for given initial conditions Calculate thermal gradients and stresses Predict the onset of thermal stress ratcheting using FEA methods Compare to ASME code prediction

Background (cont.) Thermal gradients occur due to changes in temperature of fluid flowing through piping T - Mean Temperature V - Linear Temperature Gradient, ∆T1 Peak Temperature Gradient, ∆T2

Background Bree Diagram Regions σp – Primary Stress, PD/2t E – Elastic S – Shakedown P - Plastic cyclic R - Ratcheting σp – Primary Stress, PD/2t P – Pressure D – diameter t – thickness σt – Secondary Stress, EαΔT1/2(1-v) E – Young’s modulus α – Mean coefficient of thermal expansion ∆T1 – Linear temperature gradient v – Poisson’s ratio σy – Yield Strength

Problem Description Nuclear power plants have high thermal gradients and pressures resulting in sever primary and secondary stresses Severe primary and secondary stresses result in accumulating plastic strains known as thermal ratcheting Prevention of thermal ratcheting is performed by limiting the allowable stresses

Methodology Convective heat transfer of turbulent flow inside a cylinder: Nu=0.023Re0.8Prn Nu=hd/k h – convective heat transfer coefficient d – inner diameter k – fluid thermal conductivity Re=vd/ν v – velocity ν – kinematic viscosity Pr – Prandtl number ABAQUS for solving heat transfer analysis and structural analysis Geometry Material properties Load conditions

Results Stress Vs strain for iterated pressures of 1, 2, and 3 ksi

Results (cont)

Conclusion Onset of Thermal Ratcheting is able to be predicted with ABAQUS. ABAQUS predicted 1500 psi, whereas ASME code predicted 1300 to 1600 based on different yield stress

References Bree, J. (1967). Elastic-plastic behaviour of thin tubes subject to internal pressure and intermittent high-heat fluxes with application to fast nuclear reactor fuel elements.Journal of Strain Analysis, (2), 226-38. 2010 ASME boiler & pressure vessel code an international code. (2010). New York, NY: American Society of Mechanical Engineers. ABAQUS (Version 6.13) [Software]. (2013). Providence, RI: Dassault Systèmes Simulia Corp.