Towards a Probabilistic Analysis of Pressurized Thermal Shock

Abstract

Pressurized thermal shock (PTS) in a reactor pressure vessel could lead to a sudden brittle and catastrophic cleavage fracture. The combination of radiation embrittlement, the thermal stresses, and low temperatures can cause severe conditions for the structures. Particularly thick-walled reactor pressure vessels, which contain weak spots such as welds and cracks.
In order to assess the probability for the initiation and propagation of a cleavage crack, a detailed image of the stress intensity and the temperature is needed. The critical stress intensity for brittle cleavage fracture depends on the ductile to brittle transition temperature. This complex combination of stresses, absolute temperatures and temperature gradients in combination with radiation damage requires an integral approach for the evaluation of the probability for the occurrence of cleavage fracture.
In order to get the most accurate image as possible of this problem, in previous work by the authors, simulations were performed with a combined CFD and FEM approach. Where a CFD model simulates the thermal mixing of the fluid and its effects on the reactor pressure vessel wall. The temperature profile on the reactor pressure wall is then used as input of a static structural model using FEM. Over the last few years the complexity of the models increased and different types of transients were investigated [1, 2]. Reducing the amount of modelling simplifications and assumptions should lead to the most complete picture of the risks of the accident scenario.
However in order to increase the speed of the calculations some simplifications are needed. In the coming years the simplifications will be added stepwise and their results will be checked against more complicated models. With a focus on verifying the stress intensity around a pre-existing crack, which leads directly to an increase on the probability of cleavage.
In order to correctly predict thermal mixing in the fluid, a computationally expensive 3D model is needed. However the full temperature distribution in the reactor pressure vessel at all times is not necessarily needed to determine the stress intensity. A finite element analysis has been performed on a small section of the reactor pressure vessel [3], speeding up the simulations significantly.
The largest amount of simulation time is spend on modelling the fluid using CFD. Other approaches to do this involve Thermal Hydraulic models, such as applied in the FAVOR code. The drawback of those codes is that they do not provide fluctuations which we can observe using CFD.
A first approach of a comprehensive model which features the heat transition during a transient and the resulting stress intensity. A comparison with the computationally more expensive methods is made. A significant calculation time reduction can be achieved, but more work is needed in order to perform sufficient simulations to account for a full probabilistic analysis.