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Comprehensive Modelling of Pressurized Thermal Shock With a Probabilistic Approach
Abstract
Pressurized thermal shock (PTS) may cause a quick, catastrophic cleavage fracture in a reactor pressure vessel (RPV) of a pressurized water reactor (PWR). Low temperatures, thermal strains, and radiation embrittlement can all combine to create dangerous situations for structures, specifically thick-walled reactor pressure containers with fractures and welds as weak areas. A thorough picture of the temperature and stress intensity is required to determine the likelihood of the onset and spread of a cleavage crack. The ductile to brittle transition temperature affects the critical stress intensity for brittle cleavage fracture. This complicated combination of loads, absolute temperatures, and temperature gradients is combined with radiation damage to evaluate the likelihood that cleavage fracture will occur. In earlier works, simulations were carried out using combined computational fluid dynamics (CFD) and finite element method (FEM) simulations to get the most realistic picture of this issue. However, due to the complexity of the problem, the thermal mixing of the fluid and its effects on the RPV wall are simulated by models that are simplified in terms of geometric complexity and physics. This study investigates the effect of the interaction between multiple emergency core cooling (ECC) plumes on the thermal response of the RPV wall by considering a full (360 degree) RPV geometry with two loops for the ECC fluid injection. We first perform a transient conjugate heat transfer CFD simulation to compute the spatial and temporal evolutions of RPV wall temperature. The unsteady Reynolds-averaged Navier-Stokes equations are solved on the fluid side, and the unsteady heat transfer equation is solved on the solid side.
Next, a static structural analysis using FEM is conducted using the temperature profile obtained from CFD analysis on a one-loop reactor as input. The goal of the FEM analysis is to investigate the link between the depth, length, and ratio of the crack and the probability of failure. A probabilistic approach is used to evaluate the possibility of failure. The ultimate goal of these studies is the generation of a code that can implement hydraulic models that replace the time and resource-demanding CFD and FEM analysis.
Direct Numerical Simulation (DNS) is performed for a pressurized thermal shock scenario in a reactor downcomer geometry. In the present work, a simplified representative geometry is adopted where cold fluid injected from a square duct is injected in a planar downcomer. A secondary hot inlet at the top of the downcomer is employed to enforce a downward flow of the injected emergency core cooling water, to mimic the effect of density driven flow. The Reynolds number of the impinging flow, based on bulk velocity and duct height, equals 12,500, while a unity Prandtl number fluid is used. The simulation is performed for two thermal boundary conditions, namely an isotemperature condition and an adiabatic condition, representing the two extreme scenarios of a conjugate heat transfer problem. The instantaneous and mean fields are first analysed in order to study the flow pattern and formation of vortical structures within the downcomer. The impinging flow is deflected radially outwards in the vicinity of the barrel wall, which then interacts with the surrounding hot fluid forming large vortical structures and bringing the cold fluid back to the vessel wall. The mixing of flow and penetration of colder temperatures in the downcomer is observed to be greatly influenced by interaction of these vortical structures. The descending cold plume in the downcomer is observed to form three branches separated by low-speed regions. The maximum values of turbulent kinetic energy are observed only in the vicinity of flow impingement, while high values of its production and dissipation are also observed within the shear layers of the descending plume. The maximum values of temperature fluctuations are found at the interface of the descending cold plume and surrounding hot fluid, while relatively high values are also seen at the locations of large vortical strucutres. Anisotropy in turbulence is also analysed using the componentality contour approach and a modified barycentric colour mapping scheme. Also reported herein is a comparison of mean and statistical profiles with those at lower Reynolds number reported in the literature. At higher Reynolds number, the cold impinging jet is deflected farther outwards in the downcomer. The locations of peak fluctuations in velocity and temperature are also farther away from the impingement. The magnitudes of fluctuating temperature and turbulent kinetic energy are observed to be higher for the present higher Reynolds number case. The peak Nusselt number at the barrel wall is observed to scale with a factor of Re^0.5
in the present configuration.
In a nuclear power plant, the integrity of the pressure vessel which contains the primary water is paramount. In case of an accident involving the guillotine break of primary system piping there can be a sudden loss-of-coolant accident (LOCA). During such an incident, the reactor core needs to be cooled for some period after its shut-down (residual heat removal). The emergency core cooling is achieved by the injection of cold water in the still pressurized reactor pressure vessel (RPV). The combination of pressure and thermal stresses provides a complex stress state in the RPV wall: a pressurized thermal shock (PTS). The RPV material is generally a ferritic steel. 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. This problem is simulated with a combined CFD and FEM approach. A quarter of the reactor pressure wall including the cooling nozzle is simulated during the 1000 seconds of the cooling transient. This method can accurately predict the thermal profile and the corresponding stress field. This approach is applied to a reactor pressure vessel containing pre-existing semi-elliptical cracks. The stress intensities for every time step, the temperature, the effects of radiation damage, and the material properties of two types of RPV steel; (SA-508gr.3 and SA-508gr.4N) contribute to the probability for a brittle cleavage crack to form. An estimation of the probability for cleavage fracture is made through the Master Curve approach. These probabilities are calculated for different crack locations, sizes, aspect ratios and for two different grades of RPV steel. The influence of these geometric factors and material properties under the influence of radiation have been analysed. The material just below the nozzle is cooled down further and the thermal gradient is more severe. This is reflected in a higher probability for cleavage fracture. The new generation of RPV steel; SA-508gr.4N is very promising for its resistance to radiation induced embrittlement and for its higher strength, both factors leading to a lower probability of cleavage fracture in the reactor pressure vessel. Increasing the safety of the RPV.
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.
In 2020, the CFD analyses have been performed on a whole reactor vessel model. The action of accumulators during the PTS transient was considered. Using these data, an attempt to the efficient use of sub-modelling is carried out in order to obtain a strong reduction in the computational costs compared to a full 3D analysis. The analyses were given a probabilistic view by using the Master Curve approach for determining the material(s) fracture toughness.
In parallel with these activities, a literature review work was carried out at NRG. The single temperature dependence of the Master Curve was incorporated into characterizations of fracture toughness for all RPV steels of interest such as SA 508 Grade 3 and Grade 4N for both forging and weld material. The literature review helps to prove that the Master Curve approach models the temperature dependence of fracture toughness for a generic pressure vessel before and after irradiation. This is because all of these steels have a BCC matrix phase lattice structure. Based on ASTM E1921, the types of microstructure falling under a BBC matrix, such as bainite, tempered bainite, tempered martensite, ferrite and pearlite, could also be evaluated using the Master Curve model. Furthermore, it is found that the chemical composition is one of parameter to look for as driving force in embrittlement RPV due to irradiation. For the very high nickel steels examined (SA508 Grade 4N), when not combined with copper and moderate manganese, irradiation is not a serious embrittling agent.
This paper describes the work performed at NRG in the years 2017–2020 in investigting the Pressurized Thermal Shock (PTS) phenomenon, summarizes the achievements and gives a general judgement of the lessons learned. Moreover, this paper aims to illustrate the scope of planned research on PTS and its role in the new NRG research program PIONIER 2021–2024. An overview of NRG’s effort to align itself with the international community is given. Particular attention is given to the probabilistic problematic related to PTS. In order to better understand this problematic and improve the current state of knowledge NRG will create a PFM tool. The tool aims to use the best practices from existing PFM software to try to answer to questions requiring attention (e.g. thermal-hydraulic uncertainty). The experience accumulated during the previous activities will be included in the tool.
A pressurized thermal shock (PTS) in a reactor pressure vessel (RPV) wall of a pressurized water reactor (PWR) could eventually lead to reduced integrity of the vessel. A severe PTS scenario is a Loss-of-Coolant Accident (LOCA) in which the Emergency Core Cooling (ECC) injection causes a thermal shock in the vessel wall. The traditional one-dimensional system codes fail to reliably predict the complex three-dimensional thermal mixing phenomena in the downcomer occurring during the ECC injection. Therefore, a three-dimensional computational fluid dynamics (CFD) simulation of the transient is required to provide the temperature distribution for probability analyses. The assessment of the failure probability due to a single phase PTS initiated by postulated defects in the vessel wall requires the computation of a long transient solution. Since the CFD calculation is computationally expensive, the symmetry of a four-leg PWR geometry is utilized to reduce the computational domain. In the present work, several Unsteady Reynolds Averaged Navier-Stokes (URANS) simulations are performed to select an optimal computational domain that is representative for a typical PWR. The computed temperature distribution is provided as input for the structural analyses to calculate the stress intensity factor (SIF) along several defect fronts. The SIF is then used to evaluate the potential of crack propagation initiation of this defect. As an outlook for future research, the developed method will be applied to more postulated defects with larger sizes and at different locations. Furthermore, it is required from the crack analysis point of view to compute even longer transients (up to 1000s) to achieve sufficient penetration of the thermal stratification into the RPV wall to obtain the maximum SIF for all the sets of relevant defects
The Kolmogorov-Prandtl turbulence energy hypothesis is formulated in a way which is valid for the laminar sublayer as well as the fully turbulent region of a one-dimensional flow. The necessary constants are fitted to available experimental data. Numerical solutions are obtained for Couette flow with turbulence augmentation and pressure gradient and for turbulent duct flow. Reasonable agreement with available experimental data is obtained. Some new dimensionless groups are used and shown to be superior to the ones based on the friction velocity. The effects of turbulence augmentation and pressure gradient on the velocity and temperature distribution are studied. It is found that the solutions tend to approach solutions for limiting cases. The results are plotted in some figures in Section 5.
Detailed simulation of the thermal stresses of the reactor pressure vessel (RPV) wall in case of pressurized thermal shock (PTS) requires the simulation of the thermal mixing of cold high-pressure safety injection (HPI) water injected to the cold leg and flowing further to the downcomer. The simulation of the complex mixing phenomena including, e.g., stratification in the cold leg and buoyancy driven plume in the downcomer is a great challenge for CFD methods and requires careful validation of the used modelling methods.The selected experiment of Fortum mixing test facility modelling the Loviisa VVER-440 NPP has been used for the validation of CFD methods for thermal mixing phenomena related to PTS. The experimental data includes local temperature values measured in the cold leg and downcomer. Conclusions have been made on the applicability of used CFD method to thermal mixing simulations in case with stratification in the cold leg and buoyant plume in the downcomer.
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