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Application of Computational Fluid Dynamics in Nuclear Reactor Safety Analysis

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A special issue of Fluids (ISSN 2311-5521). This special issue belongs to the section "Mathematical and Computational Fluid Mechanics".

Deadline for manuscript submissions: closed (10 December 2021) | Viewed by 23160

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Special Issue Editor

Dr. T. Hoehne

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Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden-Rossendorf (HZDR), 01328 Dresden, Germany
Interests: fluid mechanics; computational fluid dynamics; numerical simulation; numerical modeling; CFD simulation; multiphase flow; engineering thermodynamics; thermal engineering; mechanical engineering; turbulence; heat transfer; CFD coding; turbulence modeling; convection; thermodynamics; large eddy simulation; nuclear engineering; mass transfer
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Dear Colleagues,

In the last two decades, three-dimensional CFD codes have increasingly been used for the prediction of single-phase and multiphase flows under stationary or unsteady conditions in nuclear reactor applications. The motivation for this is that several important thermohydraulic phenomena cannot be predicted with the required accuracy and spatial resolution using traditional system analysis codes.

However, CFD codes contain empirical models to simulate turbulence, heat transfer, multiphase interaction, and chemical reactions. Such models must be validated before they can be confidently used in nuclear reactor applications. The necessary validation can only be performed by comparing model predictions with reliable data.

This Special Issue will focus on the following areas:

Single-phase and multi-phase CFD simulations with a focus on validation will be welcome in areas such as single-phase and multi-phase heat transfer, free-surface flows, direct contact condensation, and turbulent mixing. These should relate to nuclear reactor safety issues, such as pressurized thermal shock, critical heat flux, pool heat exchangers, boron dilution, hydrogen distribution in containments, thermal striping and fatigue, etc. The use of systematic error quantification and the application of best practice guidelines (BPGs) are strongly encouraged.
Experiments providing data suitable for CFD or CMFD validation are also welcome. These should include local measurements using multi-sensor probes, laser-based techniques (LDV, PIV, or LIF), hot-film/wire anemometry, imaging, or other advanced measuring techniques. Papers should include a discussion of measurement uncertainties.

Dr. Thomas Höhne
Guest Editor

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Keywords

single-phase and multi-phase heat transfer
free-surface flows
direct contact condensation
turbulent mixing
pressurized thermal shock
critical heat flux
pool heat exchangers
boron dilution
hydrogen distribution in containments
thermal striping and fatigue
error quantification
application of best practice guidelines (BPGs)

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Published Papers (8 papers)

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Research

29 pages, 1855 KiB

Open AccessArticle

Towards Uncertainty Quantification of LES and URANS for the Buoyancy-Driven Mixing Process between Two Miscible Fluids—Differentially Heated Cavity of Aspect Ratio 4

by Philipp J. Wenig, Ruiyun Ji, Stephan Kelm and Markus Klein

Fluids 2021, 6(4), 161; https://doi.org/10.3390/fluids6040161 - 17 Apr 2021

Cited by 6 | Viewed by 2459

Abstract

Numerical simulations are subject to uncertainties due to the imprecise knowledge of physical properties, model parameters, as well as initial and boundary conditions. The assessment of these uncertainties is required for some applications. In the field of Computational Fluid Dynamics (CFD), the reliable prediction of hydrogen distribution and pressure build-up in nuclear reactor containment after a severe reactor accident is a representative application where the assessment of these uncertainties is of essential importance. The inital and boundary conditions that significantly influence the present buoyancy-driven flow are subject to uncertainties. Therefore, the aim is to investigate the propagation of uncertainties in input parameters to the results variables. As a basis for the examination of a representative reactor test containment, the investigations are initially carried out using the Differentially Heated Cavity (DHC) of aspect ratio 4 with

R a = 2 \times 10^{9}

as a test case from the literature. This allows for gradual method development for guidelines to quantify the uncertainty of natural convection flows in large-scale industrial applications. A dual approach is applied, in which Large Eddy Simulation (LES) is used as reference for the Unsteady Reynolds-Averaged Navier–Stokes (URANS) computations. A methodology for the uncertainty quantification in engineering applications with a preceding mesh convergence study and sensitivity analysis is presented. By taking the LES as a reference, the results indicate that URANS is able to predict the underlying mixing process at

R a = 2 \times 10^{9}

and the variability of the result variables due to parameter uncertainties. Full article

(This article belongs to the Special Issue Application of Computational Fluid Dynamics in Nuclear Reactor Safety Analysis)

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21 pages, 5677 KiB

Open AccessArticle

The Tailored CFD Package ‘containmentFOAM’ for Analysis of Containment Atmosphere Mixing, H₂/CO Mitigation and Aerosol Transport

by Stephan Kelm, Manohar Kampili, Xiongguo Liu, Allen George, Daniel Schumacher, Claudia Druska, Stephan Struth, Astrid Kuhr, Lucian Ramacher, Hans-Josef Allelein, K. Arul Prakash, G. Vijaya Kumar, Liam M. F. Cammiade and Ruiyun Ji

Fluids 2021, 6(3), 100; https://doi.org/10.3390/fluids6030100 - 3 Mar 2021

Cited by 32 | Viewed by 4744

Abstract

The severe reactor accident at Fukushima Daiichi Nuclear Power Plant (2011) has confirmed the need to understand the flow and transport processes of steam and combustible gases inside the containment and connected buildings. Over several years, Computational Fluid Dynamics (CFD) models, mostly based on proprietary solvers, have been developed to provide highly resolved insights; supporting the assessment of effectiveness of safety measures and possible combustion loads challenging the containment integrity. This paper summarizes the design and implementation of containmentFOAM, a tailored solver and model library based on OpenFOAM^®. It is developed in support of Research & Development related to containment flows, mixing processes, pressurization, and assessment of passive safety systems. Based on preliminary separate-effect verification and validation results, an application oriented integral validation case is presented on the basis of an experiment on gas mixing and H₂ mitigation by means of passive auto-catalytic recombiners in the THAI facility (Becker Technologies, Eschborn, Germany). The simulation results compare well with the experimental data and demonstrate the general applicability of containmentFOAM for technical scale analysis. Concluding the paper, the strategy for dissemination of the code and measures implemented to minimize potential user errors are outlined. Full article

(This article belongs to the Special Issue Application of Computational Fluid Dynamics in Nuclear Reactor Safety Analysis)

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13 pages, 1076 KiB

Open AccessArticle

Statistical Mechanics-Based Surrogates for Scalar Transport in Channel Flow

by Molly Ross and Hitesh Bindra

Fluids 2021, 6(2), 79; https://doi.org/10.3390/fluids6020079 - 10 Feb 2021

Cited by 4 | Viewed by 2685

Abstract

Thermal hydraulics, in certain components of nuclear reactor systems, involve complex flow scenarios, such as flows assisted by free jets and stratified flows leading to turbulent mixing and thermal fluctuations. These complex flow patterns and thermal fluctuations can be extremely critical from a reactor safety standpoint. The component-level lumped approximations (0D) or one-dimensional approximations (1D) models for such components and subsystems in safety analysis codes cannot capture the physics accurately, and may introduce a large degree of modeling uncertainty. On the other hand, high-fidelity computational fluid dynamics codes, which provide numerical solutions to the Navier–Stokes equations, are accurate but computationally intensive, and thus cannot be used for system-wide analysis. An alternate way to improve reactor safety analysis is by building reduced-order emulators from computational fluid dynamics (CFD) codes to improve system scale models. One of the key challenges in developing a reduced-order emulator is to preserve turbulent mixing and thermal fluctuations across different-length scales or time-scales. This paper presents the development of a reduced-order, non-linear, “Markovian” statistical surrogate for turbulent mixing and scalar transport. The method and its implementation are demonstrated on a canonical problem of differentially heated channel flow, and high-resolution direct numerical simulations (DNS) data are used for emulator or surrogate development. This statistical surrogate model relies on Kramers–Moyal expansion and emulates the turbulent velocity signal with a high degree of accuracy. Full article

(This article belongs to the Special Issue Application of Computational Fluid Dynamics in Nuclear Reactor Safety Analysis)

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30 pages, 20153 KiB

Open AccessArticle

Two-Phase Turbulence Statistics from High Fidelity Dispersed Droplet Flow Simulations in a Pressurized Water Reactor (PWR) Sub-Channel with Mixing Vanes

by Nadish Saini and Igor A. Bolotnov

Fluids 2021, 6(2), 72; https://doi.org/10.3390/fluids6020072 - 6 Feb 2021

Cited by 3 | Viewed by 2495

Abstract

In the dispersed flow film boiling regime (DFFB), which exists under post-LOCA (loss-of-coolant accident) conditions in pressurized water reactors (PWRs), there is a complex interplay between droplet dynamics and turbulence in the surrounding steam. Experiments have accredited particular significance to droplet collision with the spacer-grids and mixing vane structures and their consequent positive feedback to the heat transfer recorded in the immediate downstream vicinity. Enabled by high-performance computing (HPC) systems and a massively parallel finite element-based flow solver—PHASTA (Parallel Hierarchic Adaptive Stabilized Transient Analysis)—this work presents high fidelity interface capturing, two-phase, adiabatic simulations in a PWR sub-channel with spacer grids and mixing vanes. Selected flow conditions for the simulations are informed by the experimental data found in the literature, including the steam Reynolds number and collision Weber number (

W e_{c} = {40, 80}

), and are characteristic of the DFFB regime. Data were collected from the simulations at an unprecedented resolution, which provides detailed insights into the continuous phase turbulence statistics, highlighting the effects of the presence of droplets and the comparative effect of different Weber numbers on turbulence in the surrounding steam. Further, axial evolution of droplet dynamics was analyzed through cross-sectionally averaged quantities, including droplet volume, surface area and Sauter mean diameter (SMD). The downstream SMD values agree well with the existing empirical correlations for the selected range of

W e_{c}

. The high-resolution data repository from the simulations herein is expected to be of significance to guide model development for system-level thermal hydraulic codes. Full article

(This article belongs to the Special Issue Application of Computational Fluid Dynamics in Nuclear Reactor Safety Analysis)

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14 pages, 5015 KiB

Open AccessArticle

Assessing the Applicability of the Structure-Based Turbulence Resolution Approach to Nuclear Safety-Related Issues

by Jinyong Feng, Liangyu Xu and Emilio Baglietto

Fluids 2021, 6(2), 61; https://doi.org/10.3390/fluids6020061 - 1 Feb 2021

Cited by 4 | Viewed by 2273

Abstract

The accuracy of computational fluid dynamics (CFD) predictions plays a fundamental role in supporting the operation of the current nuclear reactor fleet, and even more importantly the licensing of advanced high-efficiency reactor concepts, where local temperature oscillations driven by thermal striping, cycling and stratification can limit the structural performance of vessels and components. The complexity of the geometrical configurations, coupled to the long operational transients, inhibits the adoption of large eddy simulation (LES) methods, mandating the acceptance of the more efficient Reynolds-averaged Navier-Stokes (RANS)-based models, even though they are unable to provide a complete physical description of the flow in regions dominated by complex unsteady coherent structures. A new strategy has been proposed and demonstrated at Massachusetts Institute of Technology (MIT) toward the enhancement of unsteady Reynolds-averaged Navier-Stokes (URANS) predictions, using local resolution of coherent turbulence, to provide higher fidelity modeling in support of safety-related issues. In this paper, a comprehensive assessment of the recently proposed Structure-based (STRUCT-

ε

) turbulence model is presented, starting from fundamental validation of the model capabilities and later focusing on a representative safety-relevant application, i.e., thermal mixing in a T-junction. Solutions of STRUCT-

ε

, the widely used Realizable

k - ε

model (RKE) and Large Eddy Simulation with Wall-Adapting Local Eddy-viscosity subgrid scale closure (LES-WALE) are compared against the experimental data. Both the velocity and temperature fields predicted by the STRUCT-

ε

model are in close agreement with the high-fidelity data from the experiments and reference LES solutions, across all validation cases. The approach demonstrates the potential to address the accuracy requirements for application to nuclear safety-related issues, by resolving the turbulent flow structures, while the computational efficiency provides the ability to perform consistent uncertainty quantification. Full article

(This article belongs to the Special Issue Application of Computational Fluid Dynamics in Nuclear Reactor Safety Analysis)

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23 pages, 334 KiB

Open AccessArticle

First-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Critical Points in Coupled Nonlinear Systems. II: Application to a Nuclear Reactor Thermal-Hydraulics Safety Benchmark

by Dan Gabriel Cacuci

Fluids 2021, 6(1), 34; https://doi.org/10.3390/fluids6010034 - 10 Jan 2021

Cited by 1 | Viewed by 1735

Abstract

Responses defined at critical points are particularly important for reactor safety analyses and licensing (e.g., the maximum fuel and/or clad temperature). The novel mathematical framework of the first-order comprehensive adjoint sensitivity analysis methodology for critical points (1st-CASAM-CP) is applied in this work to develop a reactor safety thermal-hydraulics benchmark model which admits exact closed-form expressions for the adjoint functions and for the first-order sensitivities of responses defined at critical points (maxima, minima, saddle points) in physical systems characterized by imprecisely known parameters, external and internal boundaries. This benchmark model is designed for verifying the capabilities and accuracies of computational tools for modeling numerically thermal-hydraulics systems. The unique and extensive capabilities of the 1st-CASAM-CP methodology are demonstrated in this work by considering two responses of paramount importance in reactor safety, namely, (i) the maximum rod surface temperature, which occurs at the imprecisely known interface between the subsystem that models the heat conduction inside the heated rod and the subsystem modeling the heat convection process surrounding the rod; and (ii) the maximum temperature inside the heated rod, which has a critical point with two components, one located at a precisely known boundary of the subsystem that models the heat conduction inside the heated rod, while the other component depends on an imprecisely known boundary (i.e., the rod length). The exact analytical expressions developed in this work for the sensitivities of the maximum internal rod temperature and maximum rod surface temperature, as well as for the sensitivities of the locations where these respective maxima occur, provide exact benchmarks for verifying the accuracy of thermal-hydraulics computational tools. The sensitivities of such responses and of their critical points with respect to model parameters enable the quantification of uncertainties induced by uncertainties stemming from the system’s parameters and boundaries in the respective responses and their underlying critical points. Full article

(This article belongs to the Special Issue Application of Computational Fluid Dynamics in Nuclear Reactor Safety Analysis)

24 pages, 413 KiB

Open AccessArticle

First-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Critical Points in Coupled Nonlinear Systems. I: Mathematical Framework

by Dan Gabriel Cacuci

Fluids 2021, 6(1), 33; https://doi.org/10.3390/fluids6010033 - 10 Jan 2021

Cited by 1 | Viewed by 1733

Abstract

This work presents the novel first-order comprehensive adjoint sensitivity analysis methodology for critical points (1st-CASAM-CP), which enables the exact and efficient computation of the first-order sensitivities of responses defined at critical points (maxima, minima, saddle points) of coupled nonlinear models of physical systems characterized by imprecisely known parameters underlying the models, boundaries, and interfaces between the coupled systems. Responses defined at critical points are important in many applications, including system optimization, safety analyses and licensing. For the design and licensing of nuclear reactors, such essentially important responses include the maximum temperatures of the fuel and cladding in hot channels. The 1st-CASAM-CP presented in this work makes it possible to determine, using a single large-scale “adjoint” computation, the first-order sensitivities of the magnitude of a response defined at a critical point of a function in the phase-space of the systems’ independent variables. In addition, the 1st-CASAM-CP enables the computation of the sensitivities of the location in phase-space of the critical point at which the respective response is located: one “adjoint” computation is required for each component of the respective critical point in the phase-space of independent variables. By enabling the exact and efficient computation of the sensitivities of responses and of their critical locations to imprecisely known model parameters, boundaries, and interfaces, the 1st-CASAM-CP significantly extends the practicality of analyzing crucially important responses for large-scale systems involving many uncertain parameters, interfaces, and boundaries. Full article

(This article belongs to the Special Issue Application of Computational Fluid Dynamics in Nuclear Reactor Safety Analysis)

19 pages, 20310 KiB

Open AccessArticle

Detailed Simulation of the Nominal Flow and Temperature Conditions in a Pre-Konvoi PWR Using Coupled CFD and Neutron Kinetics

by Thomas Höhne and Sören Kliem

Fluids 2020, 5(3), 161; https://doi.org/10.3390/fluids5030161 - 22 Sep 2020

Viewed by 3214

Abstract

The aim of the numerical study was the detection of possible vortices in the upper part of the core of a Pre-Konvoi Pressurized Water Reactor (PWR) which could lead to temperature cycling. In addition, the practical application of this Computational Fluid Dynamic (CFD) simulation exists in the full 3D analysis of the coolant flow behavior in the reactor pressure vessel of a nuclear PWR. It also helps to improve the design of future reactor types. Therefore, a CFD simulation of the flow conditions was carried out based on a complex 3D model. The geometry of the model includes the entire Reactor Pressure Vessel (RPV) plus all relevant internals. The core is modelled using the porous body approach, the different pressure losses along and transverse to the main flow direction were considered. The spacer-grid levels were taken into account to the extent that in these areas no cross-flow is possible. The calculation was carried out for nominal operating conditions, i.e., for full load operation. Furthermore, a prototypical End of Cycle (EOC) power distribution was assumed. For this, a power distribution was applied as obtained from a stationary full-core calculation with the 3D neutron kinetics code DYN3D. In order to be able to adequately reproduce flow vortexes, the calculation was performed transiently with suitable Detached Eddy Simulations (DES) turbulence models. The calculation showed fluctuating transverse flow in the upper part of the core, starting at the 8th spacer grid but also revealed that no large dominant vortices exists in this region. It seems that the core acts as a rectifier attenuating large-scale vortices. The analyses included several spacer grid levels in the core and showed that in some areas of the core cross-section an upward increasingly directed transversal flow to the outlet nozzle occurs. In other areas of the core cross-section, on the other hand, there is nearly any cross-flow. However, the following limitations of the model apply: In the model all fuel elements are treated identical and cross flows due to different axial pressure losses for different FA types cannot be displayed. The complex structure of the FAs (eg. flow vanes in spacer grids) could also influence the formation of large-scale vortices. Also, the possible influence of two-phase flows was not considered. Full article

(This article belongs to the Special Issue Application of Computational Fluid Dynamics in Nuclear Reactor Safety Analysis)

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