Reduced order models (ROMs) have been regarded as an efficient alternative to conventional high-fidelity methods for accelerating the design and optimization processes in engineering applications. Many industrial facilities feature repeating geometrical patterns or contain subregions governed by distinct physical phenomena, making them well-suited to Domain Decomposition (DD) techniques. The integration of a ROM and DD is promising to further reduce computational costs by constructing local ROMs and assembling them into global solutions. Due to the complexity and necessity of coupling ROMs, many approaches have been proposed in recent years. This review provides a concise overview of existing methodologies combining ROMs and DD. We categorize existing methods into intrusive (projection-based) and non-intrusive (data-driven) frameworks. Various strategies for generating local reduced bases and coupling them across subdomains are illustrated. Particular emphasis is placed on intrusive techniques, including equations, numerical algorithms, and practical implementations. The non-intrusive framework is also discussed, highlighting its general procedures, basic formulations, and underlying principles. Finally, we summarize the state of the literature, identify open challenges, and present perspectives on future implementations from an engineering viewpoint.

Interface-resolved simulations are essential for predicting and understanding boiling heat transfer phenomena. Such simulations generally come at a high computational cost, which continues to motivate the development of efficient frameworks. In recent years, conservative second-order phase field methods have gained popularity due to their efficient representation of phase interfaces. However, their potential for simulating complex boiling phenomena has not yet been explored. To address this gap, we develop a consistent and highly efficient framework suitable for simulating large-scale boiling flows. We derive a set of mixture equations to describe the two-phase flow. The mixture equations are coupled with the accurate conservative diffuse interface method [1] to capture the interface. We present additional terms in the momentum balance equation and demonstrate that the proposed momentum balance modifications are mandatory for accurately capturing phase-change-induced pressure jumps. To solve the set of equations, an alternative Fast Fourier Transform (FFT)-based pressure solution scheme is proposed. Additionally, a modified kinetic phase change model is utilized that does not involve calculating temperature gradients and avoids problem-dependent parameters. The framework is tested against a variety of benchmark simulations, both with and without phase change. Moreover, we achieve improved accuracy when simulating bubble dynamics without phase change at high density ratios. We show that the proposed FFT-based pressure solution scheme exhibits superior performance in calculating interfacial pressure jumps compared with a commonly used FFT solver. Regardless of phase change, more accurate startup behaviour is observed. In the presence of phase change, we are successful in removing interfacial pressure oscillations. Across all phase-change benchmark simulations, the new phase change model consistently provides reliable results. Finally, we successfully simulate the dynamics of bubbles in superheated liquid subjected to gravity and validate the results with experimental data.

In this article, we study an update of the traditional subchannel approximation utilizing local reduced order bases. Through employing the symmetries and periodicity of a 7-pin bundle, the global domain is decomposed into numerous repeating subdomains following several dividing strategies. We locally study the reduced basis generated by proper orthogonal decomposition. We analyze the similarities, assessing the truncation error and the distance between the linear subspaces spanned by the reduced bases. We focus on the first stage of building a reduced order model, the generation of the reduced subspace, which is usually not regarded in detail in our application problem. Our assessment related to flow blockage in liquid metal-cooled nuclear reactors, a postulated high-risk accident that results in potential fuel damage.

The goal of the IAEA Coordinated Research Project “Benchmark of Transition from Forced to Natural Circulation Experiment with Heavy Liquid Metal Loop” (CRP—I31038) is to develop Member State advanced fast reactor analytical capabilities for simulation and design using system, CFD, and subchannel analysis codes. Here, CFD validation employing the commercial CFD code Star CCM + applied to the fuel pin simulator for forced and natural convection cases in the open phase is presented. Experimental data are provided in the benchmark specification provided by ENEA (Italian National Agency for New Technologies, Energy and Sustainable Economic Development) for the NACIE-UP facility (NAtural CIrculation Experiment-UPgrade). Considered is the fuel pin simulator with 19 pins, each consisting of a preheated lower section and heated upper sections, respectively. Three configurations: (i) all pins heated, (ii) inner 7 pins heated and (iii) asymmetric heating, are studied. For each heating configuration data for forced and natural convection are provided. Here, case (i) is studied. Temperatures at three planes are measured near the inlet, in the middle and near the end of the heated section, respectively. In addition, the axial temperature along the wall of one fuel pin simulator (in second row) is measured so that in total 67 thermocouples measure fluid and wall temperatures for validation purposes. The validation confirms that the thermohydraulic inside the fuel pin simulator can be simulated with a good accuracy. Applied is a polyhedral mesh with 2 prism layers, the k-omega SST model with all all-wall treatment and order unity y + values. Moreover, a grid-sensitivity, the importance of conjugate heat transfer inside the fuel pin simulators and the wrapper are studied. The studies indicate that it is possible to implement further simplifications without corrupting the accuracy of the simulation to reduce computational effort.

In this article, the uncertainty of a three-dimensional turbulent natural convection transient is quantified in a geometry representing an idealized spent fuel pool. The assessment is carried out through the creation of a surrogate fast model. This is build utilizing Proper Orthogonal Decomposition and Galerkin projection applied to a K-ϵ turbulent Navier–Stokes formulation. We discuss the uncertainties created by a uncertain heat release of the spent fuel elements. We consider the hypothesis of deviations that follow the normal distribution around a certain nominal value, with different standard deviations and sample size. The expected results and its uncertainty are henceforth computed by Monte–Carlo method, calculating hundreds of solutions of the Initial Value Problem with the surrogate model.

Thermal stratification in the upper plenum of the lead-cooled fast-reactor under SCRAM conditions can cause material fatigue and failure of elements critical for reactor safety. Adapting the reactor design to resist the thermohydraulic loads is an ongoing challenge addressed by a large range of experimental and numerical studies. A promising numerical approach for the efficient computation of the highly dynamic fluid behaviors in the complex geometry of the upper plenum is POD-ROM (Reduced-Order Modeling via Proper Orthogonal Decomposition). Therefore, calibration with a high-accurate solution showing the relevant physical effects is necessary. We present a spectral code capable of performing the calibration due to its high accuracy. The code which is based on the combination of Fourier and Chebyshev modes is applied to a 2D example system to show the ability for thermal stratification research. Verification is performed by computing Rayleigh–Bénard convection.

Important microfluidic phenomena, such as droplet deformation and cell motion, are impacted by the formation of Debye layers at charged interfaces. Previous studies examined interface problems with leaky dielectrics or the formation of diffuse charge layers. In most cases, the results are derived for weakly curved spherical geometries. Moreover, many studies of streaming-potential phenomena at fluid-solid interfaces lack a macroscale description of effects that are higher than first order. An asymptotic methodology capturing both complex surface geometries and an accurate description of higher-order phenomena is presented in this study. For this purpose, we consider a generic streaming-potential problem. As a result, the complex three-dimensional electrohydrodynamics in the Debye layer are entailed in two-dimensional discontinuity conditions. The latter contain a free parameter, the layer thickness, which mathematically represents the discontinuity position within the Debye layer. It can be used to derive an alternative definition of the Debye thickness capturing the influence of the ζ potential. We introduce a virtual particle whose outer boundary envelopes the solid particle plus a fraction of the Debye layer. It interacts with the macroscopic flow while incorporating the detailed electrohydrodynamics inside the layer.

A surrogate model of the Standard k-e turbulence model is created utilizing Proper Orthogonal Decomposition and Galerkin projection. This is a complex task, since the turbulence model equations exhibit multiple non-linearities. Those are treated using the Discrete Empirical Interpolation method. Nevertheless, the conventional utilization of such methodology is not possible, and a heuristic procedure has been developed to allow for its practical usage, dealing effectively with the rational functions involved in k - e model. Subsequently, the capabilities of the construct to reproduce the CFD calculation in nominal conditions are assessed. Results are studied, thoroughly checking the validity of the creation.

Fluid‐solid interfaces give rise to electro‐hydrodynamic effects at microscale. In a macroscale model, those effects can be represented by jump conditions. This report focuses on the derivation of such jump conditions for integral parameters, like mass flux, forces and charge fluxes. In particular, the effect of spatial and temporal variations in the ζ‐potential on the solid's surface are discussed, using the generic problem of a sedimenting particle.

In numerical simulations boundary layers can be treated as jump conditions inheriting detailed physical effects that emerge inside the thin layer. The presented approach, first applied by Class et al. [3], is used to determine such jump conditions in integral form. It is applied to an electro‐hydrodynamic problem with a Debye‐layer in direct vicinity to a charged solid wall.

The assessment of the inaccuracy and sensitivity of simulations of natural convection in pools is of the highest importance for the nuclear industry and concretely for the design of the 4th generation reactors. Therefore, in this article we qualify the uncertainty on the calculation of three dimensional spatio-temporal evolution of Rayleigh-Be?nard instability. This assessment is carried out through the creation of a surrogate?fast?model. The model is build utilizing Proper Orthogonal Decomposition and Galerkin projection. The most energetic modes are derived from a high fidelity CFD calculation. The governing equations are henceforth projected into the space generated. Once the model is available, we consider the uncertainties on the dimensionless numbers, Re, Pr, Ra. The expected result and its uncertainty are computed by Monte-Carlo method, calculating hundreds of solutions of the Initial Value Problem with the surrogate model. By this we have verified the applicability of the methodology to this kind of problems and the viability of the approach for uncertainty qualification.

The assessment of the inaccuracy and sensitivity of simulations of natural convection in pools is of the highest importance for the nuclear industry. Therefore, in this article we qualify the uncertainty on the calculation of three dimensional spatio-temporal evolution of Raileigh-Be`nard instability. This assessment is carried out through the creation of a surrogate fast model. The model is build utilizing Proper Orthogonal Decomposition and Galerkin projection. The Proper Orthogonal Decomposition allows finding the most energetic modes. Those are derived post-processing a high fidelity CFD calculation. Those modes constitute the vectors of a new, reduced, basis. In the Galerkin Projection the governing equations are written in this reduced basis. Once the model is available, we discuss the uncertainties on the determination of the amplitudes of each mode. Concretely, we consider the hypothesis of deviations that follow the normal distribution for each mode. This normal distribution is centered in the nominal value of the amplitude and have a standard deviation which amounts 5% of the amplitude. The expected results and its uncertainty are henceforth computed by Monte-Carlo method, calculating hundreds of solutions of the Initial Value Problem with the surrogate model.

Nuclear Power Plants (NPPs) containment study is an important part of nuclear safety analysis. With the aim of predicting the performance of hydrogen in the NPPs containment during severe accident, CFD codes are always applied as the analysis tools. With the development of computational capability, the researchers from both the academic side and industrial side try to re-study the existing simulation cases by using the refined mesh, as way to resolve more detailed information. During the pre-processing stage of CFD study, CAD is the necessary part providing geometric information on meshing. With recent development, CFD codes like GASFLOW-MPI can directly generate high resolution Cartesian mesh from CAD. However, there are still many experimental benchmarks and engineering applications where only paper-based blueprints are available for geometric information. Concerning the fact that no CAD models exist, lots of hand-based calculation and measurement need to be done by CFD analysts on geometry modeling. When some certain re-studies of the old simulation cases needed, the same work may have to be repeated multiple times, owing to the need of re-meshing in different sizes or local refinements. Therefore, a solution for reconstructing CAD from the mesh in the old simulation data is vital to improving the efficiency of CFD analysis. In this work, the reverse meshing technology with two kinds of smoothing processes, the Marching Cubes smoothing approach and Laplacian smoothing approach, are developed for CFD code GASFLOW-MPI to reconstruct the CAD geometry from the previous simulation data, which free engineers from the tedious and repetitive work on geometry construction. Three application cases are used to evaluate the performance of the two reverse meshing technologies. The results show that both reverse meshing technologies could recover the CAD geometry from Cartesian mesh of GASFLOW-MPI. Moreover, the Laplacian smoothing could fit the general surface in much smoother degree.

Hydrogen energy is one of the most promising candidates for clean and renewable energy in the coming future. Under the commission of safety study in hydrogen application, storage and transportation, CFD code analysis is always an important component in the engineering design workflow. Among the three stages of CFD analysis, the solver part has been well studied in the past two decades. However, the pre-processing and post-processing parts demand further study. The meshing process can be an important factor on the convergence speed and simulation reliability in hydrogen CFD study, which makes Cartesian mesh as an important choice in hydrogen safety codes However, traditional meshing process relies heavily on hand-based input card manipulation, which is inefficient and prone to human's improper manipulation. With the recent developments in codes like GASFLOW-MPI and FLACS, new functions have been added, which provide automatic mesh generation directly from the CAD geometry. In this work, the algorithm on automatic mesh generation will be further studied, which is more robust on the defective CAD geometries. In addition, application of the new evolving Virtual Reality technology will be implemented on the post-processing of the simulation result, which provides a better view in a real 3D environment. In the application part, three cases on a leaking hydrogen tank, a steam generator and a single car garage will be studied with regards to the validation of the new mesh generation approach. Finally, the Virtual Reality (VR) rendering performance will be studied based on the leaking hydrogen distribution in the single car garage. The work shows that the winding number based approach is an efficient and robust solution for the mesh generation of hydrogen CFD codes, and VR technology is a powerful tool for hydrogen safety simulation result rendering.

The assessment of the inaccuracy and sensitivity of simulations of natural convection in pools is of the highest importance for the nuclear industry and concretely for the design of the 4th generation reactors. Therefore, in this article we qualify the uncertainty on the calculation of three dimensional spatio-temporal evolution of Rayleigh-Bénard instability. This assessment is carried out through the creation of a surrogate–fast–model. The model is build utilizing Proper Orthogonal Decomposition and Galerkin projection. The most energetic modes are derived from a high fidelity CFD calculation. The governing equations are henceforth projected into the manifold generated considering the modes obtained as a new reduced basis. Once the model is available, we discuss the uncertainties on the determination of the amplitudes of each mode. Concretely, we consider the hypothesis of deviations that follow the normal distribution for each mode. This normal distribution is centered in the nominal value of the amplitude and have a standard deviation which amounts 5% of the amplitude. The expected results and its uncertainty are henceforth computed by Monte-Carlo method, calculating hundreds of solutions of the Initial Value Problem with the surrogate model.

Spent nuclear fuel elements contain a significant amount of fissile materials that gradually decompose generating heat and radiation. This decomposition occurs inside of deep water pools, where spent elements are cooled through natural convection. CFD calculation of all necessary cases is not feasible. Nevertheless, a light, fast and accurate model of this convection problem can be obtained utilizing Proper Orthogonal Decomposition (POD) and Galerkin Projection methods. Thus, we carry out our modeling as follows: i) Firstly, the high fidelity solver Star-CCM + is utilized to resolve the incompressible Boussinesq formulation of the pool. The results obtained constitute a set of solutions available at discrete times for each variable. ii) Subsequently, these solutions are utilized to build a special basis, which constitutes the POD. This is built considering an optimal linear combination of the solutions at different times. Notably, each reduced set of components of the basis allows for the reproduction of a maximum of the dynamics of the variables. iii) Thirdly, the system of equations is projected in this basis, Galerkin Projection. A Reduced Order Model (ROM) can be created using a small amount of the components, sufficient for the required accuracy. This simplified model is thus mathematically sound, and derived from first principles. Finally, the results of the model are compared with high fidelity solutions. The assessment includes the capabilities of the model to reproduce transients and to approach the final steady state. Additionally, we evaluate the performance of the MPI-parallelized software generated.

The Stochastic Field Method was originally derived in the field of combustion and firstly applied to a cavitation problem by our group [1]. Randomly distributed variables exist in both combustion and cavitating problems. Calculating strong nonlinear processes using mean values as input, leads to unphysical results. The consideration of the variable's probability density function (PDF) becomes mandatory. The Stochastic Field Method approximates this PDF by samples similar to methods of Lagrangian particles where imaginary particles are introduced to the flow. In contrast to Lagrangian particles methods, these samples are represented by Eulerian fields described by stochastic partial differential equations. This pure Eulerian interpretation makes the method attractive for CFD‐codes: A coupling of an Eulerian and a Lagrangian perspective becomes obsolete which results in efficient computation times ‐ especially in the presence of a vast number of bubbles. In contrast to other Eulerian methods, the calculation of an arbitrary PDF is possible at low computational cost. The representation of samples as fields allows the visualization of PDFs within every computational cell. The first implementation into a commercial CFD‐Code is presented. In addition, industrial examples, like cavitation in an automotive injection nozzle, are shown.