Casting computational fluid mechanics into a convex quadratic optimization framework

Many problems in Computational Electromagnetics (CEM) and Computational Fluid Dynamics (CFD) require millions of grid cells to properly represent the physics. Advances in parallel computing, both in hardware and software, make it feasible to solve such large scale simulations in a timely manner. The objective of this paper is to describe some of the recent work at Rockwell in performing parallel computing for providing quick-turnaround solutions to problems in CFD, CEM and other computational disciplines.

Indoor airflow field reconstruction using physics-informed neural network

The objective of this work is to gain the mechanical understanding of the water management in the proton exchange membrane fuel cell (PEMFC). Water is a by-product of the fuel cell reaction and its amount is proportion to the current of fuel cell output. Water is used to retain the proper hydration level in the PEM. At the same time, condensed water in the flowfield and the gas diffusion layer (GDL) reduces oxygen transport to the oxygen reduction reaction (ORR) area. Therefore, excess accumulation of condensed water causes to lower the performance, particularly at the higher current densities. Detailed simulation of two-phase water in the GDL is significantly important to understand the water management.This work shows the successful in development of a multi-scale calculation technique that incorporates various scales of numerical model in a fuel cell and simultaneously performed a prediction. The outcomes of this work are, (i) development of two-phase fluid model in the micro-scale porous structure of GDL, and (ii) integration of this micro-scale GDL fluid model with a state-of-the-art macro-scale flowfield fluid model to predict two-phase water in the fuel cell. Figure 1 gives the concept of modeling approach at each component of the fuel cell. The flowfield in the bipolar plate and MEA models are calculated using traditional computational fluid dynamics (CFD) method with existing PEMFC model [1-3]. The two-phase fluid in the micro-scale porous structure of GDL is numerically predicted by Lattice Boltzmann Method (LBM) [4-5]. The solution of each iteration from CFD and LBM are required to simultaneously exchange for the next iteration until all solutions are converged, especially at the interfaces. In this figure, it shows the flowfield is transformed into the macro-scale CFD model and the image of detail structured GDL is converted into micro-scale LBM model. Actual porous structure imaging of GDL is obtained by the nano-scale high special resolution x-ray computed tomography. Figure 2 shows an example of the predictions from the simulation when the macroscopic flowfield model is combined with the microscopic GDL model while performing the calculation. The predictions give the detail distributions of variables in every components of the multiscale model. In this figure, the current density distribution on MEA surface, the liquid water transport inside the GDL, and the temperature of solid and fluid phases inside the GDL are presented.

Physics-based computational models of the cardiovascular system are increasingly used to simulate hemodynamics, tissue mechanics, and physiology in evolving healthy and diseased states. While predictive models using computational fluid dynamics (CFD) originated primarily for use in surgical planning, their application now extends well beyond this purpose. In this review, we describe an increasingly wide range of modeling applications aimed at uncovering fundamental mechanisms of disease progression and development, performing model-guided design, and generating testable hypotheses to drive targeted experiments. Increasingly, models are incorporating multiple physical processes spanning a wide range of time and length scales in the heart and vasculature. With these expanded capabilities, clinical adoption of patient-specific modeling in congenital and acquired cardiovascular disease is also increasing, impacting clinical care and treatment decisions in complex congenital heart disease, coronary artery disease, vascular surgery, pulmonary artery disease, and medical device design. In support of these efforts, we discuss recent advances in modeling methodology, which are most impactful when driven by clinical needs. We describe pivotal recent developments in image processing, fluid-structure interaction, modeling under uncertainty, and reduced order modeling to enable simulations in clinically relevant timeframes. In all these areas, we argue that traditional CFD alone is insufficient to tackle increasingly complex clinical and biological problems across scales and systems. Rather, CFD should be coupled with appropriate multiscale biological, physical, and physiological models needed to produce comprehensive, impactful models of mechanobiological systems and complex clinical scenarios. With this perspective, we finally outline open problems and future challenges in the field.

Aerodynamic characteristics of a guided rocket projectile are numerically simulated. Simulations are performed in a range of flight conditions using a commercial CFD software FLUENT, and variations of lift coefficients and drag coefficients with Mach numbers and angles of attack were demonstrated. The numerical results also indicate that the angle of canard deflection has significant influence on the flow field near tailfins.

Distributed-parallel CFD computation for all fuel assemblies in PWR core

A hybrid numerical framework of potential and viscous flows for simulations of free running surface ship maneuvering in waves

<div class="section abstract"><div class="htmlview paragraph">The number of computational fluid dynamics (CFD) simulations performed during the vehicle aerodynamic development process continues to expand at a rapid rate. One key contributor to this trend is the number of analytically based designed experiments performed to support vehicle aerodynamic shape development. A second contributor is the number of aerodynamic optimization studies performed for vehicle exterior components such as mirrors, underbody shields, spoilers, etc. A third contributor is the increasing number of “what if” exploratory studies performed early in the design process when the design is relatively fluid. Licensing costs for commercial CFD solutions can become a significant constraint as the number of simulations expands. A number of alternative products (e.g., independently developed, supported and documented forks of the popular open-source OpenFOAM® toolbox [<span class="xref">1</span>]) have become available in recent years, offering a lower cost alternative to traditional commercial CFD products. This paper summarizes results from a broad and deep evaluation of the capability of iconCFD® to substitute for the more traditional commercial CFD solutions currently used to support vehicle aerodynamic development early in the program development cycle. Included in this study were detailed B-car, sedan, SUV and truck shapes as well as multiple variants of each shape. The study investigated both static and moving ground boundary conditions as well as alternative turbulence models. Trends of the predicted aerodynamic drag coefficients (<i>C<sub>d</sub></i>) are compared against experimental data. Both transient and steady state simulation ranking accuracy of total vehicle <i>C<sub>d</sub></i> were found to be equivalent to that historically observed with more traditional commercial solver results. A consistent upward bias in absolute <i>C<sub>d</sub></i> values was observed in the transient results.</div></div>

This research investigates the wake dynamics of low-Reynolds-number flow past a circular cylinder by combining high-fidelity Computational Fluid Dynamics simulations with modern data-driven analysis. The flow is simulated with the incompressible solver icoFoam in the OpenFOAM 11.0, faithfully capturing the laminar regime and its transition to unsteady vortex shedding at a Reynolds number of one hundred. These simulations provide a clear picture of wake development, the emergence of flow instabilities, and the onset of vortex shedding. Central to the study is Singular Value Decomposition, which decomposes the complex velocity field into its most energetic spatial structures. By retaining the dominant modes, Singular Value Decomposition reduces the dimensionality of the data while preserving essential flow characteristics. The velocity field reconstructed from these modes offers a compact yet accurate description of vortex formation, energy distribution, and the temporal evolution of shedding patterns. The synergy between traditional Computational Fluid Dynamics and contemporary machine-learning-inspired techniques yields a versatile and computationally efficient framework for exploring intricate fluid phenomena. Beyond accelerating calculations, this approach deepens our physical insight into the mechanisms that govern wake dynamics. By quantitatively predicting vortex-shedding onset and elucidating the underlying flow structures, the study delivers actionable knowledge for applications ranging from aerodynamic design to environmental flow management, where precise modeling of complex flow behavior is critical.

ABSTRACTA key problem in computational fluid dynamics (CFD) modelling of gravel‐bed rivers is the representation of multi‐scale roughness, which spans the range from grain size, through bedforms, to channel topography. These different elements of roughness do not clearly map onto a model mesh and use of simple grain‐scale roughness parameters may create numerical problems. This paper presents CFD simulations for three cases: a plane bed of fine gravel, a plane bed of fine gravel including large, widely‐spaced pebble clusters, and a plane gravel bed with smaller, more frequent, protruding elements. The plane bed of fine gravel is modelled using the conventional wall function approach. The plane bed of fine gravel including large, widely‐spaced pebble clusters is modelled using the wall function coupled with an explicit high‐resolution topographic representation of the pebble clusters. In these cases, the three‐dimensional Reynolds‐averaged continuity and Navier–Stokes equations are solved using the standard k − ε turbulence model, and model performance is assessed by comparing predicted results with experimental data. For gravel‐bed rivers in the field, it is generally impractical to map the bed topography in sufficient detail to enable the use of an explicit high‐resolution topography. Accordingly, an alternative model based on double‐averaging is developed. Here, the flow calculations are performed by solving the three‐dimensional double‐averaged continuity and Navier‐Stokes equations with the spatially‐averaged 〈k − ε〉 turbulence model. For the plane bed of fine gravel including large, widely‐spaced pebble clusters, the model performance is assessed by comparing the spatially‐averaged velocity with the experimental data. The case of a plane gravel bed with smaller, more frequent, protruding elements is represented by a series of idealized hypothetical cases. Here, the spatially‐averaged velocity and eddy viscosity are used to investigate the applicability of the model, compared with using the explicit high‐resolution topography. The results show the ability of the model to capture the spatially‐averaged flow field and, thus, illustrate its potential for representing flow processes in natural gravel‐bed rivers. Finally, practical data requirements for implementing such a model for a field example are given. Copyright © 2011 John Wiley & Sons, Ltd.

Research and development on digital twins of nuclear power systems has focused on high-precision real-time simulation and the prediction of local complex three-dimensional fluid dynamics. Traditional computational fluid dynamics (CFD) methods cannot take into consideration the efficiency and accuracy of fluid dynamics. In this study, a fast-flow field-prediction framework based on proper orthogonal decomposition (POD) and deep learning is proposed. Compressed data containing the original flow field information are obtained using POD and deep neural network (DNN) is used to construct the POD-DNN flow field reduction model to achieve fast flow field prediction. The calculation accuracy and speed of the reduced-order model are analyzed in detail, considering the flow field of the nuclear compressor and key flow equipment of the nuclear power system as objects. The results show that the average relative deviation of the POD-DNN is <10% and calculation time is <1% when compared to those of CFD. This research shows that the high-fidelity model constructed using model reduction and deep learning is a feasible method for the realization of digital twins of the nuclear power system in engineering.

This paper presents a novel approach to address computational challenges in predicting flow features by employing a Graph Neural Network (GNN), which is proficient in predicting flow domain values. Traditional Computational Fluid Dynamics (CFD) simulations, although effective, often require substantial computational resources and time, limiting their applicability in time-sensitive scenarios and optimization studies necessitating extensive case studies. The main objective was to evaluate the feasibility of employing node classification on a graph generated from a 2D baffle flow system to segment the domain based on relative fluid age. A second objective was to compare the computational time required for CFD simulations with the inference time of the network to quantify the efficiency gains achieved by utilizing the network. Results demonstrate the potential of utilizing graph convolutional networks for domain segmentation to predict regions of holdup and bypass. The GNN achieved 97% and 92% accuracy in predicting recirculation regions in single and double baffle cases, particularly excelling in high Reynolds number scenarios. Importantly, the proposed GNN-based approach reduces computation time by over 2100%, showcasing significant efficiency gains. Results here highlight the promise of employing graph convolutional networks for flow feature prediction, offering substantial computational efficiency improvements over traditional CFD simulations.

A supplemental main steam condenser cooling system is under development, which utilizes a phase change material (PCM). This PCM rejects heat to the cool atmosphere at night until it is fully frozen. The frozen PCM is available for condenser cooling during peak daytime electric demand. Three calcium chloride hexahydrate (CaCl2·6H2O)-based PCMs were selected for development after being characterized using differential scanning calorimetry (DSC). Additives to minimize supercooling and phase separation have demonstrated good performance after long and short-term thermal cycling. Corrosion testing under both isothermal and cycling conditions was conducted to determine long-term compatibility between several common metals and the selected PCMs. Several metals were demonstrated to have acceptably low corrosion rates for long-term operation, despite continual immersion in the selected hydrated salts. A system optimization model was developed, which utilizes a 3D modeling approach called the Layered Thermal Resistance (LTR) model. This model efficiently models the nonlinear, transient solidification process by applying analytic equations to layers of PCM. Good agreement was found between this model and more traditional computational fluid dynamics (CFD) modeling. Next phases of the work includes prototype testing and a techno-economic analysis of the technology.

Designing an excellent hull to reduce the sailing path energy consumption of UUVs is crucial for improving the energy endurance of UUVs. However, path energy consumption-based UUV hull design requires a tremendous amount of calculation due to the frequent changes in relative velocity and attack angle between a UUV and ocean current. In order to address this issue, this work developed a data-driven design methodology for energy consumption-based UUV hull design using artificial intelligence-aided design (AIAD). The design methodology in this work combined a deep learning (DL) algorithm that predicts UUVs’ resistance with different hull shapes under different velocities and attack angles with the particle swarm optimization (PSO) algorithm for UUV hull design. We tested the proposed methodology in a path energy consumption-based experiment, where the optimized UUV hull showed an 8.8% reduction in path energy consumption compared with the initial UUV hull, and design costs were greatly reduced compared with the traditional computational fluid dynamics (CFD)-based methodology. Our work demonstrates that AIAD has the potential to solve UUV design problems previously thought to be too complex by offering a data-driven engineering shape (body surface) design method.

As the preferred method for unmanned autonomous aerial refueling, soft aerial refueling technology has drawn the attention of scholars worldwide. Existing research mainly focuses on solving the problems related to the hose-drogue assembly or on vision-based drogue positioning and tracking. However, there is currently no precise and efficient docking model or strategy that can effectively guide the docking path of the receiver. Based on earlier research findings, this paper proposes a targeted-docking approach. It constructs a dataset using the bow wave model and the Kriging interpolation method. Leveraging the advantage of convolutional neural networks in extracting deep features from data, a targeted-docking model is established for the first time. Traditional computational fluid dynamics (CFD) simulations require extensive computation time about 2 days to solve the detailed flow field characteristics, but the targeted-docking model realized the prediction of the successful docking range under any steady-flow refueling condition within 10–15 s, meeting the key requirements of the aerial refueling mission. Subsequently, by comparing with the original data obtained from CFD simulations, the accuracy and practicality of the model are verified. Finally, the Sobol method is adopted to conduct a sensitivity analysis of variables under different refueling conditions, identifying the parameters that significantly influence the refueling success rate. This result enhances the interpretability of the model and provides theoretical guidance for the design of docking schemes for unmanned autonomous refueling.