High-fidelity Numerical Simulations Research Articles

A comprehensive framework to enhance numerical simulations in the spectral-element code Nek5000

A framework is presented for the spectral-element code Nek5000, which has been, and still is, widely used in the computational fluid dynamics (CFD) community to perform high-fidelity numerical simulations of transitional and high Reynolds number flows. Despite the widespread usage, there is a deficiency in having a comprehensive set of tools specifically designed for conducting simulations using Nek5000. To address this issue, we have created a unique framework that allows, inter alia, to perform stability analysis and compute statistics of a turbulent flow. The framework encapsulates modules that provide tools, run-time parameters and memory structures, defining interfaces and performing different tasks. First, the framework architecture is described, showing its non-intrusive approach. Then, the modules are presented, explaining the main tools that have been implemented and describing some of the test cases. The code is open-source and available online, with proper documentation, to-run instructions and related examples.

A generalized curvilinear solver for spherical shell Rayleigh-Bénard convection

Summary A three-dimensional finite-difference solver has been developed and implemented for Boussinesq convection in a spherical shell. The solver transforms any complex curvilinear domain into an equivalent Cartesian domain using Jacobi transformation and solves the governing equations in the latter. This feature enables the solver to account for the effects of the non-spherical shape of the convective regions of planets and stars. Apart from parallelization using MPI, implicit treatment of the viscous terms using a pipeline alternating direction implicit scheme and HYPRE multigrid accelerator for pressure correction makes the solver efficient for high-fidelity direct numerical simulations. We have performed simulations of Rayleigh-Bénard convection at two Rayleigh numbers Ra = 105 and 107 while keeping the Prandtl number fixed at unity (Pr = 1). The average radial temperature profile and the Nusselt number match very well, both qualitatively and quantitatively, with the existing literature. Closure of the turbulent kinetic energy budget, apart from the relative magnitude of the grid spacing compared to the local Kolmogorov scales, ensures sufficient spatial resolution.

High-fidelity flexible multibody model considering torsional deformation for nonequatorial space elevator

Space elevators are a promising technology for future space transportation. The primary component of a space elevator is a tether deployed from a geostationary orbit towards the Earth and into deep space. Payloads can be transported using a climber moving along the tether. However, obtaining a deeper comprehension of the precise dynamics of a space elevator is challenging. The tether could have various deformations such as elongation, bending, and torsion owing to its flexible nature and the low level of vibration damping in space. Therefore, understanding those effects on the tether is essential for the design concept of a space elevator. Reproducing the behavior of space tether systems on the ground is challenging, which is primarily due to the scale of the system and the difficulty of accurately replicating a space environment. Thus, high-fidelity numerical analysis methods are required to analyze the dynamic response of space elevators precisely. Previously proposed analysis models of space tether systems with climbers have focused on elongation, bending, and rigid body motion of the tether, and the effect of torsional deformation has been neglected. However, a tether can be twisted easily owing to its low torsional stiffness. This study established high-fidelity numerical simulation models for space elevators considering large deformations including the torsion of a tether. This study developed a flexible multibody model with a moving climber using the absolute nodal coordinate formulation with 14 degrees of freedom. Further, the gravitational perturbation caused by the non-sphericity of the Earth was considered. Using the constructed model, the motion and deformation of nonequatorial space elevators caused by the climber motion and the disturbance in the space environment were investigated. The obtained results indicate that gravitational perturbation can induce torsional deformation, particularly at higher anchor latitudes.

Aerodynamic and acoustic study of a small scale lightly loaded hovering rotor using large eddy simulation

The aerodynamics and acoustics of a small-scale lightly loaded hovering rotor operating at low Reynolds number is investigated using high-fidelity numerical simulation. A canonical geometry is considered, which allows for different flow topologies typical of transitional flows to develop along the span. Specifically, regions with laminar attached flow, trailing edge laminar separation with prominently 2D structures, and successive laminar separation, transition and reattachment with prominently 3D structures are identified. Furthermore, the lightly loaded configuration is conducive to significant blade-wake interaction, that in turn affects the dynamics of the boundary layer. The acoustic footprint of these phenomena is analyzed by correlating pressure fluctuations in the flow to those at the blade surface. It is found that the radiated noise is characterized by tonal peaks at the blade passing frequency and harmonics, and by a broadband hump at higher frequencies, consistent with experimental observations. The broadband hump exhibits distinct peaks that are found to originate from the separated shear layers on both pressure and suction sides. In particular, two noise generation mechanisms arising at two different frequencies in the broadband hump are identified. One is due to the interaction between an instability transported in the tip vortex of one blade and the leading edge of the following blade, and another one is found to rely on the interaction between an instability transported in the tip vortex and in the wake of one blade scattered by the trailing edge of the following blade.

Extreme wave impacts on a suspended box above free surface

A systematic approach incorporating precision-controlled experiments and high-fidelity numerical simulations has been employed to delve deeper into the physics of extreme wave impact pressures. Using a suite of high-speed imaging and high-resolution pressure sensing techniques that are accurately synchronized with the wave generation, a consistent and well-correlated set of data providing details of the focusing incident wave front, flow velocities, and impact pressure time histories has been successfully obtained. The numerical simulations using a validated incompressible smoothed particle hydrodynamics (ISPH) provided further details that were not tractable in the experiments. Based on the results obtained, there were five broad impact scenarios identified, ranging from focusing crest impacts to plunging jet impacts with varying entrapped air. Among these impact types, the highest impact pressures were those associated with a focusing wave crest. It has been found that high impact pressures were correlated with a convergence of the horizontally impinging overturning crest and the vertical surge of the wall boundary water mass, but with the overturning crest impingement just ahead of the arrival of the wall boundary water mass, which in essence amounted to the impingement of a focusing wave front. Depending on the relative arrival times of the impinging crest and the wall boundary upsurge, the impact scenarios could vary from an up-slosh to a jet impingement with a clear entrapped air pocket, followed by a flip-through of the incident crest. For the scenario with the highest impact pressures, broadly classified as type II impact in this paper, the peak pressures could reach as high as 85ρC2, an order of magnitude higher than impact scenarios without the focusing effect, such as the scenario with a plunging jet impact with entrapped air (classified as types III and IV impact in this study). As the volume of entrapped air for this scenario was relatively small, the one-phase ISPH model used in this study was able to capture the peak pressure characteristics, including the peak pressure amplitudes. However, in scenarios with significantly highly entrapped air during impact, a two-phase model would be necessary.

Physics-informed data-driven unsteady Reynolds-averaged Navier–Stokes turbulence modeling for particle-laden jet flows

With the assistance of deep learning (DL), we present a framework for predicting the turbulent eddy viscosity in unsteady Reynolds-averaged Navier–Stokes (URANS) simulations for particle-laden jet flows. We report a complete workflow from identifying the input flow and particle quantities in the training phase to predicting the flow and particle fields in the testing phase. The framework incorporates a deep neural network model, also known as multi-layer perceptrons, into the momentum equations of the Euler–Lagrangian gas–solid flow system. A data-driven, physics-informed DL approach was employed to predict the modeled turbulent eddy viscosity field, formulated as a function of the instantaneous flow and particle quantities. In the training phase, these regression functions were trained with an existing high-fidelity direct numerical simulation database. In the testing phase, the trained model was then used to predict the instantaneous local eddy viscosity to update the closure term and to solve the URANS equations iteratively. A series of round, turbulent particle-laden jets in a co-flow with various Stokes numbers were assessed, including those beyond the range of conditions employed for training. The proposed DL–URANS model was found to provide enhanced accuracy for predicting both flow and particle quantities when compared with the baseline URANS simulation.

Empirical loss weight optimization for PINN modeling laser bio-effects on human skin for the 1D heat equation

The application of deep neural networks towards solving problems in science and engineering has demonstrated encouraging results with the recent formulation of physics-informed neural networks (PINNs). Through the development of refined machine learning techniques, the high computational cost of obtaining numerical solutions for partial differential equations governing complicated physical systems can be mitigated. However, solutions are not guaranteed to be unique, and are subject to uncertainty caused by the choice of network model parameters. For critical systems with significant consequences for errors, assessing and quantifying this model uncertainty is essential. In this paper, an application of PINN for laser bio-effects with limited training data is provided for uncertainty quantification analysis. Additionally, an efficacy study is performed to investigate the impact of the relative weights of the loss components of the PINN and how the uncertainty in the predictions depends on these weights. Network ensembles are constructed to empirically investigate the diversity of solutions across an extensive sweep of hyper-parameters to determine the model that consistently reproduces a high-fidelity numerical simulation.

Simulation of bubble oscillations in cavitation-induced acoustic fields

Understanding bubble oscillations is critical in science, engineering and medicine. An important aspect of bubble dynamics is the transition from spherical to non-spherical oscillations when the bubble is subjected to external stimuli like time-dependent pressure fields. The mechanisms underpinning this process are not well understood for the complex pressure fields encountered in most applications. Here, we perform high-fidelity numerical simulations of the oscillations of a non-condensable gas bubble induced by the acoustic field generated by the collapse of a nearby cavitation bubble. We compare our simulation results with controlled laboratory experiments and demonstrate that our computational approach predicts spatial and temporal bubble oscillation patterns. This work opens new opportunities to understand the oscillation of bubbles induced by complex acoustic fields.

The volume of healthy red blood cells is optimal for advective oxygen transport in arterioles

Red blood cells (RBCs) are vital for transporting oxygen from the lungs to the body’s tissues through the intricate circulatory system. They achieve this by binding and releasing oxygen molecules to the abundant hemoglobin within their cytosol. The volume of RBCs affects the amount of oxygen they can carry, yet whether this volume is optimal for transporting oxygen through the circulatory system remains an open question. This study explores, through high-fidelity numerical simulations, the impact of RBC volume on advective oxygen transport efficiency through arterioles, which form the area of greatest flow resistance in the circulatory system. The results show that, strikingly, RBCs with volumes similar to those found in vivo are most efficient to transport oxygen through arterioles. The flow resistance is related to the cell-free layer thickness, which is influenced by the shape and the motion of the RBCs: at low volumes, RBCs deform and fold, while at high volumes, RBCs collide and follow more diffuse trajectories. In contrast, RBCs with a healthy volume maximize the cell-free layer thickness, resulting in a more efficient advective transport of oxygen.

A novel data-driven reduced order modelling methodology for simulation of humid blowout in wet combustion applications

Computationally inexpensive reduced order models such as Chemical Reactor Networks (CRN) are encouraging tools to obtain fast numerical solutions. However, the accuracy of such models is usually compromised compared to experiments or high-fidelity numerical simulations. Therefore, continued improvement of such models is necessary to ensure reasonable accuracy and fill the need for computationally inexpensive tools. To that end, inputs from computational fluid dynamics simulations have been used to build CRNs in the last 25 years. This can be further improved by the application of data-driven techniques. The present work uses a novel data-driven analysis based on high-fidelity simulation results where the high-dimensional data is first reduced to a low-dimensional manifold and is then clustered into chemically coherent regions. These results along with the high-fidelity simulation results are used to construct a CRN for wet combustion simulations. Wet combustion is a novel clean combustion technique, where an increase in the level of steam dilution distributes the flame, with a risk for flame extinction. This phenomenon, i.e., humid blowout (HBO), was modelled using the above-mentioned CRN. The HBO predicted by the CRN was also tested for thermal power, equivalence ratio, and fuel conditions different from its design point. The error in HBO prediction was quantified by comparing the steam-dilution level at HBO obtained using CRN and that obtained experimentally. The CRN predicted the HBO with an error magnitude less than 5% when the thermal power was unchanged. The maximum error in all tested conditions was 16.65%. Furthermore, a sensitivity analysis revealed that the inclusion of hot gas recirculation through the central recirculation zone, quantified by the mass flow split between the post-flame region and the CRZ, is important in the prediction of HBO, although its accuracy is inconsequential.

Drag coefficient for micron-sized particle in high-speed flows

The drag force on the small particle in high-speed flows is influenced by the combined effects of fluid viscosity, compressibility, and rarefaction. The existing drag coefficient models are still insufficient in accuracy and efficiency for gas-particle flow simulation. This study comprehensively considers these effects and conducts high-fidelity numerical simulations. A new drag coefficient is generated using a symbolic regression method reasonably based on the particle Mach number, Reynolds number, and Knudsen number, which are related to particle diameter, gas-particle relative velocity, and other parameters. The new drag coefficient possesses clear physical significance, high predictive accuracy, low computational cost, and consistency with theory in limiting conditions. The application of the new drag coefficient to three typical gas-solid two-phase flow cases demonstrated its excellent performance.

Simulation of nuclear fuel clad high-temperature ballooning under loss-of-coolant accident conditions considering anisotropic creep

Zirconium (Zr) alloys are standard clad material in commercial light water reactors. However, it is vulnerable to ballooning and burst under high-temperature conditions such as LOCA (Loss-Of-Coolant Accident), due to large internal/external pressure difference. Considering that clad ballooning is detrimental in terms of nuclear reactor safety especially for high-burnup fuel rod, high-fidelity numerical simulation of Zircaloy clad ballooning is desirable. This paper presented a finite-element based implementation for the simulation of Zircaloy clad ballooning. The developed simulation capability predicts progressive clad ballooning up to failure given empirical burst limits. The material models coupled together are phase transformation and high-temperature creep. Especially, anisotropic creep was considered for α phase Zircaloy. The implemented algorithm for stress update is implicit in time integration, which allows relatively large time step size to efficiently simulate the process that can last for hundreds of seconds. An analytic benchmark, the PUZRY ballooning and burst test, and the Hardy stress-rupture test were utilized to verify and validate the simulation capability. The anisotropic creep calculation conforms to the analytical solution. The comparison with PUZRY and Hardy test data shows that considering anisotropic creep in the α phase region is essential. 3D ballooning was also simulated by considering circumferential temperature difference for both conventional and novel annular clad designs. Interestingly, it is the first time to note that the risk of buckling failure is predicted for the double-cooled annular nuclear fuel clad during the accident condition, only after considering the anisotropic creep algorithm.

Revisiting the modelling framework for the unresolved scalar variance

The unresolved scalar variance in large-eddy simulations of turbulent flows is a fundamental physical and modelling parameter. Despite its importance, relatively few algebraic models have been developed for this important variable with the most prominent models to date being the classic scale-similarity and gradient models. In this work a new generalized modelling framework based on reconstruction has been developed, which in contrast to classic modelling approaches allows the construction of base static variance models of arbitrary accuracy. It is demonstrated that higher-order reconstructions naturally lead to base static variance models of increased accuracy, and that the classic scale-similarity and gradient models are subsets of more general and higher-order models. The classic scale-similarity assumption for developing dynamic models is also revisited, and it is demonstrated that this can essentially be reinterpreted as a two-level reconstruction approach. Based on this result, a new general methodology is proposed that allows the construction of dynamic models for any given base static model, and a corresponding general reconstruction operator, algebraic or iterative. Consequently, improved static and dynamic models for the scalar variance are developed. The newly developed models are then thoroughly tested a priori using two high-fidelity direct numerical simulation databases corresponding to two substantially different flame and flow configurations, and are shown to outperform classic algebraic models for the variance.

Sensitivity analysis of wall-modeled large-eddy simulation for separated turbulent flow

In this study, we conduct a parametric analysis to evaluate the sensitivities of wall-modeled large-eddy simulation (LES) with respect to subgrid-scale (SGS) models, mesh resolution, wall boundary conditions and mesh anisotropy. While such investigations have been conducted for attached/flat-plate flow configurations, systematic studies specifically targeting turbulent flows with separation are notably sparse. To bridge this gap, our study focuses on the flow over a two-dimensional Gaussian-shaped bump at a moderately high Reynolds number, which involves smooth-body separation of a turbulent boundary layer under pressure-gradient and surface-curvature effects. In the simulations, the no-slip condition at the wall is replaced by three different forms of boundary condition based on the thin boundary layer equations and the mean wall-shear stress from high-fidelity numerical simulation to avoid the additional complexity of modeling the wall-shear stress. Various statistics, including the mean separation bubble size, mean velocity profile, and dissipation from SGS model, are compared and analyzed. The results reveal that capturing the separation bubble strongly depends on the choice of SGS model. While simulations approach grid convergence with resolutions nearing those of wall-resolved LES meshes, above this limit, the LES predictions exhibit intricate sensitivities to mesh resolution. Furthermore, both wall boundary conditions and the anisotropy of mesh cells exert discernible impacts on the turbulent flow predictions, yet the magnitudes of these impacts vary based on the specific SGS model chosen for the simulation.

A LAPACK Implementation of the Dynamic Mode Decomposition

The Dynamic Mode Decomposition (DMD) is a method for computational analysis of nonlinear dynamical systems in data driven scenarios. Based on high fidelity numerical simulations or experimental data, the DMD can be used to reveal the latent structures in the dynamics or as a forecasting or a model order reduction tool. The theoretical underpinning of the DMD is the Koopman operator on a Hilbert space of observables of the dynamics under study. This paper describes a numerically robust and versatile variant of the DMD and its implementation using the state-of-the-art dense numerical linear algebra software package LAPACK . The features of the proposed software solution include residual bounds for the computed eigenpairs of the DMD matrix, eigenvectors refinements and computation of the eigenvectors of the Exact DMD, compressed DMD for efficient analysis of high dimensional problems that can be easily adapted for fast updates in a streaming DMD. Numerical analysis is the bedrock of numerical robustness and reliability of the software, that is tested following the highest standards and practices of LAPACK . Important numerical topics are discussed in detail and illustrated using numerous numerical examples.

Turbulent wake characteristics for a circular cylinder in proximity to a moving wall

This study investigates the scenario of flow past a circular cylinder in proximity to a moving wall (or equally a body translating in still fluid parallel to a stationary wall). Fifty high-fidelity three-dimensional direct numerical simulations are performed over a parameter space of turbulent Reynolds numbers (Re) of 300 to 1000 combined with gap-to-diameter ratios (G/D) of 0.2 to 3. The flow, hydrodynamic and turbulence characteristics over the (Re, G/D) parameter space are examined in detail. Small-scale rib-like mode B structures and alternate vortex shedding are observed for all cases. The streamwise location for the vortex shedding (quantified by the wake recirculation length Lr) varies strongly with both Re and G/D. The variation of Lr with Re and G/D can be explained by the spanwise circulation $\varGamma_z$ fed into the wake, where the variation trends of Lr and $\varGamma_z$ are inversely correlated. The variations of the mean drag and fluctuating lift coefficients are also governed by the variations in Lr and $\varGamma_z$ . The total kinetic energy in the wake region reduces drastically as G/D reduces below 0.8, which is contributed collectively by (i) reduction in the strength of the shed vortices, (ii) downstream movement of the location of vortex shedding and (iii) associated delayed generation of streamwise vortices. The present results on a moving wall also help to explain several flow and hydrodynamic characteristics reported in the literature for a stationary wall, because the moving wall eliminates the complex wall boundary layer and retains a ‘clean’ near-wall effect.

The breakup and instability structures of liquid jets in subsonic crossflows

The breakup of water and Jet A fuel jets injected transverse into elevated temperature (up to 425 °C), combustion pre-heated, subsonic crossflows was investigated by internally fluorescing the liquid jet column. The fluorescent dye seeded test liquids were illuminated by a pulsed laser light that was transmitted within the injector using a quartz rod light-guide. High-resolution images isolating the intact liquid column from light scattered by the surrounding dense spray facilitated precise measurement of the liquid column breakup position and the size and distribution of windward column instability waves. The injector geometry consisted of a 1 mm circular orifice with an orifice length of 20 mm with a tapered inlet. Liquid jet to gaseous crossflow momentum flux ratios were varied from 6 to 266 and the gas Weber number was varied from 10.7 to 228. Empirical correlations were derived for the liquid column breakup coordinates and breakup time in addition to the average and local maximum instability wavelength and amplitude on the liquid column windward surface. The reported correlations provided key insight into atomization physics and aim to support the quantitative validation of high-fidelity numerical simulations of the liquid jet in subsonic crossflow.

A two-field formulation for surfactant transport within the algebraic volume of fluid method

Surfactant transport plays an important role in many technical processes and industrial applications such as chemical reactors, microfluidics, printing and coating technology. High fidelity numerical simulations of two-phase flow phenomena reveal rich insights into the flow dynamics, heat, mass and species transport. In the present study, a two-field formulation for surfactant transport within the algebraic volume of fluid method is presented. The slight diffuse nature of representing the interface in the algebraic volume of fluid method is utilized to track the concentration of surfactant at the interface as a volumetric concentration. Transport of insoluble and soluble surfactants is investigated by tracking two different concentrations of the surfactant, one within the bulk of the liquid and the other one at the interface. These two transport equations are in turn coupled by source terms considering the ad-/desorption processes at a liquid–gas interface. Appropriate boundary conditions at a solid–fluid interface are formulated to ensure surfactant conservation, while also enabling to study the ad-/desorption processes at a solid–fluid interface. The developed numerical method is verified by comparing the numerical simulations with well-known analytical and numerical reference solutions and applied to a surfactant-laden drop in shear flow. The presented numerical methodology offers a seamless integration of surfactant transport into the algebraic volume of fluid method, where the latter has many advantages such as volume conservation and an inherent ability of handling large interface deformations and topological changes.

Vertical-axis turbine performance enhancement with physics-informed blade pitch control. Basic principles and proof of concept with high-fidelity numerical simulation

In this study, we developed active physics-informed turbine blade pitch control methods to conquer the inconsistent energy harvesting efficiency challenges encountered by the vertical-axis turbines (VATs) technology. Specifically, individual turbine blades were pitched by actuators following commands from the physics-informed controllers, and the turbine performance improvements as a result of the blade pitch control mechanism and the associated flow physics were studied. The aim of the blade pitch control was to maintain constant effective angles of attack (AoAs) experienced by turbine blades through active blade pitch, and the constant AoA function was designed to facilitate control mechanism implementation into real-world VATs. To gain in-depth understanding of the capability of the control, flow physics was studied for different constant AoA control strategies across a wide range of tip speed ratios and wind speeds and was compared with that from the corresponding baselines without control, and that from the sinusoidal AoA control strategy. The comparison between the turbine performance with constant AoA control and that without control showed a consistent increase in the time-averaged net power coefficient, a measure of energy harvesting efficiency taking out of the actuator loss, ranging from 27.4% to 704.0% across a wide spread of wind speeds. The superior turbine performance with constant AoA control was largely attributed to blade dynamic stall management during the blade upstream and downstream cycles and the transition between the two cycles.

Aerodynamic performance increase over an A320 morphing wing in transonic regime by numerical simulation at high Reynolds number

Purpose This study aims to investigate the morphing concepts able to manipulate the dynamics of the downstream unsteadiness in the separated shear layers and, in the wake, be able to modify the upstream shock–boundary layer interaction (SBLI) around an A320 morphing prototype to control these instabilities, with emphasis to the attenuation or even suppression of the transonic buffet. The modification of the aerodynamic performances according to a large parametric study carried out at Reynolds number of 4.5 × 106, Mach number of 0.78 and various angles of attack in the range of (0, 2.4)° according to two morphing concepts (travelling waves and trailing edge vibration) are discussed, and the final benefits in aerodynamic performance increase are evaluated. Design/methodology/approach This article examines through high fidelity (Hi-Fi) numerical simulation the effects of the trailing edge (TE) actuation and of travelling waves along a specific area of the suction side starting from practically the most downstream position of the shock wave motion according to the buffet and extending up to nearly the TE. The present paper studies through spectral analysis the coherent structures development in the near wake and the comparison of the aerodynamic forces to the non-actuated case. Thus, the physical mechanisms of the morphing leading to the increase of the lift-to-drag ratio and the drag and noise sources reduction are identified. Findings This study investigates the influence of shear-layer and near-wake vortices on the SBLI around an A320 aerofoil and attenuation of the related instabilities thanks to novel morphing: travelling waves generated along the suction side and trailing-edge vibration. A drag reduction of 14% and a lift-to-drag increase in the order of 8% are obtained. The morphing has shown a lift increase in the range of (1.8, 2.5)% for angle of attack of 1.8° and 2.4°, where a significant lift increase of 7.7% is obtained for the angle of incidence of 0° with a drag reduction of 3.66% yielding an aerodynamic efficiency of 11.8%. Originality/value This paper presents results of morphing A320 aerofoil, with a chord of 70cm and subjected to two actuation kinds, original in the state of the art at M = 0.78 and Re = 4.5 million. These Hi-Fi simulations are rather rare; a majority of existing ones concern smaller dimensions. This study showed for the first time a modified buffet mode, displaying periodic high-lift “plateaus” interspersed by shorter lift-decrease intervals. Through trailing-edge vibration, this pattern is modified towards a sinusoidal-like buffet, with a considerable amplitude decrease. Lock-in of buffet frequency to the actuation is obtained, leading to this amplitude reduction and a drastic aerodynamic performance increase.