Turbulent Case Research Articles

Freestream and shear layer effects in bluff-body-stabilized turbulent premixed flames

The effects of low and high approach flow turbulence levels on a large-scale, confined, premixed bluff-body-stabilized flame are experimentally characterized. The flame and flow are imaged using simultaneous 10-kHz-rate formaldehyde (CH2O) planar laser-induced fluorescence (PLIF), hydroxyl (OH) PLIF, particle image velocimetry (PIV), and OH* chemiluminescence. Elevated approach flow turbulence intensities of 16 % as compared to a lower value of 3 % affects the global and local flame and flow. The elevated approach flow turbulence results in a 22 % reduction in the length of the recirculation zone, despite the mean flame and mean shear layer locations being similar for both approach flow turbulence levels. Increasing the approach flow turbulence intensity does not lead to the mean flame position moving further into the reactant freestream. Both approach flow turbulence levels result in a similar growth of the flame brush thickness moving downstream until approximately 1.5 bluff-body widths, after which the flame brush for the low and high approach flow turbulence case stops growing and continues to linearly increase, respectively. This study describes the mechanisms by which high approach flow turbulence affects the global and local flame and emphasizes that the turbulent flame characteristics are influenced not only by the freestream approach flow turbulence but also by the bluff-body shear layers, recirculation zone, and wake.

Numerical Investigations of Outer-Layer Turbulent Boundary Layer Control for Drag Reduction Through Micro Fluidic-Jet Actuators

Drag reduction through turbulent boundary layer control (TBLC) is an essential way to develop green aviation technologies. Compared with traditional approaches for drag reduction, turbulence drag reduction is a relatively new technology, particularly for skin friction drag reduction, and it is becoming a hotspot problem worldwide. This paper focuses on the research of micro fluidic-jet actuators used for outer-layer boundary layer control with high-performance computing (HPC). This study aims to reduce turbulent drag by reshaping the flow structure within the turbulent boundary layer. To ensure the calculation accuracy of the core region and reduce the consumption of computing resources, a zonal LES/RANS strategy and WMLES method are proposed to simulate the effects of fluidic-actuators for outer-layer boundary control, in which high-performance computing has to be involved. The studies are performed on the classical zero-gradient turbulent flat plate cases, in which three different control strategies named “W-control,” “V-control,” and “VW-control” are used and compared to study the effects of drag reduction under a low Reynolds number at Reτ = 470 and a higher Reynolds number at Reτ = 4700. The mechanism for drag reduction is analysed via a pre-multiplied spectral method and a parallel dynamic mode decomposition (DMD) method. The results show that the present approach can effectively simulate the outer-layer turbulent boundary control where the “V-control” with the fluidic-jet actuator array behaves well to achieve an average drag reduction (DR) rate of more than 5% for the high Reynolds number case of the flat plate boundary layer. The high Reynolds shear stress and turbulent kinetic energy distribution in the boundary layer region show an obvious uplift under the effects of actuators, which is the main mechanism for drag reduction.

The Statistical Mechanics of Ideal Magnetohydrodynamic Turbulence and a Solution of the Dynamo Problem

We review and extend the theory of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence. The theory contains a solution to the ‘dynamo problem’, i.e., the problem of determining how a planetary or stellar body produces a global dipole magnetic field. We extend the theory to the case of ideal MHD turbulence with a mean magnetic field that is aligned with a rotation axis. The existing theory is also extended by developing the thermodynamics of ideal MHD turbulence based on entropy. A mathematical model is created by Fourier transforming the MHD equations and dynamical variables, resulting in a dynamical system consisting of the independent Fourier coefficients of the velocity and magnetic fields. This dynamical system has a large but finite-dimensional phase space in which the phase flow is divergenceless in the ideal case. There may be several constants of the motion, in addition to energy, which depend on the presence, or lack thereof, of a mean magnetic field or system rotation or both imposed on the magnetofluid; this leads to five different cases of MHD turbulence that must be considered. The constants of the motion (ideal invariants)—the most important being energy and magnetic helicity—are used to construct canonical probability densities and partition functions that enable ensemble predictions to be made. These predictions are compared with time averages from numerical simulations to test whether or not the system is ergodic. In the cases most pertinent to planets and stars, nonergodicity is observed at the largest length-scales and occurs when the components of the dipole field become quasi-stationary and dipole energy is directly proportional to magnetic helicity. This nonergodicity is evident in the thermodynamics, while dipole alignment with a rotation axis may be seen as the result of dynamical symmetry breaking, i.e., ‘broken ergodicity’. The relevance of ideal theoretical results to real (forced, dissipative) MHD turbulence is shown through numerical simulation. Again, an important result is a statistical solution of the ‘dynamo problem’.

Analysis of vortex structure, temperature distribution, and near-wall flow development for an inclined jet interacting with crossflow of different boundary layer conditions

In modern gas turbines, film cooling confronts complex near-wall flow conditions. Because of the low velocity ratio and the inclined injection in film cooling, the jet is more attached to the wall, making the influence of the local boundary layer critical. This paper investigates the interaction between the inclined jet and the mainstream boundary layer using large eddy simulation (LES). Four inflow boundary layer conditions were investigated, including a thin laminar case (δ/D = 0.5) and three turbulent cases with different thicknesses (δ/D = 0.5, 1.0, and 2.0). The jet velocity ratios are 0.23, 0.46, and 0.91 for each inflow condition. To consistently extract vortices of varying intensities, a local threshold was proposed using λci criterion. Based on the extracted vortices, a comprehensive analysis of the vortical strength, size, and position for horseshoe vortex (HSV), counter-rotating vortex pair (CRVP), and shear layer vortices (SLV) is performed under different inflow conditions. The results provide a clear picture of how HSV and CRVP form and evolve. Quantitative patterns are disclosed for the vortex lifting and vortical decay. Moreover, the thermal transport effects of HSV, CRVP, and SLV are examined. It was proven that these vortices dominate the coolant coverage, coolant core lifting, and thermal diffusion, respectively. Meanwhile, the jet has a significant impact on the near-wall flow development. The length of transition and the magnitude of thickening were discovered to be correlated with the jet velocity ratio and inflow thickness. Overall, these findings present a fresh perspective in understanding the flow and heat transport processes for inclined jet-in-crossflow.

Trailing-edge far-field noise and noise source characterization in high inflow turbulence conditions.

Airframe noise currently is a bottle neck in various applications, e.g., wind energy, maritime applications, and aircraft. Airframe noise is significantly increased by the presence of inflow turbulence. High inflow turbulence influences the boundary layer and wall-pressure fluctuations close to the trailing edge of airfoils. In this research, measurements of boundary layer and wall-pressure fluctuations near the trailing edge of an airfoil are conducted to investigate how the inflow turbulence affects the trailing-edge noise generation mechanism. Far-field noise measurements of additional three airfoils are shown to understand the role of the airfoil geometry in the dominant noise source for the cases of inflow turbulence and to generalize the observed increase in trailing-edge noise. Inflow turbulence leads to an increase in both the wall-pressure spectrum and spanwise correlation length. Trailing-edge noise increases due to the inflow turbulence in the entire frequency range at least 2 dB up to more than 15 dB for all the cases. The contribution of leading- and trailing-edge noise to the total noise varies with the airfoil geometry and inflow velocity, with the trailing-edge noise dominating in a larger frequency range for the thickest airfoil and for lower velocities.

Effect of differential diffusion on head-on quenching of premixed NH[formula omitted]/H[formula omitted]/air flames within turbulent boundary layers

Direct numerical simulations (DNS) have been done for premixed laminar and turbulent NH3/H2/air flames propagating towards a cold wall. Two turbulent channel flows (with well-characterized turbulent boundary layers) at Reτ = 280 and 313 have been simulated for the turbulent flame cases. Near-wall low temperature chemistry has been considered. Effect of differential diffusion on the flame head-on quenching characteristics (quenching distance and maximum wall heat flux) has been checked in detail. Finally, two underlying mechanisms determining differential diffusion effects have been identified: (a) preferential diffusion of H radical increases the reaction rates of the near-wall low temperature (radical recombination) reactions, resulting in larger quenching distance and wall heat flux; (b) differential diffusion of fuels results in smaller flame heat release, thus, larger quenching distance and smaller wall heat flux. The effect of H radical preferential diffusion is suppressed in rich H2/air turbulent flames and strengthened in lean H2/air turbulent flames, due to the differential diffusion focusing/defocusing effects. The effect of differential diffusion of fuels is suppressed in turbulent flames, due to the enhanced mixing process, especially at low Damköhler numbers typical for NH3/H2/air flames interacting with highly turbulent flows.

Flight Dynamic Characteristics of Wide-Body Aircraft with Wind Gust and Turbulence

In this research, a wide-body aircraft was analyzed with critical monitoring of its states, a function of several control inputs (wind gust, turbulence, and microburst). The aerodynamic and stability coefficients of a Boeing 747-200 were obtained from previously published works and 6- DOF equations were formulated. Simulations were conducted for various control inputs to determine the aircraft’s free response, as well as the forced response. In order to understand the nature of the atmosphere, three different models were incorporated, including (i) the Dryden Model, (ii) wind gust, and (iii) microburst. The aircraft was found to be stable in the longitudinal and lateral flight modes, with trim conditions agreeing with published data. For a vertical wind gust of −10 ft/s, the AoA and pitch rate were observed to oscillate sinusoidally and became stable with new trim conditions. These states were found to regain trim conditions once the gust was removed. In the case of 3D gust, it was found that the longitudinal modes achieved a new trim condition through Phugoid oscillations, whereas the lateral modes underwent short-period oscillations. For the case of turbulence, random fluctuations were observed for trim conditions with no unstable behavior. When considering the microburst case, it was found that the aircraft initially gained altitude in the region of the headwind; this was followed by a sharp descent under the influence of a vertical velocity component.

Evaluation of an efficient data-driven ANN model to predict agglomerate collisions within Euler–Lagrange simulations

In this study, a recently developed data-driven model for the collision-induced agglomerate breakup (CHERD 195, 2023) is evaluated. It is especially intended for Euler–Lagrange simulations of flows with high mass loadings, where coupled CFD–DEM predictions are too expensive. Therefore, a surrogate model relying on the hard-sphere approach in which agglomerates are represented by effective spheres was developed. Based on a variety of DEM simulations, artificial neural networks were trained to predict the post-collision number of arising fragments, their size distribution and their velocities. In the present contribution, the agglomerate collision model is assessed using the particle-laden flow through a T-junction. Since two fluid streams with agglomerates are injected at both opposite ends, the setup is particularly suitable for investigating breakage caused by collisions. Two flow configurations (laminar flow at Re = 130 and turbulent flow at Re = 8000) and two different powders (primary particle diameter of 0.97 and 5.08 micrometers) are taken into account. The latter allows to study the influence of the strength of the agglomerates on the collision-induced breakage. The laminar case offers the possibility to evaluate the effect of the collision angle in detail. The collision-induced breakage proves to be the most dominant deagglomeration mechanism in both the laminar and turbulent flow scenario. Nevertheless, the role of the fluid stresses and especially the drag stress becomes more prominent in the turbulent case, while in the laminar flow their effects are negligible.

Surrogate Modeling of the Aeroacoustics of an NM80 Wind Turbine

Wind turbines play a major role in the European Green Deal for clean energy transition. Noise is a critical aspect among open technological issues, as it determines the possibility of onshore installations near inhabited places and the possible detrimental effects on wildlife when offshore. This paper assesses the accuracy of different approaches to predicting the sound pressure level (SPL) of a wind turbine. The 2.75 MW Neg Micon NM80 horizontal axis wind turbine (HWAT) was simulated in OpenFOAM, modeling the turbine with the actuator line method (ALM) implemented in the turbinesFoam library. Two different inflow conditions were considered: a stationary inflow with a typical atmospheric boundary layer profile and a time-dependent inflow derived from a precursor channel with fully turbulent conditions. The surrogate model for noise prediction used for this work is based on the synthetic/surrogate acoustics models (SAMs) of Amiet and Brooks-Pope-Marcolini (BPM). This approach allows for blade motion modeling and the prediction of the SPL of the URANS postprocessing results. The SPL spectrum obtained was then compared to the results from the other aeroacoustic solvers of IEA Task 39 participants, showing the best performance in the fully turbulent case. The results demonstrate that coupling between the ALM and surrogate acoustics provides more accurate results than the blade element momentum (BEM) approach.

Length-scales for efficient CFL conditions in high-order methods with distorted meshes: Application to local-timestepping for [formula omitted]-multigrid

We propose a strategy to estimate the maximum stable time-steps for explicit time-stepping methods for hyperbolic systems in a high-order flux reconstruction framework. The strategy is derived through a von-Neumann analysis (VNA) framework for the advection–diffusion equation on skewed two- and three-dimensional meshes. It directly incorporates the spatial polynomial- and mesh-discretization in estimating the convective and diffusive length-scales. The strategy is extended to the density-based Navier–Stokes system of equations, taking into account the omnidirectionality of the speed of sound.We compare the performance of this strategy with three other popular choices of length-scales across a wide range of polynomial-orders, meshes of drastically varying cell-quality, and flow-physics. The proposed strategy shows robust behavior across all test-scenarios with limited variation of the maximum stable CFL-number (0.1 to 1) for polynomial-orders 1 through 10, unlike other strategies where the CFL-number varies sharply. Finally, we show the advantage of the proposed methodology for local-timestepping for p-multigrid through a RANS-modeled steady-state turbulent flow case, on a mesh with large disparity of mesh elements and aspect ratios.

Wall-pressure spectra, spanwise correlation, and far-field noise measurements of a NACA 0008 airfoil under uniform and turbulent inflows

This paper discusses unique measurements of wall-pressure fluctuations (WPFs), spanwise correlation length, and far-field noise of a NACA 0008 airfoil subjected to uniform, non-turbulent and turbulent inflows. From these measurements, the near-field characteristics of trailing-edge (TE) and leading-edge (LE) noise of a thin airfoil are analyzed. The competing nature of the LE and TE noise mechanisms of an airfoil subjected to a turbulent inflow is also investigated. Experiments were performed in the Aeroacoustic Wind Tunnel of the University of Twente for a chord-based Reynolds number ranging from 3.2×105 to 9×105 for a uniform inflow and a rod-generated turbulent inflow with a turbulence intensity of approximately 18%. The effective angles of attack ranged from -5∘ to 5∘. Measurements of the boundary layer at the TE, the WPFs along the chord and span, and the far-field radiated noise were performed. For the uniform inflow case, laminar-boundary-layer noise, turbulent-boundary-layer (TBL) noise, and blunt TE noise sources are identified. The far-field noise spectrum presents similar components in the frequency domain as the WPF spectrum and the spanwise correlation length at the TE. The angle of attack mainly affects the WPF spectrum and spanwise correlation length for chord-based Strouhal numbers St<10. The angle of attack slightly affects the TE noise with a maximum variation of 3 dB for 10<St<60. For the turbulent inflow case, it is observed that the turbulence significantly affects the WPFs and spanwise correlation length along the chord, increasing considerably compared to the case of uniform inflow. The highest WPF spectral level and the larger spanwise correlation length occur at positions close to the LE. The results show that the turbulent inflow yields a higher WPF spectral level and larger spanwise correlation length at the TE, resulting in higher levels of TE noise. However, LE noise is still the dominant noise source for St<25.2. For higher frequencies, the TE noise level is expected to become higher than the LE noise level.

Toward the use of LES for industrial complex geometries. Part II: Reduce the time-to-solution by using a linearised implicit time advancement

The strong increase in computational power observed during the last few years has allowed to use Large Eddy Simulation (LES) for industrial configurations. Nevertheless, the time-to-solution is still too large for a daily use in the design phases. The objective of this work is to develop a new time integration method to reduce the time-to-solution of LES of incompressible flows by allowing the use of larger time step. The projection method, probably the most commonly used method in the context of LES of incompressible flow, is generally applied using explicit time advancement which constrains the time-step value for stability reasons (CFL and Fourier constraints). The time step can then be small with respect to the physical characteristic times of the studied flow. In this case, an implicit time advancement method, which is unconditionally stable, can be used. However, this leads to non-linear resolution of momentum equation which can strongly increase time-to-solution because of non-linear iterations inside a physical iteration. To relax the stability constraints while minimising the computational cost of an iteration, a linearised implicit time advancement based on Backward Differentiation Formula (BDF) scheme is proposed in this work. The linearisation is performed using an extrapolated velocity field based on the previous fields. This time integration is first evaluated on a turbulent pipe test case. It is observed a time-to-solution up to five times lower than the explicit time integration while keeping the same accuracy in terms of mean and fluctuating velocity fields. To incorporate this new time advancement method in the automatic mesh convergence developed in Part I, a time-step control method based on the local truncation error is used. The resulting automatic time-step and mesh procedure is evaluated on a turbulent round jet case and on PRECCINSTA configuration, a swirl burner which is a representative case of an industrial aeronautical injection system. This new procedure leads to a time-to-solution up to three times lower than the previous procedure, presented in Part I.

A data-driven approach to model enstrophy transfers in large eddy simulation of forced two-dimensional turbulence

Contemporary research on the application of data-driven techniques to modeling subgrid closure in two-dimensional turbulence has been limited. Furthermore, the incorporation of the enstrophy cascade and other two-dimensional turbulence-specific physics has received insufficient attention. To address these gaps, a novel physics-based shallow feed-forward neural network framework was designed in this study to model subgrid closure in three selected cases of forced two-dimensional turbulence with a forcing that provides energy and enstrophy at a particular wavenumber. As a novel approach, we trained our framework to learn the subgrid vorticity transport vector from a set of appropriate resolved flow variables. Another framework used in recent works which directly learned the subgrid forcing field was also investigated. Both frameworks were assessed using a priori and a posteriori tests for two selected filter widths. Both frameworks performed accurately for the lower filter width but less accurately for the higher filter width. However, we demonstrate that our new framework has wider usefulness for model diagnosis. Ad hoc clipping procedures were used to make the models more generalizable to higher filter widths, and stable and consistent a posteriori tests were observed for all test cases and filter widths when the subgrid forcing field was modified to enhance the model's subgrid dissipative characteristics. In contrast, modifying the enstrophy fluxes did not perform as consistently. These findings demonstrate the potential of the novel physics-based framework for improving subgrid modeling in two-dimensional turbulence.

Performance investigation of multi-aperture digital combining algorithm for satellite-to-ground coherent optical communication

An important component of the future communication network will include satellite-to-ground communication technology. In the meantime, the community of communication network also has a huge capacity as one of its purposes. In this situation, the free-space optical (FSO) communication technology is a potential option for satellite-to-ground communications. A major drawback of FSO communication systems, nevertheless, is atmospheric turbulence. Multi-aperture receiver with digital combining architecture is an effective approach to overcoming the effect of atmospheric turbulence on the performance of free-space optical (FSO) communication. In this paper, a blind digital combining algorithm for coherent FSO communication is proposed. To verify the effectiveness of the proposed combining algorithm, a 10-Gbps data rate single polarization 16-ary quadrature amplitude modulation (SP-16QAM) offline four-aperture simulated turbulence experiment is performed, and the performance of multi-aperture spatial diversity and signal processing is emulated through the experimental data. The results confirm that the proposed blind digital combining algorithm has an excellent performance in average bit error rate (BER). Compared with the single-aperture system, the receiver sensitivity of the four-aperture is increased by 1.2, 4.6, and 6.8 dB for the cases of weak, moderate, and strong turbulence at the SD-FEC threshold, respectively.

Learning Similarity Metrics for Volumetric Simulations with Multiscale CNNs

Simulations that produce three-dimensional data are ubiquitous in science, ranging from fluid flows to plasma physics. We propose a similarity model based on entropy, which allows for the creation of physically meaningful ground truth distances for the similarity assessment of scalar and vectorial data, produced from transport and motion-based simulations. Utilizing two data acquisition methods derived from this model, we create collections of fields from numerical PDE solvers and existing simulation data repositories. Furthermore, a multiscale CNN architecture that computes a volumetric similarity metric (VolSiM) is proposed. To the best of our knowledge this is the first learning method inherently designed to address the challenges arising for the similarity assessment of high-dimensional simulation data. Additionally, the tradeoff between a large batch size and an accurate correlation computation for correlation-based loss functions is investigated, and the metric's invariance with respect to rotation and scale operations is analyzed. Finally, the robustness and generalization of VolSiM is evaluated on a large range of test data, as well as a particularly challenging turbulence case study, that is close to potential real-world applications.

When a Series’ Main Protagonist Gets Stolen and Sold – A Study of NFTs and Their Approaches to Copyright Licensing

Abstract Over the past two years non-fungible tokens (NFTs) have become a highly popular, though extremely volatile trade asset. As mere data sets on the blockchain, NFTs are challenging the law to define the legal positions they entail. This article examines NFTs from the angle of copyright licensing, looking at it from a European perspective with the main focus on German law. Based on the technical specifics of NFTs, the paper evaluates the relevant legal position required for a permitted use of tokenized copyrighted content and how such a position may be obtained in the context of NFT trading. A review of the copyright schemes of 21 of the most sought-after NFT collections sets out the current state of licensing and identifies the prevailing legal uncertainties. The fact that these are not merely theoretical is then shown by the turbulent case of a ‘stolen’ ape avatar, tokenized by an NFT, that was set to star in a live-action animated series.

Direct numerical simulations of oscillatory boundary layers over rough walls

Numerical simulations of turbulent oscillatory flow over a bed made of fixed, identical spherical particles have been performed. Oscillations are imposed through a shear-driven forcing by means of an harmonic velocity boundary condition on the bed. A parametric study on the effect of the particle size and Reynolds number, spanning from the laminar to the fully-turbulent regimes, has been performed. Results show that the temporal evolution of the flow over the rough bed is modified compared to the classical Stokes’ solution for smooth-wall laminar boundary layers. In the turbulent cases, the phase shift in the velocity at various distances from the bed is reduced compared to the laminar case. The phase shift reduction seems predominantly dependent on the Reynolds number rather than the bed morphology, which suggests that a unique curve may exist for large enough values of the Reynolds number. Turbulence is observed during the deceleration phases of the cycle, with the presence of a logarithmic layer in the velocity profile, and “canonical” distribution of Reynolds shear stress and turbulent kinetic energy production. During the acceleration, the logarithmic region is suppressed and the Reynolds shear stress changes sign. Nevertheless, the turbulent kinetic energy production becomes only slightly negative, because the shear is also very small during these phases. A good correlation between Reynolds and shear stresses is also evidenced from the eddy viscosity profiles, which show the presence of plateau in the outer layers approximately constant across the phases of the cycle. Turbulence in the outer layers is related to structures which develop during previous cycles and propagate from the bed to the bulk of the channel. When the flow is fully developed, anisotropy maps show similar distributions to unidirectional wall-bounded flows, while departures from canonical distributions during the transient phases are mild, because the flow responds very rapidly to the time-varying forcing.

Transition to Equilibrium and Coherent Structure in Ideal MHD Turbulence, Part 2

We continue our study of the transition of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence from non-equilibrium initial conditions to equilibrium using long-time numerical simulations on a 1283 periodic grid. A Fourier spectral transform method is used to numerically integrate the dynamical equations forward in time. The six runs that previously went to near equilibrium are here extended into equilibrium. As before, we neglect dissipation as we are primarily concerned with behavior at the largest scale where this behavior has been shown to be essentially the same for ideal and real (forced and dissipative) MHD turbulence. These six runs have various combinations of imposed rotation and mean magnetic field and represent the five cases of ideal, homogeneous, incompressible, and MHD turbulence: Case I (Run 1), with no rotation or mean field; Case II (Runs 2a and 2b), where only rotation is imposed; Case III (Run 3), which has only a mean magnetic field; Case IV (Run 4), where rotation vector and mean magnetic field direction are aligned; and Case V (Run 5), which has non-aligned rotation vector and mean field directions. Statistical mechanics predicts that dynamic Fourier coefficients are zero-mean random variables, but largest-scale coherent magnetic structures emerge and manifest themselves as Fourier coefficients with very large, quasi-steady, mean values compared to their standard deviations, i.e., there is ‘broken ergodicity.’ These magnetic coherent structures appeared in all cases during transition to near equilibrium. Here, we report that, as the runs were continued, these coherent structures remained quasi-steady and energetic only in Cases I and II, while Case IV maintained its coherent structure but at comparatively low energy. The coherent structures that appeared in transition in Cases III and V were seen to collapse as their associated runs extended into equilibrium. The creation of largest-scale, coherent magnetic structure appears to be a dynamo process inherent in ideal MHD turbulence, particularly in Cases I and II, i.e., those cases most pertinent to planets and stars. Furthermore, the statistical theory of ideal MHD turbulence has proven to apply at the largest scale, even when dissipation and forcing are included. This, along with the discovery and explanation of dynamically broken ergodicity, is essentially a solution to the ‘dynamo problem’.

Spatiotemporal parallel physics-informed neural networks: A framework to solve inverse problems in fluid mechanics

Physics-informed neural networks (PINNs) are widely used to solve forward and inverse problems in fluid mechanics. However, the current PINNs framework faces notable challenges when presented with problems that involve large spatiotemporal domains or high Reynolds numbers, leading to hyper-parameter tuning difficulties and excessively long training times. To overcome these issues and enhance PINNs' efficacy in solving inverse problems, this paper proposes a spatiotemporal parallel physics-informed neural networks (STPINNs) framework that can be deployed simultaneously to multi-central processing units. The STPINNs framework is specially designed for the inverse problems of fluid mechanics by utilizing an overlapping domain decomposition strategy and incorporating Reynolds-averaged Navier–Stokes equations, with eddy viscosity in the output layer of neural networks. The performance of the proposed STPINNs is evaluated on three turbulent cases: the wake flow of a two-dimensional cylinder, homogeneous isotropic decaying turbulence, and the average wake flow of a three-dimensional cylinder. All three turbulent flow cases are successfully reconstructed with sparse observations. The quantitative results along with strong and weak scaling analyses demonstrate that STPINNs can accurately and efficiently solve turbulent flows with comparatively high Reynolds numbers.

3D Radiation-hydrodynamic Simulations Resolving Interior of Rapidly Accreting Primordial Protostar

Direct collapse of supermassive stars is a possible pathway to form supermassive black hole seeds at high redshifts. Whereas previous three-dimensional (3D) simulations demonstrate that supermassive stars form via rapid mass accretion, those resolving the stellar interior have been limited. Here, we report 3D radiation-hydrodynamic (RHD) simulations following the evolution of rapidly accreting protostars resolving the stellar interior. We use an adaptive mesh refinement code with our newly developed RHD solver employing an explicit M1 closure method. We follow the early evolution until the stellar mass reaches ∼10 M ⊙ from two different initial configurations of spherical and turbulent clouds. We demonstrate that, in both cases, a swollen protostar whose radius is 100–1000 R ⊙ appears, as predicted by the stellar evolution calculations. Its effective temperature remains a few thousand Kelvin, and the radiative feedback by ionizing photons is too weak to disturb the accretion flow up to the epoch examined in this work. In the turbulent case, the protostar rotates rapidly at more than 0.4 times the Keplerian velocity owing to the angular momentum provided by the initial turbulence. The protostar approximates an oblate spheroid, and its equatorial radius is more than twice the polar radius. Our results suggest that we need to consider the rapid stellar rotation to elucidate the realistic 3D protostellar evolution in the supermassive star formation.