Turbulent Problems Research Articles

A high-order generalised differential quadrature element method for simulating 2D and 3D incompressible flows on unstructured meshes

In this paper, a high-order generalised differential quadrature element method (GDQE) is proposed to simulate two-dimensional (2D) and three-dimensional (3D) incompressible flows on unstructured meshes. In this method, the computational domain is decomposed into unstructured elements. In each element, the high-order generalised differential quadrature (GDQ) discretisation is applied. Specifically, the GDQ method is utilised to approximate the partial derivatives of flow variables and fluxes with high-order accuracy inside each element. At the shared interfaces between different GDQ elements, the common flux is computed to account for the information exchange, which is achieved by the lattice Boltzmann flux solver (LBFS) in the present work. Since the solution in each GDQ element solely relies on information from itself and its direct neighbouring element, the developed method is authentically compact, and it is naturally suitable for parallel computing. Furthermore, by selecting the order of elemental GDQ discretisation, arbitrary accuracy orders can be achieved with ease. Representative incompressible flow problems, including 2D laminar flows as well as 3D turbulent simulations, are considered to evaluate the accuracy, efficiency, and robustness of the present method. Successful numerical simulations, especially for scale-resolving 3D turbulent flow problems, confirm that the present method is efficient and high-order accurate.

Assessment of RANS turbulence models based on the cell-based smoothed finite element model for prediction of turbulent flow

There is a growing body of literature that recognizes the importance of Smoothed Finite Element Method (S-FEM) in computational fluid dynamics (CFD) fields and, to a lesser extent, in complex turbulent flow problems. This study evaluates the performance of Reynolds-averaged Navier-Stokes (RANS) turbulence models within the S-FEM framework for predicting incompressible turbulent flows. Our assessment of three turbulence models based on the cell-based S-FEM (CS-FEM) is convincingly supported by testing on three flow problems. It is found that the CS-FEM exhibits superior mesh robustness compared to the Finite Volume Method (FVM) and achieves higher computational accuracy than the Finite Element Method (FEM). Notably, the CS-FEM combined with the standard k-epsilon model (CS-FEM-SKE) and the realizable k-epsilon model (CS-FEM-RKE) demonstrate robust performance in handling severely distorted meshes, with CS-FEM-RKE outperforming in regions of strong flow separation and convection. The Spalart-Allmaras model with CS-FEM (CS-FEM-SA) offers faster computational speed but shows poor mesh robustness. The hexcore mesh based on CS-FEM-RKE is employed to evaluate the aerodynamic performance of High-speed train (HST), resulting in enhanced computational efficiency. The outcomes show good agreement with other numerical studies and experimental data. Overall, it also highlights the latent capability of CS-FEM in solving complex engineering problems.

Numerical investigation of lattice Boltzmann method-based large-eddy simulation in non-isothermal enclosed cavity airflow

This study implemented the lattice Boltzmann method-based large-eddy simulation (LBM-LES) in a wall-heated cavity turbulent flow problem with the Rayleigh number reaching 5.33 × 109. The effects of crucial parameters in LBM temperature simulation, including discrete time intervals, discrete external force models by temperature effect, and temperature discrete velocity schemes, were investigated to obtain the suggested values. In addition, the simulations' accuracy and computational efficiency were compared with those of FVM-LES. LBM-LES generally agreed with experiments, and the accuracy was comparable to FVM-LES. However, exceedingly small discrete time intervals induced numerical oscillations in velocity and temperature at high frequencies, yielding significant errors. The accuracy of the discrete external force model satisfied Guo model > primitive model > He model. For temperature particles' discrete velocity scheme, D3Q7 was already sufficiently accurate, and higher schemes (D3Q19 and D3Q27) did not increase the accuracy further. LBM-LES and FVM-LES were concordant with respect to predicting various physical quantities, and the accuracy of LBM-LES in the near-wall region was slightly higher than that of the FVM-LES. Single-core and multicore computational speeds of LBM-LES were 4–8 fold higher than FVM-LES. The multicore parallelism of LBM-LES also exceeded FVM-LES and became more evident as CPU cores increased.

A time-averaged method to analyze slender rods moving in tubes

The motion of slender rods in narrow tubes involves the coupling of axial movements and transverse vibrations, in which the transverse vibration exhibits high frequency and chaotic characteristics. These characteristics render the computational cost of the time integration to the motions of rods and tubes expensive. To solve this problem, this paper proposes a novel time-averaged method, which contains two innovations: 1) By time averaging the traditional dynamic equations, the time-averaged dynamic equations describing the rod-tube system are established based on the time-averaged concept used in turbulence problems; 2) Two time-averaged contact models are developed, by fitting the time-averaged sample set using the polishing function and the machine learning, respectively, to construct the relationship between the time-averaged contact gaps and the time-averaged contact forces. The time-averaged method can use a large time step, which is far larger than that required for the time integration of traditional methods, thus reducing the computational cost. Inclined and rolling experiments of the rod-tube system, as well as numerical experiments of the control rod drop in a nuclear reactor, are conducted to validate the accuracy of the time-averaged method. Comparative analyses are carried out between the time-averaged method and six continuous contact models, demonstrating the high computational efficiency of the proposed method. Moreover, the experimental results can provide benchmark data for algorithm verification for scholars studying dynamic contact algorithms.

Large-eddy simulation of wall-bounded incompressible turbulent flows based on multi-moment finite volume formulation

The multi-moment based numerical model is proposed for performing large-eddy simulation (LES) of wall-bounded incompressible turbulent flows on the unstructured grids. In this model, velocity is defined as volume integral average (VIA) and point values (PVs) which are updated as prognostic variables simultaneously in time. Using VIA and PV in each cell, this method constructs higher-order polynomial on a compact stencil and more importantly, provides a new approach to design subgrid-scale (SGS) models for LES. Various SGS models are developed in this framework where the eddy-viscosity is computed separately at both VIA and PVs using the least-square method on different interpolation stencils. Compared with conventional finite volume schemes, the proposed method effectively reduces numerical dissipation and largely suppresses the sensitivity of numerical solution on SGS models and resolves more elaborated flow structures on the same mesh resolution. It also reduces solution dependence on the shape and quality of grid elements, as demonstrated by comparing numerical results on the different types of grids. The proposed method can attain high-fidelity simulation without loss of numerical efficiency and robustness, which is highly appealing for complex turbulent problems with high Reynolds numbers and complicated geometries.

The unsolved problem of solar-wind turbulence

The solar wind forms the largest wind tunnel for plasma and magnetofluid turbulence that is accessible to Earth. It evolves from what is thought to be a turbulent source that continues to drive nonlinear turbulent dynamics as it expands outward via large-scale, energy-containing wind shear and shocks. In the outer heliosphere, once the gradients in the flow have coalesced and they no longer provide an adequate source for the turbulence, the excitation of wave energy by the injection of interstellar pickup ions becomes the dominant source of energy that continues to drive the turbulence. While there are established formalisms for the determination of the strength of the turbulence and the evolution of the turbulent spectra is well-established, the actual nonlinear dynamics that are responsible for its formation and evolution remain unresolved and the subject of considerable debate. We examine the evidence and attempt to illuminate the various theories while demonstrating what is needed to resolve the debates and bring the subject of plasma turbulence into a new level of understanding.

Adaptive detached eddy simulation of turbulent combustion with the subgrid dissipation concept

Detached eddy simulation has become a widely used method in eddy simulations due to its balance between cost and accuracy. The recently developed subgrid dissipation concept (SDC) combustion model [Liu et al., “On the subgrid dissipation concept for large eddy simulation of turbulent combustion,” Combust. Flame 258, 113099 (2023)] is found to be more reasonable and accurate than the conventional eddy dissipation concept model in large eddy simulation (LES). In this paper, the SDC model is adapted to the ℓ2-ω adaptive detached eddy simulation framework, named DES-SDC. The required key quantities, including the fine structure mass fraction and dissipation rate, are appropriately blended across Reynolds-averaged Navier–Stokes and LES regions. The DES-SDC approach is validated using premixed bluff body stabilized flame, non-premixed swirl flame, and premixed swirl flame with complex geometry. It is much more tolerant to coarse mesh resolution than pure LES, yet it preserves the capability of resolving the key unsteady feature critical for the combustion process, as it is designed to be. The DES-SDC approach is relatively insensitive to the grid resolution. The present research provides a promising approach for accurately simulating practical unsteady turbulent combustion problems at an affordable computational cost.

Numerical Simulation of Airflow Velocity and Temperature Distribution in an Aircraft Cabin

In this work, a computational fluid dynamics (CFD) model is established to calculate the airflow distribution in the cabin of a single-channel Boeing 737-800 airplane. The RNG k-ε model, considering the calculation of turbulence kinetic energy and its rate of dissipation, is adopted to solve turbulence problems in physical field simulation. The proposed three-dimensional model is able to consider the particular physical factors and spatial structures, which can simulate the detailed distributions of complex physical fields, compared with the one-dimensional lumped parameter model. The velocity and temperature fields under different air supply velocities are then numerically investigated. The calculation results show that when the air velocity at the top air supply inlet is 1.4 m/s, the velocity and temperature distribution inside the cabin can both meet the comfort requirements of humans in the airworthiness standards. The results from this work can help to design an aircraft environmental control system.

A variational data assimilation approach for sparse velocity reference data in coarse RANS simulations through a corrective forcing term

The Reynolds-averaged Navier–Stokes (RANS) equations provide a computationally efficient method for solving fluid flow problems in engineering applications. However, the use of closure models to represent turbulence effects can reduce their accuracy. To address this issue, recent research has explored data-driven techniques such as data assimilation and machine learning.An efficient variational data assimilation (DA) approach is presented to enhance steady-state eddy viscosity based RANS simulations. To account for model deficiencies, a corrective force term is introduced in the momentum equation. In the case of only velocity reference data, this term can be represented by a potential field and is divergence-free. The DA implementation relies on the discrete adjoint method and approximations for efficient gradient evaluation.The implementation is based on a two-dimensional coupled RANS solver in OpenFOAM, which is extended to allow the computation of the adjoint velocity and pressure as well as the adjoint gradient. A gradient-based optimizer is used to minimize the difference between the simulation results and the reference data. To evaluate this approach, it is compared with alternative data assimilation methods for canonical stationary two-dimensional turbulent flow problems. For the data assimilation, sparsely distributed reference data from averaged high-fidelity simulation results are used.The results suggest that the proposed method achieves the optimization goal more efficiently compared to applying data assimilation for obtaining the eddy viscosity, or a field modifying the eddy viscosity, directly. The method works well for different reference data configurations and runs efficiently by leveraging coarse meshes.

A note on cascade flux laws for the stochastically-driven nonlinear Schrödinger equation

In this note we point out some simple sufficient (plausible) conditions for ‘turbulence’ cascades in suitable limits of damped, stochastically-driven nonlinear Schrödinger equation in a d-dimensional periodic box. Simple characterizations of dissipation anomalies for the wave action and kinetic energy in rough analogy with those that arise for fully developed turbulence in the 2D Navier–Stokes equations are given and sufficient conditions are given which differentiate between a ‘weak’ turbulence regime and a ‘strong’ turbulence regime. The proofs are relatively straightforward once the statements are identified, but we hope that it might be useful for thinking about mathematically precise formulations of the statistically-stationary wave turbulence problem.

Simulating variable‐order fractional Brownian motion and solving nonlinear stochastic differential equations

Stochastic differential equations (SDEs) are very useful in modeling many problems in biology, economic data, turbulence, and medicine. Fractional Brownian motion (fBm) and variable‐order fractional Brownian motion (vofBm) are suitable alternatives to standard Brownian motion (sBm) for describing and modeling many phenomena, since the increments of these processes are dependent of the past and for these increments have the property of long‐term dependence. Classical mathematical techniques such as Ito's calculus do not work for stochastic computations on fBm and vofBm due to they are not semi‐Martingale for . Therefore, solving these equations is much more difficult than solving SDEs with sBm. On the other hand, these equations do not have an analytical solution, so we have to use numerical methods to find their solution. In this paper, a computational approach based on hybrid of block‐pulse and parabolic functions (HBPFs) has been introduced for simulating vofBm and solving a modern class of SDEs. The mechanism of this approach is based on stochastic and fractional integration operational matrices, which transform the intended problem to a nonlinear system of algebraic equations. Thus, the complexity of solving the mentioned problem is reduced significantly. Also, convergence analysis of the expressed method has been theoretically examined. Finally, the accuracy and efficiency of the proposed algorithm have been experimentally investigated through some test problems and comparison of obtained results with results of previous papers. High accurate numerical results are obtained by using a small number of basic functions. Therefore, this method deals with smaller matrices and vectors, which is one of the most important advantage of our suggested method. Also, presenting an applicable procedure to construct vofBm is another innovation of this work. To gain this aim, at first, discretized sBm is generated via fundamental features of this process, and afterward, block‐pulse functions (BPFs) and HBPFs are utilized for simulating discretized vofBm. Finally, spline interpolation method has been employed to provide a continuous path of vofBm.

On the Sensitivity of Large-Eddy Simulations of the Atmospheric Boundary Layer Coupled with Realistic Large-Scale Dynamics

Abstract We present a new ensemble of 36 numerical experiments aimed at comprehensively gauging the sensitivity of nested large-eddy simulations (LES) driven by large-scale dynamics. Specifically, we explore 36 multiscale configurations of the Weather Research and Forecasting (WRF) Model to simulate the boundary layer flow over the complex topography at the Perdigão field site, with five nested domains discretized at horizontal resolutions ranging from 11.25 km to 30 m. Each ensemble member has a unique combination of the following input factors: (i) large-scale initial and boundary conditions, (ii) subgrid turbulence modeling in the gray zone of turbulence, (iii) subgrid-scale (SGS) models in LES, and (iv) topography and land-cover datasets. We probe their relative importance for LES calculations of velocity, temperature, and moisture fields. Variance decomposition analysis unravels large sensitivities to topography and land-use datasets and very weak sensitivity to the LES SGS model. Discrepancies within ensemble members can be as large as 2.5 m s−1 for the time-averaged near-surface wind speed on the ridge and as large as 10 m s−1 without time averaging. At specific time points, a large fraction of this sensitivity can be explained by the different turbulence models in the gray zone domains. We implement a horizontal momentum and moisture budget routine in WRF to further elucidate the mechanisms behind the observed sensitivity, paving the way for an increased understanding of the tangible effects of the gray zone of turbulence problem. Significance Statement Several science and engineering applications, including wind turbine siting and operations, weather prediction, and downscaling of climate projections, call for high-resolution numerical simulations of the lowest part of the atmosphere. Recent studies have highlighted that such high-resolution simulations, coupled with large-scale models, are challenging and require several important assumptions. With a new set of numerical experiments, we evaluate and compare the significance of different assumptions and outstanding challenges in multiscale modeling (i.e., coupling large-scale models and high-resolution atmospheric simulations). The ultimate goal of this analysis is to put each individual assumption into the wider perspective of a realistic problem and quantify its relative importance compared to other important modeling choices.

The Generation of 150 km Echoes Through Nonlinear Wave Mode Coupling

AbstractA fundamental problem in plasma turbulence is understanding how energy cascades across multiple scales. In this paper, a new weak turbulence theory is developed to explain how energy can be transferred from Langmuir and Upper‐Hybrid waves to ion‐acoustic waves. A kinetic approach is used where the Boltzmann equation is Fourier‐Laplace transformed, and the nonlinear term is retained. A unique feature of this approach is the ability to calculate power spectra at low frequencies, for any wavelength or magnetic aspect angle. The results of this theory explain how the predominant type of 150‐km radar echoes are generated in the ionosphere. First, peaks in the suprathermal electron velocity distribution drive a bump‐on‐tail like instability that excites the Upper‐Hybrid mode. This excited wave then couples nonlinearly to the ion‐acoustic mode, generating the ∼10 dB enhancement observed by radars. This theory also explains why higher frequency radars like ALTAIR do not observe these echoes.

Turbulence calculation based on the extended Navier–Stokes equations

In this study, phenomenological observations and the Kreuer interpretation of the origin of viscosity were used to develop a computational method for solving the turbulence problem of incompressible viscous Newtonian fluids based on extended Navier–Stokes (N–S) equations. The shear process in fluid flow was hypothesized to be accompanied by eddy formation, and the effects of eddies on the convection and diffusion were considered. The classical N–S equations were improved to obtain extended N–S equations. The extended equations are closed, and the sources of the velocity fluctuations are explicitly considered to be additional convection and diffusion. The extended equations are compatible with the classical N–S equations; thus, they can describe laminar and turbulent flows in a unified manner. In fluid flow simulations, the equations describing the mean flow quantities could be directly obtained from the extended N–S equations without any additional turbulence models. A numerical investigation was carried out to verify the extended equations by exploring the flow over a cube placed in a channel. The simulation results were compared with both the large eddy simulation and experimental results.

Calibrating sub-grid scale models for high-order wall-modeled large eddy simulation

AbstractHigh-order methods have demonstrated orders of magnitude reduction in computational cost for large eddy simulation (LES) over low-order methods in the past decade. Most such simulations are wall-resolved implicit LES (ILES) without an explicit sub-grid scale (SGS) model. The use of high-order ILES for severely under-resolved LES such as wall-modeled LES (WMLES) often runs into robustness and accuracy issues due to the low dissipation embedded in these methods. In the present study, we investigate the performance of several popular SGS models, the static Smagorinsky model, the wall-adapting local eddy-viscosity (WALE) model and the Vreman model, to improve the robustness and accuracy of under-resolved LES using high-order methods. The models are implemented in the high-order unstructured grid LES solver called hpMusic based on the discontinuous flux reconstruction method. The length scales in these SGS models are calibrated using the direct numerical simulation (DNS) database for the turbulent channel flow problem. The Vreman model has been found to produce the most accurate and consistent results with a proper choice of the length scale for WMLES.

Study on the stability and its simulation algorithm of a nonlinear impulsive ABC-fractional coupled system with a Laplacian operator via F-contractive mapping

In this paper, we study the solvability and generalized Ulam–Hyers (UH) stability of a nonlinear Atangana–Baleanu–Caputo (ABC) fractional coupled system with a Laplacian operator and impulses. First, this system becomes a nonimpulsive system by applying an appropriate transformation. Secondly, the existence and uniqueness of the solution are obtained by an F-contractive operator and a fixed-point theorem on metric space. Simultaneously, the generalized UH-stability is established based on nonlinear analysis methods. Thirdly, a novel numerical simulation algorithm is provided. Finally, an example is used to illustrate the correctness and availability of the main results. Our study is a beneficial exploration of the dynamic properties of viscoelastic turbulence problems.

A cell-based smoothed finite element model for the analysis of turbulent flow using realizable k-ε model and mixed meshes

Smoothed finite element method (S-FEM) has been widely employed in computational mechanics, particularly in computational solid mechanics (CSM) and, to a lesser extent, in computational fluid dynamics (CFD). The present work focuses on the development of S-FEM for solving three-dimensional incompressible turbulent flow problems using the realizable k-ε model. The Streamline Upwind Petrov-Galerkin approach combined with Stabilized Pressure Gradient Projection (SUPG/SPGP) was used to restrain/control the spatial oscillation and instability in conjunction with mixed meshes employed to discretize complex geometries. The presented turbulent cell-based S-FEM (CS-FEM) was validated under several common flow types, including mesh turbulence, turbulent channel flow, turbulent flow past a circular cylinder, flow separation around an obstacle, flow in the dimpled channel, and flow in the upper human airway. In particular, the presented work exhibited the latent capability of the CS-FEM in solving turbulent flows near boundary regions and strong convection regions. Meanwhile, the results of the CS-FEM were compared to those of the lowest equal-order finite element method (i.e. P1–P1 or Q1–Q1 elements) in simulating turbulent flows, and it was found that the CS-FEM had better agreement with other published works.

Persistence in active turbulence.

Active fluids such as bacterial swarms, self-propelled colloids, and cell tissues can all display complex spatiotemporal vortices that are reminiscent of inertial turbulence. This emergent behavior, despite the overdamped nature of these systems, is the hallmark of active turbulence. In this Letter, using a generalized hydrodynamic model, we present a study of the persistence problem in active turbulence. We report that the persistence time of passive tracers inside the coherent vortices follows a Weibull probability density whose shape and scale are decided by the strength of activity-contrary to inertial turbulence that displays power-law statistics in this region. In the turbulent background, the persistence time is exponentially distributed that is remindful of inertial turbulence. Finally we show that the driver of persistence inside the coherent vortices is the temporal decorrelation of the topological field, whereas it is the vortex turnover time in the turbulent background.

Ensemble flow reconstruction in the atmospheric boundary layer from spatially limited measurements through latent diffusion models

Due to costs and practical constraints, field campaigns in the atmospheric boundary layer typically only measure a fraction of the atmospheric volume of interest. Machine learning techniques have previously successfully reconstructed unobserved regions of flow in canonical fluid mechanics problems and two-dimensional geophysical flows, but these techniques have not yet been demonstrated in the three-dimensional atmospheric boundary layer. Here, we conduct a numerical analogue of a field campaign with spatially limited measurements using large-eddy simulation. We pose flow reconstruction as an inpainting problem, and reconstruct realistic samples of turbulent, three-dimensional flow with the use of a latent diffusion model. The diffusion model generates physically plausible turbulent structures on larger spatial scales, even when input observations cover less than 1% of the volume. Through a combination of qualitative visualization and quantitative assessment, we demonstrate that the diffusion model generates meaningfully diverse samples when conditioned on just one observation. These samples successfully serve as initial conditions for a large-eddy simulation code. We find that diffusion models show promise and potential for other applications for other turbulent flow reconstruction problems.

Influence of LES Inflow Conditions on Simulations of a Piloted Diffusion Flame

This study investigates the influence of different turbulent inflow conditions on the Large Eddy Simulation (LES) of turbulent combustion problems. Four turbulent inflow conditions are studied, including two Synthetic turbulence methods (White Noise and Random Spot), and two Precursor simulation methods (Library and Library-Rescale). The simulation results are compared with experimental measurements. While the White Noise method yields a longer flame with poor agreement against experiments, the Random Spot method has good predictions initially but overpredicts turbulent fluctuations downstream. The results obtained by the Library and Library-Rescale methods are similar, and the discrepancies mainly lie in the region around the centerline. By rescaling the turbulent inlet library to match the experimental profiles, the Library Rescale method improves the prediction of turbulence fluctuations near the nozzle. The present study shows the pronounced sensitivity of LES accuracy in turbulent jet flames to the choice of turbulent inflow conditions.