Direct Numerical Simulation Results Research Articles

Scaling Law of Flow and Heat Transfer Characteristics in Turbulent Radiative Rayleigh-Bénard Convection of Optically Thick Media

Radiative natural convection is of vital importance in the process of energy storage, power generation, and thermal storage technology. As the attenuation coefficients of many heat transfer media in these fields are high enough to be considered as optically thick media, like nanofluids or molten salts in concentrated solar power or phase change thermal storage, Rosseland approximation is commonly used. In this paper, we delve into the impact of thermal radiation on the Rayleigh-Bénard (RB) convection. Theoretical analysis has been conducted by modifying the Grossmann-Lohse (GL) model. Based on turbulent dissipation theory, the corresponding scaling laws in four main regimes are proposed. Direct numerical simulation (DNS) was also performed, revealing that radiation exerts a notable influence on both flow and heat transfer, particularly on the formation of large-scale circulation. By comparing with DNS results, it is found that due to the presence of radiation, the modified Nu scaling law in small Pr range of the GL model is more suitable for predicting the transport characteristics of optical thick media with large Pr. The maximum deviation between the results of DNS and prediction model is about 10%, suggesting the summarized scaling law can effectively predict the Nu of radiative RB convection.

Super-resolution reconstruction of turbulence for Newtonian and viscoelastic fluids with a physical constraint

Super-resolution reconstruction (SR) of turbulent flow fields with high physical fidelity from low-resolution turbulence data is a novel and cost-effective way in a turbulence study. However, some naive image-to-image machine learning methods often produce nonphysical features inconsistent with the physical characteristics of turbulence. The present work proposes, respectively, convolutional neural network and generative adversarial network-based turbulence SR models using the kinetic energy spectra of turbulence flow as a physical constraint. The models have been validated in turbulence SR reconstruction for a Newtonian fluid under the flow condition of homogeneous isotropic turbulence at Reynolds number, Re=3140 and 4710 and viscoelastic fluid at the same Re numbers and Weisenberg number, Wi=0.796 and 1.194 (the elasticity number El=Wi/Re=0.000 254), respectively. The results show that with the energy spectra constraint (ESC), not only the nonphysical features occurred in the energy spectra of velocity field could be eliminated by the SR models, the errors of their reconstructed vorticity fields in comparison with the results of direct numerical simulation are also significantly smaller than those of the SR models without ESC. Therefore, incorporation of physical constraints is vital in preserving physical characteristics in SR of turbulent flow.

Receptivity of Rayleigh-Taylor instability to acoustic pulses: Theoretical explanation of pulse propagation

Direct numerical simulation (DNS) of Rayleigh-Taylor instability (RTI) has been reported in “Three-dimensional (3D) DNS of RTI triggered by acoustic excitation - Sengupta, et al. Phys. Fluids 34(5), 054108 (2022)” using more than 4 billion points with initial time steps of 7.69 ×10−8s. The set-up consists of quiescent heavy (cold) fluid atop lighter (hot) fluid initially separated by an insulated partition. Removal of this partition creates acoustic pulses in the directions normal to the interface, which provides the receptivity route of RTI to transient acoustic pulses spread over several mega-Hz frequencies, far in excess of ultrasonic frequencies. The DNS and its analysis reveal the pulses to be severely attenuated, which cannot be explained by the classical wave equation. In the present research, after demonstrating the features of the DNS results, we report in detail, the theoretical development of a wave equation incorporating losses based on the Navier-Stokes equation without Stokes' hypothesis for a quiescent ambience. Apart from the physical properties of this altered wave equation, the numerical solution of the same is obtained. The governing partial differential equation (PDE) for the propagation of disturbances in the spectral plane, provides the dispersion relation between wavenumber and circular frequency in the dissipative medium accounting for viscous losses. The presented analysis provides physical properties using the global spectral analysis (GSA). This shows the far-field perturbation to propagate either as attenuated waves or strictly in a diffusive manner depending upon the wavenumber. The PDE is solved numerically by a high-accuracy compact scheme and the four-stage, Runge-Kutta scheme for time advancement. The computed solution is shown to match not only with the developed theoretical analysis but also explains the DNS results for RTI at early times when the computed flow field truly represents the quiescent ambience.

Experimental evidence of the correlation between the flow rolling structures and momentum transfer in Rayleigh–Bénard convection

The formation of large-scale circulating structures (LSC) is one of the critical characteristics of turbulent Rayleigh–Bénard convection (RBC). Although the effect of LSC in turbulent RBC was disputed due to conflicting results, recently, the results of three-dimensional direct numerical simulation [Zwirner et al., “Elliptical instability and multiple-roll flow modes of the large-scale circulation in confined turbulent Rayleigh-Bénard convection,” Phys. Rev. Lett. 125, 54502 (2020)] confirmed that in RBC flows with a low Prandtl number, Pr=0.1 within Oberbeck–Boussinesq assumption, the formation of higher number of LSC leads to a decrease in heat and momentum transfer. However, it was shown that for higher Prandtl numbers, heat/momentum transfer is not correlated with the number of LSC. Experimental evidence is investigated of an inverse correlation between the momentum transfer and small-scale rolling structures for high Prandtl non-Oberbeck–Boussinesq condition. Experiments were undertaken at a Prandtl number of Pr=7 and Rayleigh number of Ra=5.3×107 in a cubical convection cell with an unit aspect ratio. Particle image velocimetry along with a robust combinatorial vortex detection algorithm was used to capture the flow field, detect the rolling structures, and estimate their size. It was found that although the flow structures were dominated by the LSC, the number of smaller rolling structures was significant. The results also showed that after the initiation of convection while the flow was still undeveloped, the majority of rolling structures were small scale. For this state, an inverse correlation between the number of rolling structures and momentum transfer was observed highlighting the influence of flow rolling structures regardless of the formation of the LSC.

DNS of laboratory-scale turbulent premixed counterflow flames under elevated gravity conditions

In the present work, direct numerical simulations (DNSs) of laboratory-scale turbulent premixed counterflow flames are performed to understand the effect of elevated gravity on flame structures. In the DNS, a turbulent jet of CH4/N2/O2 mixture is injected in opposition to a stream of combustion product. Three cases were considered, i.e., one case with normal gravity and two cases with elevated gravity in different directions. The DNS results of the case under normal gravity conditions were found to be in good agreement with the experimental data. The turbulent flame speed is the highest in the case with elevated gravity aligned with the mean flame propagating direction, which is due to the increase in flame surface area and stretch factor. The gravity levels have a substantial influence on the flame extinction characteristics. It was observed that the flame front is pushed toward the direction of the gravity. When the elevated gravity antialigns with the mean flame propagating direction, the flame front travels across the stagnation plane toward the combustion product stream, leading to significant reactant dilution and flame extinction. The flame normal vector preferentially aligns with the most compressive strain rate for various gravity conditions. The tangential strain rate is the greatest (smallest) when elevated gravity antialigns (aligns) with the mean flame propagating direction. The impact of elevated gravity on the tangential strain rate at the flame fronts ultimately leads to a displacement in the flame front location relative to the stagnation plane, thereby influencing flame extinction.

On dissipation timescales of the basic second-order moments: the effect on the energy and flux budget (EFB) turbulence closure for stably stratified turbulence

Abstract. The dissipation rates of the basic second-order moments are the key parameters playing a vital role in turbulence modelling and controlling turbulence energetics and spectra and turbulent fluxes of momentum and heat. In this paper, we use the results of direct numerical simulations (DNSs) to evaluate dissipation rates of the basic second-order moments and revise the energy and flux budget (EFB) turbulence closure theory for stably stratified turbulence. We delve into the theoretical implications of this approach and substantiate our closure hypotheses through DNS data. We also show why the concept of down-gradient turbulent transport becomes incomplete when applied to the vertical turbulent flux of potential temperature under stable stratification. We reveal essential feedback between the turbulent kinetic energy (TKE), the vertical turbulent flux of buoyancy, and the turbulent potential energy (TPE), which is responsible for maintaining shear-produced stably stratified turbulence for any Richardson number.

High-Order Models for Gas Transport in Multiscale Coal Rock.

The coal reservoirs exhibit great heterogeneity and strong anisotropy in multiscale pore/fracture structures. Developing highly accurate multiscale models for real-time prediction of microgaseous flow in complicated porous media with pronounced contrast in transport coefficients is crucial but not yet available, which is time-consuming, expensive, and even computationally impossible. In this study, a multiscale approximate solution of the gas flow and pressure field is derived in this paper for predicting coalbed methane (CBM) transport in macro-microscopic two-scale porous media of typical coal rocks in Guizhou Province, China, and the detailed finite element algorithm is established. The multiscale approximate solutions are constructed from the first- and second-order auxiliary cell functions and low- or high-order derivatives of the homogenized pressure field, which can accurately approximate the solution of the original problem to a certain extent. The numerical accuracy and validity of the multiscale approximate solutions under various working conditions are analyzed in detail by comparing and verifying the results with the direct numerical simulation results of fine-mesh high-precision finite elements. The results show that the homogenized approximate solution can only roughly capture the characteristics of the macroscopic pressure evolution, the first-order approximate solution can partially reproduce the macro-microscopic pressure oscillation phenomenon, and the second-order approximate solution can accurately predict the pressure profile and its evolution law with time in porous media with macro-micro configuration under various complex conditions. The second- and high-order two-scale approximate solutions constructed in this paper exhibit high numerical accuracy and excellent computational efficiency. We also develop multiscale approximate solutions for predicting microgaseous flow at a low reservoir pressure where the slippage effects are very pronounced. Potential applications of our high-order models to the coal reservoirs with a hierarchical matrix and fractures are discussed. The developed multiscale models exhibit excellent applicability to investigating the crossflow effects and coupling mechanisms between the matrix and cleats or fractures with multiple configurations in the CBM and shale gas reservoirs, which is crucial for the effective implementation of hydraulic fracturing technology. This study provides a fundamental understanding of gas transport in multiscale matrix-fracture networks, which helps to improve the optimization design of hydraulic fracturing in tight reservoirs.

Evaluation of a Volume-Averaged Species Transport Model with Micro-Macro Coupling for Breakthrough Curve Prediction.

In porous water filters, the transport and entrapment of contaminants can be modeled as a classic mass transport problem, which employs the conventional convection-dispersion equation to predict the transport of species existing in trace amounts. Using the volume-averaging method (VAM), the upscaling has revealed two possible macroscopic equations for predicting contaminant concentrations in the filters. The first equation is the classical convection-dispersion equation, which incorporates a total dispersion tensor. The second equation involves an additional transport coefficient, identified as the adsorption-induced vector. In this study, the aforementioned equations were solved in 1D for column tests using 3D unit cells. The simulated breakthrough curves (BTCs), using the proposed micro-macro-coupling-based VAM model, are compared with the direct numerical simulation (DNS) results based on BCC-type unit cells arranged one-after-another in a daisy chain manner, as well as with three previously reported experimental works, in which the functionalized zeolite and zero-valent iron fillings were used as an adsorbent to remove phosphorous and arsenic from water, respectively. The disagreement of VAM BTC predictions with DNS and experimental results reveals the need for an alternative closure formulation in VAM. Detailed investigations reveal time constraint violations in all the three cases, suggesting this as the main cause of VAM's failure.

An improved viscoelastic k- ε -v2-f turbulence model for intermediate and high drag reduction regimes

In this work, an improved anisotropic k-ε-v2-f model based on the finite extensible nonlinear elastic model with the Peterlin approximation for viscoelastic channel flows is proposed. This model is tested using direct numerical simulation (DNS) data for friction Reynolds numbers (Reτ) in the range of 120–1000, friction Wiesenberg numbers (Wiτ) in the range of 25–116, viscosity ratios (β) in the range of 0.6–0.9, and maximum polymer extensibility values (L2) in the range of 900–14 400. The flow characteristics of viscoelastic fluids with various parameters obtained from the new model agree well with existing DNS results. By adding closures for the flow, shear, and transverse components, the incomplete prediction of nonlinear terms from interactions between the fluctuating components of the conformation and velocity gradient tensors is improved. Compared with DNS results, these closures can fully obtain each component and significantly improve the accuracy of the flow direction component in the intermediate and high drag reduction regimes. Furthermore, the model in this paper retains the advantages of an anisotropic model, does not require a damping function, is simple to construct, and is easily extended to a variety of bounded flows.

Application of machine learning technique for a fast forecast of aggregation kinetics in space-inhomogeneous systems

Modelling of aggregation processes in space-inhomogeneous systems is extremely numerically challenging since complicated aggregation equations, Smoluchowski equations, are to be solved at each space point along with the computation of particle propagation. Low rank approximation for the aggregation kernels can significantly speed up the solution of Smoluchowski equations, while the particle propagation could be done in parallel. Yet the numerics with many aggregate sizes remains quite resource-demanding. Here, we explore the way to reduce the amount of direct computations by replacing the actual numerical solution of the Smoluchowski equations with the respective density transformations learned with the application of one of machine learning (ML) methods, the conditional normalising flow. We demonstrate that the ML predictions for the space distribution of aggregates and their size distribution require drastically shorter computation time and agree fairly well with the results of direct numerical simulations. Such an opportunity of a quick forecast of space-dependent particle size distribution could be important in practice, especially for the fast (on the timescale of data reading) prediction and visualisation of pollution processes, providing a tool with a reasonable trade off between the prediction accuracy and the computational time.

Spontaneous ignition and flame propagation in hydrogen/methane wrinkled laminar flames at reheat conditions: Effect of pressure and hydrogen fraction

Direct numerical simulations (DNS) with detailed chemical kinetics and chemical explosive mode analysis (CEMA) are performed to investigate the effect of operating pressure and hydrogen–methane blending on laminar wrinkled flames at reheat combustion conditions. Building upon previous three-dimensional DNS datasets of reheat hydrogen flames, the present work considers two-dimensional configurations that render computationally-feasible simulations of high-pressure combustion and significantly more complex hydrocarbon chemistry. A geometrically-simplified representation of the reheat combustor is adopted and the thermodynamic states considered in the simulations are carefully chosen to mimic gas turbine operation conditions, which are constrained to achieve a target flame position and flame temperature. The two-dimensional DNS results are first assessed against the available three-dimensional data and then analyzed to extract the main trends exhibited by the reheat combustion process with respect to the fraction of the fuel consumed by spontaneous ignition and flame propagation, for increasing pressures and hydrogen fractions. Due to significant differences in the characteristic features of the velocity and thermal boundary layers between the three-dimensional and the two-dimensional configurations, a different global flame shape is observed (V-shaped flame vs W-shape flame) together with a ∼10% bias in the fraction of fuel consumed by spontaneous ignition. Crucially, results from the scaling studies reveal very clear trends with a significant decrease in the fuel consumption by spontaneous ignition for increasing pressures and hydrogen fractions, at the conditions investigated. Finally, this study highlights the important role that first-principle direct numerical simulations, even when conducted in computationally affordable two-dimensional simplified geometrical configurations, can play in obtaining detailed insights and quantitative trends useful for the characterization of complex reactive flows.Novelty and significanceThe reheat burners of the two-stage sequential gas turbine combustors are designed to stabilize flames primarily due to spontaneous ignition. However, prior numerical simulations revealed the presence of an additional assisted-ignition mode aided by recirculation zones. In this study, we used practically feasible two-dimensional direct numerical simulations of premixed hydrogen–air mixtures under lean conditions to quantify the roles of the two flame stabilization modes at different operating pressures. Achieving fundamental understanding of the effect of pressure and hydrogen fraction on flame stabilization is crucial to the development of two-stage sequential combustion and the present two-dimensional calculations provide important new insights. We show that at high pressures, both modes consume fuel to a similar extent. We also investigated the effect of methane blending on flame stabilization. This study also discusses how two-dimensional direct numerical simulations can be leveraged in the design optimization of reheat burners at low technology readiness levels.

A novel subgrid-scale stress model considering the influence of combustion on turbulence: A priori and a posteriori assessment

Most classical turbulence models were proposed and developed based on non-reacting flows without considering the effects of combustion on turbulence. The flow structure in turbulent combustion is more complex, creating challenges to the applicability of traditional turbulence models. Given this, a novel flame surface and k-equation-based gradient model (FKGM) considering combustion effects is proposed for the modeling of the subgrid-scale (SGS) stress in large eddy simulation (LES). The SGS stress is calculated based on the SGS kinetic energy (kSGS) and normalized velocity gradient. The velocity gradient incorporates first-order gradients at multiple stencil locations and considers the anisotropy of the stress near the flame surface. The FKGM model is first validated by the a priori analysis based on the direct numerical simulation (DNS) database of a premixed swirling flame. The closure terms of the kSGS equation are well validated, and the predicted SGS stress using the FKGM model achieves good agreement with the filtered DNS results. In the a posteriori LES study, the FKGM model demonstrates better performance compared with the traditional dynamic Smagorinsky model and velocity gradient model, providing more accurate predictions for mean and fluctuation velocities. The error analysis for SGS kinetic energy is further conducted by comparing the LES results with the DNS data, and the results indicate that the underestimation of the generation term of the kSGS equation is the main source of error.

Thermal convection of a liquid metal under an alternating magnetic field

The objective of this work is to measure the heat transfer of a liquid metal in a cylindrical cell under the conjugate effects of a temperature difference and a Lorentz force generated by an alternating current in a coil. The experimental results are compared to recent direct numerical simulations (DNS) (Guillou et al., 2022). 25 experiments are performed for a large range of frequency f, ac intensity amplitude I0 and temperature difference between the top and bottom walls ΔT0: 15≤f≤1000Hz, 2≤I0≤67 A and 6≤ΔT0≤11 K. In these experiments, the Hartmann number Ha, the shielding parameter Sω and Rayleigh number Ra vary in the following range: 6≤Ha≤200, 1≤Sω≤70, 2.3×106≤Ra≤4.1×106. The experiments with an ac magnetic field are compared with the Rayleigh–Bénard convection (RBC) experiments under the same thermal conditions. Three rings of thermocouples allow characterizing the fluid temperature distribution during the convection. The heat flux at the bottom and top walls are also measured. We observe a very good agreement between the experimental results and the DNS results. As previously shown by numerical simulations, a master curve of Nu/Peω vs. QJ/Qc allows predicting the evolution of the heat transfer under different conditions of temperature difference and Lorentz force. Here Nu and Peω are the Nusselt number and a Péclet number based on the Lorentz force, and QJ and Qc are the total power deposited by the Joule effect and the total conduction heat flux without motion, respectively. The experiments show that Nu/Peω∼(QJ/Qc)−2/5.

Towards Direct Numerical Simulations of Reactivity-Controlled Compression Ignition Engine Using n-Octanol/Ethanol Fuel Blends

AbstractThe results of a two-dimensional direct numerical simulation of a lean n-octanol-ethanol fuel blend under Reactivity Controlled Compression Ignition (RCCI) conditions are presented in this paper. Stratified temperature and high reactivity fuel fields of Gaussian, bi-modal, and log-normal distributions are studied for uncorrelated and correlated scenarios. The pimple loop is made to run twice to achieve compression heating. A chemical mechanism with 171 species and 734 reactions was developed to capture autoignition characteristics and flame propagation reasonably well. Diagnosing techniques published in the literature are used to determine whether the flame fronts are spontaneously propagating or not. As reported previously for other fuel blends under RCCI conditions, both deflagration and spontaneous ignition flame fronts are observed to co-exist. Gaussian, bi-modal, and log-normal fields respectively move towards a spontaneously igniting mode. Correlating temperature and high reactivity fuel fields not only makes combustion more spontaneously igniting but also more premixed. The analysis reveals the sensitivity of the DNS results with respect to the initial conditions which accordingly should be chosen with care.

The Effect of Domain Length and Initialization Noise on Direct Numerical Simulation of Shear Stratified Turbulence

Direct numerical simulation (DNS) has been employed with success in a variety of oceanographic applications, particularly for investigating the internal dynamics of Kelvin–Helmholtz (KH) billows. However, it is difficult to relate these results directly with observations of ocean turbulence due to the significant scale differences involved (ocean shear layers are typically on the order of tens to hundreds of meters in thickness, compared to DNS studies, with layers on the order of one to tens of centimeters). As efforts continue to inform our understanding of geophysical-scale turbulence by extrapolating DNS results, it is important to understand the impact of model setup and initial conditions on the resulting turbulent quantities. Given that geophysical-scale measurements, whether through microstructures or other techniques, can only provide estimates of averaged TKE quantities (e.g., TKE dissipation or buoyancy flux), it may be necessary to compare mean turbulent quantities derived from DNS (i.e., across one or more complete billow evolutions) with ocean measurements. In this study, we analyze the effect of domain length and initial velocity noise on resulting turbulent quantities. Domain length is important, as dimensions that are not integer multiples of the natural KH billow wavelength may compress or stretch the billows and impact their energetics. The addition of random noise in the initial velocity field is often used to trigger turbulence and suppress secondary instabilities; however, the impact of noise on the resulting turbulent energetics is largely unknown. In this study, we conclude that domain lengths on the order of 1.5 times the natural wavelength or less can affect the resulting turbulent energetics by a factor of two or more. We also conclude that increasing the amplitude of random initial velocity noise decreases the resulting turbulent energetics, but that different realizations of the random noise field may have an even greater impact than amplitude. These results should be considered when designing a DNS experiment.

A compact open boundary treatment for a pure thermal plume by direct numerical simulation

This study introduces a novel open boundary treatment method for simulating thermal plumes in natural convection, utilizing a combination of the Perfectly Matched Layer (PML) and local one-dimensional inviscid (LODI) methods within a compressible flow solver for Direct Numerical Simulation (DNS). This innovative approach significantly reduces the size of the computational domain yet effectively captures the complex transition from laminar to turbulent flow. Validation of the proposed methodology includes comparisons with existing empirical formulations, experimental data, and well-resolved DNS results, incorporating both time-averaged and spectral analyses. Additionally, the buoyancy-induced laminar-turbulent transition is investigated to enhance understanding of the dynamics and behaviors of thermal plumes. The findings offer insights into optimizing computational efficiency without compromising the accuracy needed to analyze intricate fluid dynamics in thermal engineering applications.

High-flexibility reconstruction of small-scale motions in wall turbulence using a generalized zero-shot learning

This study proposes a novel super-resolution (or SR) framework for generating high-resolution turbulent boundary layer (TBL) flow from low-resolution inputs. The framework combines a super-resolution generative adversarial neural network (SRGAN) with down-sampling modules (DMs), integrating the residual of the continuity equation into the loss function. The DMs selectively filter out components with excessive energy dissipation in low-resolution fields prior to the super-resolution process. The framework iteratively applies the SRGAN and DM procedure to fully capture the energy cascade of multi-scale flow structures, collectively termed the SRGAN-based energy cascade reconstruction framework (EC-SRGAN). Despite being trained solely on turbulent channel flow data (via ‘zero-shot transfer’), EC-SRGAN exhibits remarkable generalization in predicting TBL small-scale velocity fields, accurately reproducing wavenumber spectra compared to direct numerical simulation (DNS) results. Furthermore, a super-resolution core is trained at a specific super-resolution ratio. By leveraging this pretrained super-resolution core, EC-SRGAN efficiently reconstructs TBL fields at multiple super-resolution ratios from various levels of low-resolution inputs, showcasing strong flexibility. By learning turbulent scale invariance, EC-SRGAN demonstrates robustness across different TBL datasets. These results underscore the potential of EC-SRGAN for generating and predicting wall turbulence with high flexibility, offering promising applications in addressing diverse TBL-related challenges.

Particle and wave dynamics of nonlocal solitons in external potentials

We study nonlocal bright solitons subject to external spatially nonuniform potentials. If the potential is slowly varying on the soliton scale, we derive analytical soliton solutions behaving like Newtonian particles. If the potential has the form of an attractive delta-like point defect, we identify different dynamical regimes, defined by the relative strength of the nonlocality and the point defect. In these regimes, the soliton can be trapped at the defect's location, via a nonlinear resonance with a defect mode –which is found analytically– reflected by or transmitted through the defect, featuring a wave behavior. Our analytical predictions are corroborated by results of direct numerical simulations.

Drag, lift, and torque correlations for axi-symmetric rod-like non-spherical particles in linear wall-bounded shear flow

This paper presents novel correlations to predict the drag, lift, and torque coefficients of axi-symmetric non-spherical rod-like particles in a wall-bounded linear shear flow. The particle position and orientation relative to the wall are varied to systematically investigate the influence of the wall on the hydrodynamic forces. The newly derived correlations for drag, lift, and torque on the particle depend on various parameters, including the particle Reynolds number, the orientation angle between the major axis of the particle and the main local flow direction, the aspect ratio of the particle, and the dimensionless distance from the particle centre to the wall. The impact of the wall on the hydrodynamic forces is accounted for as a function of a multiplication factor on the drag force in case of locally uniform flow, and an additional force contribution for the lift and the torque, modifying the resultant forces experienced by a particle in a locally uniform flow. The changes in the hydrodynamic forces prove to be substantial, emphasizing the necessity of accounting for wall effects across all particle types and flow conditions investigated in this study. The coefficients of the correlations are determined through a fitting process utilizing the data generated from our previous study on the interaction forces between a locally uniform flow and an axi-symmetric non-spherical rod-like particles, as well as from data of novel direct numerical simulations (DNS) performed in this work of flow past axi-symmetric rod-like particles near a wall. The proposed correlations exhibit a good agreement compared to the DNS results, with median errors of 2.89%, 5.37%, and 11.00%, and correlation coefficients of 0.99, 0.99, and 0.96 for the correlations accounting for the drag, lift, and torque coefficients of a non-spherical particle in wall-bounded linear shear flow profile, respectively. These correlations can be used in large-scale simulations using an Eulerian–Lagrangian or a CFD/DEM framework to predict the behaviour of axi-symmetric rod-like non-spherical particles in wall-bounded shear flow to locally uniform flow conditions.

Investigations on the turbulentnon-turbulent interface in supersonic compressible plate turbulent boundary layer

The turbulent boundary layer (TBL) is a widely existing flow phenomenon in nature and engineering applications. Its strong mixing effect can achieve more sufficient material mixing, heat transport, etc. The understanding of the entrainment process and mechanism of irrotational fluids entering the turbulent region can be promoted by studying the geometric and dynamic characteristics of turbulent ${/}$ non-turbulent interfaces (TNTI). In compressible flow, it is unclear whether the properties of TNTI will change and whether the entrainment will show different features due to the influence of compressibility. Based on the direct numerical simulation results of supersonic compressible plate TBLs with Mach number of 2.9, the geometric and dynamic characteristics of TNTI are investigated in this paper. The interface is identified by the enstrophy method, and the height, thickness, fractal dimension, enstrophy transportation and entrainment characteristics of the interface are investigated. It is found that for the enstrophy transportation in a TBL, the contribution of compressibility-related terms accounts for approximately 13.4 % of the total enstrophy transportation, which tends to transfer the enstrophy of turbulence near the interface to both directions vertical to the interface. This promotes the expansion of the turbulent region towards the non-turbulent region, and the mean height, thickness and entrainment velocity are increased by approximately 3.7 %, 7.0 % and 8.5 %, respectively, while the fractal dimension is basically unaffected. Different from the incompressible flow, the contribution of the compressibility-related terms to the entrainment velocity is independent of the local curvature, and the intense entrainment process is more likely to occur on a highly curved concave surface.