Three-dimensional Direct Numerical Simulations Research Articles

Impact of pressure anisotropy on the cascade rate of Hall magnetohydrodynamic turbulence with biadiabatic ions

The impact of ion pressure anisotropy on the energy cascade rate of Hall-MHD turbulence with biadiabatic ions and isothermal electrons is evaluated in three-dimensional direct numerical simulations, using the exact (or third-order) law derived by Simon and Sahraoui in 2022. It is shown that pressure anisotropy can enhance or reduce the cascade rate, depending on the scales, in comparison with the prediction of the exact law with isotropic pressure, by an amount that correlates well with pressure anisotropy, ap=p⊥p∥≠1, that develops in simulations initialized with an isotropic pressure (ap0=1). A simulation with initial pressure anisotropy ap0=4 confirms this trend, exhibiting a stronger impact on the cascade rate, both in the inertial range and at larger scales, close to the forcing scales. Furthermore, a Fourier-based numerical method, to compute exact laws in numerical simulations in the full (ℓ⊥,ℓ∥) increment plane, is presented. Published by the American Physical Society 2025

How interfacial tension enhances drag in turbulent Taylor–Couette flow with neutrally buoyant and equally viscous droplets

The presence of dispersed-phase droplets can result in a notable increase in a system's drag. However, our understanding of the mechanism underlying this phenomenon remains limited. In this study, we use three-dimensional direct numerical simulations with a modified multi-marker volume-of-fluid method to investigate liquid–liquid two-phase turbulence in a Taylor–Couette geometry. The dispersed phase has the same density and viscosity as the continuous phase. The Reynolds number $Re\equiv r_i\omega _i d/\nu$ is fixed at 5200, the volume fraction of the dispersed phase is up to $40\,\%$ , and the Weber number $We\equiv \rho u^2_\tau d/\sigma$ is approximately 8. It is found that the increase in the system's drag originates from the contribution of interfacial tension. Specifically, droplets experience significant deformation and stretching in the streamwise direction due to shear near the inner cylinder. Consequently, the rear end of the droplets lags behind the fore head. This causes opposing interfacial tension effects on the fore head and rear end of the droplets. For the fore head of the droplets, the effect of interfacial tension appears to act against the flow direction. For the rear end, the effect appears to act in the flow direction. The increase in the system's drag is attributed primarily to the effect of interfacial tension on the fore head of the droplets which leads to the hindering effect of the droplets on the surrounding continuous phase. This hindering effect disrupts the formation of high-speed streaks, favouring the formation of low-speed ones, which are generally associated with higher viscous stress and drag of the system. This study provides new insights into the mechanism of drag enhancement reported in our previous experiments.

Unsteady motion of nearly spherical particles in viscous fluids: a second-order asymptotic theory

The motion of small non-spherical particles is often studied using the unsteady Stokes equations. Zhang & Stone (J. Fluid Mech., vol. 367, 1998, pp. 329–358) reported an asymptotic treatment for nearly spherical particles, to first order in particle non-sphericity, i.e. $O(\epsilon )$ , where $\epsilon$ quantifies the shape deviation from a sphere. Importantly, key physical phenomena are absent at $O(\epsilon )$ , including (1) coupling between the torque experienced by the particle and its linear translation, (2) coupling between the force the particle experiences and its rotation and (3) the effect of non-sphericity on the orientation averages of these forces and torques. We present an explicit asymptotic theory to second order in particle non-sphericity, i.e. $O(\epsilon ^2)$ , for the force and torque acting on a particle in a general unsteady Stokes flow. The derived analytical formulae apply to particles of arbitrary shape, providing the leading-order asymptotic theory for the three above-mentioned phenomena. The theory is demonstrated for several example nearly spherical particles including a spheroid, a ‘pear-shaped’ particle and a simple model for a SARS-CoV-2 virion. This includes formulae for force and torque as a function of particle orientation and their corresponding orientation averages. Our study reveals that the orientation-averaged forces and torques experienced by a nearly spherical particle cannot be generally represented by a perfect sphere. The reported formulae are validated using finite-amplitude three-dimensional direct numerical simulations of the Navier–Stokes equations. A Mathematica notebook is also provided, facilitating implementation of the theory for particle shapes of the user's choosing.

Turbulence modulation in liquid–liquid two-phase Taylor–Couette turbulence

We investigate the coupling effects of the two-phase interface, viscosity ratio and density ratio of the dispersed phase to the continuous phase on the flow statistics in two-phase Taylor–Couette turbulence at a system Reynolds number of $6\times 10^3$ and a system Weber number of 10 using interface-resolved three-dimensional direct numerical simulations with the volume-of-fluid method. Our study focuses on four different scenarios: neutral droplets, low-viscosity droplets, light droplets and low-viscosity light droplets. We find that neutral droplets and low-viscosity droplets primarily contribute to drag enhancement through the two-phase interface, whereas light droplets reduce the system's drag by explicitly reducing Reynolds stress due to the density dependence of Reynolds stress. In addition, low-viscosity light droplets contribute to greater drag reduction by further reducing momentum transport near the inner cylinder and implicitly reducing Reynolds stress. While interfacial tension enhances turbulent kinetic energy (TKE) transport, drag enhancement is not strongly correlated with TKE transport for both neutral droplets and low-viscosity droplets. Light droplets primarily reduce the production term by diminishing Reynolds stress, whereas the density contrast between the phases boosts TKE transport near the inner wall. Therefore, the reduction in the dissipation rate is predominantly attributed to decreased turbulence production, causing drag reduction. For low-viscosity light droplets, the production term diminishes further, primarily due to their greater reduction in Reynolds stress, while reduced viscosity weakens the density difference's contribution to TKE transport near the inner cylinder, resulting in a more pronounced reduction in the dissipation rate and consequently stronger drag reduction. Our findings provide new insights into the physics of turbulence modulation by the dispersed phase in two-phase turbulence systems.

ML enhanced measurement of the electrostatic charge distribution of powder conveyed through a duct

The electrostatic charge acquired by powders during transport through ducts can cause devastating dust explosions. Our recently developed laser-optical measurement technique can resolve the powder charge along a one-dimensional (1D) path. However, the charge across the duct’s complete two-dimensional (2D) cross-section, which is the critical parameter for process safety, is generally unavailable due to limited optical access. To estimate the complete powder charge distribution in a conveying duct, we propose a machine learning (ML) approach using a shallow neural network (SNN). The ML algorithm is trained with cross-sectional data extracted from four different three-dimensional direct numerical simulations of a turbulent duct flow with varying particle size. Through this training with simulation data, the ML algorithm can estimate the powder charge distribution in the duct’s cross-section based on only 1D measurements. The results reveal an average L1-error of the reconstructed 2D cross-section of 1.63%.

Intrinsic characteristics of three-dimensional flow around a wall-mounted conical cylinder

To investigate the flow characteristics around a wall-mounted conical cylinder, three-dimensional direct numerical simulations are carried out for a conical cylinder with an end diameter ratio ranging from 0.5 to 1.5 at three low Reynolds numbers (Re = 100, 150, 200). The flow features are examined in terms of time-mean streamlines, singularity points location, topological structure, time-mean streamwise vortices, and instantaneous spanwise vortices denoted with different vortex identification methods. The downwash effect also happens even without a free end. The upwash streamlines clash with the downwash streamlines and then coalesce to the saddle (impingement) point P2. The occurrence of the symmetry plane belongs to a new topology, where the saddle point on the bottom wall is an attachment point (NA), instead of the separation point (SS). The singular point verifies the topological existence of the attachment–attachment combination of the horseshoe vortex system. The “Quadrupole Type,” “Sextupole Type,” and “Octupole Type” are identified. The “Octupole Type” is reported first, consisting of a pair of “time-mean streamwise tip vortices,” two pairs of “time-mean streamwise base vortices” and a pair of “time-mean streamwise bottom vortices.” Moreover, the vorticity magnitude cannot represent the occurrence of vortices. The instantaneous iso-surfaces of Q = 0.2 and λ2 = –0.2 in the wake are similar to the threshold of Ω = 0.52. In contrast, the Liutex/Rortex method is easier to identify the streamwise bottom vortices than the former two methods.

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 Sengupta, et al. (2022) [35] 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.

The influence of non-Newtonian behaviors of blood on the hemodynamics past a bileaflet mechanical heart valve

This study employs extensive three-dimensional direct numerical simulations to investigate the hemodynamics around a bileaflet mechanical heart valve. In particular, this study focuses on assessing whether non-Newtonian rheological behaviors of blood, such as shear-thinning and yield stress behaviors, exert an influence on hemodynamics compared to the simplistic Newtonian behavior under both steady inflow and physiologically realistic pulsatile flow conditions. Under steady inflow conditions, the study reveals that blood rheology impacts velocity and pressure field variations, as well as the values of clinically important surface and time-averaged parameters like wall shear stress (WSS) and pressure recovery. Notably, this influence is most pronounced at low Reynolds numbers, gradually diminishing as the Reynolds number increases. For instance, surface-averaged WSS values obtained with the non-Newtonian shear-thinning power-law model exceed those obtained with the Newtonian model. At Re=750, this difference reaches around 67%, reducing to less than 1% at Re=5000. Correspondingly, pressure recovery downstream of the valve leaflets is lower for the shear-thinning blood than the constant viscosity one, with the difference decreasing as the Reynolds number increases. On the other hand, in pulsatile flow conditions, jets formed between the leaflets and the valve housing wall are shorter than steady inflow conditions. Additionally, surface-averaged wall shear stress and blood damage (BD) parameter values are higher (with differences more than 13% and 47%, respectively) during the peak stage of the cardiac cycle, especially for blood exhibiting non-Newtonian yield stress characteristics compared to the shear-thinning or constant viscosity characteristics. Therefore, blood non-Newtonian behaviors, including shear-thinning and yield stress behaviors, exert a considerable influence on the hemodynamics around a mechanical heart valve. All in all, the findings of this study demonstrate the importance of considering non-Newtonian blood behaviors when designing blood-contacting medical devices, such as mechanical heart valves, to enhance functionality and performance.

A meshless model for three-dimensional direct numerical simulation of local scour around cylinder bridge foundation

A meshless local scour model for cylinder bridge foundation based on the smoothed particle hydrodynamics (SPH) method is proposed in this paper. Differing from the traditional Eulerian mesh model used for monopile local scour, it overcomes the high requirements of mesh quality and density for capturing large deformations at the fluid interface. Unlike the transient sediment erosion SPH model used for dam-break, sediment flushing, and water jet, the meshless approach is innovatively applied to the continuous simulation of bridge local scour under steady flow conditions. The present SPH model is established based on the SPH multi-phase fluid model, integrating a classical fluid model combined with numerical stabilization algorithms to govern water particle motion and a sediment model from Zhang et al. (2024) to govern sediment evolution, and tests a new scheme for boundary treatment in the model based on DualSPHysics. Furthermore, a novel scour visualization method that aims at extracting both visible and actual bed surfaces from discrete particles is proposed. The model is validated through comparison with rigid bed and live bed experiments, demonstrating favorable agreement in terms of flow and scour simulation. Importantly, the model results reveal a discrepancy between the elevation of the post-scour visible bed surface derived from the conventional Eulerian mesh model and experimental data, compared to the actual bed surface unaffected by water flow erosion. This indicates the necessity for incorporating a safety margin in foundation design when utilizing experimental results to determine the maximum scour depth.

Direct Numerical Simulation of Tandem-Wing Aerodynamic Interactions at Low Reynolds Number

A three-dimensional direct numerical simulation was conducted to investigate the vortex–wing interactions through two NACA 0012 stationary wings placed in tandem at a low Reynolds number Re=10,000. The aerodynamic characteristics and three-dimensional flow structures were analyzed for the tandem wings. The back wing disturbed by the upstream vortices gained an evident increase in aerodynamic performance, where the advantage is related to the suppression of the large-scale vortex formation near the trailing edge. The Liutex method was applied to visualize the vortical structures for investigating the three-dimensional evolution and instability when interacting with the back wing. The upstream wake triggered dual-secondary vortices and intensified the secondary instability on the back wing. The induced vortices contributed to the lift enhancement because they provided an extra low-pressure region when propagating downstream on the suction side of the back wing. Because of the three-dimensional destabilization, the vortex interaction in the evolution process accelerated the transition and injection of the high-momentum flow into the boundary layer attached to the back wing, energizing the turbulent boundary layer and eliminating the large-scale separation near the trailing edge. This study provided a new perspective on the enhanced aerodynamic performance of tandem layout.

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.

Vortex-shedding modes of a pair of side-by-side thin pitching plates

We have conducted three-dimensional (3D) direct numerical simulations to analyze vortex-shedding modes past vertically arranged, side-by-side 3D pitching plates, considering cases where the plates are in the same, opposite, and different phases. The simulations are performed at a Reynolds number Re=1000, with a dimensionless pitching frequency St=1, and a maximum pitching angle θmax=15°. The vortex-shedding modes reveal horseshoe vortices transforming into distorted hairpin-like structures in the far wake for in-phase plates. Opposite phase plates exhibit helical distortion and core bifurcation, while different phase angles produce meridionally twisted, entangled hairpins. We observe a reverse von Kármán vortex street for in- and different-phase plates, while the opposite shows a reverse Kármán vortex street for the upper plate and a Kármán vortex street for the lower plate. The streakline visualizations reveal wake compression and spoke-like structures symmetrically emanating from the shear layer extremities around the plates' central region. We find leapfrog-like cross-stream vortex interaction when the plates are in phase. The line-time diagram reveals alternating patches of low-intensity cells, switching between negative and positive, alongside continuous bands of both positive and negative cells. Both plates produce similar thrust for the parameters examined in this study.

A Comparison Between Conventional and MILD Combustion Processes of Turbulent Stratified Mixtures

ABSTRACT The relative enhancements of volume-integrated burning rate and flame surface area under turbulence and heat release rate contributions due to different combustion and flame propagation modes have been compared between conventional and Moderate or Intense Low Oxygen Dilution (MILD) combustion of stratified mixtures (for a global mean equivalence ratio of 0.8) for the first time using three-dimensional Direct Numerical Simulation (DNS) data. The burning rate enhancement under turbulence is found to be comparable to the enhancement of flame surface area for the conventional stratified flames considered here, whereas the burning rate enhancement is found to be considerably greater than flame area augmentation in the MILD cases analyzed here. It has been found that almost all the heat release rate arises due to the lean-premixed mode of combustion for the conventional stratified flame cases considered here. In contrast, the lean premixed mode of combustion accounts for about 50% of the total heat release rate for the MILD cases where rich-premixed and non-premixed modes of combustion contribute significantly to the overall heat release rate. Under the conditions analyzed here, more than 75% of heat release rate arises from the propagation-dominated regions for both MILD combustion and stratified flame cases, but the trend is stronger in the conventional stratified mixture combustion. More than 80% of heat release rate in the globally lean conventional stratified flame cases considered here originates from back-supported flame propagation, whereas both front and back-supported flame propagation modes have comparable contributions to heat release in the MILD combustion cases. The non-premixed mode of combustion has been found to play a more important role in the MILD combustion cases than in the case of conventional stratified flames. This implies that the closures, which work reasonably well for MILD combustion of homogeneous mixtures, may not be sufficient for modeling of MILD combustion of stratified/inhomogeneous mixtures.

Direct numerical simulations of pure and partially cracked ammonia/air turbulent premixed jet flames

Ammonia has been identified as a promising fuel to diminish greenhouse gas emission. However, ammonia combustion presents certain challenges including low reactivity and high NO emission. In the present study, three-dimensional direct numerical simulations (DNS) of ammonia/air premixed slot jet flames with varying Karlovitz numbers (Ka) and cracking ratios were performed. Three cases were considered, including two pure ammonia/air flames with different turbulence intensities and one partially cracked ammonia/air flame with high turbulence intensity. The effects of turbulence intensity and partial ammonia cracking on turbulence–flame interactions and NO emission characteristics of the flames were investigated. It was shown that the turbulent flame speed is higher for the flames with high turbulence intensity. In general, the flame displacement speed is negatively correlated with curvature in negative curvature regions, while the correlation is weak in the positive curvature regions for highly turbulent flames. Most flame area is consumed in negatively curved regions and produced in positively curved regions. It was found that the NO mass fraction is higher in the flame with partial ammonia cracking compared to the pure ammonia/air flames. The NO pathway analysis shows that the NH → NO pathway is enhanced, while the NO consumption pathway is suppressed in the partially cracked ammonia/air flame. The NO mass fraction is higher in regions of negative curvature than positive curvature. Interestingly, the NO mass fraction is found to be negatively correlated with the local equivalence ratio, which is consistent in both the DNS and the corresponding laminar premixed flames.

Dynamics and Wake Interference Mechanism of Long Flexible Circular Cylinders in Side-by-Side Arrangements

The vortex-induced vibrations of two side-by-side flexible cylinders in a uniform flow were studied using a three-dimensional direct numerical simulation at Reynolds number Re = 350 with an aspect ratio of 100, and a center-to-center spacing ratio of 2.5. A mixture of standing-traveling wave pattern was induced in the in-line (IL) vibration, while the cross-flow (CF) vibration displayed a standing-wave characteristic. The ninth vibration mode prominently occurred in both IL and CF directions, along with competition between multiple modes. Proximity effects from the neighboring cylinder caused the primary frequency to be consistent between IL and CF vibrations for each cylinder, deviating from the IL to CF ratio of 2:1 in isolated cylinder conditions. Repulsive mean lift coefficients were observed in both stationary and vibrating conditions for the two cylinders due to asymmetrical vortex shedding in this small gap. Comparatively, lift and drag coefficients were notably increased in the vibrating condition, albeit with a lower vortex shedding frequency. Positive energy transfer was predominantly excited along the span via vortex shedding from the cylinder itself and the neighboring one, leading to increasing lower-mode vibration amplitudes. The flip-flopping (FF) wake pattern was excited in the stationary and vibrating cylinders, causing spanwise vortex dislocations and wake transition over time, with the FF pattern being more regular in the stationary cylinder case.

Fingering convection in a spherical shell

We use $123$ three-dimensional direct numerical simulations to study fingering convection in non-rotating spherical shells. We investigate the scaling behaviour of the flow length scale, the non-dimensional heat and compositional fluxes $Nu$ and $Sh$ and the mean convective velocity over the fingering convection instability domain defined by $1 \leq R_\rho < Le$ , $R_\rho$ being the ratio of density perturbations of thermal and compositional origins and $Le$ the Lewis number. We show that the chemical boundary layers are marginally unstable and adhere to the laminar Prandtl–Blasius model, hence explaining the asymmetry between the inner and outer spherical shell boundary layers. We develop scaling laws for two asymptotic regimes close to the two edges of the instability domain, namely $R_\rho \lesssim Le$ and $R_\rho \gtrsim 1$ . For the former, we develop novel power laws of a small parameter $\epsilon$ measuring the distance to onset, which differ from theoretical laws published to date in Cartesian geometry. For the latter, we find that the Sherwood number $Sh$ gradually approaches a scaling $Sh\sim Ra_\xi ^{1/3}$ when $Ra_\xi \gg 1$ ; and that the Péclet number accordingly follows $Pe \sim Ra_\xi ^{2/3} |Ra_T|^{-1/4}$ , $Ra_T$ and $Ra_{\xi}$ being the thermal and chemical Rayleigh numbers. When the Reynolds number exceeds a few tens, we report on a secondary instability which takes the form of large-scale toroidal jets which span the entire spherical domain. Jets distort the fingers, resulting in Reynolds stress correlations, which in turn feed the jet growth until saturation. This nonlinear phenomenon can yield relaxation oscillation cycles.

Evaluation of the wall heat flux in filtered premixed turbulent combustion

The paper focuses on modelling the heat flux through the isothermal wall boundary in premixed turbulent combustion. In a statistically stationary configuration, the distorted flames, advected by the incoming flow toward the wall, can be either head-on or entrained. The wall heat flux model with respect to the head-on and entrained parts are constructed differently to describe their distinct behaviours. In model validation, to exclude the interference from various inaccuracies, either numerically or experimentally, the filtered three-dimensional direct numerical simulation (DNS) fields are adopted as benchmark. Results justify that the newly proposed model is able to capture the wall heat flux statistics. The predictions are consistently satisfactory at different filter widths, performing clearly better than direct evaluation from the filtered temperature gradient and effective diffusivity. In addition, it is also straightforward to integrate this model together with existing flow solvers.

Investigation of Sidewall and Reynolds Number Effects in a Ribbed Square Duct

This paper presents a comprehensive three-dimensional Direct Numerical Simulation (DNS) investigation of flow characteristics over a roughened wall in a duct, exploring bulk Reynolds number variations from 4400 to 13,200 and considering the influence of side walls. Notably, a significant increase in friction factor highlights heightened resistance to flow due to surface roughness, emphasizing the importance of considering surface conditions in engineering applications. The study reveals three recirculation zones in the streamwise direction, indicating intricate separation phenomena caused by the interaction between the ribbed wall and the flow. Furthermore, the presence of sidewalls creates two major vortices perpendicular to the flow direction, highlighting the complexity of the vortical structures in this configuration, crucial for predicting flow behavior and optimizing system performance. The study demonstrates that the influence of the Reynolds number on these vortices is not well-scalable with respect to outer units, in contrast with respect to smooth ducts. Investigating side-wall effects, increased turbulent production rate, and non-equilibrium turbulence along the side walls highlight the sensitivity of turbulent stresses to Reynolds number and side-wall proximity. In conclusion, the paper provides novel insights into the interplay between Reynolds numbers, roughened surfaces, and boundary conditions in turbulent flows, laying a foundation for a deeper understanding of the flow in duct with high roughness.

Connecting finite-time Lyapunov exponents with supersaturation and droplet dynamics in a turbulent bulk flow.

The impact of turbulent mixing on an ensemble of initially monodisperse water droplets is studied in a turbulent bulk that serves as a simplified setup for the interior of a turbulent ice-free cloud. A mixing model was implemented that summarizes the balance equationsof water vapor mixing ratio and temperature to an effective advection-diffusion equationfor the supersaturation field s(x,t). Our three-dimensional direct numerical simulations connect the velocity and scalar supersaturation fields in the Eulerian frame of reference to an ensemble of cloud droplets in the Lagrangian frame of reference. The droplets are modeled as point particles with and without effects due to inertia. The droplet radius is subject to growth by vapor diffusion. We report the dependence of the droplet size distribution on the box size, initial droplet radius, and the strength of the updraft, with and without gravitational settling. In addition, the three finite-time Lyapunov exponents λ_{1}≥λ_{2}≥λ_{3} are monitored which probe the local stretching properties along the particle tracks. In this way, we can relate regions of higher compressive strain to those of high local supersaturation amplitudes. For the present parameter range, the mixing process in terms of the droplet evaporation is always homogeneous, while it is inhomogeneous with respect to the relaxation of the supersaturation field. The probability density function of the third finite-time Lyapunov exponent, λ_{3}<0, is related to the one of the supersaturation s by a simple one-dimensional aggregation model. The probability density function (PDF) of λ_{3} and the droplet radius r are found to be Gaussian, while the PDF of the supersaturation field shows sub-Gaussian tails.