3D Direct Numerical Simulations Research Articles

Investigation of the derivation and consistency of the quasi-two-dimensional flamelet models for non-premixed flames

Three non-premixed quasi-two-dimensional flamelet (Q2DF) models can be derived via integrating one-dimensional flamelet libraries, which are generated by premixing the third stream with the fuel stream or (and) the oxidizer stream as the premix fraction (η) varied from zero to unity. These models are attractive and considered effective substitutes for two-dimensional flamelet (2DF) formulations; however, the connections between these Q2DF models and 2DF equations have not been clearly illustrated formerly. In this work, the 2DF formulations are converted from the space defined by two mixture fractions (Z1×Z2) to that used for each Q2DF model (ξ×η) in which ξ designates a newly defined mixture fraction. For moderate Reynolds number conditions, it is considered that the Q2DF models and the 2DF formulations are equivalents as the one-dimensional (1D) flamelet elemental libraries are integrated upon sufficient grids of η. To confirm this, the two-dimensional (2D) direct numerical simulations (DNS) and three-dimensional (3D) large-eddy simulation (LES) are performed to provide reference data since it is readily to associate the 2DF formulations with variable transports in physical space. The 2D DNS cases present various three-feed systems characterized by different third streams and ensure a well-mixed mixture in moderate η, while the 3D LES case is performed with a large flux of pure CO2 as the third stream. Three Q2DF models are compared by using the same tracking parameters obtained from, respectively, the DNSs and LES. The comparisons based on the DNS cases demonstrate that the Q2DF models can reproduce the DNS data with quite satisfying accuracy, and it is confirmed that the accuracy has nothing to do with the type of the third stream. Through the LES results and the related comparisons, it can be concluded that the Q2DF models are reliable to predict the experimental measurements, and on the condition of a sufficient η resolution, the three Q2DF models can give the same prediction in the whole range of η.

The flow dynamics in a short annulus with rotating end-walls

The paper reports on the 3D direct numerical simulation (DNS) results of the flow in a short annulus of aspect ratios 3.8–4.8 and radius ratios 0.45, 0.5 with end-walls attached to a rotating inner cylinder. The research is focused on the bifurcation processes occurring in the local unsteady area, existing at very low Reynolds numbers (Re = 90–164) - this unsteady area is associated with the presence of the codimension-2 point occurring in this range of parameters. The study has revealed many interesting phenomena, e.g. the period-doubling, the homoclinic collision and the second modulated wave. New bifurcation lines have been determined. The DNS results are analyzed in the light of experimental data published so far. At higher Reynolds numbers the next unsteady area occurs, dynamical features of which have been studied in detail for Re up to 1000. The computations have also been performed for the configurations with cylinders rotating in the co- and counter-rotating systems with rotational rate Ωout/Ωin = ± 0.1 and ± 0.2, to determine the impact of these new boundary conditions on the bifurcation processes.

A simplified two-mixture-fraction-based flamelet modelling and its validation on a non-premixed staged combustion system

A simplified two-mixture-fraction-based flamelet model is proposed in this work for a non-premixed staged combustion mode in which three feeds are introduced into the flow field. As the third stream is injected downstream of the main port, the system can be considered a special case of the two-mixture-fraction-based systems. It is considered that if a well-mixing is achieved in the upper stream prior to the third-stream injection, the simplification of the two-mixture-fraction-based flamelet model is feasible. In this work, a simplified model is proposed which can greatly reduce the library size compared to the complete two-mixture-fraction-based flamelet library providing identical resolutions for the fuel stream mixture fraction and the progress variable, respectively. Analysis associated with the interpolation strategy has been implemented. Extension of the current model for the cases in which the well-mixing state is not attained is also analysed, as well as the consideration of heat loss. To validate the model, two adiabatic cases of two-dimensional (2D) direct numerical simulations (DNS) have been performed in this work. To describe the chemical events, one is using finite-rate chemistry (FRC), while the other one is realised by means of the current flamelet model (FLM). An a priori test case that directly looks up the libraries by using the tracking parameters obtained from the FRC case is also considered. It is observed that the interpolation along the primary oxidiser mixture fraction direction outperforms that along directions for both fuel and primary oxidiser mixture fractions. It is also found that three one-mixture-fraction-based flamelet libraries which form the current model are sufficient for simulation of the non-premixed staged combustion, while the extended one which composes five libraries is expected to gain higher accurateness. In the FLM case, although the distributions of tracking parameters deviate from the FRC case slightly, good agreements can be obtained in terms of temperature and species mass fractions. The a priori test shows that the current model can reproduce the reacting flow accurately when the tracking parameters are identical to the FRC case. It is confirmed that the current model can be used to predict the characteristics of the reacting flow in the non-premixed staged combustion.

Spiral- and scroll-wave dynamics in mathematical models for canine and human ventricular tissue with varying Potassium and Calcium currents

We conduct a systematic, direct-numerical-simulation (DNS) study, in mathematical models for ventricular tissue, of the dependence of spiral- and scroll-wave dynamics on GKr, the maximal conductance of the delayed rectifier Potassium current (IKr) channel, and the parameter γCao, which determines the magnitude and shape of the current ICaL for the L-type calcium-current channel, in both square and anatomically realistic, whole-ventricle simulation domains. We study canine and human models. In the former, we use a canine-ventricular geometry, with fiber-orientation details, obtained from diffusion-tensor-magnetic-resonance-imaging (DTMRI) data; and we employ the physiologically realistic Hund-Rudy-Dynamic (HRD) model for a canine ventricular myocyte. To focus on the dependence of spiral- and scroll-wave dynamics on GKr and γCao, we restrict ourselves to an HRD-model parameter regime, which does not produce spiral- and scroll-wave instabilities because of other, well-studied causes like a very sharp action-potential-duration-restitution (APDR) curve or early after depolarizations (EADs) at the single-cell level. We find that spiral- or scroll-wave dynamics are affected predominantly by a simultaneous change in ICaL and IKr from their original values in the model, rather than by a change in any one of these currents; other currents do not have such a large effect on these wave dynamics in this parameter regime of the HRD model. In particular, we examine spiral-wave dynamics for ten different values of GKr and ten different values of γCao in our 2D DNSs. For our 3D DNSs in an anatomically realistic domain, we chose 16 parameter sets. In the parameter regime we begin with, the system displays broken spiral or scroll states with S1–S2 initial conditions (see below). We show that, by simultaneously increasing GKr and reducing γCao, we can get to a parameter regime in which the system displays single, stable rotating spirals or scroll waves. We obtain stability diagrams (or phase diagrams) in the GKr−γCao plane; and we find that these diagrams are significantly different in our 2D and 3D studies. In the 3D case, the geometry of the domain itself supports the confinement of the scroll waves and makes them more stable compared to their spiral-wave counterparts in our flat, 2D simulation domain. Thus, a combination of functional and geometrical mechanisms produce different dynamics for 3D scroll waves and their 2D spiral-wave counterparts. In particular, the former do not break easily because, in an anatomically realistic ventricular geometry, they are not easily absorbed at boundaries, nor do they break near boundaries. We have also carried out a comparison of our HRD results with their counterparts for the human-ventricular TP06 model; and we have found important differences between wave dynamics in these two models. The region in parameter space, where we obtain broken spiral or scroll waves in the HRD model is the region of stable rotating waves in the TP06 model; the default parameter values produce broken waves in the HRD model, but stable scrolls in the TP06 model. In both these models, to make a transition, (most simply, from broken-wave to stable-scroll states) we must simultaneously increase IKr and decrease ICaL; a modification of only one of these currents is not enough to effect this transition. Furthermore, the converse, i.e., an increase in ICaL along with a decrease in IKr does not yield any interesting dynamical transitions in the HRD model, for, in this range of currents, this model does not sustain spiral or scroll waves or broken waves.

Supercritical and subcritical rotating convection in a horizontally periodic box with no-slip walls at the top and bottom

The study of instabilities in the convection of rotating fluids is one of the classical topics of research. However, in spite of more than five decades of research, the instabilities and related transition scenarios near the onset of rotating convection of low Prandtl number fluids are not well understood. Here, we investigate the transition scenario in rotating Rayleigh–Bénard convection with no-slip boundary conditions by performing 3D direct numerical simulations (DNS) and low-dimensional modeling. The governing parameters, namely, the Taylor number (Ta), Rayleigh number (Ra), and Prandtl number (Pr), are varied in the ranges 0<Ta≤8×103, 0<Ra<1×104, and 0<Pr≤0.35, where convection appears as a stationary cellular pattern. In DNS, for Pr<0.31, the supercritical or subcritical onset of convection appears, according as Ta>Tac(Pr) or Ta<Tac(Pr), where Tac(Pr) is a Pr dependent threshold of Ta. On the other hand, only supercritical onset of convection is observed for Pr≥0.31. At the subcritical onset, both finite amplitude stationary and time dependent solutions are manifested. The origin of these solutions are explained using a low dimensional model. DNS show that as Ra is increased beyond the onset of convection, the system becomes time dependent and depending on Pr, standing and traveling wave solutions are observed. For very small Pr (≤0.045), interestingly, finite amplitude time dependent solutions are manifested at the onset for higher Ta.

Onset of turbulence in channel flows with scale-invariant roughness

Using 3D direct numerical simulations of the Navier--Stokes equations, we study the effect of a self-affine wall roughness on the onset of turbulence in channel flow. We quantify the dependence of the turbulent intensity (proportional to the mean-squared velocity fluctuations) on the Reynolds number $\mathrm{Re}$ for different roughness amplitudes $A$. We find that for sufficiently high amplitudes, $A>{A}_{b}$, the transition changes its nature from being subcritical (as is known at $A=0$) to supercritical, i.e., the boundary roughness renders the flow unstable for $\mathrm{Re}>{\mathrm{Re}}_{l}$, where the critical ${\mathrm{Re}}_{l}$ decays nontrivially with increasing $A$. The dependence of the friction factor on $\mathrm{Re}$ is found to follow a generalized Forchheimer law, which interpolates between the laminar and inertial asymptotes. The transition between these two asymptotes occurs at a second critical ${\mathrm{Re}}_{\text{c}}$ which is comparable in magnitude to ${\mathrm{Re}}_{l}$. This implies that transitional flow is an integral part of flow in open fractures when $\mathrm{Re}$ is sufficiently high, and should be accounted for in effective modeling approaches.

Investigating microscale patchiness of motile microbes under turbulence in a simulated convective mixed layer.

Microbes play a primary role in aquatic ecosystems and biogeochemical cycles. Spatial patchiness is a critical factor underlying these activities, influencing biological productivity, nutrient cycling and dynamics across trophic levels. Incorporating spatial dynamics into microbial models is a long-standing challenge, particularly where small-scale turbulence is involved. Here, we combine a fully 3D direct numerical simulation of convective mixed layer turbulence, with an individual-based microbial model to test the key hypothesis that the coupling of gyrotactic motility and turbulence drives intense microscale patchiness. The fluid model simulates turbulent convection caused by heat loss through the fluid surface, for example during the night, during autumnal or winter cooling or during a cold-air outbreak. We find that under such conditions, turbulence-driven patchiness is depth-structured and requires high motility: Near the fluid surface, intense convective turbulence overpowers motility, homogenising motile and non-motile microbes approximately equally. At greater depth, in conditions analogous to a thermocline, highly motile microbes can be over twice as patch-concentrated as non-motile microbes, and can substantially amplify their swimming velocity by efficiently exploiting fast-moving packets of fluid. Our results substantiate the predictions of earlier studies, and demonstrate that turbulence-driven patchiness is not a ubiquitous consequence of motility but rather a delicate balance of motility and turbulent intensity.

System Identification For Enhanced Flow Description From Multi-Pulse PIV

We propose a novel approach to obtain a time-resolved description from non-time-resolved PIV measurements. The method needs in input velocity and acceleration fields from ( at least) 3-pulse PIV data, without time r esolution. A sparse identification of nonlinear dynamics (based on the SINDy technique) is carried out to estimate the time history of coordinates in a low-dimensional space from Proper Orthogonal Decomposition (POD). The output is a reduced-order model of the dynamics which can be integrated to obtain time-resolved velocity fields using t he s napshots as i nitial c onditions. The t ime-resolved e volution of t he pressure fields is th en derived from the momentum equation. The time history of the velocity and pressure fields is obtained through a weighted Backward-Forward Integration (BFI) of the identified s ystem. Time super-sampling can be achieved by integration between consecutive non-time-resolved realizations. In alternative, simple one-directional time integration can be used for short-time prediction starting from individual snapshots. The algorithm is validated using a synthetic test case from 2D Direct Numerical Simulation of the wake of a fluidic pinball at a Reynolds number Re equal to 130, and PIV measurements of the wake of a NACA 0018 wing profile with Re = 4 800. We show that the method is able to reconstruct the flow dynamics for horizons of several convective times, provided that the basis for the data reduction is sufficiently c ompact. Our results suggest that manifold learning and data assimilation can be combined to obtain an enhanced flow description.

Energetics and Mixing of Stratified, Rotating Flow over Abyssal Hills

Abstract One of the proposed mechanisms for energy loss in the ocean is through dissipation of internal waves, in particular above rough topography where internal lee waves are generated. Rates of dissipation and diapycnal mixing are often estimated using linear internal wave generation theory and a constant value for mixing efficiency. However, previous oceanographic measurements found that nonlinear dynamics may be important close to topography. To investigate the role of nonlinear interactions, we conduct idealized 3D direct numerical simulations (DNS) of steady flow over 1D topography and vary the topographic height, which correlates to the degree of flow nonlinearity. We analyze the spatial distribution of energy transfer rates between internal waves and the nongeostrophic portion of the time-mean flow, and of dissipation and diapycnal mixing rates. In our simulations with taller, more nonlinear topographies, energy transfer rates are similar to previously unexplained oceanographic observations near topography: internal waves gain energy from time-mean flow through horizontal straining and lose energy through vertical shearing. In the tall topography simulations, buoyancy fluxes also play a significant role, consistent with observations but contrary to linear wave theory, suggesting that quasigeostrophy-based approximations and linear theory may not hold in some regions above rough topography. Both dissipation and mixing rates increase with topographic height, but their vertical distributions differ between topographic regimes. As such, the vertical profile of mixing efficiency is different for linear and nonlinear topographic regimes, which may need to be incorporated into parameterizations of small-scale processes in models and estimates of ocean energy loss.

Capillary equilibration of trapped ganglia in porous media: A pore-network modeling approach

Ganglia, or bubbles, trapped by capillary forces inside porous materials occur in a wide range of subsurface and manufacturing applications. In geologic CO2 storage, ganglia are desired as they render the injected CO2 hydrodynamically immobile. But they may evolve by dissolution or mass exchange across the brine, called ripening. In fuel cells and electrolyzers, water/oxygen ganglia must be removed to ensure optimal performance of the device. In both applications, the porous microstructure plays a key role in how the geometry/topology of ganglia evolve as they grow/shrink in size. This dependence is poorly understood but important for controlling ganglion dynamics. Pore-scale models are useful tools for probing the physics, but existing ones are either computationally expensive (e.g., CFD) or incapable of accurately simulating ganglia spanning multiple pores (e.g., pore networks). Our main contribution is a new pore-network model (PNM) that removes this barrier. The PNM can simulate the evolution of multi-pore occupying ganglia due to diffusive mass transfer by ripening or an external concentration field. We validate the PNM against published microfluidic experiments, 2D direct numerical simulations, and an analytical solution previously derived by the authors for a 2D homogeneous domain. We then use the PNM to study quasi-static growth-shrinkage cycles of trapped ganglia inside heterogeneous porous media. The findings constitute our second contribution, generalizing previous theoretical results by the authors from 2D homogeneous to 3D-planar heterogeneous microstructures. They include: (1) the interfacial area of a ganglion depends approximately linearly on its volume; (2) if the throat-to-pore aspect ratio is large, growth is percolation-like; but (3) if it is small, a hitherto unreported intermittent growth regime precedes percolation, in which ganglia repeatedly fragment and reconnect. These outcomes have implications for selecting optimal storage sites for CO2 and designing fuel cells and electrolyzers with finetuned porous microstructures.

Simulation of three-dimensional forced compressible isotropic turbulence by a redesigned discrete unified gas kinetic scheme

In this paper, we implemented the Boltzmann-equation-based mesoscopic model, developed recently by Chen et al. [“Inverse design of mesoscopic models for compressible flow using the Chapman–Enskog analysis,” Adv. Aerodyn. 3, 5 (2021)], to simulate three-dimensional (3D) forced compressible isotropic turbulence. In this model, both the Prandtl number and the ratio of bulk to shear viscosity can be arbitrary prescribed. The statistically stationary turbulent flow is driven by a large-scale momentum forcing in the Fourier space, with the internal heating due to the viscous dissipation at small scales being removed by a thermal cooling function. Under the framework of discrete unified gas kinetic scheme (DUGKS), a 3D direct numerical simulation code has been developed, incorporating a generalized Strang-splitting scheme. The weighted essentially non-oscillatory (WENO) scheme is used to increase local spatial accuracy in the reconstruction of particle distribution functions at the cell interface. A 3D discrete particle velocity model with a ninth-order Gauss–Hermite quadrature accuracy is used to ensure accurate evaluation of viscous stress and heat flux in the continuum regime. We simulate forced compressible isotropic turbulence at both low and high turbulent Mach numbers. A direct comparison is performed with the results obtained from a hybrid compact finite difference-WENO scheme solving directly the Navier–Stokes–Fourier system. The comparison validates our DUGKS code and indicates that DUGKS is a reliable and promising tool for simulating forced compressible isotropic turbulence. The work represents a first study to directly simulate forced compressible turbulence by a mesoscopic method based on the Boltzmann equation.

Modeling and simulation of static and dynamic behavior in composite sandwich plates with hourglass lattice cores based on reduced-order model

The composite sandwich plate with hourglass lattice cores (CSP-HLC) is a novel cellular structure that can increase the width-to-length ratio and reduce the inter-node spacing. However, its static and dynamic behaviors are difficult to analyze due to the complex microstructures. In this work, a computational homogenization method is proposed for calculating the constitutive parameters. A reduced-order plate model is then derived through dimensional reduction from the three-dimensional orthotropic thermoelasticity framework. The effectiveness and accuracy of the proposed model were verified by comparing with the static-displacement and free-vibration results of 3D direct numerical simulations. The parameter analysis showed that the different material and structural parameters of the hourglass lattice core had different effects on the equivalent stiffnesses and natural frequencies of the CSP-HLC. Compared with the composite sandwich plate with pyramidal lattice cores, the displacement of the CSP-HLC was smaller under the same load and boundary conditions, and the natural frequencies were also smaller, which may have been because the additional equivalent density of the CSP-HLC influenced the frequency more predominantly than the extra equivalent stiffness.

Solving Burgers\u2019 equation with quantum computing

Computational fluid dynamics (CFD) simulations are a vital part of the design process in the aerospace industry. Although reliable CFD results can be obtained with turbulence models, direct numerical simulation of complex bodies in three spatial dimensions (3D) is impracticable due to the massive amount of computational elements. For instance, a 3D direct numerical simulation of a turbulent boundary-layer over the wing of a commercial jetliner that resolves all relevant length scales using a serial CFD solver on a modern digital computer would take approximately 750 million years or roughly 20% of the earth’s age. Over the past 25 years, quantum computers have become the object of great interest worldwide as powerful quantum algorithms have been constructed for several important, computationally challenging problems that provide enormous speed-up over the best-known classical algorithms. In this paper, we adapt a recently introduced quantum algorithm for partial differential equations to Burgers’ equation and develop a quantum CFD solver that determines its solutions. We used our quantum CFD solver to verify the quantum Burgers’ equation algorithm to find the flow solution when a shockwave is and is not present. The quantum simulation results were compared to: (i) an exact analytical solution for a flow without a shockwave; and (ii) the results of a classical CFD solver for flows with and without a shockwave. Excellent agreement was found in both cases, and the error of the quantum CFD solver was comparable to that of the classical CFD solver.

A comparative study of flame-wall interaction and flame-cooling air interaction

This paper presents a three-dimensional (3D) direct numerical simulation (DNS) study of flame-wall interaction (FWI) and flame-cooling air interaction (FCAI). A preheated, methane/air mixture enters a channel with constant temperature walls, where the top wall is effusion cooled. An imposed vertical hot sheet near the inlet creates two flame branches interacting with the top and bottom walls. The flame is observed to be leaner in the region where it interacts with the effusion cooling jets. In this region, the flame is longer and features reduced CO mass fraction. The fluctuations in the heat release rate (HRR) and CO mass fraction are also relatively small near the top wall. Near the bottom wall, finger-like flame structures are formed due to the interaction of turbulent vortices with the flame surface. These flame structures initially move away from the wall as they propagate further downstream before eventually collapsing at the wall. This leads to the creation of regions of high wall heat flux and CO. While analysis of the CO thermochemical state shows a complex picture near the bottom wall, two-dimensional (2D) manifolds can be identified near the top wall. Therefore, a framework to estimate CO mass fraction due to FCAI based on 1D freely-propagating flame solutions is proposed showing a good agreement with the DNS results.

Preferential concentration by mechanically driven turbulence in the two-fluid formalism

Preferential concentration is thought to play a key role in promoting particle growth, which is crucial to processes such as warm rain formation in clouds, planet formation, and industrial sprays. In this work, we investigate preferential concentration using 3D Direct Numerical Simulations adopting the Eulerian-Eulerian two-fluid approach, where the particles are treated as a continuum field with its own momentum and mass conservation laws. We consider particles with Stokes number $St \lesssim O(0.01)$ in moderately turbulent flows with fluid Reynolds number $Re \leq 600$. In our previous work (Nasab & Garaud, Physical Review Fluids. doi: 10.1103/PhysRevFluids.5.114308, 2020), we established scaling laws to predict maximum and typical particle concentration enhancements in the context of the particle-driven convective instability. Here we verify that the same results apply when turbulence is externally driven, extending the relevance of our model to a wider class of particle-laden flows. We find in particular that (i) the maximum particle concentration enhancement above the mean scales as $u_{rms}^2 \tau_p / \kappa_p$, where $u_{rms}$ is the rms fluid velocity, $\tau_p$ is the particle stopping time, and $\kappa_p$ is the assumed particle diffusivity from the two-fluid equations; (ii) the typical particle concentration enhancement over the mean scales as $(u_{rms}^2 \tau_p / \kappa_p)^{1/2}$; and (iii) the probability distribution function of the particle concentration enhancement over the mean has an exponential tail whose slope scales like $(u_{rms}^2 \tau_p /\kappa_p)^{-1/2}$. We conclude by discussing the caveats of our model and its implications in a relevant cloud application.

Comparison of Flame Propagation Statistics Based on Direct Numerical Simulation of Simple and Detailed Chemistry. Part 2: Influence of Choice of Reaction Progress Variable

Flame propagation statistics for turbulent, statistically planar premixed flames obtained from 3D Direct Numerical Simulations using both simple and detailed chemistry have been evaluated and compared to each other. To achieve this, a new database has been established encompassing five different conditions on the turbulent combustion regime diagram, using nearly identical numerical methods and the same initial and boundary conditions. The discussion includes interdependencies of displacement speed and its individual components as well as surface density function (i.e., magnitude of the reaction progress variable) with tangential strain rate and curvature. For the analysis of detailed chemistry Direct Numerical Simulation data, three different definitions of reaction progress variable, based on CH4,H2O and O2 mass fractions will be used. While the displacement speed statistics remain qualitatively and to a large extent quantitatively similar for simple chemistry and detailed chemistry, there are pronounced differences for its individual contributions which to a large extent depend on the definition of reaction progress variable as well as on the chosen isosurface level. It is concluded that, while detailed chemistry simulations provide more detailed information about the flame structure, the choice of the reaction progress variable definition and the choice of the resulting isosurface give rise to considerable uncertainty in the interpretation of displacement speed statistics, sometimes even showing opposing trends. Simple chemistry simulations are shown to provide (a) the global flame propagation statistics which are qualitatively similar to the corresponding results from detailed chemistry simulations, (b) remove the uncertainties with respect to the choice of reaction progress variable, and (c) are more straightforward to compare with theoretical analysis or model assumptions that are mostly based on simple chemistry assumptions.

Dynamics of flow reversals in the presence of a vertical magnetic field (a) (a)Contribution to the Focus Issue Turbulent Thermal Convection edited by Mahendra Verma and Jörg Schumacher.

We investigate the dynamics of flow reversals close to the onset of Rayleigh-Bénard convection (RBC) of electrically conducting low Prandtl number (Pr) Boussinesq fluids in the presence of an external vertical magnetic field. The investigation is carried out by performing three-dimensional (3D) direct numerical simulations (DNS) of the related mathematical model considering the quasi-static approximation. The numerical investigation reveals a rich dynamics of the flow reversals close to the onset of convection. Three qualitatively different kinds of flow reversals, namely chaotic, intermittent and periodic are identified and all are found to occur in the presence of weak magnetic field, measured in terms of the Chandrasekhar number (Q). Explored ranges of the Prandtl number (Pr), the Rayleigh number (Ra) and the Chandrasekhar number are , and , respectively. Out of the three different types of flow reversals, intermittent flow reversal is new and has not been reported so far in convective system to the best of our knowledge. The probability density function of the time interval of occurrences of chaotic flow reversals is found to decay exponentially. The heat transfer properties of the system are also numerically investigated and it is observed that magnetic field facilitates the heat transfer in the considered ranges of the parameter space.

Impact of high- and low-vorticity turbulence on cloud–environment mixing and cloud microphysics processes

Abstract. Turbulent mixing of dry air affects the evolution of the cloud droplet size spectrum via various mechanisms. In a turbulent cloud, high- and low-vorticity regions coexist, and inertial clustering of cloud droplets can occur in low-vorticity regions. The nonuniformity in the spatial distribution of the size and in the number of droplets, variable vertical velocity in vortical turbulent structures, and dilution by entrainment/mixing may result in spatial supersaturation variability, which affects the evolution of the cloud droplet size spectrum via condensation and evaporation processes. To untangle the processes involved in mixing phenomena, a 3D direct numerical simulation of turbulent mixing followed by droplet evaporation/condensation in a submeter-sized cubed domain consisting of a large number of droplets was performed in this study. The analysis focused on the thermodynamic and microphysical characteristics of the droplets and the flow in high- and low-vorticity regions. The impact of vorticity generation in turbulent flows on mixing and cloud microphysics is illustrated.

Hydrodynamic interaction and coalescence of two inline bubbles rising in a viscoelastic liquid

In this paper, direct numerical simulations (DNS) are performed to investigate the inline rise of a pair of three-dimensional (3D) air bubbles in a viscoelastic liquid using the volume-of-fluid approach with an adaptive mesh refinement technique. The exponential Phan-Thien–Tanner model is used as the non-linear viscoelastic constitutive equation for the liquid. The numerical model has been validated by comparison with previously published results, including the terminal velocity jump discontinuity of an isolated bubble rising in a viscoelastic fluid, when its volume exceeds a certain critical value. Focusing on the inline rising bubble pair in such a viscoelastic medium with different configurations, we found that the wake of the small leading bubble attracts a larger trailing bubble, whereas for a supercritical bubble in front of a subcritical bubble, they tend to further separate. Before reaching a critical volume, the two subcritical bubbles remain close to each other after approaching each other, forming a stable chain. For pairs containing a supercritical trailing bubble, however, a drafting–kissing scenario occurs before the bubble–bubble coalescence. The long-range repulsion and the short-range attraction due to fluid elasticity are critical to the aforementioned bubble pair interactions. Interestingly, the terminal rise velocities of the stable bubble chain and the coalesced bubble both increase with the initial spacing. The squeezing flow near the growing bubble neck seems to delay the coalescence process. The capillary wave propagating down to the coalesced bubble tip together with the extensional flow behind the stretched bubble determines the generation of satellite microdroplets along the tail of the coalesced bubble. To the best of our knowledge, this is the first 3D DNS on a bubble pair ascending in viscoelastic fluids.

Existence of dual solutions and three-dimensional instability in helical pipe flow

Three-dimensional (3D) direct numerical simulations (DNS) of the viscous incompressible fluid flow through a helical pipe with circular cross section were performed. The flow is governed by three parameters: the Dean number (or the Reynolds number), curvature, and torsion. First, we obtained steady solutions by steady 3D calculations, where dual solutions were found, one was uniform in the pipe axial direction and the other varied very slowly, if torsion exceeded a critical value. Then, the instability of the steady solutions obtained was studied by unsteady 3D calculations. We obtained critical Reynolds numbers of steady to unsteady transition by observing the behaviors of the unsteady solutions. The present results of the critical Reynolds number nearly agreed with those by the 2D linear stability analysis (Yamamoto et al. [9]) except for the lowest critical Reynolds number region, where the present study gave the critical Reynolds number much less than that obtained by the 2D linear stability analysis. We found the vortical structures in the form of a standing wave slightly above the marginal instability state, which is a trigger of explosive 3D instability.