Recent Direct Numerical Simulations Research Articles

Modulation of flow, heat, and mass transfer in turbulent double-diffusive convection

The present study addresses numerical simulations of the double-diffusive convection in a turbulent regime. The characteristic concentration and temperature Prandtl numbers (PrC = 700 and PrT = 7) correspond to the typical seawater properties. Here, we applied the Large-Eddy Simulation (LES) approach, with relatively simple subgrid turbulence closures of momentum, concentration, and temperature for the unresolved scales. The wall-resolved LES approach proved to work well on significantly coarser numerical mesh than used in recent Direct Numerical Simulation (DNS) studies of Yang et al. (2016) in the intermediate range of working parameters, 107 ≤ RaC ≤ 109, 0 ≤ RaT ≤ 106, which covers the quasi-Rayleigh-Bénard, fingering, and damping flow regimes. A good agreement between concentration and temperature Nusselt numbers is obtained. The instantaneous Nusselt numbers distribution revealed a significant impact of the imposed strong thermal stratification (RaT = 106) in comparison to the neutral case (RaT = 0).

Stratified inclined duct: two-layer hydraulics and instabilities

The stratified inclined duct (SID) sustains an exchange flow in a long, gently sloping duct as a model for continuously forced density-stratified flows such as those found in estuaries. Experiments have shown that the emergence of interfacial waves and their transition to turbulence as the tilt angle is increased appears to be linked to a threshold in the exchange flow rate given by inviscid two-layer hydraulics. We uncover these hydraulic mechanisms by (i) using recent direct numerical simulations (DNS) providing full flow data in the key flow regimes (Zhu et al., J. Fluid Mech., vol. 969, 2023, A20), (ii) averaging these DNS into two layers, and (iii) using an inviscid two-layer shallow-water and instability theory to diagnose interfacial wave behaviour and provide physical insight. The laminar flow is subcritical and stable throughout the duct and hydraulically controlled at the ends of the duct. As the tilt is increased, the flow becomes supercritical everywhere and unstable to long waves. An internal jump featuring stationary waves first appears near the centre of the duct, then leads to larger-amplitude travelling waves, and to stronger jumps, wave breaking and intermittent turbulence at the largest tilt angle. Long waves described by the (nonlinear) shallow-water equation are interpreted locally as linear waves on a two-layer parallel base flow described by the Taylor–Goldstein equation. This link helps us to interpret long-wave instability and contrast it with short-wave (e.g. Kelvin–Helmholtz) instability. Our results suggest a transition to turbulence in SID through long-wave instability relying on vertical confinement by the top and bottom walls.

Selection of vortex ripple dimensions in sinusoidal oscillatory flows. Part 1. Ripple dimensions and fluid kinematics

Subaqueous vortex ripples in equilibrium are characterized by their unique geometry and dimensions. Motivated by the recent direct numerical simulation study of oscillatory turbulent flow over a wavy bottom by Önder & Yuan (J. Fluid Mech., vol. 858, 2019, pp. 264–314), the objective of this study is to further investigate the fluid dynamical controls that determine the distinctive equilibrium dimensions of vortex ripples. We use direct numerical simulations to investigate the differences in flow kinetics between sinusoidal oscillatory flow over equilibrium and out-of-equilibrium vortex ripples. In comparison with the equilibrium case, the spanwise coherent vortices, the averaged bottom shear stress on overlying flow and the shear stress distribution on the ripple surface are identified as the key fluid dynamical controls on equilibrium dimensions. Based on these controls, we propose mechanisms in the selection of vortex ripple dimensions. We observe that the flow adjusts in such a way that the interaction between overlying flow and vortex ripples tends to generate the strongest coherent vortices while the ripple surface (or overlying flow) experiences the smallest shear stress averaged over ripple wavelength during the selection process. Through a triple decomposition of the flow, the component of the ripple-induced fluctuation is found to dictate these fluid dynamical controls, which implies that this component plays an important role in the evolution of vortex ripples.

Modeling simultaneous momentum and passive scalar transfer in turbulent annular Poiseuille flow

AbstractSimultaneous momentum and passive scalar transfer in weakly heated pressure‐driven turbulent concentric annular pipe flow is numerically investigated using the cylindrical formulation of the stochastic one‐dimensional turbulence (ODT) model, which is utilized here as standalone tool. In the present study, we focus on the model calibration for heated annular pipes based on recent reference direct numerical simulations (DNS) from Bagheri and Wang (Int. J. Heat Fluid Flow 86, 108725, 2020; Phys. Fluids 33, 055131, 2021). It is shown that the model is able to individually capture scalar and momentum transfer, but not both equally well at the same time. We attribute this to less dissimilar scalar and momentum transport in the model at the low Reynolds number investigated. It is argued that the model prefers a fully developed turbulent state due to its construction. Nevertheless, it is demonstrated that ODT is able to reasonably capture the radial inner‐outer asymmetry of the scalar and momentum boundary layers which yields better predictive capabilities than wall‐function‐based approaches.

Compressibility effects on Reynolds stress amplification and shock structure in shock–isotropic turbulence interactions

Recent direct numerical simulation studies of canonical shock–isotropic turbulence interactions (SITIs) in the highly compressible regime exhibit streamwise Reynolds stress amplification that is significantly higher in some cases than in previous studies; an explanation is offered based on a relatively high Mach number combined with significant dilatational energy in the incident flow. Some cases exhibit a loss of amplification that is associated with a highly perturbed shock structure as the flow parameters approach the threshold between the wrinkled and broken shock regimes. The shock structure perturbations due to the highly compressible incident turbulence match those proposed by Donzis (Phys. Fluids, vol. 24, 2012, 126101) relatively well, but due to the presence of thermodynamic fluctuations in addition to velocity fluctuations in the incident flow, we propose a generalized parametrization based on the root-mean-square Mach number fluctuation in place of the turbulence Mach number. This is found to improve the collapse of the shock structure data, suggesting that the wrinkled–broken shock regime threshold determined previously for vortical turbulence (Donzis, Phys. Fluids, vol. 24, 2012, 126101; Larsson et al., J. Fluid Mech., vol. 717, 2013, pp. 293–321) can be applied to more general isotropic inflow fields using the proposed parametrization.

Density waves in protoplanetary discs excited by eccentric planets: linear theory

ABSTRACT Spiral density waves observed in protoplanetary discs have often been used to infer the presence of embedded planets. This inference relies both on simulations as well as the linear theory of planet–disc interaction developed for planets on circular orbits to predict the morphology of the density wake. In this work, we develop and implement a linear framework for calculating the structure of the density wave in a gaseous disc driven by an eccentric planet. Our approach takes into account both the essential azimuthal and temporal periodicities of the problem, allowing us to treat any periodic perturbing potential (i.e. not only that of an eccentric planet). We test our framework by calculating the morphology of the density waves excited by an eccentric, low-mass planet embedded in a globally isothermal disc and compare our results to the recent direct numerical simulations (and heuristic wavelet analysis) of the same problem by Zhu and Zhang. We find excellent agreement with the numerical simulations, capturing all the complex eccentric features including spiral bifurcations, wave crossings, and planet-wave detachments, with improved accuracy and detail compared with the wavelet method. This illustrates the power of our linear framework in reproducing the morphology of complicated time-dependent density wakes, presenting it as a valuable tool for future studies of eccentric planet–disc interactions.

Onset of large-scale convection in wall-bounded turbulent shear flows

Large-scale coherent rolls are observed frequently in unstably stratified turbulent wall-bounded flows where they influence strongly the turbulent transport and the mean flow properties. Here we address the question of their genesis by means of a linear stability analysis of the turbulent mean flow where a model of turbulent Reynolds stresses is embedded in the linear stability operator. We use the unstably stratified turbulent channel flow as a testbed for the analysis. We show that the onset of large-scale convection is associated to the linear instability of the mean flow to large-scale streamwise-uniform coherent rolls of aspect ratio$A \approx 3\unicode{x2013}3.3$when the friction Richardson number exceeds$|Ri_{\tau,c}|=0.86$. This corresponds to critical Rayleigh numbers that increase with the Reynolds number approximately as$Ra_c \approx 0.04\,Re_b^{1.8}$. These results are consistent with those obtained in recent direct numerical simulations performed in the same setting. It is also found that if turbulent Reynolds stresses are not modelled in the linear operator used in the stability analysis, then predictions are not consistent with direct numerical simulations results.

Heat transport in Rayleigh-Bénard convection with linear marginality.

Recent direct numerical simulations (DNS) and computations of exact steady solutions suggest that the heat transport in Rayleigh-Bénard convection (RBC) exhibits the classical [Formula: see text] scaling as the Rayleigh number [Formula: see text] with Prandtl number unity, consistent with Malkus-Howard's marginally stable boundary layer theory. Here, we construct conditional upper and lower bounds for heat transport in two-dimensional RBC subject to a physically motivated marginal linear-stability constraint. The upper estimate is derived using the Constantin-Doering-Hopf (CDH) variational framework for RBC with stress-free boundary conditions, while the lower estimate is developed for both stress-free and no-slip boundary conditions. The resulting optimization problems are solved numerically using a time-stepping algorithm. Our results indicate that the upper heat-flux estimate follows the same [Formula: see text] scaling as the rigorous CDH upper bound for the two-dimensional stress-free case, indicating that the linear-stability constraint fails to modify the boundary-layer thickness of the mean temperature profile. By contrast, the lower estimate successfully captures the [Formula: see text] scaling for both the stress-free and no-slip cases. These estimates are tested using marginally-stable equilibrium solutions obtained under the quasi-linear approximation, steady roll solutions and DNS data. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.

The logarithmic variance of streamwise velocity and conundrum in wall turbulence

The logarithmic dependence of streamwise turbulence intensity has been observed repeatedly in recent experimental and direct numerical simulation data. However, its spectral counterpart, a well-developed $k^{-1}$ spectrum ( $k$ is the spatial wavenumber in a wall-parallel direction), has not been convincingly observed from the same data. In the present study, we revisit the spectrum-based attached eddy model of Perry and co-workers, who proposed the emergence of a $k^{-1}$ spectrum in the inviscid limit, for small but finite $z/\delta$ and for finite Reynolds numbers ( $z$ is the wall-normal coordinate, and $\delta$ is the outer length scale). In the upper logarithmic layer (or inertial sublayer), a reexamination reveals that the intensity of the spectrum must vary with the wall-normal location at order of $z/\delta$ , consistent with the early observation argued with ‘incomplete similarity’. The streamwise turbulence intensity is subsequently calculated, demonstrating that the existence of a well-developed $k^{-1}$ spectrum is not a necessary condition for the approximate logarithmic wall-normal dependence of turbulence intensity – a more general condition is the existence of a premultiplied power-spectral intensity of $O(1)$ for $O(1/\delta ) < k < O(1/z)$ . Furthermore, it is shown that the Townsend–Perry constant must be weakly dependent on the Reynolds number. Finally, the analysis is semi-empirically extended to the lower logarithmic layer (or mesolayer), and a near-wall correction for the turbulence intensity is subsequently proposed. All the predictions of the proposed model and the related analyses/assumptions are validated with high-fidelity experimental data (Samie et al., J. Fluid Mech., vol. 851, 2018, pp. 391–415).

Influence of molecular transport on burning rate and conditioned species concentrations in highly turbulent premixed flames

Apparent inconsistency between (i) experimental and direct numerical simulation (DNS) data that show the significant influence of differential diffusion on the turbulent burning rate and (ii) recent complex-chemistry DNS data that indicate mitigation of the influence of differential diffusion on conditioned profiles of various local flame characteristics at high Karlovitz numbers, is explored by analysing new DNS data obtained from lean hydrogen–air turbulent flames. Both aforementioned effects are observed by analysing the same DNS data provided that the conditioned profiles are sampled from the entire computational domain. On the contrary, the conditioned profiles sampled at the leading edge of the mean flame brush do not indicate the mitigation, but are significantly affected by differential diffusion phenomena, e.g. because reaction zones are highly curved at the leading edge. This observation is consistent with a significant increase in the computed turbulent burning velocity with decreasing Lewis number, with all the results considered jointly being consonant with the leading point concept of premixed turbulent combustion. The concept is further supported by comparing DNS data obtained by allowing for preferential diffusion solely for a single species, either atomic or molecular hydrogen.

Transient linear stability of pulsating Poiseuille flow using optimally time-dependent modes

Time-dependent flows are notoriously challenging for classical linear stability analysis. Most progress in understanding the linear stability of these flows has been made for time-periodic flows via Floquet theory focusing on time-asymptotic stability. However, little attention has been given to the transient intracyclic linear stability of periodic flows since no general tools exist for its analysis. In this work, we explore the potential of using the recent framework of the optimally time-dependent (OTD) modes (Babaee & Sapsis, Proc. R. Soc. Lond. A, vol. 472, 2016, 20150779) to extract information about both the transient and the time-asymptotic linear stability of pulsating Poiseuille flow. The analysis of the instantaneous OTD modes in the limit cycle leads to the identification of the dominant instability mechanism of pulsating Poiseuille flow by comparing them with the spectrum and the eigenmodes of the Orr–Sommerfeld operator. In accordance with evidence from recent direct numerical simulations, it is found that structures akin to Tollmien–Schlichting waves are the dominant feature over a large range of pulsation amplitudes and frequencies but that for low pulsation frequencies these modes disappear during the damping phase of the pulsation cycle as the pulsation amplitude is increased beyond a threshold value. The maximum achievable non-normal growth rate during the limit cycle was found to be nearly identical to that in plane Poiseuille flow. The existence of subharmonic perturbation cycles compared with the base flow pulsation is documented for the first time in pulsating Poiseuille flow.

A DNS study of extreme and leading points in lean hydrogen-air turbulent flames - part II: Local velocity field and flame topology

Data obtained in recent direct numerical simulations (Lee et al.) of statistically one-dimensional and planar, lean complex-chemistry hydrogen-air flames characterized by three different Karlovitz numbers Ka ranging from 3 to 33 are further analyzed in order to explore local characteristics and structure of (i) extreme points characterized by the peak (over the computational domain) Fuel Consumption Rate (FCR) or Heat Release Rate (HRR) and (ii) leading points that are also characterized by a high FCR or HRR, but advance furthest into unburned reactants. Results show that, on the one hand, common characteristics of flame perturbations (curvature, strain and stretch rates, displacement speed) fluctuate significantly in the extreme or leading, FCR or HRR points and are different in different flames. Moreover, other two-point local quantities such as the local gradients of combustion progress variables or species (e.g., the radical H) mass fractions are different in different flames. Therefore, a common simple configuration of a perturbed laminar flame cannot be used as a catchall model of the entire local structure of zones surrounding the discussed points at various Ka. On the other hand, single-point local characteristics (temperature, species mass fractions, rates of their production) of the FCR extreme points are comparable in all three turbulent flames and in the critically strained planar laminar flame. In particular, the FCRs in the extreme points fluctuate weakly and are approximately equal to each other and to the peak FCR in the critically strained laminar flame. The latter finding implies that (i) the maximum FCR evaluated in the critically strained laminar flame could be used to characterize, in a first approximation, the local FCR in the extreme or leading points in turbulent flames, thus, supporting the leading point concept, and (ii) almost the same extreme FCR can be reached in substantially different local burning structures.

A macroscopic two-length-scale model for natural convection in porous media driven by a species-concentration gradient

The modelling of natural convection in porous media is receiving increased interest due to its significance in environmental and engineering problems. State-of-the-art simulations are based on the classic macroscopic Darcy–Oberbeck–Boussinesq (DOB) equations, which are widely accepted to capture the underlying physics of convection in porous media provided the Darcy number, $Da$ , is small. In this paper we analyse and extend the recent pore-resolved direct numerical simulations (DNS) of Gasow et al. (J. Fluid Mech, vol. 891, 2020, p. A25) and show that the macroscopic diffusion, which is neglected in DOB, is of the same order (with respect to $Da$ ) as the buoyancy force and the Darcy drag. Consequently, the macroscopic diffusion must be modelled even if the value of $Da$ is small. We propose a ‘two-length-scale diffusion’ model, in which the effect of the pore scale on the momentum transport is approximated with a macroscopic diffusion term. This term is determined by both the macroscopic length scale and the pore scale. It includes a transport coefficient that solely depends on the pore-scale geometry. Simulations of our model render a more accurate Sherwood number, root mean square (r.m.s.) of the mass concentration and r.m.s. of the velocity than simulations that employ the DOB equations. In particular, we find that the Sherwood number $Sh$ increases with decreasing porosity and with increasing Schmidt number $(Sc)$ . In addition, for high values of $Ra$ and high porosities, $Sh$ scales nonlinearly. These trends agree with the DNS, but are not captured in the DOB simulations.

Connecting large-scale velocity and temperature bursts with small-scale intermittency in stratified turbulence

Non-Gaussian statistics of large-scale fields are routinely observed in data from atmospheric and oceanic campaigns and global models. Recent direct numerical simulations (DNSs) showed that large-scale intermittency in stably stratified flows is due to the emergence of sporadic, extreme events in the form of bursts in the vertical velocity and the temperature. This phenomenon results from the interplay between waves and turbulent motions, affecting mixing. We provide evidence of the enhancement of the classical small-scale (or internal) intermittency due to the emergence of large-scale drafts, connecting large- and small-scale bursts. To this aim we analyze a large set of DNSs of the stably stratified Boussinesq equations over a wide range of values of the Froude number –1). The variation of the buoyancy field kurtosis with Fr is similar to (though with smaller values than) the kurtosis of the vertical velocity, both showing a non-monotonic trend. We present a mechanism for the generation of extreme vertical drafts and vorticity enhancements which follows from the exact equations for field gradients.

Conceptual Limitations of the Probability Density Function Method for Modeling Turbulent Premixed Combustion and Closed-Form Description of Chemical Reactions’ Effects

In this paper, we critically analyzed possibilities of probability density function (PDF) methods for the closed-form description of combustion chemical effects in turbulent premixed flames. We came to the conclusion that the concept of a closed-form description of chemical effects in the classical modeling strategy in the PDF method based on the use of reaction-independent mixing models is not applicable to turbulent flames. The reason for this is the strong dependence of mixing on the combustion reactions due to the thin-reaction-zone nature of turbulent combustion confirmed in recent optical studies and direct numerical simulations. In this case, the chemical effect is caused by coupled reaction–diffusion processes that take place in thin zones of instantaneous combustion. We considered possible alternative modeling strategies in the PDF method that would allow the chemical effects to be described in a closed form and came to the conclusion that this is possible only in a hypothetical case where instantaneous combustion occurs in reaction zones identical to the reaction zone of the undisturbed laminar flame. For turbulent combustion in the laminar flamelet regime, we use an inverse modeling strategy where the model PDF directly contains the characteristics of the laminar flame. For turbulent combustion in the distributed preheat zone regime, we offer an original joint direct/inverse modeling strategy. For turbulent combustion in the thickened flamelet regime, we combine the joint direct/inverse and inverse modeling strategies correspondingly for simulation of the thickened flamelet structure and for the determination of the global characteristics of the turbulent flame.

Effect of spatial dimension on a model of fluid turbulence

A numerical study of the $d$ -dimensional eddy damped quasi-normal Markovian equations is performed to investigate the dependence on spatial dimension of homogeneous isotropic fluid turbulence. Relationships between structure functions and energy and transfer spectra are derived for the $d$ -dimensional case. Additionally, an equation for the $d$ -dimensional enstrophy analogue is derived and related to the velocity derivative skewness. Comparisons are made to recent four-dimensional direct numerical simulation results. Measured energy spectra show a magnified bottleneck effect which grows with dimension whilst transfer spectra show a varying peak in the nonlinear energy transfer as the dimension is increased. These results are consistent with an increased forward energy transfer at higher dimensions, further evidenced by measurements of a larger asymptotic dissipation rate with growing dimension. The enstrophy production term, related to the velocity derivative skewness, is seen to reach a maximum at around five dimensions and may reach zero in the limit of infinite dimensions, raising interesting questions about the nature of turbulence in this limit.

Extension to various thermal boundary conditions of the elliptic blending model for the turbulent heat flux and the temperature variance

Abstract

Low- and High-Drag Intermittencies in Turbulent Channel Flows.

Recent direct numerical simulations (DNS) and experiments in turbulent channel flow have found intermittent low- and high-drag events in Newtonian fluid flows, at between 70 and 100, where , h and are the friction velocity, channel half-height and kinematic viscosity, respectively. These intervals of low-drag and high-drag have been termed “hibernating” and “hyperactive”, respectively, and in this paper, a further investigation of these intermittent events is conducted using experimental and numerical techniques. For experiments, simultaneous measurements of wall shear stress and velocity are carried out in a channel flow facility using hot-film anemometry (HFA) and laser Doppler velocimetry (LDV), respectively, for between 70 and 250. For numerical simulations, DNS of a channel flow is performed in an extended domain at = 70 and 85. These intermittent events are selected by carrying out conditional sampling of the wall shear stress data based on a combined threshold magnitude and time-duration criteria. The use of three different scalings (so-called outer, inner and mixed) for the time-duration criterion for the conditional events is explored. It is found that if the time-duration criterion is kept constant in inner units, the frequency of occurrence of these conditional events remain insensitive to Reynolds number. There exists an exponential distribution of frequency of occurrence of the conditional events with respect to their duration, implying a potentially memoryless process. An explanation for the presence of a spike (or dip) in the ensemble-averaged wall shear stress data before and after the low-drag (or high-drag) events is investigated. During the low-drag events, the conditionally-averaged streamwise velocities get closer to Virk’s maximum drag reduction (MDR) asymptote, near the wall, for all Reynolds numbers studied. Reynolds shear stress (RSS) characteristics during these conditional events are investigated for = 70 and 85. Except very close to the wall, the conditionally-averaged RSS is higher than the time-averaged value during the low-drag events.

Computing the aerodynamic drag of fractal aggregates in free-molecular and transition regimes

For fine particles moving in the gas different regimes of aerodynamic drag are distinguished depending on their sizes and dust to gas relative velocities. In the Epstein or free-molecular regime, the drag force depends on the projected area or cross-section of the body, and in the Stokes or transition regime, on its linear size. Finding the linear size and the projected area for nonspherical particles is a non-trivial task. To describe the mobility of some type of nonspherical particles - fluffy aggregates, considered as a set of spheres - monomers, the value Df called fractal dimension is often used. For such aggregates with fixed fractal dimension D0, several authors suggested the approximations of the linear size (called Smoluchowski radius Rs) and projected area PA as a function of N - the number of monomers in the aggregate. These authors validated their approximations on experimental data. On the other hand, new direct numerical simulation (DNS) data on mobility of fractal aggregates have been obtained recently. In the paper we constructed new functions PA(Df,N) and Rs(Df, N) interpolating available from the literature approximations of PA(Df = D0,N) and Rs(Df = D0,N) and minimizing the deviation from recent DNS data. These functions are designed for global simulations of protoplanetary discs dynamics and planet formation, but can be used in different applications.

Generalised Eddy Dissipation Concept for MILD combustion regime at low local Reynolds and Damköhler numbers. Part 2: Validation of the model

The generalised Eddy Dissipation Concept (EDC) developed in the first part of this article is thoroughly validated against twelve flames from the Delft and Adelaide jet-in-hot-coflow (JHC) burners. These flames emulate Moderate or Intense Low Oxygen Dilution (MILD) conditions. Modelling of turbulence-chemistry interactions in this regime is a non trivial problem and many standard combustion models may fail. Recent Direct Numerical Simulation studies revealed a distributed appearance of the reaction zone indicating non-flamelet regime, which justified the use of reactor type modelling approaches. Those kind of models are of empirical nature and are sometimes criticized for being dependent on a number of tunable parameters. Also, most of new concepts are validated against a limited number of experiments. In this study, using the same modelling setup, twelve flames with different jet Reynolds number, level of oxidizer dilution with various fuel mixture were simulated. It turned out that the generalised EDC model considerably improved predictions with respect to the standard model for all the considered flames. Even though the predictions of the other EDC extensions provided better results in some regions, only the proposed generalised approach could cover the broad tange of operating conditions, proving its “universality” and reliability.