Three-dimensional Direct Numerical Simulations Research Articles

High Grashof number turbulent natural convection on an infinite vertical wall

The present study concerns a temporally evolving turbulent natural convection boundary layer (NCBL) adjacent to an isothermally heated vertical wall, with Prandtl number 0.71. Three-dimensional direct numerical simulations (DNS) are carried out to investigate the turbulent flow up to $\textit {Gr}_\delta =1.21\times 10^8$ , where $\textit {Gr}_\delta$ is the Grashof number based on the boundary layer thickness $\delta$ . In the near-wall region, there exists a constant heat flux layer, similar to previous studies for the spatially developing flows (e.g. George & Capp, Intl J. Heat Mass Transfer, vol. 22, 1979, pp. 813–826). Beyond a wall-normal distance $\delta _i$ , the NCBL can be characterised as a plume-like region. We find that this region is well described by a self-similar integral model with profile coefficients (cf. van Reeuwijk & Craske, J. Fluid Mech., vol. 782, 2015, pp. 333–355) which are $\textit {Gr}_\delta$ -independent after $\textit {Gr}_\delta =10^7$ . In this Grashof number range both the outer plume-like region and the near-wall boundary layer are turbulent, indicating the beginning of the so-called ultimate turbulent regime (Grossmann & Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56; Grossmann & Lohse, Phys. Fluids, vol. 23, 2011, 045108). Solutions to the self-similar integral model are analytically obtained by solving ordinary differential equations with profile coefficients empirically obtained from the DNS results. In the present study, we have found the wall heat transfer of the NCBL is directly related to the top-hat scales which characterise the plume-like region. The Nusselt number is found to follow $\textit {Nu}_\delta \propto \textit {Gr}_\delta ^{0.381}$ , slightly higher than the empirical $1/3$ -power-law correlation reported for spatially developing NCBLs at lower $\textit {Gr}_\delta$ , but is shown to be consistent with the ultimate heat transfer regime with a logarithmic correction suggested by Grossmann & Lohse (Phys. Fluids, vol. 23, 2011, 045108). By modelling the near-wall buoyancy force, we show that the wall shear stress would scale with the bulk velocity only at asymptotically large Grashof numbers.

Global POD-Galerkin ROMs for Fluid Flows with Moving Solid Structures

Traditional proper orthogonal decomposition (POD)-Galerkin projection for reduced-order models (ROMs) of fluid flows is based on a fixed domain. The current method removes this limitation by considering a single combined domain of fluid and solid, whereas the original solid boundary conditions are reinforced by additional ROM terms. The combined domain requires a new inner product defined in the same combined domain to compute POD modes and the projection of equations. Solid motion is considered first as a continuous motion, then a decomposed motion, represented by a few solid modes to further reduce the computational cost. This new global approach was applied first on a two-dimensional direct numerical simulation (DNS) database of the flow past an oscillatory cylinder, and then on a three-dimensional DNS database of the flow past an oscillatory sphere. Last, the approach was applied on a high-resolution particle image velocimetry database from an experiment at higher Reynolds number of the flow past a pitching-up NACA0012 airfoil. The ROMs derived by the global POD-Galerkin projection approach, for all three moving-boundary cases, have shown adequate accuracy in the reconstruction of flow fields and the prediction of key aerodynamic features while keeping very low computational costs.

Effects of spatial distribution of CO2 dilution on localised forced ignition of stoichiometric biogas-air mixtures

ABSTRACT The localized forced ignition and subsequent flame propagation have been analyzed for stoichiometric biogas-air mixtures ( blend) with different spatial distributions (uniform, Gaussian and bimodal) and mean levels of dilution (i.e. mole fraction of ) for different flow conditions (e.g. quiescent laminar condition and different turbulence intensities) using three-dimensional Direct Numerical Simulations. A two-step chemical mechanism with sufficient accuracy is used to capture the effects of dilution on the laminar burning velocity of the . A parametric analysis in terms of the mean, standard deviation and integral length scale of the initial Gaussian and bimodal distributions of spatial dilution in the unburned gas has been conducted. Qualitatively similar behavior has been observed for all three initial spatial distributions of . A departure from uniform conditions was found to increase the range of reaction rate magnitudes of , which impacts the burned gas volume and, in turn, increases the variability of the outcomes of the ignition event (successful thermal runaway and subsequent self-sustained propagation or misfire). Turbulence intensity and the mean level of dilution were found to have significant impacts on the outcome of the localized forced ignition, and an increase of either quantity acts to reduce the burned gas volume irrespective of mixture composition due to the enhancement of heat transfer from the hot gas kernel, and the heat sink effects of , respectively. An increase of the integral length scale for the spatial distribution of dilution increased the probability of a successful outcome of the ignition event. A uniform initial spatial distribution was found to be optimal, and in the case of a departure from non-uniform conditions, larger variability in the outcome are obtained for a Gaussian initial distribution of dilution than a bimodal one. The variance of the dilution distribution has been found to have a negligible impact on the outcomes observed, as it was dominated by the effects arising from turbulence intensity, nature of initial distribution and integral length scale of dilution.

Direct numerical simulation of confined weak round fountains in homogeneous ambient

Fountains (negatively buoyant jets) are commonly used in numerous engineering applications, such as the natural ventilation in buildings and the smoke spread in compartment fires. In this study, the long-term behavior of weak round fountains in homogeneous ambient confined in a cylindrical container was analyzed using three-dimensional direct numerical simulation over a range of the Froude number (Fr), Reynolds number (Re), dimensionless radius of the container (λ), respectively. The confined weak round fountain behaves in the manner of a ‘fountain filling box’ flow, experiencing five development stages, i.e., the formation of the fountain flow, the intrusion flow, the wall fountain, the reversed flow and the stratification. Three stages of the development of the bulk entrainment rate are identified and the dominant mechanisms involved are analyzed. Fr = 1 and 2 are identified as the approximate critical values to distinguish the behavior of the intrusion, wall fountain and stratification. Re = 200 is determined as the approximate critical value to distinguish the influence of Re. These are consistent with the existing results about the round fountains.

Effect of heating on topology of vortex breakdown in Vogel–Escudier flow

This paper examines the effect of unstable thermal stratification on vortex breakdown in Vogel–Escudier flow. A three-dimensional direct numerical simulation of Navier–Stokes and energy equations are used to simulate a flow inside a cylindrical container generated by rotating the top lid. The top and bottom are kept at two constant temperatures such that unstable stratification is maintained. The rotation speed is related to the Reynolds number (Re), and buoyancy is linked to the Rayleigh number (Ra). The streamline and vertical velocity contour plots indicate different regimes of the flow depending on the Re and Ra. The convection dominated (CD) regime has a characteristic large-scale circulation similar to the Rayleigh–Bénard convection, and the rotation dominated (RD) regime has a central axial vortex and breakdowns. A transitional regime between RD and CD regimes is also identified from energy consideration. The influence of Ra on a vortex breakdown bubble and its relation to azimuthal vorticity is investigated in detail. Consistent with the literature on Vogel–Escudier flow, the azimuthal vorticity is shown to be essential for the breakdown in the presence of buoyancy as well. In the low Re limits, the energy of flow tends to be associated with the r–z plane velocity field, while at large Re, the energy is associated with the out-of-the-plane velocity field. Thermal plumes align along the axis for large rotations and are affected by the vortex breakdown bubble. The velocity perturbation structures and plumes show a remarkable distinction between rotation and convection-dominated regimes in the topology.

The effect of Schmidt number on gravity current flows: The formation of large-scale three-dimensional structures

The Schmidt number, defined as the ratio of scalar to momentum diffusivity, varies by multiple orders of magnitude in real-world flows, with large differences in scalar diffusivity between temperature, solute, and sediment driven flows. This is especially crucial in gravity currents, where the flow dynamics may be driven by differences in temperature, solute, or sediment, and yet the effect of Schmidt number on the structure and dynamics of gravity currents is poorly understood. Existing numerical work has typically assumed a Schmidt number near unity, despite the impact of Schmidt number on the development of fine-scale flow structure. The few numerical investigations considering high Schmidt number gravity currents have relied heavily on two-dimensional simulations when discussing Schmidt number effects, leaving the effect of high Schmidt number on three-dimensional flow features unknown. In this paper, three-dimensional direct numerical simulations of constant-influx solute-based gravity currents with Reynolds numbers 100≤Re≤3000 and Schmidt number 1 are presented, with the effect of Schmidt number considered in cases with (Re,Sc)=(100,10), (100,100), and (500, 10). These data are used to establish the effect of Schmidt number on different properties of gravity currents, such as density distribution and interface stability. It is shown that increasing Schmidt number from 1 leads to substantial structural changes not seen with increased Reynolds number in the range considered here. Recommendations are made regarding lower Schmidt number assumptions, usually made to reduce computational cost.

Simulating Relic Gravitational Waves from Inflationary Magnetogenesis

Abstract We present three-dimensional direct numerical simulations of the production of magnetic fields and gravitational waves (GWs) in the early universe during a low energy scale matter-dominated post-inflationary reheating era, and during the early subsequent radiative era, which is strongly turbulent. The parameters of the model are determined such that it avoids a number of known physical problems and produces magnetic energy densities between 0.03% and 0.5% of the critical energy density at the end of reheating. During the subsequent development of a turbulent magnetohydrodynamic cascade, magnetic fields and GWs develop a spectrum that extends to higher frequencies in the millihertz (nanohertz) range for models with reheating temperatures of around 100 GeV (150 MeV) at the beginning of the radiation-dominated era. However, even though the turbulent cascade is fully developed, the GW spectrum shows a sharp drop for frequencies above the peak value. This suggests that the turbulence is less efficient in driving GWs than previously thought. The peaks of the resulting GW spectra may well be in the range accessible to space interferometers, pulsar timing arrays, and other facilities.

Motion of a tightly fitting axisymmetric object through a lubricated elastic tube

We consider the translation of a rigid, axisymmetric, tightly fitting object through a cylindrical elastic tube filled with viscous fluid, using a combination of theory and direct numerical simulations. The intruding object is assumed to be wider than the undeformed tube radius, forcing solid–solid contact in the absence of relative motion. The motion of the object establishes a thin fluid film that lubricates this contact. Our theory couples lubrication theory to a geometrically nonlinear membrane description of the tube's elasticity, and applies to a slender intruding object and a thin tube with negligible bending rigidity. We show using asymptotic and numerical solutions of the theory, that the thickness of the thin fluid film scales with the square root of the relative speed for small speeds, set by a balance of hoop stresses, membrane tension and fluid pressure. While membrane tension is relatively small at the entrance of the film, it dominates near the exit and produces undulations of the film thickness, even in the limit of vanishing speeds and slender objects. We find that the drag force on the intruding object depends on the slope of its surface at the entrance to the thin fluid film, and scales as the square root of the relative speed. The predictions of the lubricated membrane theory for the shape of the film and the force on the intruder are in quantitative agreement with three-dimensional direct numerical simulations of the coupled fluid–elastic problem.

Comparison of Flame Propagation Statistics Extracted from Direct Numerical Simulation Based on Simple and Detailed Chemistry—Part 1: Fundamental Flame Turbulence Interaction

In the present study, flame propagation statistics from turbulent statistically planar premixed flames obtained from simple and detailed chemistry, three-dimensional Direct Numerical Simulations, were evaluated and compared to each other. To this end, a new database was established encompassing five different conditions on the turbulent premixed combustion regime diagram, using nearly identical numerical methods and the same initial and boundary conditions. A detailed discussion of the advantages and limitations of both approaches is provided, including the difference in carbon footprint for establishing the database. It is shown that displacement speed statistics and their interrelation with curvature and tangential strain rate are in very good qualitative and reasonably good quantitative agreement between simple and detailed chemistry Direct Numerical Simulations. Hence, it is concluded that simple chemistry simulations should retain their importance for future combustion research, and the environmental impact of high-performance computing methods should be carefully chosen in relation to the goals to be achieved.

Lagrangian coherent track initialization

Advances in time-resolved three-dimensional Particle Tracking Velocimetry (4D-PTV) techniques have consistently revealed more accurate Lagrangian particle motions. A novel track initialization technique as a complementary part of 4D-PTV, based on local temporal and spatial coherency of neighbor trajectories, is proposed. The proposed Lagrangian Coherent Track Initialization (LCTI) applies physics-based Finite Time Lyapunov Exponent (FTLE) to build four frame coherent tracks. We locally determine Lagrangian coherent structures among neighbor trajectories by using the FTLE boundaries (i.e., ridges) to distinguish the clusters of coherent motions. To evaluate the proposed technique, we created an open-access synthetic Lagrangian and Eulerian dataset of the wake downstream of a smooth cylinder at a Reynolds number equal to 3900 obtained from three-dimensional direct numerical simulation. Performance of the proposed method based on three characteristic parameters, temporal scale, particle concentration (i.e., density), and noise ratio, showed robust behavior in finding true tracks compared to the recent initialization algorithms. Sensitivity of LCTI to the number of untracked and wrong tracks is also discussed. We address the capability of using the proposed method as a function of a 4D-PTV scheme in the Lagrangian particle tracking challenge. We showed that LCTI prevents 4D-PTV divergence in flows with high particle concentrations. Finally, the LCTI behavior was demonstrated in a jet impingement experiment. LCTI was found to be a reliable tracking tool in complex flow motions, with a strength revealed for flows with high velocity and acceleration gradients.

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.

Three-dimensional direct numerical simulation of flow induced by an oscillating sphere close to a plane boundary

The dynamic interaction of submerged spherical structures with ocean waves alters the local flow field and is responsible for the movement of sediments over the seabed, which would have detrimental effects on the ecosystems. The present research aims to gain insight into the effect of a plane boundary on the vorticity dynamics and shear modifications on the plane boundary induced by the flow due to an oscillating sphere. The flow field around an oscillating sphere close to a plane boundary is investigated numerically by three-dimensional direct numerical simulation of the Navier–Stokes equations. The sphere oscillates perpendicular to the plane boundary modeling the seabed. The flow structure, resulting mean and fluctuating shear stress distribution on the plane boundary, and the Lagrangian particle transport are investigated as a function of the sphere oscillation amplitude, Reynolds number, and the distance of the sphere from the plane boundary. The systematic correlations for the variation of maximum shear stress on the plane boundary are estimated from scaling parameters. The time-mean results are then linked to the Lagrangian particle transport where it is observed that the Lagrangian path lines track the mean streamlines closely. Further, the particles at the stagnation zone cease drifting and oscillate about a constant mean position. The practical significance of this result is that a ring of zero mean shear on the seabed is found toward where particles congregate. This provides a guide for the optimum location for the mooring anchors, minimizing the risk of anchor scour or undermining.

On wake modulation and interaction features of a pair of dual-step circular cylinders in side-by-side arrangements

The proximity interference and the vortex dislocation are fundamental fluid dynamic features that determine a wake pattern of dual-step circular cylinders in a side-by-side arrangement. Each dual-step cylinder consists of two coaxial cylinders with different diameters. A complex wake modulation is expected due to an intrinsic interaction between the vortex shedding of the larger-diameter cylinder (LC) and the smaller-diameter cylinder (SC), and to the cross-wake interaction of side-by-side cylinders in a uniform flow. To understand the physics of fluid wake modulations, three-dimensional direct numerical simulations of the flow around a pair of dual-step circular cylinders in side-by-side arrangements are performed and investigated. Six simulation cases are presented with different combinations of diameter ratio (1.33–2.00), gap ratio (1.00–3.17), and the Reynolds number (60–200) in a laminar flow regime, providing key insights into the two distinct LC-dominated and SC-governing wake modulation characteristics. For the LC-dominated wake modulation, the wake pattern of side-by-side cylinders is determined by the predominant vortex dynamics in the LC wake. For the SC-governing wake modulation, the LC wake pattern becomes modulated and controlled by the SC wake through the connections of vortex tubes shed downstream of the two nonuniform cylinders. Owing to the proximity interference and vortex dislocation, these new evolutionary wake modulations result in distinct wake patterns, vortex structures, and associated hydrodynamic force features for the pair of side-by-side dual-step circular cylinders.

Fluidic Oscillators, Feedback Channel Effect under Compressible Flow Conditions.

Fluidic oscillators are often used to modify the forces fluid generates on any given bluff body; they can also be used as flow, pressure or acoustic sensors, with each application requiring a particular oscillator configuration. Regarding the fluidic oscillators’ main performance, a problem which is not yet clarified is the understanding of the feedback channel effect on the oscillator outlet mass flow frequency and amplitude, especially under compressible flow conditions. In order to bring light to this point, a set of three-dimensional Direct Numerical Simulations under compressible flow conditions are introduced in the present paper; four different feedback channel lengths and two inlet Reynolds numbers = 12,410 and = 18,617 are considered. From the results obtained, it is observed that as the inlet velocity increases, the fluidic oscillator outlet mass flow frequency and amplitude increase. An increase of the feedback channel length decreases the outlet mass flow oscillating frequency. At large feedback channel lengths, the former main oscillation tends to disappear, the jet inside the mixing chamber simply fluctuates at high frequencies. Once the Feedback Channel (FC) length exceeds a certain threshold, the oscillation stops. Under all conditions studied, pressure waves are observed to be traveling along the feedback channels, their origin and interaction with the jet entering the mixing chamber are thoroughly evaluated. The paper proves that jet oscillations are pressure-driven.

Insights on the interaction of serpentine channels and gas diffusion layer in an operating polymer electrolyte fuel cell: Numerical modeling across scales

Three-dimensional direct numerical simulations were performed for investigating the flow in a serpentine channel and the under-laying porous gas diffusion layer (GDL) of a micro polymer electrolyte fuel cell (PEFC). The flow field comprised three straight sections and two U-turns. The geometry was acquired with high-resolution (2.9 μm) in situ X-ray tomographic measurements on an operating cell. Simulations considered the GDL under dry and partially saturated conditions, whereby saturation was established via electrochemically produced water. A lattice Boltzmann (LB) methodology was adopted for simulating the single-phase (gas) transport in the actual 3D channel and porous GDL geometry. The global pressure drop in the dry GDL was dominated by the turns in the gas channel, while the pressure drops were quite small along the straight channel sections. In the wet GDL case, however, the pressure drop was mainly dictated by the neck-shaped passages created by the large water clusters inside the channel. Owing to the water blockage, the local accumulated cross-flows along the serpentine channel length, when normalized by the inlet channel flow, were substantially higher in the wet GDL, reaching local values up to 45% compared to 18% for the dry GDL. The implications are that in an electrochemically operating cell, the GDL under the rib would receive more gas (and thus O2). The creation of cross-flows through the porous GDL would enhance cell performance under the ribs since diffusion will not be the main driving mechanism for oxygen transport and water evaporation. The analysis indicated that the flow field, although designed as serpentine, behaved like half-interdigitated (with a rib of 1.5 mm, half-serpentine flow field, depending on the state of channel flooding).

Role of surfactant-induced Marangoni stresses in drop-interface coalescence

We study the effect of surfactants on the dynamics of a drop-interface coalescence using full three-dimensional direct numerical simulations. We employ a hybrid interface-tracking/level-set method, which takes into account Marangoni stresses that arise from surface-tension gradients, interfacial and bulk diffusion and sorption kinetic effects. We validate our predictions against the experimental data of Blanchette and Bigioni (Nat. Phys., vol. 2, issue 4, 2006, pp. 254–257) and perform a parametric study that demonstrates the delicate interplay between the flow fields and those associated with the surfactant bulk and interfacial concentrations. The results of this work unravel the crucial role of the Marangoni stresses in the flow physics of coalescence, with particular attention paid to their influence on the neck reopening dynamics in terms of stagnation-point inhibition, and near-neck vorticity generation. We demonstrate that surfactant-laden cases feature a rigidifying effect on the interface compared with the surfactant-free case, a mechanism that underpins the observed surfactant-induced phenomena.

Assessment of Extrapolation Relations of Displacement Speed for Detailed Chemistry Direct Numerical Simulation Database of Statistically Planar Turbulent Premixed Flames

A three-dimensional Direct Numerical Simulation (DNS) database of statistically planar H_{2} - air turbulent premixed flames with an equivalence ratio of 0.7 spanning a large range of Karlovitz number has been utilised to assess the performances of the extrapolation relations, which approximate the stretch rate and curvature dependences of density-weighted displacement speed S_{d}^{*}. It has been found that the correlation between S_{d}^{*} and curvature remains negative and a significantly non-linear interrelation between S_{d}^{*} and stretch rate has been observed for all cases considered here. Thus, an extrapolation relation, which assumes a linear stretch rate dependence of density-weighted displacement speed has been found to be inadequate. However, an alternative extrapolation relation, which assumes a linear curvature dependence of S_{d}^{*} but allows for a non-linear stretch rate dependence of S_{d}^{*}, has been found to be more successful in capturing local behaviour of the density-weighted displacement speed. The extrapolation relations, which express S_{d}^{*} as non-linear functions of either curvature or stretch rate, have been found to capture qualitatively the non-linear curvature and stretch rate dependences of S_{d}^{*} more satisfactorily than the linear extrapolation relations. However, the improvement comes at the cost of additional tuning parameter. The Markstein lengths LM for all the extrapolation relations show dependence on the choice of reaction progress variable definition and for some extrapolation relations LM also varies with the value of reaction progress variable. The predictions of an extrapolation relation which involve solving a non-linear equation in terms of stretch rate have been found to be sensitive to the initial guess value, whereas a high order polynomial-based extrapolation relation may lead to overshoots and undershoots. Thus, a recently proposed extrapolation relation based on the analysis of simple chemistry DNS data, which explicitly accounts for the non-linear curvature dependence of the combined reaction and normal diffusion components of S_{d}^{*}, has been shown to exhibit promising predictions of S_{d}^{*} for all cases considered here.

Effects of turbulent length scale on the bending effect of turbulent burning velocity in premixed turbulent combustion

The effects of turbulent integral length scale to flame thickness ratio on the bending effect of turbulent burning velocity variation have been analysed based on a three-dimensional Direct Numerical Simulation database of statistically planar turbulent premixed flames with a characteristic Lewis number of unity propagating into forced unburned gas turbulence. It has been demonstrated that Damköhler's first hypothesis remains valid for the cases considered here and this has been utilised to explain the bending effect by analysing the terms in the generalised Flame Surface Density (FSD) transport equation. Under steady-state, the flame surface area generation by the FSD tangential strain rate term remains in equilibrium with the flame surface destruction by the FSD curvature term. It has been found that the length scale ratio influences the relative contributions of the dilatation and normal strain rate to the flame surface area generation due to tangential strain rate. Similarly, relative contributions of the flame surface area destruction due to the curvature terms arising from the combined reaction and normal diffusion component of displacement speed, and the tangential diffusion component of displacement speed are affected by the length scale ratio. The propensity of the flame area generation due to the normal strain rate term and the dominance of the flame area destruction arising from the tangential diffusion component of displacement speed are strengthened with decreasing length scale ratio. The flame surface area destruction due to the FSD curvature term arising from tangential diffusion component of displacement speed strengthens with increasing turbulence intensity and it becomes the major contributor to the destruction of flame surface area for large turbulence intensities. However, the inner cut-off scale, which also limits maximum possible flame area generation by the FSD strain rate term under statistically stationary state, determines the maximum possible destruction of flame surface area for a given length scale ratio and this is manifested in the bending effects of turbulent burning velocity and flame surface area. At high turbulence intensities, the turbulent burning velocity levels off at a smaller value for the smaller length scale ratio, which is consistent with Damköhler's second hypothesis and has been explained based on scaling arguments utilising the leading order balance between the strain rate and curvature contributions to the flame surface area evolution for large turbulence intensities characterised by large Karlovitz number and small Damköhler number values.

On the role of roughness valleys in turbulent Rayleigh–Bénard convection

Three-dimensional direct numerical simulations are used to characterize turbulent buoyant convection in a box-shaped Rayleigh–Bénard cavity with a rough bottom plate made of a series of square based blocks separated by valleys. The cavity is filled with water. The Rayleigh number varies over five decades up to $10^{10}$ . As mentioned in the literature, three successive heat transfer regimes are identified: from inactive roughness (I) to a regime (III) where the heat transfer increase is larger than that expected from only surface increase due to roughness. The heat transfers of the transitional regime II are particularly intense. After validation against experimental and numerical data from the literature, we highlight the role of the fluid retained within valleys (the inner fluid). It is shown that only the heat transfer across the fluid interface between the cavity bulk and the inner fluid is responsible for changes in the overall heat transfer at the rough plate, with an exponent of the heat transfer scaling law close to $1/2$ in regime II. The valley flow typifies the limits of this regime: the blocks protrude from the thermal boundary layer while remaining within the kinetic boundary layer. As compared with regimes I and III, regime II is characterized by larger temperature fluctuations, especially near the rough plate, and a larger friction coefficient. A fluctuating rough fluid layer overlaying both blocks and valleys appears in regime III, in addition to the classic boundary layers formed along the plate geometry.

Assessment of Bray Moss Libby formulation for premixed flame-wall interaction within turbulent boundary layers: Influence of flow configuration

Three-dimensional direct numerical simulations (DNS) of two different flow configurations have been performed for premixed flames interacting with chemically inert isothermal walls at the unburned gas temperature in fully developed turbulent boundary layers. The first configuration is an oblique flame-wall interaction (FWI) of a V-flame in a turbulent channel flow and the second configuration is a head-on quenching planar flame in a turbulent boundary layer. These simulations are representative of stoichiometric methane-air mixture at unity Lewis number under atmospheric conditions. The turbulence in the non-reacting conditions for these simulations is representative of the friction velocity based Reynolds number of Reτ=110. Differences in the statistical behaviours of the mean values of progress variable, temperature, and density during the FWI process have been reported for the two configurations. It is found that the mean flame brush thickens in the near wall region leading to significant departures from the strict Bray Moss Libby (BML) formulation limit during the FWI process and that is reflected in the probability density function (PDF) distributions of c for both flame configurations. The closures from the BML formulation for Reynolds averaged progress variable c¯ and the Favre averaged variance of the progress variable c′′2˜ have also been investigated and it is found that these closures need to be modified to account for the FWI process even when the flame away from the wall represents high Damköhler number premixed turbulent combustion. Furthermore, the statistical behaviours of the quantities required for Flame Surface Density (FSD) based mean reaction rate closure including the flame orientation factor σy, the flamelet length scale Ly and the flame stretch factor I0 have been interrogated from the DNS data for the two flame configurations. The flamelet length scale and the stretch factor extracted from the DNS data are compared with the closures for these quantities proposed in the literature. It is found that σy exhibits significant spatial variation for both cases. The existing closures for Ly and I0 which exhibit the best quantitative agreement with DNS data have been identified. It has been found that the models for Ly and I0 have scopes for further improvement to enable satisfactory predictions of these quantities during the FWI process within turbulent boundary layers.