Three-dimensional Direct Numerical Simulations Research Articles

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

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

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

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

Fingering convection in a spherical shell

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

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

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

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

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

Magnetized Fingering Convection in Stars

Fingering convection (also known as thermohaline convection) is a process that drives the vertical transport of chemical elements in regions of stellar radiative zones where the mean molecular weight increases with radius. Recently, Harrington & Garaud used three-dimensional direct numerical simulations (DNS) to show that a vertical magnetic field can dramatically enhance the rate of chemical mixing by fingering convection. Furthermore, they proposed a so-called “parasitic saturation” theory to model this process. Here, we test their model over a broad range of parameter space, using a suite of DNS of magnetized fingering convection, varying the magnetic Prandtl number, magnetic field strength, and composition gradient. We find that the rate of chemical mixing measured in the simulations is not always predicted accurately by their existing model, in particular when the magnetic diffusivity is large. We then present an extension of the Harrington & Garaud model which resolves this issue. When applied to stellar parameters, it recovers the results of Harrington & Garaud except in the limit where fingering convection becomes marginally stable, where the new model is preferred. We discuss the implications of our findings for stellar structure and evolution.

On the Definition of Reaction Progress Variable in Exhaust Gas Recirculation Type Turbulent MILD Combustion of Methane and n-Heptane

Three-dimensional Direct Numerical Simulations of Exhaust Gas Recirculation (EGR)-type Moderate or Intense Low Oxygen Dilution (MILD) combustion of homogeneous mixtures of methane- and n-heptane–air have been conducted with skeletal chemical mechanisms. The suitability of different choices of reaction progress variable (which is supposed to increase monotonically from zero in the unburned gas to one in fully burned products) based on the mass fractions of different major species and non-dimensional temperature have been analysed in detail. It has been found that reaction progress variable definitions based on oxygen mass fraction, and linear combination of CO, CO2, H2 and H2O mass fractions (i.e. cO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${c}_{O2}$$\\end{document} and cc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${c}_{c}$$\\end{document}) capture all the extreme values of the major species in the range between zero and one under MILD conditions. A reaction progress variable based on fuel mass fraction is found to be unsuitable for heavy hydrocarbons, such as n-heptane, since the fuel breaks down to smaller molecules before the major reactants (products) are completely consumed (formed). Moreover, it has been found that the reaction rates of cO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${c}_{O2}$$\\end{document} and cc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${c}_{c}$$\\end{document} exhibit approximate linear behaviours with the heat release rate in both methane and n-heptane MILD combustion. The interdependence of different mass fractions in the EGR-type homogeneous mixture combustion is considerably different from the corresponding 1D unstretched premixed flames. The current findings indicate that the tabulated chemistry approach based on premixed laminar flames may need to be modified to account for EGR-type MILD combustion. Furthermore, both the reaction rate and scalar dissipation rate of cO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${c}_{O2}$$\\end{document} and cc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${c}_{c}$$\\end{document} are found to be non-linearly related in both methane and n-heptane MILD combustion cases but the qualitative nature of this correlation for n-heptane is different from that in methane. This suggests that the range of validity of SDR-based turbulent combustion models can be different for homogeneous MILD combustion of different fuels.

Turbulent wake characteristics for a circular cylinder in proximity to a moving wall

This study investigates the scenario of flow past a circular cylinder in proximity to a moving wall (or equally a body translating in still fluid parallel to a stationary wall). Fifty high-fidelity three-dimensional direct numerical simulations are performed over a parameter space of turbulent Reynolds numbers (Re) of 300 to 1000 combined with gap-to-diameter ratios (G/D) of 0.2 to 3. The flow, hydrodynamic and turbulence characteristics over the (Re, G/D) parameter space are examined in detail. Small-scale rib-like mode B structures and alternate vortex shedding are observed for all cases. The streamwise location for the vortex shedding (quantified by the wake recirculation length Lr) varies strongly with both Re and G/D. The variation of Lr with Re and G/D can be explained by the spanwise circulation $\varGamma_z$ fed into the wake, where the variation trends of Lr and $\varGamma_z$ are inversely correlated. The variations of the mean drag and fluctuating lift coefficients are also governed by the variations in Lr and $\varGamma_z$ . The total kinetic energy in the wake region reduces drastically as G/D reduces below 0.8, which is contributed collectively by (i) reduction in the strength of the shed vortices, (ii) downstream movement of the location of vortex shedding and (iii) associated delayed generation of streamwise vortices. The present results on a moving wall also help to explain several flow and hydrodynamic characteristics reported in the literature for a stationary wall, because the moving wall eliminates the complex wall boundary layer and retains a ‘clean’ near-wall effect.

Flame self-interactions in MILD combustion of homogeneous and inhomogeneous mixtures

Flame self-interaction (FSI) events in Moderate or Intense Low-Oxygen Dilution (MILD) combustion of homogeneous and inhomogeneous mixtures of methane and oxidiser have been analysed using three-dimensional Direct Numerical Simulations (DNS). The simulations have been conducted at the same global equivalence ratio (⟨ϕ⟩=0.8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle \\phi \\rangle = 0.8$$\\end{document}) for different levels of O2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathrm {O_2}$$\\end{document} concentration (dilution) and initial turbulence intensities. It has been reported that both homogeneous and inhomogeneous mixture MILD combustion cases exhibit significant occurrences of FSI events, with the peak frequency of FSI events occurring towards the burned gas side in all cases. Moreover, the frequency of FSI events increases with increasing dilution level and turbulence intensity, but the presence of mixture inhomogeneity leads to a reduction in total FSI events. In all cases, the cylindrical FSI topologies (i.e. tunnel formation and tunnel closure) were found to have a higher likelihood of occurrence compared to spherical FSI topologies (i.e. unburned and burned gas pockets). The geometries of FSI topologies were also analysed using the mean and Gaussian curvatures. It has been shown that the inward propagating spherical FSI topologies (i.e. unburned gas pockets) are associated with negative mean curvature, while outward propagating spherical FSI topologies (i.e. burned gas pockets) are associated with positive mean curvature. Moreover, tunnel formation (tunnel closure) FSI topologies predominantly exhibit either elliptic geometries with positive (negative) mean curvature or hyperbolic saddle geometries with negative (positive) mean curvature. It has been shown for the first time in MILD combustion that the mean values of kinematic restoration and dissipation terms in the transport equation of the magnitude of the reaction progress variable conditional upon the reaction progress variable tend to cancel each other in the vicinity of the critical points associated with cylindrical topologies. Thus, the singular contributions in these terms, which are obtained from analytical descriptions in the vicinity of tunnel formation and tunnel closure topologies, do not affect the balance equation of the magnitude of the gradient of the reaction progress variable. Consequently, there is no need for a separate model treatment for singularities in modelling approaches based on the magnitude of the gradient of the reaction progress variable. The FSI events in the reaction dominated and propagating flame regions of MILD combustion have also been analysed for the first time. It has been found that more FSI events occur in the reaction dominated region, particularly towards the burned gas side. However, the majority of spherical FSI topologies are found in the propagating flame region. The findings from this study indicate that turbulence intensity, dilution level and mixture inhomogeneity effects need to be considered in any attempt to extend flame surface-based modelling approaches to MILD combustion.

Carrier-Phase DNS of Ignition and Combustion of Iron Particles in a Turbulent Mixing Layer

Three-dimensional carrier-phase direct numerical simulations (CP-DNS) of reacting iron particle dust clouds in a turbulent mixing layer are conducted. The simulation approach considers the Eulerian transport equations for the reacting gas phase and resolves all scales of turbulence, whereas the particle boundary layers are modelled employing the Lagrangian point-particle framework for the dispersed phase. The CP-DNS employs an existing sub-model for iron particle combustion that considers the oxidation of iron to FeO and that accounts for both diffusion- and kinetically-limited combustion. At first, the particle sub-model is validated against experimental results for single iron particle combustion considering various particle diameters and ambient oxygen concentrations. Subsequently, the CP-DNS approach is employed to predict iron particle cloud ignition and combustion in a turbulent mixing layer. The upper stream of the mixing layer is initialised with cold particles in air, while the lower stream consists of hot air flowing in the opposite direction. Simulation results show that turbulent mixing induces heating, ignition and combustion of the iron particles. Significant increases in gas temperature and oxygen consumption occur mainly in regions where clusters of iron particles are formed. Over the course of the oxidation, the particles are subjected to different rate-limiting processes. While initially particle oxidation is kinetically-limited it becomes diffusion-limited for higher particle temperatures and peak particle temperatures are observed near the fully-oxidised particle state. Comparing the present non-volatile iron dust flames to general trends in volatile-containing solid fuel flames, non-vanishing particles at late simulation times and a stronger limiting effect of the local oxygen concentration on particle conversion is found for the present iron dust flames in shear-driven turbulence.

Direct numerical simulation of oblique-wave transition in concave boundary layer

Investigation of transition in a concave boundary layer is conducted via three-dimensional direct numerical simulation at Mach 3. The model consists of a flat plate and a concave plate, connected smoothly. The development of the boundary layer in the unperturbed flow is computed initially. It is found that the boundary layer thickness rapidly increases due to the separation bubble, caused by an adverse pressure gradient. Subsequently, spanwise vortices are generated by the Kelvin–Helmholtz instability, which develops within the strong shear layer. Then, a pair of oblique waves is introduced at the inlet of the computational domain through suction and blowing slot to examine the impact of oblique waves on transition and separation of the concave plate boundary layer. The investigation reveals that oblique waves significantly reduce the separation bubble and the boundary layer thickness and weaken the Kelvin–Helmholtz instability. Oblique waves generate streamwise vortices, while high-amplitude oblique waves lead to a three-dimensional checkerboard structure and staggered Λ vortices. The findings demonstrate that oblique breakdown can advance to a fully developed turbulent boundary layer, hence operating as a relevant mechanism for transition in supersonic concave boundary layers.

Predicting the upper bound of two-dimensional flow regimes of symmetric objects through two-dimensional computations

The onset of secondary wake instability is generally predicted via experiments, linear stability analysis, and three-dimensional direct numerical simulations. The current work stems from an open question that is very intriguing and fundamental: Can the upper bound of a two-dimensional flow be predicted purely on the basis of two-dimensional computational results? It is found that spatial distribution of a field variable, i.e., streamwise velocity in the vortex formation region, aids in determining the upper limit of a two-dimensional flow regime of a symmetric object. The vortex formation length attains its least value at the second critical Reynolds number. In addition, streamwise extents of mean wake and vortex formation region along wake axis become the same. Under this circumstance, the streamwise velocity at the terminal point of vortex formation region is such that its mean value vanishes while intensity of fluctuations or corresponding Reynolds stress becomes the maximum. The predicted values of critical Reynolds numbers for circular, square, and diamond cross sections exhibit excellent agreement with the results available in the literature.

Direct numerical simulations on oscillating flow past surface-mounted finite-height circular cylinder

In this work, a surface-mounted circular cylinder with a fixed aspect ratio (ratio of height of the cylinder to its diameter) of 5 is subjected to a non-zero mean oscillating flow with a range of frequencies and amplitudes. Three-dimensional direct numerical simulations are then conducted on this finite-height cylinder. The mass and momentum equations are resolved using the finite volume-based Open Source Field Operation and Manipulation (OpenFOAM). A fixed Reynolds number Re=UoD/ν of 250 is used in this study, which is defined based on mean velocity at the inlet ( Uo ) and cylinder diameter (D). Here ν is the kinematic viscosity of the working fluid. Non-dimensional velocity oscillation amplitude ( A∗=a/Uo ) is varied from 0.1 to 0.3, while the non-dimensional oscillation frequency ( f∗=f/fo ) takes the values of 0.33, 0.5, 1, 2, and 3. Here a and f are the dimensional oscillation amplitude and frequency, respectively and fo is the vortex shedding frequency corresponding to a uniform flow at Re = 250. The three-dimensional vortex structures, presented with the help of iso-Q surfaces, show that the oscillating flow changes the size and shape of the hairpin-shaped vortices. Wake is found to be synchronized with the oscillation frequency at f* = 2 for each value of the A* and results in the maximum lift force on the cylinder. Hilbert Huang transformation analysis of the transverse velocity signals at a specific point in the wake reveals that the wake is more complex and aperiodic in nature for f* values of 0.33, 0.5, and 1, whereas it is periodic for f* = 2 and 3. In order to further disclose the nonlinearity associated with the oscillating flow, the degree of stationarity is discussed corresponding to each value of A* and f*. Dynamic mode decomposition is exploited to obtain information about the coherent vortical structures and their spatial and temporal behavior in the wake with a change in the value of f*. Effects of A* and f* on the dynamic characteristics are also investigated.

Opposite effects of flame-generated potential and solenoidal velocity fluctuations on flame surface area in moderately intense turbulence

To explore the influence of dilatational and rotational motions on iso-scalar surface area within a premixed turbulent flame, three-dimensional compressible direct numerical simulation data obtained by Dave et al. (2018) from a lean, complex-chemistry, hydrogen-air flame propagating in intense small-scale turbulence (a ratio of laminar flame thickness to Kolmogorov length scale is about 20) in a box are analyzed using Helmholtz–Hodge decomposition of velocity field into solenoidal and potential components. The obtained results indicate that the flame surface area is created by potential velocity fluctuations generated due to combustion-induced thermal expansion, whereas the rotational motion acts to smooth wrinkles of iso-scalar surfaces within local preheat and reaction zones and, consequently, to reduce the flame surface area. The latter finding challenges the classical concept of flame-generated turbulence and is attributed to flame-generated solenoidal velocity fluctuations. Specifically, the incoming tangential (to the flame) vorticity is suppressed by baroclinic torque, which also generates vorticity in another tangential direction, with the latter (flame-generated) solenoidal velocity fluctuations working to smooth the flame surface. Thus, even under conditions of moderately intense turbulence, flame surface area can primarily be created by potential velocity perturbations caused by combustion-induced thermal expansion.

Wake suppression of a cylinder immersed in turbulence using rotating rods

In this study, we conducted three-dimensional direct numerical simulations to investigate the control performance of the free-stream turbulence past a circular cylinder with two small rotating rods at Re = 3900. In the case A and case B, two control rods with different rotating ratio α are positioned symmetrically at the circumferential angle θ=±45° and θ=±120° from the forward stagnation point of the main cylinder, respectively. Here, α is the ratio of the tangential velocity of the control rod surface ur to the inflow velocity U∞. Compared to the bare cylinder immersed in turbulence, both installation positions of the rotating rods at α = 2 result in a significant suppression on the wake flow. Specifically, the time-averaged drag coefficient Cd¯ was reduced by 25%, and the root mean square value of the lift coefficient measured to reduce by up to 30%. Statistical analysis is then performed, in terms of the Reynolds stresses, mean field, and the turbulent wake visualization to show variations in the flow dynamics. As expected, the front-mounted control rods inject kinetic energy into the boundary layer, effectively suppressing the turbulence fluctuations on both sides of the main cylinder. The work done by viscous forces around the rotating control rods and the suppression of turbulent fluctuations contribute to the pressure recovery observed in the rear-mounted control rod case. Proper orthogonal decomposition method is further employed to analyze the key features of the controlled wake of two cases with α = 2.

An Assessment of the Validity of Damköhler’s Hypotheses for Different Choices of Reaction Progress Variable in Homogenous Mixture Moderate or Intense Low-Oxygen Dilution (MILD) Combustion

The applicability of Damköhler’s hypotheses for homogenous mixture (i.e. constant equivalence ratio) moderate or intense low-oxygen dilution (MILD) combustion processes (with methane as the fuel) has been assessed using three-dimensional direct numerical simulation data with a skeletal mechanism. Two homogeneous MILD combustion cases with different levels of O2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\ ext{O}}}_{2}$$\\end{document} concentration (4.8% and 3.5% by volume) and different turbulence intensities have been investigated to analyse the influence of dilution level, turbulence intensity and the choice of the reaction progress variable definition (i.e. different choices of major species for turbulent burning velocity and flame surface area evaluations) on the applicability of Damköhler’s hypotheses in MILD combustion. It has been found that the normalized volume-integrated burning rate remains of the same order of magnitude as that of the normalized flame surface area only for the reaction progress variable definition based on a species mass fraction which has a Lewis number close to unity (e.g. CH4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\ ext{CH}}}_{4}$$\\end{document}) but the level of applicability deteriorates when the Lewis number of the species mass fraction, based on which the reaction progress variable is defined, deviates significantly from unity (e.g. CO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\ ext{CO}}}_{2}$$\\end{document}). Moreover, it has been demonstrated that the flame surface area calculation from the OH mole fraction-based information can lead to significant departures from Damköhler’s first hypothesis. It is also found that the relative magnitudes of normalised volume-integrated burning rate and normalised flame surface area are significantly affected by the level of dilution and the choice of the reaction progress variable definition. Damköhler’s second hypothesis, which provides a relation between the normalised turbulent burning velocity and the ratio of turbulent to molecular diffusivities, has been found to hold in an order of magnitude sense in homogeneous mixture MILD combustion only for the reaction progress variable definition based on species that has a Lewis number close to unity (e.g. CH4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\ ext{CH}}}_{4}$$\\end{document}) but the level of disagreement increases as the Lewis number of the reaction progress variable deviates significantly from unity (e.g. CO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\ ext{CO}}}_{2}$$\\end{document}).

Three-Dimensional Direct Numerical Simulation of Flow past A Near-Wall Circular Cylinder: Combined Effects of Gap Ratio and Boundary Layer Thickness on Flow Profiles and Pressure Distribution

Three-Dimensional Direct Numerical Simulation of Flow past A Near-Wall Circular Cylinder: Combined Effects of Gap Ratio and Boundary Layer Thickness on Flow Profiles and Pressure Distribution

Wall mode dynamics and transition to chaos in magnetoconvection with a vertical magnetic field

Quasistatic magnetoconvection of a fluid with low Prandtl number ( ${\textit {Pr}}=0.025$ ) with a vertical magnetic field is considered in a unit-aspect-ratio box with no-slip boundaries. At high relative magnetic field strengths, given by the Hartmann number ${\textit {Ha}}$ , the onset of convection is known to result from a sidewall instability giving rise to the wall-mode regime. Here, we carry out three-dimensional direct numerical simulations of unprecedented length to map out the parameter space at ${\textit {Ha}} = 200, 500, 1000$ , varying the Rayleigh number ( ${\textit {Ra}}$ ) over the range $6\times 10^5 \lesssim {\textit {Ra}} \lesssim 5\times 10^8$ . We track the development of stable equilibria produced by this primary instability, identifying bifurcations leading to limit cycles and eventually to chaotic dynamics. At ${\textit {Ha}}=200$ , the steady wall-mode solution undergoes a symmetry-breaking bifurcation producing a state that features a coexistence between wall modes and a large-scale roll in the centre of the domain, which persists to higher ${\textit {Ra}}$ . However, under a stronger magnetic field at ${\textit {Ha}}=1000$ , the steady wall-mode solution undergoes a Hopf bifurcation producing a limit cycle which further develops to solutions that shadow an orbit homoclinic to a saddle point. Upon a further increase in ${\textit {Ra}}$ , the system undergoes a subsequent symmetry break producing a coexistence between wall modes and a large-scale roll, although the large-scale roll exists only for a small range of ${\textit {Ra}}$ , and chaotic dynamics primarily arise from a mixture of chaotic wall-mode dynamics and arrays of cellular structures.

Analysis of high-speed drop impact onto deep liquid pool

The present work is devoted to the analysis of drop impact on a deep liquid pool, focusing on the high-energy splashing regimes caused by large raindrops at high velocities. Such cases are characterized by short time scales and complex mechanisms, thus they have received very little attention until now. The BASILISK open-source solver is used to perform three-dimensional direct numerical simulations. The capabilities of octree adaptive mesh refinement techniques enable capturing of the small-scale features of the flow, while the volume of fluid approach combined with a balanced-force surface-tension calculation is applied to advect the volume fraction of the liquids and reconstruct the interfaces. The numerical results compare well with experimental visualizations: both the evolution of crown and cavity, the emanation of ligaments, the formation of bubble canopy and the growth of a downward-moving spiral jet that pierces through the cavity bottom, are correctly reproduced. Reliable quantitative agreements are also obtained regarding the time evolution of rim positions, cavity dimensions and droplet distributions through an observation window. Furthermore, simulation gives access to various aspects of the internal flows, which allows us to better explain the observed physical phenomena. Details of the early-time dynamics of bubble ring entrapment and splashing performance, the formation/collapse of bubble canopy and the spreading of drop liquid are discussed. The statistics of droplet size show the bimodal distribution in time, corroborating distinct primary mechanisms of droplet production at different stages.

Compressible turbulent convection in highly stratified adiabatic background

Buoyancy-driven turbulent convection leads to a fully compressible flow with a prominent top-down asymmetry of first- and second-order statistics when the adiabatic equilibrium profiles of temperature, density and pressure change very strongly across the convection layer. The growth of this asymmetry and the formation of an increasingly thicker stabilized sublayer with a slightly negative mean convective heat flux$J_c(z)$at the top of the convection zone is reported here by a series of highly resolved three-dimensional direct numerical simulations beyond the Oberbeck–Boussinesq and anelastic limits for dimensionless dissipation numbers,$0.1 \le D\le 0.8$, at fixed Rayleigh number$Ra=10^6$and superadiabaticity$\epsilon =0.1$. The highly stratified compressible convection regime appears for$D &gt; D_{crit}\approx 0.65$, when density fluctuations collapse to those of pressure; it is characterized by an up to nearly 50 % reduced global turbulent heat transfer and a sparse network of focused thin and sheet-like thermal plumes falling through the top sublayer deep into the bulk.