Direct Numerical Simulation of Differential Scalar Diffusion in Three-Dimensional Stratified Turbulence

Large eddy simulations of non-reacting H2/CO2 jets mixing with air are performed and the calculations are compared with the experiments reported by Smith et al. [“Laser Raman scattering measurements of differential molecular diffusion in non-reacting turbulent jets of H2/CO2 mixing with air,” Phys. Fluids 7, 1455–1466 (1995)]. The influence of differential diffusion effects for Reynolds numbers Re = 1000–8000 is analyzed and a differential diffusion parameter, ξ, is defined on the basis of normalized H2 and CO2 concentrations in order to quantify the effects of differential diffusion with increasing Reynolds number. The analysis is made not only in physical space but also with scatter plots and histograms. The simulation results reveal that differential diffusion effects are significant at downstream locations (more than 15 nozzle diameters away from the inlet) only for the lower Reynolds numbers (Re = 1000–2000). However, differential diffusion effects are present for all Reynolds numbers examined close to the inlet (closer than 10 nozzle diameters). This is not only confirmed by the mean results of the differential diffusion parameter, ξ, but also by looking at the histograms of ξ. This is an important indication that differential diffusion can be important in turbulent reacting flows if laminarization of the flow or weakening of turbulent diffusion occurs. Including differential diffusion effects in turbulent reactive flows involving mixtures with vastly different mass diffusivities can, therefore, improve the accuracy of numerical simulations. Results obtained assuming equal species mass diffusivities revealed that differential diffusion effects do not have any significant influence in the velocity field.

Differential diffusion of a passive scalar and an active scalar/density in stratified shear flow is considered when both the density and the passive scalar have a mean vertical gradient. The vertical diffusion coefficient of the passive scalar {ie397-01} (c: passive scalar fluctuation, \-c(x3): mean passive scalar distribution) has been obtained by the rapid distortion theory (RDT), and the comparison with the density diffusion coefficient {ie397-02} (ρ: density fluctuation, {ie397-03} mean density distribution) shows that the difference between Kc and Kρ comes from the initial density fluctuations. Namely, passive scalar flux has a ‘slow mode’ which oscillates at half frequency of the density flux, whose magnitude is proportional to the initial potential energy due to density fluctuations.

Effects of differential diffusion on turbulent burning velocity and flame surface area in NH3/H2/N2-air premixed flames

The modelling of differential diffusion with a conditional moment closure (CMC) method is considered. Direct numerical simulations for scalar fields in homogeneous isotropic decaying turbulence are used to quantify the non-unity Schmidt number effects. Unlike the equal molecular diffusion case, where terms involving deviations from the conditional average usually make a negligible contribution, these terms contribute significantly to the equations governing the evolution of the conditional average scalar in the presence of different molecular diffusion coefficients. Together with the conditional scalar dissipation they come to balance conditional scalar diffusion, the driving force of the differential diffusion effects. The shape of the conditional averages of these terms in mixture fraction space coincides with the approximate shape of the conditional average differential diffusion, Qz. Therefore, dividing by Qz they are only functions of time. Conditional moment closure leads to good predictions of Qz provided the time function is properly modelled. A model for the time scale is suggested.

A Consistent Flamelet Formulation for Non-Premixed Combustion Considering Differential Diffusion Effects

Differential diffusion in binary scalar mixing and reaction

The stratified inclined duct (SID) is a relatively new experimental paradigm that produces a sustained shear flow between two counterflowing layers of fluid supplied by reservoirs at each end of the duct containing fluids of different density. The duct can be tilted at a small angle θ to the horizontal and, for a given fluid, the flow is determined by two nondimensional parameters θ and the Reynolds number. We have observed four different flow regimes in SID: Laminar when the interface between the layers remains undisturbed, Holmboe characterised by sharp cusped waves on the interface, Intermittent when the flow has bursts of turbulence followed by relatively calm periods and Turbulent when the turbulence occurs throughout the duct and is sustained in time. The laminar regime occurs at low Re and θ, and transitions to the other regimes occur successively as Re and θ increase, so SID allows a systematic study of the different regimes. One of the most important questions in stratified turbulence is the efficiency with which the fluid is mixed. When the stratification is stable, with density decreasing with height, work needs to be done against gravity to move light fluid downwards and dense fluid upwards so that irreversible mixing can occur. The ‘tax’ that this irreversible mixing imposes on the kinetic energy of the flow, the so-called ‘mixing efficiency’ is important to parameterise mixing in ocean and climate models. In this talk I will discuss the philosophy behind SID and explain why the experiment is relevant to this issue, particularly in the context of the energetics of the flow. We focus first on the self-organisation properties of the flows, wherein more strongly turbulent flows tend to an asymptotic state characterised by a uniform gradient Richardson number of order 0.1-0.2 across the shear layer. We then summarise our results on turbulent energetics and mixing statistics. We derive the kinetic and scalar energy budgets and explain the specificity and scalings of SID turbulence. We assess the relevance of standard mixing parameterisations models, and we compare representative values with the literature. The dependence of these measures of mixing on controllable flow parameters provides asymptotic estimates that may be extrapolated to more strongly turbulent flows. Complementing the experiments we introduce the first accurate 3D DNS for SID. Implementing a suitable forcing method and boundary conditions allow us to maintain steady exchange flow for an arbitrarily long time at a minimal computational cost. With the newly developed numerical model, we explore the diverse transitions in SID from a numerical perspective.

We investigate the possibility of determining the local turbulent flame speed by measuring the individual terms in the balance of a mean progress of reaction variable for the case of a low turbulence methane-air Bunsen flame in the thin flame regime. Velocity distributions and flame edge positions were measured by particle image velocimetry techniques at 3 kHz for a flame stabilized by a surrounding pilot of the same stoichiometry, for a turbulent Reynolds number around 66 and Karlovitz numbers of the order of 4. The conservation equation for mean progress variable was analyzed along different streamlines as a balance of terms expressed as velocities, including terms for convection, turbulent diffusion, mean reaction, and turbulent and molecular diffusion. Each term was estimated from local velocities and flame locations using a thin flame approximation, and their uncertainty was evaluated based on propagation of experimentally measured statistical correlations. The largest terms were the convective and reaction terms, as expected, with smaller roles for turbulent and molecular diffusion across the flame brush. Countergradient diffusion and transition to gradient diffusion were observed across the flame brush. Closure of the balance of terms in the conservation equations using independently measured terms was not consistently achieved across the flame brush within the reckoned uncertainties, arriving at a balance within 20–30% of the absolute value. Testable hypotheses are offered for the possible reasons for the mismatch, including the role of spatial filtering and 3D effects on the reaction rate term. Finally, the experiments identify the inaccuracies in measuring a true local turbulent flame speed, and suggest a consistent methodology to reduce errors in such estimations. This is the first time such a detailed experimental closure is attempted for any configuration. The results suggest that the significant improvements in spatial resolution are necessary for a full closure.

Oceanographers use the term “differential diffusion” to express a greater value of bulk turbulent diffusivity of temperature within the ocean than the value of bulk diffusivity of salinity, the ratio quantified by Lewis number. Investigation of horizontal thermohaline convection at Prandtl number 1 and infinity over the range reveals a variety of new flow patterns. The chamber has a linearly changing temperature T and salinity S along the top extending from the cold, fresh “polar” end to the hot, salty “tropics” end. It has an aspect ratio of 8 and sides and bottom are insulated and impermeable. Five transition flow patterns occur with little hysteresis for a fixed salinity Rayleigh number Ras of order 105 as Rayleigh number Ra changes from 3.2 × 106 down to 1. They are: 1. A steady T-cell with sinking at the cold end flowing into a bottom flow that feeds up into a top thermal boundary layer. 2. Salty blobs in the boundary layer that amplify and move from the hot to cold end. Each cold end arrival triggers a sudden increase in overturning velocity. 3. A “stripes” pattern where top to bottom cells (alternating T and S cells) move toward the cold end. 4. An S-cell that is a mirror image of the T-cell near the top along with small T-cells lying at the bottom that move toward the cold end 5. A steady S-cell. Each pattern has a distinct volumetric signature in a T-S diagram. Ranges of Ra with various patterns are sizeable at Ras=7.5 × 105 if Le >4/3 but insensitive to Pr. Balanced convection at Ra = Ras >106 adopts a large unsteady supercell containing smaller T and S cells. Exact ranges of the supercell are unknown. Since differential diffusion produces a large collection of flows compared to thermal convection alone, it might produce unexpected new results if added into numerical models of the ocean.

LES of oxy-fuel jet flames using the Eulerian Stochastic Fields method with differential diffusion

Molecular diffusion and phase stability in high-pressure combustion

On the competing roles of turbulence and differential diffusion in facilitated ignition

Syngas is an attractive alternative to currently popular hydrocarbon fuels due to its ability to be synthesized from multiple sources and lower carbon content. Direct Numerical Simulation (DNS) studies on premixed and non-premixed syngas flames have recently received attention. In this light, DNS of turbulent premixed syngas has been performed. Influence of turbulence and differential diffusion effects on chemical pathways of fuels like Hydrogen and methane has been studied in the past. Similar study on syngas flame has not been reported in the literature. Two cases with variation in the intensity of turbulence have been reported in this study. Effect of differential diffusion and turbulence on heat release rate and fuel consumption rate has been discussed. The behavior of heat release rate and fuel consumption rate was largely similar between laminar and turbulent flames considered in this study. Influence of species Lewis number was found to be more pronounced than that of turbulence.

Relatively strongly stratified turbulent flows tend to self-organise into a ‘layered anisotropic stratified turbulence’ (LAST) regime, characterised by relatively deep and well-mixed density ‘layers’ separated by relatively thin ‘interfaces’ of enhanced density gradient. Understanding the associated mixing dynamics is a central problem in geophysical fluid dynamics. It is challenging to study LAST mixing, as it is associated with Reynolds numbers$Re := UL/\nu \gg 1$and Froude numbers$Fr :=(2{\rm \pi} U)/(L N) \ll 1$($U$and$L$being characteristic velocity and length scales,$\nu$the kinematic viscosity and$N$the buoyancy frequency). Since a sufficiently large dynamic range (largely) unaffected by stratification and viscosity is required, it is also necessary for the buoyancy Reynolds number$Re_{b} := \epsilon /(\nu N^{2}) \gg 1$, where$\epsilon$is the (appropriately volume-averaged) turbulent kinetic energy dissipation rate. This requirement is exacerbated for oceanically relevant flows, as the Prandtl number$Pr := \nu /\kappa = {O}(10)$in thermally stratified water (where$\kappa$is the thermal diffusivity), thus leading (potentially) to even finer density field structures. We report here on four forced fully resolved direct numerical simulations of stratified turbulence at various Froude ($Fr=0.5, 2$) and Prandtl ($Pr=1, 7$) numbers forced so that$Re_{b}=50$, with resolutions up to$30\,240 \times 30\,240 \times 3780$. We find that, as$Pr$increases, emergent ‘interfaces’ become finer and their contribution to bulk mixing characteristics decreases at the expense of the small-scale density structures populating the well-mixed ‘layers’. However, extreme mixing events (as quantified by significantly elevated local destruction rates of buoyancy variance$\chi _0$) are always preferentially found in the (statically stable) interfaces, irrespective of the value of$Pr$.

Scalar fluxes in decaying stratified turbulence are investigated when vertical mean gradients of density and passive scalar coexist. While there have been many studies on stratified turbulence, behavior of passive scalars in that system has rarely been studied. In this study, we have compared the DNS results with RDT(rapid distortion theory)[1], particularly for the time development of turbulent diffusion coefficients of density \(K_p = - \overline {pw} /N^2 \) w: vertical velocity, N: Brunt-Vaisala frequency) and passive scalar \(K_c = - \overline {cw} /(d\bar c/dz),\bar c(z)\) mean passive scalar distribution), and investigated the effects of molecular diffusions and initial conditions which might lead to differential diffusions of density (active scalar) and passive scalar[2].