Simulations Of Mixing Layers Research Articles

Direct numerical simulation of supercritical oxy-methane mixing layers with CO2 substituted counterparts

Direct numerical simulations of temporally developing, three-dimensional, CH4/CO2, CH4/O2, and CO2/O2 mixing layers are conducted at a supercritical pressure of 300 atm. To effectively model the supercritical regime, the employed formulation includes the compressible form of the governing equations, the cubic Peng–Robinson equation of state and a generalized formulation for heat and mass flux vectors derived from non-equilibrium thermodynamics and fluctuation theory. A linear inviscid stability analysis is also performed for each case, to determine its most unstable wavelength. Flow visualizations reveal the presence of high density gradient magnitude regions for all three mixing layers, with conditional averages indicating increased presence of heavier fluid species within these regions. No significant departures are observed from perfect gas behavior, with compressibility factors very close to unity for all three mixing cases. Applicability of presumed probability density function methods is examined for the three supercritical mixing layers. An a priori analysis is also conducted to investigate various simplifying assumptions employed in modeling various subgrid scale (SGS) flux models. Two additional terms are identified in the large eddy simulation equations, the gradient of SGS contribution of pressure in the momentum equation and the gradient of SGS contribution of heat flux in energy equation, whose magnitudes are similar and comparable with their respective resolved terms. The performance of the scale similarity model to represent these additional terms is investigated. Finally, the performance of Smagorinsky, gradient, and scale similarity models is also investigated.

Large eddy simulation of the variable density mixing layer

In this paper we perform large eddy simulations of variable density mixing layers, which originate from initially laminar conditions. The aim of this work is to capture the salient flow physics present in the laboratory flow. This is achieved through varying the nature of the inflow condition, and assessing the vortex structure present in the flow. Two distinct inflow condition types are studied; the first is an idealised case obtained from a mean inflow velocity profile with superimposed pseudo-white-noise, and the second is obtained from an inflow generation technique. The inflow conditions generated have matching mean and root mean squared statistics. Validation of the simulations is achieved through grid dependency and subgrid-scale model testing. Regardless of the inflow condition type used, the change in growth rate of the mixing layer caused by the density ratio is captured. It is found that the spacing of the large-scale spanwise structure is a function of the density ratio of the flow. Detailed interrogation of the simulations shows that the streamwise vortex structure present in the mixing layer depends on the nature of the imposed inflow condition. Where white-noise fluctuations provide the inflow disturbances, a spatially-stationary streamwise structure is absent. Where the inflow generator is used, a spatially stationary streamwise structure is present, which appears as streaks in plan-view visualisations. The stationary streamwise structure evolves such that the ratio of streamwise structure wavelength to local vorticity thickness asymptotes to unity, independent of the density ratio. This value is in agreement with previous experimental studies. Recommendations are made on the requirements of inflow condition modelling for accurate mixing layer simulations.

Variable-density effects in incompressible non-buoyant shear-driven turbulent mixing layers

Abstract

Mesoscale elements description of turbulent flow

• Description of turbulent flow as an ensemble of finite size, or mesoscale , Lagrangian elements is formulated. • Mesoscale element has no deterministic position but a probability of presence and a region of influence growing with time. • Consideration of finite size elements allows explicit account of molecular transport described through pairwise interactions. • The method applied to a mixing layer in grid turbulence yielded scalar statistics in quantitative agreement with experiments. This work proposes to describe a turbulent flow using a set of mesoscale elements, that is fluid elements of small, but finite, size the properties of which are representative of larger region surrounding them. Consideration of fluid elements of finite dimensions allows one to formulate a small scale mixing model with an explicit dependency on the molecular transport coefficients. The dimensions of a mesoscale element are determined from an evolution equation accounting for the molecular diffusion and the strain rate induced by small-scale turbulence while its position is determined by convection by large-scale velocity components. In addition to consideration of the fluid elements of a finite size, the second key new concept is the notion of radius of influence over which such an element contributes to the statistics of the flow; this radius grows with time. It is shown that the proposed method satisfies the mass conservation and normalisation of the probability density functions of scalar quantities . The proposed method is illustrated with simulations of thermal mixing layer in grid turbulence.

Topology-based characterization of compressibility effects in mixing layers

Direct numerical simulations of high-speed mixing layers are used to characterize the effects of compressibility on the basis of local streamline topology and vortical structure. Temporal simulations of the mixing layers are performed using a finite volume gas-kinetic scheme for convective Mach numbers ranging from $M_{c}=0.2$ to $M_{c}=1.2$. The focus of the study is on the transient development and the main objectives are to (i) investigate and characterize the turbulence suppression mechanism conditioned upon local streamline topology; and (ii) examine changes in the vortex vector field – distribution, magnitude and orientation – as a function of Mach number. We first reaffirm that kinetic energy suppression with increasing Mach number is due to a decrease in pressure–strain redistribution. Then, we examine the suppression mechanism conditioned upon topology and vortex structure. Conditional statistics indicate that (i) at a given Mach number, shear-dominated topologies generally exhibit more effective pressure–strain redistribution than vortical topologies; and (ii) for a given topology, the level of pressure–strain correlation mostly decreases with increasing Mach number. At each topology, with increasing Mach number, there is a corresponding decrease in turbulent shear stress and production leading to reduced kinetic energy. Further, as $M_{c}$ increases, the proportion of vortex-dominated regions in the flow increases, leading to further reduction in the turbulent kinetic energy of the flow. Then, the orientation of vortical structures and direction of fluid rotation are examined using the vortex vector approach of Tian et al. (J. Fluid Mech., vol. 849, 2018, pp. 312–339). At higher $M_{c}$, the vortex vectors tend to be more aligned in the streamwise direction in contrast to low $M_{c}$ wherein larger angles with streamwise direction are preferred. The connection between vortex orientation and kinetic energy production is also investigated. The findings lead to improved insight into turbulence suppression dynamics in high Mach number turbulent flows.

Simulations of radiative turbulent mixing layers

ABSTRACTRadiative turbulent mixing layers should be ubiquitous in multi-phase gas with shear flow. They are a potentially attractive explanation for the high ions such as O vi seen in high-velocity clouds and the circumgalactic medium (CGM) of galaxies. We perform 3D magnetohydrohynamics (MHD) simulations with non-equilibrium (NEI) and photoionization modelling, with an eye towards testing simple analytic models. Even purely hydrodynamic collisional ionization equilibrium (CIE) calculations have column densities much lower than observations. Characteristic inflow and turbulent velocities are much less than the shear velocity, and the layer width $h \propto t_{\mathrm{cool}}^{1/2}$ rather than h ∝ tcool. Column densities are not independent of density or metallicity as analytic scalings predict, and show surprisingly weak dependence on shear velocity and density contrast. Radiative cooling, rather than Kelvin–Helmholtz instability, appears paramount in determining the saturated state. Low pressure due to fast cooling both seeds turbulence and sets the entrainment rate of hot gas, whose enthalpy flux, along with turbulent dissipation, energizes the layer. Regardless of initial geometry, magnetic fields are amplified and stabilize the mixing layer via magnetic tension, producing almost laminar flow and depressing column densities. NEI effects can boost column densities by factors of a few. Suppression of cooling by NEI or photoionization can, in principle, also increase O vi column densities, but, in practice, is unimportant for CGM conditions. To explain observations, sightlines must pierce hundreds or thousands of mixing layers, which may be plausible if the CGM exists as a ‘fog’ of tiny cloudlets.

The influence of velocity ratio on the evolution of streamwise vortices in the simulated plane mixing layer

Abstract In this paper we perform Large Eddy Simulations of the plane turbulent mixing layer, to assess the effect of the velocity ratio parameter on the evolution of the streamwise vortex structure in the flow. The mixing layers originate from a physically-correlated inflow condition. A simulation performed against reference experimental flow conditions produces reliable flow statistics, and the velocity ratio parameter is subsequently varied by changing the low-speed freestream velocity of the flow. It is found that the residual streamwise vorticity in the flow upstream of the splitter plate is amplified, and subsequently realigns into a single row of spatially stationary streamwise vortices. The distance required for this realignment process decreases with increasing values of the velocity ratio parameter. Once formed, the average spacing of the spatially stationary streamwise vortices evolves in a stepwise fashion, with the overall spanwise wavelength of the streamwise structure scaling linearly with the local vorticity thickness. This scaling is independent of the velocity ratio parameter for all values tested here.

Droplet dynamics and fine-scale structure in a shearless turbulent mixing layer with phase changes

Three-dimensional direct numerical simulations of a shearless mixing layer in a small fraction of the cloud–clear air interface are performed to study the response of an ensemble of cloud water droplets to the turbulent entrainment of clear air into a cloud filament. The main goal of this work is to understand how mixing of cloudy and clear air evolves as turbulence and thermodynamics interact through phase changes, and how the cloud droplets respond. In the main simulation case, mixing proceeds between a higher level of turbulence in the cloudy filament and a lower level of turbulence in the clear air environment – the typical shearless mixing layer set-up. Fluid turbulence is driven solely by buoyancy, which incorporates feedbacks from the temperature, the vapour content and the liquid water content fields. Two different variations on the core set of shearless mixing layer simulations are discussed, a simulation in a larger domain and a simulation with the same turbulence level inside the filament and its environment. Overall, it is found that, as evaporation occurs for the droplets that enter subsaturated clear air regions, buoyancy comes to dominate the subsequent evolution of the mixing layer. The buoyancy feedback leads initially to downdraughts at the cloudy–clear air interface and to updraughts in the bulk regions. The strength of the turbulence after initial transients depends on the domain size, showing that the range of scales is an important parameter in the shearless mixing layer set-up. In contrast, the level of turbulence in the clear air is found to have little effect on the evolution of the mixing process. The distributions of cloud water droplet size, supersaturation at the droplet positions and vertical velocity are more sensitive to domain size than to the details of the turbulence profile, suggesting that the evolution of cloud microphysics is more sensitive to large-scale as opposed to small-scale properties of the flow.

Compressibility and heat release effects in high-speed reactive mixing layers II. Structure of the stabilization zone and modeling issues relevant to turbulent combustion in supersonic flows

Three-dimensional direct numerical simulations of spatially-developing mixing layers have been conducted and analyzed for three distinct values of the convective Mach number Mc in both inert and reactive conditions. For reactive mixing layers, depending on the value of Mc, the thermal runaway occurs in either the mixing layer development zone (small value of Mc) or the fully developed turbulence region (larger value of Mc). For the smallest values of Mc, there is a significant increase in temperature in the auto-ignition zone at values of the mixture fraction slightly lower than the most reactive one and for sufficiently small values of the scalar dissipation rate (SDR). The combustion mode here is predominantly non-premixed as deduced from the Takeno index. This is in sharp contrast with the complexity of the flow observed in the fully turbulent region where combustion takes place in a spotty regime featuring premixed pockets of fuel and oxidizer where the maximum levels of heat release follow quite closely the stoichiometric isoline. It is thus evidenced that, in the most compressible regime, where ignition occurs in the fully developed turbulent region, the contribution of premixed combustion becomes quite significant, a conclusion that differs from previous computational studies of supersonic combustion. Finally, the paper ends with the inspection of some assumptions that are currently retained in the modeling of supersonic reactive flows of non-premixed reactants.

Lagrangian properties of the entrainment across turbulent/non-turbulent interface layers

Lagrangian statistics obtained from direct numerical simulations of turbulent planar jets and mixing layers are reported for the separation distance between the tracer particles at the outer edge of the turbulent/non-turbulent interface layer, and the entrained fluid particles. In the viscous superlayer (VSL) the mean square particle distance exhibits a ballistic evolution, while the Richardson-like scaling for relative dispersion prevails inside the turbulent sublayer (TSL). The results further support the existence of two different regimes within the interface layer, where small-scale outward enstrophy diffusion governs the entrained particles in the VSL, while inviscid small-scale motions govern the TSL.

On streamwise vortices in Large Eddy Simulations of initially laminar plane mixing layers

This paper details the influence of the nature of imposed inflow fluctuations on Large Eddy Simulations of a spatially developing turbulent mixing layer originating from laminar boundary layers. A simulation with imposed white-noise random fluctuations, commonly used in numerical simulations, produces mean-flow statistics that agree well with reference experimental data. Whilst flow visualisation images show evidence for streamwise vorticity in this simulation, quantitative statistics do not reveal the presence of statistically stationary streamwise vortices. A further simulation that uses physically-correlated inflow fluctuations also produces good mean-flow statistical agreement with reference data. From secondary shear stress contours it can be inferred that this simulation does, however, predict the presence of statistically stationary streamwise vortices. The properties of the streamwise vortices are in good agreement with experimental data. The data presented here indicate that, even for initially laminar conditions, plane mixing layer simulations require accurate physically correlated inflow conditions in order to reproduce the flow features found experimentally.

Initial condition effects on large scale structure in numerical simulations of plane mixing layers

In this paper, Large Eddy Simulations are performed on the spatially developing plane turbulent mixing layer. The simulated mixing layers originate from initially laminar conditions. The focus of this research is on the effect of the nature of the imposed fluctuations on the large-scale spanwise and streamwise structures in the flow. Two simulations are performed; one with low-level three-dimensional inflow fluctuations obtained from pseudo-random numbers, the other with physically correlated fluctuations of the same magnitude obtained from an inflow generation technique. Where white-noise fluctuations provide the inflow disturbances, no spatially stationary streamwise vortex structure is observed, and the large-scale spanwise turbulent vortical structures grow continuously and linearly. These structures are observed to have a three-dimensional internal geometry with branches and dislocations. Where physically correlated provide the inflow disturbances a “streaky” streamwise structure that is spatially stationary is observed, with the large-scale turbulent vortical structures growing with the square-root of time. These large-scale structures are quasi-two-dimensional, on top of which the secondary structure rides. The simulation results are discussed in the context of the varying interpretations of mixing layer growth that have been postulated. Recommendations are made concerning the data required from experiments in order to produce accurate numerical simulation recreations of real flows.

Mixing Driven by Radiative and Evaporative Cooling at the Stratocumulus Top

Abstract The stratocumulus-top mixing process is investigated using direct numerical simulations of a shear-free cloud-top mixing layer driven by evaporative and radiative cooling. An extension of previous linear formulations allows for quantifying radiative cooling, evaporative cooling, and the diffusive effects that artificially enhance mixing and evaporative cooling in high-viscosity direct numerical simulations (DNS) and many atmospheric simulations. The diffusive cooling accounts for 20% of the total evaporative cooling for the highest resolution (grid spacing ~14 cm), but this can be much larger (~100%) for lower resolutions that are commonly used in large-eddy simulations (grid spacing ~5 m). This result implies that the κ scaling for cloud cover might be strongly influenced by diffusive effects. Furthermore, the definition of the inversion point as the point of neutral buoyancy allows the derivation of two scaling laws. The in-cloud scaling law relates the velocity and buoyancy integral scales to a buoyancy flux defined by the inversion point. The entrainment-zone scaling law provides a relationship between the entrainment velocity and the liquid evaporation rate. By using this inversion point, it is shown that the radiative-cooling contribution to the entrainment velocity decouples from the evaporative-cooling contribution and behaves very similarly as in the smoke cloud. Finally, evaporative and radiative cooling have similar strengths, when this strength is measured by the integrated buoyancy source. This result partially explains why current entrainment parameterizations are not accurate enough, given that most of them implicitly assume that only one of the two mechanisms rules the entrainment.

Evaporative cooling amplification of the entrainment velocity in radiatively driven stratocumulus

AbstractEvaporative cooling monotonically increases as the thermodynamical properties of the inversion allow for more evaporation in shear‐free radiatively driven stratocumulus. However, the entrainment velocity can deviate from the evaporative cooling trend and even become insensitive to variations in the inversion properties. Here the efficiency of evaporative cooling at amplifying the entrainment velocity is quantified by means of direct numerical simulations of a cloud top mixing layer. We demonstrate that variations in the efficiency modulate the effect of evaporative cooling on entrainment, explaining the different trends. These variations are associated with the evaporation of droplets in cloud holes below the inversion point. The parametrization of the efficiency provides the evaporative amplification of the entrainment velocity as a function of a single parameter that characterizes the inversion. The resulting entrainment velocities match our experiments and previous measurements to within ±25%. The parametrization also predicts the transition to a broken‐cloud field consistently with observations.

Simulation of spatial high speed mixing layers using LES

The present paper is concerned with the simulation of the spatial supersonic mixing layer using large eddy simulation, with PISO algorithm, using one equation eddy viscosity model for sub grid scale stress modelling, a fourth order spatial and a second order temporal scheme. The size of the domain is of a similar to that of experiments, and encompases the splitter plate effect. The calculations are ascertained to be grid independent for grid sizes of 1200×260,800×200 and 600×160. The calculations are shown to match the experiments of Goebel and Dutton (1990) [1] and Papamoschou and Roshko (1988) [2] reasonably well, and are able to capture the effect of the reduced growth rate with increased Mc within the tolerance of experiments. The simulations are used further to study the removal of velocity deficit and the attainment of self similarity with increasing Mc.

Organised large structure in the post-transition mixing layer. Part 2. Large-eddy simulation

AbstractThree-dimensional large-eddy simulations of two-stream mixing layers developing spatially from laminar boundary layers are presented, replicating wind-tunnel experiments carried out in Part 1 of this study. These simulations have been continued through the mixing transition and into the fully turbulent self-similar flow beyond. In agreement with the experiments, the simulations show that the familiar mechanism of growth by vortex amalgamation is replaced at the mixing transition by a previously unrecognised mechanism in which the spanwise-coherent large structures individually undergo continuous linear growth. In the post-transition flow it is this continuous linear growth of the individual structures that produces the self-similar growth of the mixing-layer thickness, the large-structure interactions occurring as a consequence of the growth, not its cause. New information is also presented on the topography of the organised post-transition flow and on its cyclical evolution through the lifetimes of the individual large structures. The dynamic and kinematic implications of these findings are discussed and shown to define quantitatively the growth rate of the homogeneous post-transition mixing layer in its organised state.

Reynolds averaged Navier-Stokes simulations of compressible mixing layers of similar and dissimilar gases: Performance of k–ɛ turbulence model

The issue of growth rate reduction of high speed mixing layer with convective Mach number is examined for similar and dissimilar gases using Reynolds averaged Navier-Stokes (RANS) methodology with k–ɛ turbulence model. It is observed that the growth rate predicted using RANS simulations closely matches with that predicted using model free simulations. Velocity profiles do not depend on the modelled value of Prt and Sct; while the temperature and species mass fraction distributions depend heavily on them. Although basic k–ɛ turbulence model could not capture the reduced growth rate for the mixing layer formed between similar gases, it predicts very well the reduced growth rate for the mixing layer for the dissimilar gases. It appears that density ratio changes caused by temperature changes for the dissimilar gases have profound effect on the growth rate reduction.

Impacts of Parameterized Langmuir Turbulence and Nonbreaking Wave Mixing in Global Climate Simulations

Abstract The impacts of parameterized upper-ocean wave mixing on global climate simulations are assessed through modification to Large et al.’s K-profile ocean boundary layer parameterization (KPP) in a coupled atmosphere–ocean–wave global climate model. The authors consider three parameterizations and focus on impacts to high-latitude ocean mixed layer depths and related ocean diagnostics. The McWilliams and Sullivan parameterization (MS2000) adds a Langmuir turbulence enhancement to the nonlocal component of KPP. It is found that the Langmuir turbulence–induced mixing provided by this parameterization is too strong in winter, producing overly deep mixed layers, and of minimal impact in summer. The later Smyth et al. parameterization modifies MS2000 by adding a stratification effect to restrain the turbulence enhancement under weak stratification conditions (e.g., winter) and to magnify the enhancement under strong stratification conditions. The Smyth et al. scheme improves the simulated winter mixed layer depth in the simulations herein, with mixed layer deepening in the Labrador Sea and shoaling in the Weddell and Ross Seas. Enhanced vertical mixing through parameterized Langmuir turbulence, coupled with enhanced lateral transport associated with parameterized mesoscale and submesoscale eddies, is found to be a key element for improving mixed layer simulations. Secondary impacts include strengthening the Atlantic meridional overturning circulation and reducing the Antarctic Circumpolar Current. The Qiao et al. nonbreaking wave parameterization is the third scheme assessed here. It adds a wave orbital velocity to the Reynolds stress calculation and provides the strongest summer mixed layer deepening in the Southern Ocean among the three experiments, but with weak impacts during winter.

DNS with detailed and tabulated chemistry of engine relevant igniting systems

Developments in modern engine technology are moving towards a regime with fuel injection uncoupled from combustion. Auto-ignition is an essential characteristic in these systems. The accurate prediction of this chemical process is of paramount importance. Tabulation techniques can provide a detailed chemistry description which is needed to represent the subtle processes that occur during ignition. Strictly, only chemical sources are stored in a look-up table, while assumptions have been made about the mixing process in this pre-processing step.In this study, the validity of Flamelet Generated Manifolds (FGM’s) in a series of canonical configurations representative for compression ignition combustion processes is investigated. To this purpose, the FGM approach is applied to 0D perfectly stirred reactor (PSR), igniting 1D counterflow diffusion flame (CD-flame) and igniting 2D mixing layer simulations for a wide range of relevant engine conditions. An FGM table generated with homogeneous reactor simulations is able to correctly predict reaction progress in PSR cases which include mixing. On the other hand, an FGM table generated with a single igniting CD-flame at a constant strain rate predicts the trend in auto-ignition delay for varying strain rates qualitatively correct. Ignition in a 2D mixing layer, where a straining field due to vortical structures exists, is also well predicted with this FGM. To improve the quantitative auto-ignition prediction near the ignition limit, an extra controlling variable is needed.

Large Eddy Simulations of Turbulent Mixing Layers Excited with Two Frequencies

In this study, we investigate the energy transfer during the pairing and merging process of two vortices into one in an excited turbulent mixing layer using Large Eddy Simulations. We present simulations of natural and periodically excited mixing layers for validation purposes and study the vortex pairing dynamics by exciting the mixing layer by two frequencies. The results help in understanding the effects of the energy transfer in the long-wave turbulent spectrum and assessing the role of backscatter.