Analysis of Mixing Models for use in Simulations of Turbulent Spray Combustion

The present study concerns the investigation of different mixing models for use in the transported probability density function (PDF) modeling of turbulent (reacting) spray flows. The modeling of the turbulent mixing and other characteristic scalar variables such as gas enthalpy using transported (joint) PDFs has become an important method to describe turbulent (reacting) spray flows since the evaporation process causes the PDF of the mixture fraction to deviate from the widely used β function, which is typically used in models for turbulent gas flows. In the PDF transport equation, the molecular mixing does not appear in closed form so that modeling strategies are required. For gas combustion, the interaction-by-exchange-with-the-mean (IEM) model, the modified Curl (MC) model, and the Euclidean minimum spanning tree (EMST) models are used. More recently, a new mixing model, the PSP model, which is based on parameterized scalar profiles has been developed. The present study focuses on the use and analysis of the IEM, MC and PSP models for turbulent spray flames. For this purpose, the models are reconsidered with respect to the evaporation process that must be included and evaluated if spray combustion is considered. For model evaluation, turbulent ethanol/air spray flames are simulated, and the results are compared to experimental data by A. Masri, University of Sydney, Australia.     

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.     

Wall-Resolved Large Eddy Simulations of the Transient Turbulent Fluid Mixing in a Closed System Replicating a Pressurized Thermal Shock

The isothermal mixing of a heavy and a light liquid of different physical properties is numerically investigated by means of Large Eddy Simulations. The validation is based on experimental data held in a system reproducing various components of a pressurized water nuclear reactor, during a scenario of cold water injection at a low Atwood number of 0.05. The flow has two distinct stages: first a buoyancy-driven phase is characterized by a fluid front development in the cold leg and gives rise to Kelvin–Helmholtz whorls under the action of density changes. Then, the heavy liquid discharges into the downcomer filled with light liquid, which causes a turbulent mixing. These phenomena are analyzed through a single-phase approach where the density of the working fluid is either variable or modeled by the Boussinesq approximation. The influence of grid refinement is deeply examined, which shows that the mesh convergence is well achieved for the main flow quantities, unlike the low-magnitude spanwise components. Overall, the numerical solutions are found to reproduce the experimental measurements with a fair accuracy for both physical models used. These latter exhibit similar trends, due to the small density difference under consideration. The predictions in the downcomer appear to be more challenging owing to a strongest turbulence than in the cold leg, some flow features being not properly captured. However, the experimental data in the downcomer are found to be incomplete and somewhat dubious for a strict validation of the numerical simulations. Lastly, the flow distribution in the dowcomer is investigated, providing further insight on the mixing process.

     

Impact of Turbulent Flow and Mean Mixture Fraction Results on Mixing Model Behavior in Transported Scalar PDF Simulations of Turbulent Non-premixed Bluff Body Flames

Numerical simulation results are presented for three turbulent jet diffusion flames, stabilized behind a bluff body (Sydney Flames HM1-3). Interaction between turbulence and combustion is modeled with the transported joint-scalar PDF approach. The focus of the study is on the impact of the quality of simulation results in physical space on the behavior of two micro-mixing models in composition space: the Euclidean Minimum Spanning Tree (‘EMST’) model and the modified Curl coalescence dispersion (‘CD’) model. Profiles of conditional means and variances of thermo-chemical quantities, conditioned on the mixture fraction, are discussed in the recirculation region and in the neck zone behind. The impact of the flow and mixing fields in physical space on the mixing model behavior in composition space is strong for the CD model and increases as the turbulence – chemistry interaction becomes stronger. The EMST conditional profiles, on the contrary, are hardly affected.     

Presumed Mapping Functions for Eulerian Modelling of Turbulent Mixing

The mapping closure of Chen et al. [Phys. Rev. Lett., 63, 1989] is a transported probability density function (PDF) method that has proven very efficient for modelling of turbulent mixing in homogeneous turbulence. By utilizing a Gaussian reference field, the solution to the mapping function (in homogeneous turbulence) can be found analytically for a range of initial conditions common for turbulent combustion applications, e.g. for binary or trinary mixing. The purpose of this paper is to investigate the possibility of making this solution a presumed mapping function (PMF) for inhomogeneous flows. The PMF in turn will imply a presumed mixture fraction PDF that can be used for a wide range of models in turbulent combustion, e.g. flamelet models, the conditional moment closure (CMC) or large eddy simulations. The true novelty of the paper, though, is in the derivation of highly efficient, closed algebraic expressions for several existing models of conditional statistics, e.g. for the conditional scalar dissipation/diffusion rate or the conditional mean velocity. The closed form expressions nearly eliminates the overhead computational cost that usually is associated with nonlinear models for conditional statistics. In this respect it is argued that the PMF is particularly well suited for CMC that relies heavily on manipulations of the PDF for consistency. The accuracy of the PMF approach is shown with comparison to DNS of a single scalar mixing layer to be better than for the β-PDF. Not only in the shape of the PDF itself, but also for all conditional statistics models computed from the PDF.     

Numerical Simulations of High-Speed Turbulent Cavity Flows

Detached-Eddy Simulations (DES) of flows over clean and controlled cavities with and without doors are presented in this paper. Mach and Reynolds numbers (based on cavity length) were 0.85 and one million respectively. Spectral analyses showed that the DES computations were able to correctly predict the frequencies of the Rossiter modes for both uncontrolled and controlled cases. Flow visualisations revealed that the impact of the shear layer formed along the cavity on a slanted aft wall no longer creates a large source of acoustic noise. Therefore little acoustic propagation was seen up the cavity. This was confirmed by the analysis of the cavity wall forces, which showed that the oscillations of the shear layer were reduced when the wall was slanted. This aided in reducing the overall Sound Pressure Levels throughout the cavity and far-field. Comparisons of the flow-fields suggested that the addition of the doors also aided in stabilising the shear layer, which was also shown in the analysis of the wall forces. As a result, the addition of the doors was found to affect the clean cavity configuration significantly more than the controlled one.     

Spectral-Dynamic Model for Large-Eddy Simulations of Turbulent Rotating Channel Flow

A new subgrid-scale model called the spectral-dynamic model is proposed. It consists of a refinement of spectral eddy-viscosity models taking into account nondeveloped turbulence in the subgrid-scales. The proposed correction, which is derived from eddy-damped quasi-normal Markovian statistical theory, is based on an adjustment of the turbulent eddy-viscosity coefficient to the deviation of the spectral slope (at small scales) with respect to the standard Kolmogorov law. The spectral-dynamic model is applied to large eddy simulation (LES) of rotating and nonrotating turbulent plane channel flows. It is shown that the proposed refinement allows for clear improvement of the statistical predictions due to a correct prediction of the near-wall behavior. Cases of rotating and nonrotating low (DNS) and high Reynolds (LES) numbers are then compared. It is shown that the principal structural features of the rotating turbulent channel flow are reproduced by the LES, such as the presence of the near-zero mean absolute vorticity region, the modification of the anisotropic character of the flow (with respect to the nonrotating case), the enhancement of flow organization, and the inhibition of the high- and low-speed streaks near the anticyclonic wall. Only a moderate Reynolds number dependence is exhibited, resulting in a more unstable character of the longitudinal large-scale roll cells at high Reynolds number, and a slight increase of the laminarization tendency on the cyclonic side of the channel. Received 16 October 1997 and accepted 1 October 1998     

Direct Numerical Simulations of Localised Forced Ignition in Turbulent Mixing Layers: The Effects of Mixture Fraction and Its Gradient

The effects of mixture fraction value ξ and the magnitude of its gradient |∇ξ| at the ignitor location on the localised forced ignition of turbulent mixing layers under decaying turbulence is studied based on three-dimensional compressible Direct Numerical Simulations (DNS) with simplified chemistry. The localised ignition is accounted for by a spatial Gaussian power distribution in the energy transport equation, which deposits energy over a prescribed period of time. In successful ignitions, it is observed that the flame shows a tribrachial structure. The reaction rate is found to be greater in the fuel rich side than in stoichiometric and fuel-lean mixtures. Placing the ignitor at a fuel-lean region may initiate ignition, but extinction may eventually occur if the diffusion of heat from the hot gas kernel overcomes the heat release due to combustion. It is demonstrated that ignition in the fuel lean region may fail for an energy input for which self-sustained combustion has been achieved in the cases of igniting at stoichiometric and fuel-rich locations. It is also found that the fuel reaction rate magnitude is negatively correlated with density-weighted scalar dissipation rate in the most reactive region. An increase in the initial mixture fraction gradient at the ignition centre for the ignitor placed at stoichiometric mixture decreases the spreading of the burned region along the stoichiometric mixture fraction isosurface. By contrast, the mass of the burned region increases with an increase in the initial mixture fraction gradient at the ignition location, as for a given ignition kernel size the thinner mixing layer includes more fuel-rich mixture, which eventually makes the overall burning rate greater than that compared to a thicker mixing layer where relatively a smaller amount of fuel-rich mixture is engulfed within the hot gas kernel. Submitted as a full-length article to Flow Turbulence and Combustion.     

Large-Eddy Simulations of Forced Three-Dimensional Impinging Jets

Large-eddy simulations of the flow field around twin three-dimensional impinging jets were carried out to simulate the near-ground hover configuration of a vertical takeoff and landing (VTOL) aircraft. Both the impinging jet and the upwash caused by the collision of the wall jets are modeled in this study. The evolution of the vortical structures in the impinging jet flow field, due to the introduction of axisymmetric and azimuthal perturbations at the jet exit, has been investigated. The vortical structures formed in the jet shear layer due to azimuthal forcing, show significant three-dimensional vortex stretching effects when compared to the structures formed during axisymmetric forcing. Breakdown of the large-scale structures into smaller vortices also occurs much earlier during azimuthal forcing. When compared to the upwash formed during axisymmetric forcing, the azimuthally perturbed jet forms an upwash that is less coherent and results in a weaker upload or lift-off force on the aircraft undersurface. Comparison with available experimental data indicates good agreement for the centerline velocity decay, the wall pressure variation and the phase speed of the vortical structures.     

Modeling of Three-Dimensional Turbulent Jet and Boundary-Layer Flows

New anisotropic algebraic constitutive relations for the Reynolds stress tensor are formulated. These relations make it possible to model correctly three-dimensional turbulent flows which cannot be described on the basis of traditional modern semi-empirical models of turbulence. Along with the well-known nonlinear Saffman term, these relations contain new nonlinear terms which take the wall effect into account. Several two- and three-dimensional turbulent flows are calculated nu\-merically using the averaged Navier-Stokes equations. The calculation results are compared with known experimental data.     

Simulations of Turbulent Flow in a Plane Asymmetric Diffuser

Large-eddy simulations (LES) of a planar, asymmetric diffuser flow have been performed. The diverging angle of the inclined wall of the diffuser is chosen as 8.5°, a case for which recent experimental data are available. Reasonable agreement between the LES and the experiments is obtained. The numerical method is further validated for diffuser flow with the diffuser wall inclined at a diverging angle of 10°, which has served as a test case for a number of experimental as well as numerical studies in the literature (LES, RANS). For the present results, the subgrid-scale stresses have been closed using the dynamic Smagorinsky model. A resolution study has been performed, highlighting the disparity of the relevant temporal and spatial scales and thus the sensitivity of the simulation results to the specific numerical grids used. The effect of different Reynolds numbers of the inflowing, fully turbulent channel flow has been studied, in particular, Re _b  = 4,500, Re _b  = 9,000 and Re _b  = 20,000 with Re _b being the Reynolds number based on the bulk velocity and channel half width. The results consistently show that by increasing the Reynolds number a clear trend towards a larger separated region is evident; at least for the studied, comparably low Reynolds-number regime. It is further shown that the small separated region occurring at the diffuser throat shows the opposite behaviour as the main separation region, i.e. the flow is separating less with higher Re _b . Moreover, the influence of the Reynolds number on the internal layer occurring at the non-inclined wall described in a recent study has also been assessed. It can be concluded that this region close to the upper, straight wall, is more distinct for larger Re _b . Additionally, the influence of temporal correlations arising from the commonly used periodic turbulent channel flow as inflow condition (similar to a precursor simulation) for the diffuser is assessed.     

Measurements of Turbulent Jet Mixing in a Turbulent Co-Flow Including the Influence of Periodic Forcing and Heating

In this work, the turbulent mixing of a confined coaxial jet in air is investigated by means of simultaneous particle image velocimetry and planar laser induced fluorescence of the acetone seeded flow injection. The jet is injected into a turbulent duct flow at atmospheric pressure through a 90 ^° pipe bend. Measurements are conducted in a small scale windtunnel at constant mass flow rates and three modes of operation: isothermal steady jet injection at a Dean number of 20000 (R e _d =32000), pulsed isothermal injection at a Womersley number of 65 and steady injection at elevated jet temperatures of ΔT=50 K and ΔT=100 K. The experiment is aimed at providing statistically converged quantities of velocity, mass fraction, turbulent fluctuations and turbulent mass flux at several downstream locations. Stochastic error convergence over the number of samples is assessed within the outer turbulent shear layer. From 3000 samples the statistical error of time-averaged velocity and mass fraction is below 1 % while the error of Reynolds shear stress and turbulent mass flux components is in the of range 5-6 %. Profiles of axial velocity and turbulence intensity immediately downstream of the bend exit are in good agreement with hot-wire measurements from literature. During pulsed jet injection strong asymmetric growing of shear layer vortices lead to a skewed mass fraction profile in comparison with steady injection. Phase averaging of single shot PLIF-PIV measurements allows to track the asymmetric shear layer vortex evolvement and flow breakdown during a pulsation cycle with a resolution of 10^°. Steady injection with increased jet temperature supports mixing downstream from 6 nozzle diameters onward.     

Transport, Mixing and Agglomeration of Particles in Turbulent Flows

This paper describes methods and approaches that have been used to simulate and model the transport, mixing and agglomeration of small particles in a flowing turbulent gas. The transported particles because of their inertia are assumed not to follow the motion of the large scales of the turbulence and or the motion of the small dissipating scales of the turbulence. We show how both these behaviours can be represented by a PDF approach analogous to that used in classical kinetic theory. For large scale dispersion the focus is on transport in simple generic flows like statistically stationary homogeneous and isotropic turbulence and simple shear flows. Special consideration is given to the transport and deposition of particles in turbulent boundary layers. For small scale transport the focus is on how the small scales of turbulence together with the particle inertial response enhance collision processes like particle agglomeration. In this case the importance of segregation and the formation of caustics, singularities and random uncorrelated motion is highlighted and discussed.     

Large Eddy Simulations of the Darmstadt Turbulent Stratified Flames with REDIM Reduced Kinetics

Turbulent stratified combustion is often found in practical combustion devices, however, for large eddy simulations (LES) of it is still a challenge. In the present work, LES of the Darmstadt turbulent stratified flame (TSF) cases are conducted. In total, one isothermal flow case A-i2 and four reacting cases with different combinations of stratification and shear, i.e., A-r, C-r, E-r, G-r cases, are simulated. The employed sub-grid scale (SGS) combustion model is the REDIM-PFDF model, in which the chemical kinetics is reduced into a two-dimensional chemistry look-up table by the reaction-diffusion manifolds (REDIM) method, which performs a model reduction based on the coupling of the chemical kinetics with molecular transport. The fluctuation of scalars within the LES filter volume is modeled by the presumed filtered density function (PFDF). The overall good agreement of the statistics of velocity, temperature and species with the experimental data demonstrates the capability of the REDIM-PFDF model for TSF. Additionally, the probability distributions of the alignment angle, α, between the reaction layer and mixing layer, are analyzed in detail. It is shown that the probability distributions of the alignment angel vary with the axial distance from the jet nozzle. It also reveals that, with a stronger turbulence, the stratification effect can be weakened and the probability difference for finding ‘back-supported’ and ‘front-supported’ flame modes tends to decrease.