Aspects of turbulent shear-layer mixing are investigated over a range of shear-layer Reynolds numbers, $Re_{\unicode[STIX]{x1D6FF}}=\unicode[STIX]{x0394}U\unicode[STIX]{x1D6FF}/\unicode[STIX]{x1D708}$, based on the shear-layer free-stream velocity difference, $\unicode[STIX]{x0394}U$, and mixing-zone thickness, $\unicode[STIX]{x1D6FF}$, to probe the role of initial conditions in mixing stages and the evolution of the scalar-field probability density function (p.d.f.) and variance. Scalar transport is calculated for unity Schmidt numbers, approximating gas-phase diffusion. The study is based on direct-numerical simulation (DNS) and large-eddy simulation (LES), comparing different subgrid-scale (SGS) models for incompressible, uniform-density, temporally evolving forced shear-layer flows. Moderate-Reynolds-number DNS results help assess and validate LES SGS models in terms of scalar-spectrum and mixing estimates, as well as other metrics, to $Re_{\unicode[STIX]{x1D6FF}}\lesssim 3.3\times 10^{4}$. High-Reynolds-number LES investigations to $Re_{\unicode[STIX]{x1D6FF}}\lesssim 5\times 10^{5}$ help identify flow parameters and conditions that influence the evolution of scalar variance and p.d.f., e.g. marching versus non-marching. Initial conditions that generate shear flows with different mixing behaviour elucidate flow characteristics in each flow regime and identify elements that induce p.d.f. transition and scalar-variance behaviour. P.d.f. transition is found to be largely insensitive to local flow parameters, such as $Re_{\unicode[STIX]{x1D6FF}}$, or a previously proposed vortex-pairing parameter based on downstream distance, or other equivalent criteria. The present study also allows a quantitative comparison of LES SGS models in moderate- and high-$Re_{\unicode[STIX]{x1D6FF}}$ forced shear-layer flows.

Geometrical optics ray-tracing is used to derive schlieren and shadowgraph images from large-eddy simulation (LES) data of a jet in supersonic crossflow and to compare with experimental data. Including the components of the optical system that forms the image in the simulation is found to be important. The technique produces images that replicate flow physics more faithfully than straight-line path integration and other techniques, and more efficiently than physical-optics techniques. Applications of these simulated images are demonstrated in supersonic flows. Time-correlated pairs of shadowgraph images taken from the LES using this technique are used in conjunction with an image-correlation velocimetry technique to compare the estimated convection velocity field in the LES to that of experiments of the same flow. Agreement between the two is good with a maximum variance of 5% by some metrics. This technique can aid in the validation of LES results, allowing quantitative comparison between experiment and simulation, and to extract information unattainable by experiment alone. Comparisons of simulated and experimental jet penetration into the supersonic freestream are also made.

Numerical schemes for scalar transport and mixing in turbulent flows must be high-order accurate, and observe conservation and boundedness constraints. Discretization accuracy can be evaluated from the truncation error, and assessed by its dispersion and dissipation properties. Dispersion errors can cause violation of physical scalar bounds, whereas numerical dissipation is key to mitigating those violations. Numerical dissipation primarily alters the energy at small scales that are critical to turbulent mixing. Influence of additional dissipation on scalar mixing in large-eddy simulations (LES) of incompressible temporally evolving shear flow is examined in terms of the resolved passive-scalar field, Z¯. Scalar fields in flows with different mixing behavior, exhibiting both uniform and non-uniform mixed-fluid composition across a shear layer, are compared for different grid resolutions, subgrid-scale models, and scalar-convection schemes. Scalar mixing is assessed based on resolved passive scalar probability density function (PDF), variance, and spectra. The numerical-dissipation influence on mixing is found to depend on the nature of the flow. Mixing metrics sensitive to numerical dissipation are applied to examine the performance of limiting methods employed to mitigate unphysical scalar excursions. Two approaches, using a linear-scaling limiter for finite-volume schemes and a monotonicity-preserving limiter for finite-difference schemes, are studied. Their performance with respect to accuracy, conservation, and boundedness is discussed.

We discuss turbulent dynamics and mixing of a variable-density flow subject to a uniformacceleration field. The flow resulting from initial misalignments of pressure and density gradients is investigated for small to large density ratios, with evidence that the smalldensity ratio flow is described by the Boussinesq approximation. A new shear-layer growth rate is reported. Spectra collapse when properly scaled for variable density.

Simulations of combustion in high-speed and supersonic flows need to account for autoignition phenomena, compressibility, and the effects of intense turbulence. In the present work, the evolution-variable manifold framework of Cymbalist and Dimotakis ("On Autoignition-Dominated Supersonic Combustion," AIAA Paper 2015-2315, June 2015) is implemented in a computational fluid dynamics method, and Reynolds-averaged Navier–Stokes and wall-modeled large-eddy simulations are performed for a hydrogen–air combustion test case. As implemented here, the evolution-variable manifold approach solves a scalar conservation equation for a reaction-evolution variable that represents both the induction and subsequent oxidation phases of combustion. The detailed thermochemical state of the reacting fluid is tabulated as a low-dimensional manifold as a function of density, energy, mixture fraction, and the evolution variable. A numerical flux function consistent with local thermodynamic processes is developed, and the approach for coupling the computational fluid dynamics to the evolution-variable manifold table is discussed. Wall-modeled large-eddy simulations incorporating the evolution-variable manifold framework are found to be in good agreement with full chemical kinetics model simulations and the jet in supersonic crossflow hydrogen–air experiments of Gamba and Mungal ("Ignition, Flame Structure and Near-Wall Burning in Transverse Hydrogen Jets in Supersonic Crossflow," Journal of Fluid Mechanics, Vol. 780, Oct. 2015, pp. 226–273). In particular, the evolution-variable manifold approach captures both thin reaction fronts and distributed reaction-zone combustion that dominate high-speed turbulent combustion flows.

Dynamics and mixing of a variable-density turbulent flow subject to an externally imposed acceleration field in the zero-Mach-number limit are studied in a series of direct numerical simulations. The flow configuration studied consists of alternating slabs of high- and low-density fluid in a triply periodic domain. Density ratios in the range of $1.05\leqslant R\equiv \unicode[STIX]{x1D70C}_{1}/\unicode[STIX]{x1D70C}_{2}\leqslant 10$ are investigated. The flow produces temporally evolving shear layers. A perpendicular density–pressure gradient is maintained in the mean as the flow evolves, with multi-scale baroclinic torques generated in the turbulent flow that ensues. For all density ratios studied, the simulations attain Reynolds numbers at the beginning of the fully developed turbulence regime. An empirical relation for the convection velocity predicts the observed entrainment-ratio and dominant mixed-fluid composition statistics. Two mixing-layer temporal evolution regimes are identified: an initial diffusion-dominated regime with a growth rate ${\sim}t^{1/2}$ followed by a turbulence-dominated regime with a growth rate ${\sim}t^{3}$. In the turbulent regime, composition probability density functions within the shear layers exhibit a slightly tilted (‘non-marching’) hump, corresponding to the most probable mole fraction. The shear layers preferentially entrain low-density fluid by volume at all density ratios, which is reflected in the mixed-fluid composition.

For combustion in high-speed flows, radical-formation time scales and ignition delay times may be similar to, or dominate, relevant flow time scales. Reliable modeling of induction and autoignition processes is critical to the prediction of combustor performance. The evolution-variable manifold (EVM) approach of Cymbalist and Dimotakis uses a transported scalar to track the evolution of the reaction processes, from induction leading to autoignition and subsequent robust combustion. In the present work, the EVM method is implemented in a computational fluid dynamics code in which wall-modeled large-eddy simulations are performed for two ethylene-air high-speed combustion cases. The detailed thermochemical state of the reacting fluid is tabulated as a function of a reduced number of state variables that include density, energy, mixture fraction, and the reaction-evolution variable. A thermodynamically consistent numerical flux function is developed and the approach for coupling the large-eddy simulation to the EVM framework is discussed. It is found that particular attention must be given to the solution of the energy equation to obtain accurate and computationally stable results. The results show that the LES-EVM approach shows promise for the simulation of turbulent combustion of hydrocarbons in high-speed flows, including those dominated by ignition delay, and encompass regions of thin reaction fronts as well as distributed reaction zones.

We discuss turbulent dynamics and mixing of a variable-density flow subject to a uniform-acceleration field. The flow and misalignments of pressure and density gradients are investigated for small to large density ratios, with evidence that the small-density ratio flow is described by the Boussinesq approximation. A new shear-layer growth rate is reported, along with an extension of uniform-density flow vorticity-alignment statistics in the variable-density ow studied. Spectra collapse when properly scaled for variable density.

Supersonic combustion in hydrocarbon-fueled scramjets, in the lower limits of hypersonic flight Mach numbers, is expected to occur as autoignition-dominated distributed reactions. At relevant conditions, including leading to autoignition is not well-captured by detailed chemical-kinetic models at present. This paper introduces an evolution-variable manifold (EVM) framework for modeling autoignition-dominated distributed reactions in both compressible and incompressible flows. This framework combines a data-driven model for induction with a Lagrangian-reactor-generated (discretized) state-space manifold method for post-ignition combustion. As a first-order validation, EVM captures the temperature evolution in a rapidly-mixing well-stirred reactor (WSR).

The present work carries out large-eddy simulations of the low-speed, high-Reynolds number, chemically-reacting mixing layer experiments by Slessor et al. 1 In particular, we study the low-heat release case with prescribed turbulent inflow conditions.The objective of the present work is to gain insight into the physics of the reacting shear layer and to address some associated computational challenges.This set of experiments are at subsonic conditions and use hydrogen and fluorine as the fuel and oxidizer, respectively.The hypergolic reaction between H2 and F2, as it was run in the Slessor et al. experiments, is characterized by a large Damköhler number, making the chemistry fast compared to the flow time scales: the product formation and temperature-rise in the flow is mixing-limited.In this work, we attempt to address the issue of overshoots and undershoots of species mass-fractions, often observed in LES of high-Reynolds number flows, by modifying the convective fluxes.We observe that the modified fluxes eliminate the global excursions of species mass-fraction concentration.A three dimensional simulation is performed by imposing synthetic turbulence at the inflow, generated using the digital filter approach of Klein et al., 2 to mimic the experimental flow conditions.The velocity profiles, growth rate, and product thickness obtained from the simulations show a good match with the experimental data, but the peak value of temperature-rise is slightly over predicted.

We study a class of chemically reacting, spatially evolving, supersonic mixing layers via large eddy simulation. Specifically, the goal is to reproduce the experimental results on molecular mixing and heat release performed at Caltech by Bonanos et al. Here, the mixing layer is formed as a result of the interaction of supersonic and subsonic streams: the supersonic stream expands over a 30° perforated ramp and interacts with a subsonic stream of fluid injected into the combustor through the ramp. The primary (top, supersonic) stream contains a small amount of H_2 as the fuel. The secondary stream (injected through the ramp) contains a fractional amount of F_2 which acts as the oxidizer. The hypergolic reaction between hydrogen and fluorine is characterized by a large Damkohler number, making the chemistry fast compared with the flow time scales. Hence, the product formation and temperature-rise in the flow is mixing limited. Both reacting and non-reacting simulations are performed with two turbulence models (Smagorinsky and Vreman) and the comparisons are made with the available experimental data. The reconstructed species concentrations, used in the flux evaluation, are limited using ideas from a recent paper by Zhang and Shu in order to ensure boundedness for these quantities. The simulations show close agreement of the velocity profiles and the temperature-rise profiles to those measured in the experiment.

Baroclinic torque plays an important role in the dynamics of variable-density flows. Large eddy simulations using Favre-filtered resolved-scale velocities mask the explicit dependence of resolved-scale dynamics on subgrid-scale pressure-gradient-density interactions. The effect of subgrid-scale baroclinic torque on resolved scales is implicitly included in the subgrid-scale stress and subgrid-scale scalar fluxes through the resolved-scale vorticity it generates. LES closure models must therefore incorporate this effect in the computations. We explore the physics of subgrid-scale baroclinic torque within the structural framework of the Stretched-Vortex model. Fine-scale simulations of supersonic flows and direct numerical simulations of variable-density turbulence are investigated. Such flows have regions of active baroclinic torque and serve to set up flow configurations to assess the model.

The range of values of scalar fields in turbulent flows is bounded by their boundary values, for passive scalars, and by a combination of boundary values, reaction rates, phase changes, etc., for active scalars. The current investigation focuses on the local conservation of passive scalar concentration fields and the ability of the large-eddy simulation (LES) method to observe the boundedness of passive scalar concentrations. In practice, as a result of numerical artifacts, this fundamental constraint is often violated with scalars exhibiting unphysical excursions. The present study characterizes passive-scalar excursions in LES of a shear flow and examines methods for diagnosis and assesment of the problem. The analysis of scalar-excursion statistics provides support of the main hypothesis of the current study that unphysical scalar excursions in LES result from dispersive errors of the convection-term discretization where the subgrid-scale model (SGS) provides insufficient dissipation to produce a sufficiently smooth scalar field. In the LES runs three parameters are varied: the discretization of the convection terms, the SGS model, and grid resolution. Unphysical scalar excursions decrease as the order of accuracy of non-dissipative schemes is increased, but the improvement rate decreases with increasing order of accuracy. Two SGS models are examined, the stretched-vortex and a constant-coefficient Smagorinsky. Scalar excursions strongly depend on the SGS model. The excursions are significantly reduced when the characteristic SGS scale is set to double the grid spacing in runs with the stretched-vortex model. The maximum excursion and volume fraction of excursions outside boundary values show opposite trends with respect to resolution. The maximum unphysical excursions increase as resolution increases, whereas the volume fraction decreases. The reason for the increase in the maximum excursion is statistical and traceable to the number of grid points (sample size) which increases with resolution. In contrast, the volume fraction of unphysical excursions decreases with resolution because the SGS models explored perform better at higher grid resolution.