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In this paper we discuss the formulation of the fuctuating Navier-Stokes(FNS) equations for multi-species, non-reactive fluids. In particular, weestablish a form suitable for numerical solution of the resulting stochasticpartial differential equations. An accurate and efficient numerical scheme,based on our previous methods for single species and binary mixtures, ispresented and tested at equilibrium as well as for a variety of non-equilibriumproblems. These include the study of giant nonequilibrium concentrationfluctuations in a ternary mixture in the presence of a diffusion barrier, thetriggering of a Rayleigh-Taylor instability by diffusion in a four-speciesmixture, as well as reverse diffusion in a ternary mixture. Good agreement withtheory and experiment demonstrates that the formulation is robust and can serveas a useful tool in the study of thermal fluctuations for multi-species fluids.The extension to include chemical reactions will be treated in a sequel paper.

Large-scale simulations are increasingly being used to study complex scientific and engineering phenomena. As a result, advanced visualization and data analysis are also becoming an integral part of the scientific process. Often, a key step in extracting insight from these large simulations involves the definition, extraction, and evaluation of features in the space and time coordinates of the solution. However, in many applications, these features involve a range of parameters and decisions that will affect the quality and direction of the analysis. Examples include particular level sets of a specific scalar field, or local inequalities between derived quantities. A critical step in the analysis is to understand how these arbitrary parameters/decisions impact the statistical properties of the features, since such a characterization will help to evaluate the conclusions of the analysis as a whole. We present a new topological framework that in a single-pass extracts and encodes entire families of possible features definitions as well as their statistical properties. For each time step we construct a hierarchical merge tree a highly compact, yet flexible feature representation. While this data structure is more than two orders of magnitude smaller than the raw simulation data it allows us to extract a set of features for any given parameter selection in a postprocessing step. Furthermore, we augment the trees with additional attributes making it possible to gather a large number of useful global, local, as well as conditional statistic that would otherwise be extremely difficult to compile. We also use this representation to create tracking graphs that describe the temporal evolution of the features over time. Our system provides a linked-view interface to explore the time-evolution of the graph interactively alongside the segmentation, thus making it possible to perform extensive data analysis in a very efficient manner. We demonstrate our framework by extracting and analyzing burning cells from a large-scale turbulent combustion simulation. In particular, we show how the statistical analysis enabled by our techniques provides new insight into the combustion process.

There is considerable technological interest in developing new fuel-flexible combustion systems that can burn fuels such as hydrogenor syngas. Lean premixed systems have the potential to burn these types of fuels with high efficiency and low NOx emissions due to reduced burnt gas temperatures. Although traditional scientific approaches based on theory and laboratory experiment have played essential roles in developing our current understanding of premixed combustion, they are unable to meet the challenges of designing fuel-flexible lean premixed combustion devices. Computation, with itsability to deal with complexity and its unlimited access to data, hasthe potential for addressing these challenges. Realizing this potential requires the ability to perform high fidelity simulations of turbulent lean premixed flames under realistic conditions. In this paper, we examine the specialized mathematical structure of these combustion problems and discuss simulation approaches that exploit this structure. Using these ideas we can dramatically reduce computational cost, making it possible to perform high-fidelity simulations of realistic flames. We illustrate this methodology by considering ultra-lean hydrogen flames and discuss how this type of simulation is changing the way researchers study combustion.

This paper introduces an adaptive mesh and algorithm refinement method for fluctuating hydrodynamics. This particle-continuum hybrid simulates the dynamics of a compressible fluid with thermal fluctuations. The particle algorithm is direct simulation Monte Carlo (DSMC), a molecular-level scheme based on the Boltzmann equation. The continuum algorithm is based on the Landau-Lifshitz Navier-Stokes (LLNS) equations, which incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. It uses a recently-developed solver for LLNS, based on third-order Runge-Kutta. We present numerical tests of systems in and out of equilibrium, including time-dependent systems, and demonstrate dynamic adaptive refinement by the computation of a moving shock wave. Mean system behavior and second moment statistics of our simulations match theoretical values and benchmarks well. We find that particular attention should be paid to the spectrum of the flux at the interface between the particle and continuum methods, specifically for the non-hydrodynamic (kinetic) time scales.

Using examples from active research areas in combustion and astrophysics, we demonstrate a computationally efficient numerical approach for simulating multiscale low Mach number reacting flows. The method enables simulations that incorporate an unprecedented range of temporal and spatial scales, while at the same time, allows an extremely high degree of reaction fidelity. Sample applications demonstrate the efficiency of the approach with respect to a traditional time-explicit integration method, and the utility of the methodology for studying the interaction of turbulence with terrestrial and astrophysical flame structures.

Type Ia supernovae (SNe Ia) are the largest thermonuclear explosions in the Universe. Their light output can be seen across great stances and has led to the discovery that the expansion rate of the Universe is accelerating. Despite the significance of SNe Ia, there are still a large number of uncertainties in current theoretical models. Computational modeling offers the promise to help answer the outstanding questions. However, even with today's supercomputers, such calculations are extremely challenging because of the wide range of length and time scales. In this paper, we discuss several new algorithms for simulations of SNe Ia and demonstrate some of their successes.

We present three-dimensional, time-dependent simulations of the flowfield of a laboratory-scale slot burner. The simulations are performed using an adaptive time-dependent low Mach number combustion algorithm based on a second-order projection formulation that conserves both species mass and total enthalpy. The methodology incorporates detailed chemical kinetics and a mixture model for differential species diffusion. Methane chemistry and transport are modeled using the DRM-19 mechanism along with its associated thermodynamics and transport databases. Adaptive mesh refinementdynamically resolves the flame and turbulent structures. Detailedcomparisons with experimental measurements show that the computational results provide a good prediction of the flame height, the shape of the time-averaged parabolic flame surface area, and the global consumption speed (the volume per second of reactants consumed divided by the area of the time-averaged flame). The thickness of the computed flamebrush increases in the streamwise direction, and the flamesurface density profiles display the same general shapes as the experiment. The structure of the simulated flame also matches the experiment; reaction layers are thin (typically thinner than 1 mm) and the wavelengths of large wrinkles are 5--10 mm. Wrinkles amplify to become long fingers of reactants which burn through at a neck region, forming isolated pockets of reactants. Thus both the simulated flame and the experiment are in the "corrugated flamelet regime."

The convective period leading up to a Type Ia supernova (SN Ia) explosion is characterized by very low Mach number flows, requiring hydrodynamical methods well-suited to long-time integration. We continue the development of the low Mach number equation set for stellar scale flows by incorporating the effects of heat release due to external sources. Low Mach number hydrodynamics equations with a time-dependent background state are derived, and a numerical method based on the approximate projection formalism is presented. We demonstrate through validation with a fully compressible hydrodynamics code that this low Mach number model accurately captures the expansion of the stellar atmosphere as well as the local dynamics due to external heat sources. This algorithm provides the basis for an efficient simulation tool for studying the ignition of SNe Ia.

We introduce a low Mach number equation set for the large-scale numerical simulation of carbon-oxygen white dwarfs experiencing a thermonuclear deflagration. Since most of the interesting physics in a Type Ia supernova transpires at Mach numbers from 0.01 to 0.1, such an approach enables both a considerable increase in accuracy and savings in computer time compared with frequently used compressible codes. Our equation set is derived from the fully compressible equations using low Mach number asymptotics, but without any restriction on the size of perturbations in density or temperature. Comparisons with simulations that use the fully compressible equations validate the low Mach number model in regimes where both are applicable. Comparisons to simulations based on the more traditional anelastic approximation also demonstrate the agreement of these models in the regime for which the anelastic approximation is valid. For low Mach number flows with potentially finite amplitude variations in density and temperature, the low Mach number model overcomes the limitations of each of the more traditional models and can serve as the basis for an accurate and efficient simulation tool.

Successfully attacking underground storage facilities for chemical and biological (C/B) weapons is an important mission area for the Department of Defense. The fate of a C/B agent during an attack depends critically on the pressure and thermal environment that the agent experiences. The initial environment is determined by the blast wave from an explosive device. The byproducts of the detonation provide a fuel source that burn when mixed with oxidizer (after burning). Additional energy can be released by the ignition of the C/B agent as it mixes with the explosion products and the air in the chamber. Hot plumes venting material from any openings in the chamber can provide fuel for additional energy release when mixed with additional oxidizer. Assessment of the effectiveness of current explosives as well as the development of new explosive systems requires a detailed understanding of all of these modes of energy release. Using methodologies based on the use of higher-order Godunov schemes combined with Adaptive Mesh Refinement (AMR), implemented in aparallel adaptive framework suited to the massively parallel computer systems provided by the DOD High-Performance Computing Modernization program, we use a suite of programs to develop predictive models forthe simulation of the energetics of blast waves, deflagration waves and ejecta plumes. The programs use realistic reaction kinetic and thermodynamic models provided by standard components (such as CHEMKIN) as well as other novel methods to model enhanced explosive devices. The work described here focuses on the validation of these models against a series of bomb calorimetry experiments performed at the Ernst-Mach Institute. In this paper, we present three-dimensional simulations of the experiments, examining the explosion dynamics and the role of subsequent burning on the explosion products on the thermal and pressure environment within the calorimeter. The effects of burning are quantified by comparing two sets of computations, one in which the calorimeter is filled with nitrogen so there is no after burning and a second in which the calorimeter contains air.

Recent progress in simulation methodologies and high-performance parallel computers have made it is possible to perform detailed simulations of multidimensional reacting flow phenomena using comprehensive kinetics mechanisms. As simulations become larger and more complex, it becomes increasingly difficult to extract useful information from the numerical solution, particularly regarding the interactions of the chemical reaction and diffusion processes. In this paper we present a new diagnostic tool for analysis of numerical simulations of reacting flow. Our approach is based on recasting an Eulerian flow solution in a Lagrangian frame. Unlike a conventional Lagrangian view point that follows the evolution of a volume of the fluid, we instead follow specific chemical elements, e.g., carbon, nitrogen, etc., as they move through the system . From this perspective an "atom" is part of some molecule of a species that is transported through the domain by advection and diffusion. Reactions cause the atom to shift from one chemical host species to another and the subsequent transport of the atom is given by the movement of the new species. We represent these processes using a stochastic particle formulation that treats advection deterministically and models diffusion and chemistry as stochastic processes. In this paper, we discuss the numerical issues in detail and demonstrate that an ensemble of stochastic trajectories can accurately capture key features of the continuum solution. The capabilities of this diagnostic are then demonstrated by applications to study the modulation of carbon chemistry during a vortex-flame interaction, and the role of cyano chemistry in rm NO_x production for a steady diffusion flame.

Many turbulent premixed flames of practical interest are statistically stationary. They occur in combustors that have anchoring mechanisms to prevent blow-off and flashback. The stabilization devices often introduce a level of geometric complexity that is prohibitive for detailed computational studies of turbulent flame dynamics. As a result, typical detailed simulations are performed in simplified model configurations such as decaying isotropic turbulence or inflowing turbulence. In these configurations, the turbulence seen by the flame either decays or, in the latter case, increases as the flame accelerates toward the turbulent inflow. This limits the duration of the eddy evolutions experienced by the flame at a given level of turbulent intensity, so that statistically valid observations cannot be made. In this paper, we apply a feedback control to computationally stabilize an otherwise unstable turbulent premixed flame in two dimensions. For the simulations, we specify turbulent inflow conditions and dynamically adjust the integrated fueling rate to control the mean location of the flame in the domain. We outline the numerical procedure, and illustrate the behavior of the control algorithm. We use the simulations to study the propagation and the local chemical variability of turbulent flame chemistry.

Ammonia often occurs in combustion gases as a product of fuel-nitrogen. Since either NO or N2 may predominate as the product of ammonia oxidation, there is considerable interest in understanding the factors responsible for selecting the final products. In flames the selectivity is known to depend on whether the reaction zones are premixed or non-premixed. This paper reports on a combined experimental and modeling investigation of ammonia chemistry in a hot combustion environment that is below flame temperatures, such as in post combustion gases. Experiments that mix highly diluted ammonia-methane and oxygen-water streams are interpreted in terms of a plug-flow model, a simplified mixing reactor model, and a two-dimensional direct numerical simulation. The study finds that the final products of ammonia oxidation remain sensitive to mixing even at temperatures below those of self-sustaining flames. At low temperatures ammonia oxidation occurs in a premixed reaction zone, but at sufficiently high temperatures a nonpremixed reaction zone may develop that produces significantly less NO than the equivalent premixed system. A direct numerical simulation is required to predict the behavior over the full range of conditions investigated experimentally, while a simplified reactor model captures the essential features as long as the radial gradients are not too steep.

We present three-dimensional, time-dependent simulations of a full-size laboratory-scale rod-stabilized premixed turbulent V-flame. The computations use an adaptive projection method based on a low Mach number formulation that incorporates detailed chemical kinetics and transport. The simulations are performed without introducing models for turbulence or turbulence chemistry interaction. We outline the numerical procedure and experimental setup, and compare computed results to mean flame location and surface wrinkling statistics gathered from experiment.

In this paper we discuss the application of a new diagnostic tool for analysis of flame simulations. This methodologogy is based on following specific chemical elements, e.g., carbon or nitrogen, as they move through the system. From this perspective an "atom" is a component of a molecule that is being transported through the simulation domain by advection and diffusion. Reactions cause the atom to shift from one species to another with the subsequent transport of the atom determined by the movement of the new species.

In this paper we use numerical simulation to investigate shock-induced ignition and combustion of a hydrocarbon gas. The focus of this paper is on quantifying the effect of fidelity in the chemical kinetics on the overall solution. We model the system using the compressible Navier Stokes equations for a reacting mixture. These equations express conservation of species mass, momentum, total energy.

With adaptive-grid computational methodologies and judicious use of compressible and low Mach number combustion models, we are carrying out three-dimensional, time-dependent direct numerical simulations of a laboratory-scale turbulent premixed methane burner. In the laboratory experiment, turbulence is generated by a grid located in the throat of a 50mm diameter circular nozzle; swirl is be introduced by four tangential air jets spaced uniformly around the circumference of the nozzle just above the turbulence grid. A premixed methane flame is stabilized above the nozzle in the central core region where a velocity deficit is induced by the swirling flow. The time-dependent flow field inside the nozzle, from the turbulence grid and the high-speed jets, to the nozzle exit plane is simulated using an adaptive-grid embedded-boundary compressible Navier-Stokes solver. The compressible calculation then provides time-dependent boundary conditions for an adaptive low Mach number model of the swirl-stabilized premixed flame. The low Mach model incorporates detailed chemical kinetics and species transport using 20 species and 84 reactions. Laboratory diagnostics available for comparisons include characterizations of the flow field just down stream of the nozzle exit plane, and flame surface statistics, such as mean location, wrinkling and crossing frequencies.

This conference paper considers how to use reaction path diagrams to better understand the output of reacting flow simulations. Briefly, these diagrams have long been used to depict the reactants and products in networks of chemical reactions. The diagrams can be generated in several ways from computer simulations of chemically reacting fluids to depict how the fluid moderates the chemistry by determining which species are brought into contact to react in quantity. The concept of a conditional diagram is introduced which depicts the reactions occurring in only a portion of the fluid domain, thus enabling comparisons between different regions of the fluid and the overall reaction network. Several examples are provided of the paths occurring in methane diffusion flames.

This paper reports on a combined experimental and modeling investigation of NOx formation in nitrogen-diluted laminar methane diffusion flames seeded with ammonia. The methane-ammonia mixture is a surrogate for biomass fuels which contain significant fuel-bound nitrogen. The experiments use flue-gas sampling to measure the concentration of stable species in the exhaust gas, including NO, O2, CO, and CO2. The computations evolve a two-dimensional low Mach number model using a solution-adaptive projection algorithm to capture fine-scale features of the flame. The model includes detailed thermodynamics and chemical kinetics, differential diffusion, buoyancy, and radiative losses. The model shows good agreement with the measurements over the full range of experimental NH3 seeding amounts. As more NH3 is added, a greater percentage is converted to N2 rather than to NO. The simulation results are further analyzed to trace the changes in NO formation mechanisms with increasing amounts of ammonia in the fuel.

In this paper we study the behavior of a premixed turbulent methane flame in three dimensions using numerical simulation. The simulations are performed using an adaptive time-dependent low Mach number combustion algorithm based on a second-order projection formulation that conserves both species mass and total enthalpy. The species and enthalpy equations are treated using an operator-split approach that incorporates stiff integration techniques for modeling detailed chemical kinetics. The methodology also incorporates a mixture model for differential diffusion. For the simulations presented here, methane chemistry and transport are modeled using the DRM-19 (19-species, 84-reaction) mechanism derived from the GRIMech-1.2 mechanism along with its associated thermodynamics and transport databases. We consider a lean flame with equivalence ratio 0.8 for two different levels of turbulent intensity. For each case we examine the basic structure of the flame including turbulent flame speed and flame surface area. The results indicate that flame wrinkling is the dominant factor leading to the increased turbulent flame speed. Joint probability distributions are computed to establish a correlation between heat release and curvature. We also investigate the effect of turbulent flame interaction on the flame chemistry. We identify specific flame intermediates that are sensitive to turbulence and explore various correlations between these species and local flame curvature. We identify different mechanisms by which turbulence modulates the chemisry of the flame.

In this paper we study the formation of NO in laminar, nitrogen diluted methane diffusion flames that are seeded with ammonia in the fuel stream. We have performed numerical simulations with detailed chemistry as well as laser-induced fluorescence imaging measurements for a range of ammonia injection rates. For comparison with the experimental data, synthetic LIF images are calculated based on the numerical data accounting for temperature and fluorescence quenching effects. We demonstrate good agreement between measurements and computations. The LIF corrections inferred from the simulation are then used to calculate absolute NO mole fractions from the measured signal.The NO formation in both doped and undoped flames occurs in the flame sheet. In the undoped flame, four different mechanisms including thermal and prompt NO appear to contribute to NO formation. As the NH3 seeding level increases, fuel-NO becomes the dominant mechanism and N2 shifts from being a net reactant to being a net product. Nitric oxide in the undoped flame as well as in the core region of the doped flames are underpredicted by the model; we attribute this mainly to inaccuracies in the NO recycling chemistry on the fuel-rich side of the flame sheet.

Recent progress in simulation methodologies and new, high-performance parallel architectures have made it is possible to perform detailed simulations of multidimensional combustion phenomena using comprehensive kinetics mechanisms. However, as simulation complexity increases, it becomes increasingly difficult to extract detailed quantitative information about the flame from the numerical solution, particularly regarding the details of chemical processes. In this paper we present a new diagnostic tool for analysis of numerical simulations of combustion phenomena. Our approach is based on recasting an Eulerian flow solution in a Lagrangian frame. Unlike a conventional Lagrangian viewpoint in which we follow the evolution of a volume of the fluid, we instead follow specific chemical elements, e.g., carbon, nitrogen, etc., as they move through the system. From this perspective an "atom" is part of some molecule that is transported through the domain by advection and diffusion. Reactions cause the atom to shift from one species to another with the subsequent transport given by the movement of the new species. We represent these processes using a stochastic particle formulation that treats advection deterministically and models diffusion as a suitable random-walk process. Within this probabilistic framework, reactions can be viewed as a Markov process transforming molecule to molecule with given probabilities. In this paper, we discuss the numerical issues in more detail and demonstrate that an ensemble of stochastic trajectories can accurately capture key features of the continuum solution. We also illustrate how the method can be applied to studying the role of cyanochemistry on NOx production in a diffusion flame.

Axisymmetric numerical simulations continue to provide insight into how the structure, dynamics, and maximum windspeeds of tornadoes, and other convectively-maintained vortices, are influenced by the surrounding environment. This work is continued with a new numerical model of axisymmetric incompressible flow that incorporates adaptive mesh refinement. The model dynamically increases or decreases the resolution in regions of interest as determined by a specified refinement criterion. Here, the criterion used is based on the cell Reynolds number dx dv / nu, so that the flow is guaranteed to be laminar on the scale of the local grid spacing. The model is used to investigate how the altitude and shape of the convective forcing, the size of the domain, and the effective Reynolds number (based on the choice of the eddy viscosity nu) influence the structure and dynamics of the vortex. Over a wide variety of domain and forcing geometries, the vortex Reynolds number Gamma / nu (the ratio of the far-field circulation to the eddy viscosity) is shown to be the most important parameter for determining vortex structure and behavior. Furthermore, it is found that the vertical scale of the convective forcing only affects the vortex inasmuch as this vertical scale contributes to the total strength of the convective forcing. The horizontal scale of the convective forcing, however, is found to be the fundamental length scale in the problem, in that it can determine both the circulation of the fluid that is drawn into the vortex core, and also influences the depth of the swirling boundary layer. Higher mean windspeeds are sustained as the eddy viscosity is decreased; however, it is observed that the highest windspeeds are found in the high-swirl, two-celled vortex regime rather than in the low-swirl, one-celled regime, which is in contrast with some previous results. The conclusions drawn from these results are applied to dimensional simulations with scales similar to the mesocyclone/thunderstorm environment. Tornado-like vortices are reproduced, using a constant eddy viscosity with such values as 40 m2s-1, which have maximum windspeeds, radii of maximum winds, and boundary layer depths which are quite similar t o those recently observed with portable Doppler radar. Based on the results of both nondimensional and tornado-scale simulations, scaling laws are empirically derived for the internal length scales in tornado-like vortices, such as the depth of the boundary layer and the radius of maximum winds.

The dominant computational cost in modeling turbulent combustion phenomena numerically with high fidelity chemical mechanisms is the time required to solve the ordinary differential equations associated with chemical kinetics. One approach to reducing that computational cost is to develop an inexpensive surrogate model that accurately represents evolution of chemical kinetics. One such approach, PRISM, develops a polynomial representation of the chemistry evolution in a local region of chemical composition space. This representation is then stored for later use. As the computation proceeds, the chemistry evolution for other points within the same region are computed by evaluating these polynomials instead of calling an ordinary differential equation solver. If initial data for advancing the chemistry is encountered that is not in any region for which a polynomial is defined, the methodology dynamically samples that region and constructs a new representation for that region. The utility of this approach is determined by the size of the regions over which the representation provides a good approximation to the kinetics and the number of these regions that are necessary to model the subset of composition space that is active during a simulation. In this paper, we assess the PRISM methodology in the context of a turbulent premixed flame in two dimensions. We consider a range of turbulent intensities ranging from weak turbulence that has little effect on the flame to strong turbulence that tears pockets of burning fluid from the main flame. For each case, we explore a range of sizes for the local regions and determine the scaling behavior as a function of region size and turbulent intensity.

The interaction of a vortex pair with a premixed flame serves as an important prototype for premixed turbulent combustion. In this study, we investigate the interaction of a counter-rotating vortex pair with an initially flat premixed methane flame. We focus on characterizing the mechanical nature of the flame-vortex interaction and on the features of the interaction strongly affected by fuel equivalence ratio. We compare computational solutions obtained using a time-dependent, two-dimensional adaptive low Mach number combustion algorithm that incorporates GRI-Mech 1.2 for the chemistry, thermodynamics and transport of the chemical species. We find that the circulation around the vortex scours gas from the preheat zone in front of the flame, making the interaction extremely sensitive to equivalence ratio. For nearly stoichiometric cases, the peak mole fraction of CH across the flame is relatively insensitive to the vortex whereas for richer flames we observe a substantial and rapid decline in the peak CH mole fraction, commencing early in the flame-vortex interaction. The peak concentration of HCO is found to correlate, in both space and time, with the peak heat release across a broad range of equivalence ratios. The model also predicts a measurable increase in C2H2 as a result of interaction with the vortex, and a marked increase in the low temperature chemistry activity.

Reacting flow simulations for combustion applications require extensive computing capabilities. Leveraging the AMReX library, the Pele suite of combustion simulation tools targets the largest supercomputers available and future exascale machines. We introduce PeleC, the compressible solver in the Pele suite, and detail its capabilities, including complex geometry representation, chemistry integration, and discretization. We present a comparison of development efforts using both OpenACC and AMReX's C++ performance portability framework for execution on multiple GPU architectures. We discuss relevant details that have allowed PeleC to achieve high performance and scalability. PeleC's performance characteristics are measured through relevant simulations on multiple supercomputers. The success of PeleC's design for exascale is exhibited through demonstration of a 160 billion cell simulation and weak scaling onto 100% of Summit, an NVIDIA-based GPU supercomputer at Oak Ridge National Laboratory. Our results provide confidence that PeleC will enable future combustion science simulations with unprecedented fidelity. [ABSTRACT FROM AUTHOR]