Michael E. Mueller

Manifold-based models offer a computationally efficient alternative to directly transporting the thermochemical state in computational simulations of turbulent reacting flows, projecting the high-dimensional thermochemical state-space onto a low-dimensional manifold. Recent efforts have yielded a manifold-based model applicable to multi-modal combustion, enabling reconstruction of the thermochemical state from solutions to two-dimensional manifold equations in mixture fraction and generalized progress variable that are parameterised by three scalar dissipation rates. In coarse-grained simulations such as Large Eddy Simulation (LES), closure of the multi-modal manifold equations and subfilter variances/covariance requires closure of three filtered scalar dissipation rates. The present work adopts a data-based approach, providing closure for the three filtered scalar dissipation rates via deep neural networks (DNNs). High-fidelity datasets corresponding to an autoigniting n-dodecane jet flame and a bluff body swirl-stabilized confined lifted spray flame of two aviation fuels (Jet-A and C1) with different ignition propensities are leveraged to generate training data that spans a diverse range of thermodynamic conditions and combustion modes, including low- and high-temperature ignition regimes in addition to premixed and nonpremixed behaviour. A final DNN model is trained to enforce inherent physical constraints by learning nonlinear functional transformations of the three filtered scalar dissipation rates. The generalizability of this constrained DNN model is demonstrated a priori via conditional statistics evaluated on the lifted spray flame with C1–a configuration that had not been included in the training data. Excellent DNN agreement with conditional DNS statistics is observed, and integrated gradients are computed to identify the most sensitive input variables. The similarity of the marginal PDFs of the most informative input variables and outputs across configurations are quantified via the Wasserstein metric, demonstrating that data-based models may successfully generalize to unseen parametric conditions so long as the most informative input variables share similar distributions across training and testing datasets.

Temperature- and size-based collision efficiencies for the collision of dimerizing gas-phase species and for the condensation of dimers onto soot particles were estimated based on theoretical principles. These collision efficiencies were then implemented within a detailed soot model with the Hybrid Method of Moments (HMOM). For the size dependence, taking advantage of the inherent ability of HMOM to demarcate nucleation and aggregation modes of the soot size distribution, a different condensation collision efficiency is used for each mode to account for the substantial differences in size between the two modes and the effect on condensation collision efficiency. Simulations were performed using detailed chemistry for laminar ethylene flames and were validated for premixed atmospheric, premixed pressurized, and coflow atmospheric diffusion flames. Compared to the base model with constant collision efficiency for a given dimerizing species and 100% collision efficiency for condensation, the proposed model results in a change in the budget of nucleation and condensation rates with increased nucleation and decreased condensation. This change was found to increase the surface growth rate due to an increase in the number of primary particles resulting from increased nucleation/reduced condensation and the corresponding increase in soot surface area. This change was found to improve the prediction of soot volume fraction significantly for growth-dominated flames. For the coflow diffusion flame in particular, the maximum soot volume fraction shifted from the centerline to the wings of the flame, consistent with experimental measurements, in stark contrast to the base model with limited soot in the wings of the flame. • Size-based collision efficiency for condensation in a moment-based method. • Model validated for laminar flames (premixed and coflow diffusion). • Soot in wings of coflow diffusion flame captured accurately.

Large Eddy Simulation (LES) was used to investigate the evolution of the soot size distribution in a series of turbulent nonpremixed bluff body flames, with different bluff body diameters. The new Bivariate Multi-Moment Sectional Method (BMMSM) is employed to characterize the size distribution. BMMSM combines elements of sectional methods and methods of moments and is capable of reproducing fractal aggregate morphology, thanks to its joint volume-surface formulation, all at relatively low computational costs with fewer transported soot scalars compared to traditional sectional methods. LES results show soot volume fraction profiles agreeing correctly with the experimental measurements, exhibiting significant improvement compared to previous work using the HMOM. The evolution of the particle size distribution function (PSDF) was examined across the flame series and show that the size distribution is less sensitive to the bluff body diameter than the overall soot volume fraction, which increases with increasing bluff body diameter. The PSDF across the flame exhibit different features compared to turbulent nonpremixed jet flames. The long residence times in the recirculation zone leads to a nearly bimodal size distribution, which eventually becomes bimodal in the downstream jet-like region. Further analysis indicates that a size distribution model is needed to correctly predict the soot evolution. Remarkably, due to improved descriptions of oxidation with BMMSM compared to HMOM, significant nucleation and condensation rates in both the recirculation zone and jet-like region were found using BMMSM, on the same order of magnitude as surface growth and oxidation, leading to the improved prediction of mean soot volume fraction compared to HMOM. This work reveals that the need of size distribution is crucial to both predict global soot quantities accurately and reproduce fundamental mechanisms.

Filtered two-fluid models (fTFMs) for gas–solid flows, supplemented with models for the effects of subgrid-scale structures, are frequently used to simulate industrial-scale fluidized beds because of the prohibitively high cost of fine-grid simulations of two-fluid models (TFMs). Previous studies have shown that the subgrid correction to the interphase interaction force (specifically, the drag force) is critical for accurate prediction of the flow hydrodynamics via fTFM simulations. Although early studies focused on analytical models for subgrid contributions, machine learning-based models have appeared in recent years. In the present study, an automated framework based on Bayesian optimization was used to train an artificial neural network (ANN) to predict the drag force in fTFMs. This optimized ANN model revealed a linear dependence of the filtered drag force on the filtered gas pressure gradient over most of the particle volume fraction range and filter sizes for various gas–solid systems. A constrained ANN model in which the linear dependence of the drag force on the filtered gas pressure gradient was explicitly enforced was found to be comparable to that of the unconstrained ANN model in accuracy, but its on-the-fly utilization in simulations could be less expensive from a computational perspective. The constrained ANN model, when introduced into the fTFM, shows that the overall dependence on the gas pressure gradient is altered upon filtering the drag force term, which has previously been shown to be equivalent to the emergence of an apparent added mass force term.

Ammonia (NH3) is a zero-carbon fuel that has been receiving increasing attention for power generation and even transportation. Compared to H2, NH3's volumetric energy density is higher, is not as explosive, and has well established transport and storage technologies. Yet, NH3 has poor flammability and flame stability characteristics and more reactive nitrogen (RN: NOx, N2O) emissions than hydrocarbon fuels, at least with traditional combustion processes. Partially cracking NH3 (into a NH3-H2-N2 mixture, AHN) addresses its flammability and stability issues. RN emissions remain a challenge, and mechanisms of their emissions are fundamentally different in NH3 and hydrocarbon combustion. While rich-quench-lean NH3 combustion strategies have shown promise, the largest contributions to RN emissions are the unrelaxed emissions in the fuel-rich stage due to overshoot of thermodynamic equilibrium within the reaction zone of premixed flames coupled with finite residence times available for relaxation to equilibrium. This work introduces a rush-to-equilibrium concept for AHN combustion, which aims to reduce the unrelaxed RN emissions in finite residence times by accelerating the approach to equilibrium. In the concept, a flow particle is subjected to a decaying mixing rate as it transits the premixed flame. This mitigates the mixing effects that prevents the particle approach to equilibrium, and promotes the chemistry effects to push the particle toward equilibrium, all while considering finite residence times. Evaluated with a state-of-the-art combustion model at gas turbine conditions, the concept shows the potential to reduce RN emissions by an order of magnitude, and that works irrespective of cracking extent, pressure, temperature, etc. A brief discussion of possible practical implementation reveals reasonable geometric and flow parameters characteristic of modern gas turbine combustors.

Abstract Accurate understanding and prediction of how ocean waves affect offshore wind farms are critical to their siting, design, and operation. This study presents a computational framework for simulating finite offshore wind farms using Large Eddy Simulation (LES) and a Dynamic Wave Spectrum Model (Dyn-WaSp). Implementation of the Dyn-WaSp with and without a correction for swell modes is compared to a static roughness (wave phase-averaged) model, which has a similar computational cost. Impacts of the different wave models on the wind’s mean velocity and turbulent kinetic energy profiles in the finite offshore wind farm are examined, and ideal available power at hub height is compared. The dynamic wave spectrum model is shown to predict lower mean velocities in comparison to the phase-averaged approach and predicts higher shear and turbulent kinetic energy, suggesting that loading on turbines is greater than would be estimated by a static roughness model.

A joint volume-surface formalism of the Multi-Moment Sectional Method (MMSM) is developed to describe the evolution of soot size distribution in turbulent reacting flows. The bivariate MMSM (or BMMSM) considers three statistical moments per section, including the total soot number density, total soot volume, and total soot surface area per section. A linear profile along the volume coordinate is considered to reconstruct the size distribution within each section, which weights a delta function along the surface coordinate. The closure for the surface considers that the primary particle diameter is constant so the surface/volume ratio constant within each section. The inclusion of the new variable in BMMSM allows for the description of soot's fractal aggregate morphology compared to the strictly spherical assumption of its univariate predecessor. BMMSM is shown to reproduce bimodal soot size distributions in simulations of one-dimensional laminar sooting flames as in experimental measurements. To demonstrate its performance in turbulent reacting flows, BMMSM is coupled to a Large Eddy Simulation framework to simulate a laboratory-scale turbulent nonpremixed jet flame. Computational results are validated against available experimental measurements of soot size distribution, showing the ability of BMMSM to reproduce the evolution of the size distribution from unimodal to bimodal moving downstream in the flame. In general, varying the number of sections has limited influence on results, and accurate results are obtained with as few as eight sections so 24 total degrees of freedom. The impact of using a different statistical model for soot (HMOM) is also investigated. The total computational cost of using BMMSM as low as approximately 44% more than the cost of HMOM. The new formulation results in a computationally efficient approach for the soot size distribution in turbulent reacting flows.

A joint volume-surface formalism of the Multi-Moment Sectional Method (MMSM) is developed to describe the evolution of soot size distribution in turbulent reacting flows. The bivariate MMSM (or BMMSM) considers three statistical moments per section, including the total soot number density, total soot volume, and total soot surface area per section. A linear profile along the volume coordinate is considered to reconstruct the size distribution within each section, which weights a delta function along the surface coordinate. The closure for the surface considers that the primary particle diameter is constant so the surface/volume ratio constant within each section. The inclusion of the new variable in BMMSM allows for the description of soot's fractal aggregate morphology compared to the strictly spherical assumption of its univariate predecessor. BMMSM is shown to reproduce bimodal soot size distributions in simulations of one-dimensional laminar sooting flames as in experimental measurements. To demonstrate its performance in turbulent reacting flows, BMMSM is coupled to a Large Eddy Simulation framework to simulate a laboratory-scale turbulent nonpremixed jet flame. Computational results are validated against available experimental measurements of soot size distribution, showing the ability of BMMSM to reproduce the evolution of the size distribution from unimodal to bimodal moving downstream in the flame. In general, varying the number of sections has limited influence on results, and accurate results are obtained with as few as eight sections so 24 total degrees of freedom. The impact of using a different statistical model for soot (HMOM) is also investigated. The total computational cost of using BMMSM as low as approximately 44% more than the cost of HMOM. The new formulation results in a computationally efficient approach for the soot size distribution in turbulent reacting flows.

Large Eddy Simulation (LES) was used to investigate the evolution of the soot size distribution in a series of turbulent nonpremixed bluff body flames, with different bluff body diameters. The new Bivariate Multi-Moment Sectional Method (BMMSM) is employed to characterize the size distribution. BMMSM combines elements of sectional methods and methods of moments and is capable of reproducing fractal aggregate morphology, thanks to its joint volume-surface formulation, all at relatively low computational costs with fewer transported soot scalars compared to traditional sectional methods. LES results show soot volume fraction profiles agreeing correctly with the experimental measurements, exhibiting significant improvement compared to previous work using the HMOM. The evolution of the particle size distribution function (PSDF) was examined across the flame series and show that the size distribution is less sensitive to the bluff body diameter than the overall soot volume fraction, which increases with increasing bluff body diameter. The PSDF across the flame exhibit different features compared to turbulent nonpremixed jet flames. The long residence times in the recirculation zone leads to a nearly bimodal size distribution, which eventually becomes bimodal in the downstream jet-like region. Further analysis indicates that a size distribution model is needed to correctly predict the soot evolution. Remarkably, due to improved descriptions of oxidation with BMMSM compared to HMOM, significant nucleation and condensation rates in both the recirculation zone and jet-like region were found using BMMSM, on the same order of magnitude as surface growth and oxidation, leading to the improved prediction of mean soot volume fraction compared to HMOM. This work reveals that the need of size distribution is crucial to both predict global soot quantities accurately and reproduce fundamental mechanisms.

Abstract Combustion encompasses multiscale, multiphase reacting flow physics spanning a wide range of scales from the molecular scales, where chemical reactions occur, to the device scales, where the turbulent flow is affected by the geometry of the combustor. This scale disparity and the limited measurement capabilities from experiments make modeling combustion a significant challenge. Recent advancements in high-performance computing (HPC), particularly with the Department of Energy's Exascale Computing Project (ECP), have enabled high-fidelity simulations of practical applications to be performed. The major physics submodels, including chemical reactions, turbulence, sprays, soot, and thermal radiation, exhibit distinctive computational characteristics that need to be examined separately to ensure efficient utilization of computational resources. This paper presents the multiphysics solver for the Pele code suite, called PeleMP, which consists of models for spray, soot, and thermal radiation. The mathematical and algorithmic aspects of the model implementations are described in detail as well as the verification process. The computational performance of these models is benchmarked on multiple supercomputers, including Frontier, an exascale machine. Results are presented from production simulations of a turbulent sooting ethylene flame and a bluff-body swirl stabilized spray flame with sustainable aviation fuels to demonstrate the capability of the Pele codes for modeling practical combustion problems with multiphysics. This work is an important step toward the exascale computing era for high-fidelity combustion simulations providing physical insights and data for predictive modeling of real-world devices.

Manifold-based models are an efficient modeling framework for turbulent combustion but, in their basic formulation, do not account for the compressibility effects of high-speed flows. To include the effects of compressibility, ad hoc corrections have been proposed but result in an inconsistent thermodynamic state between the manifold and flow simulation. In this work, an iterative algorithm to consistently incorporate compressibility effects into manifold-based models is developed. The manifold inputs (fuel and oxidizer temperatures and pressure) are determined iteratively to reflect the nonnegligible variations in thermodynamic state (expressed in terms of density and internal energy in flow simulations) that are characteristic of supersonic combustion. The algorithm is demonstrated on data from simulations of high-speed reacting mixing layers and is significantly more accurate than established approaches that only partially couple the manifold in compressible flow simulations. The proposed approach eliminates partial coupling approximation errors in excess of 10 and 20% for temperature and water source term.

Due to the multitude of scales present in realistic oceanic conditions, resolving the surface stress is computationally intensive, motivating modeling approaches. In this work, a dynamic wave drag model is developed for large eddy simulation (LES) to quantify the effects of multiscale dynamically rough surfaces on the atmospheric boundary layer. The waves are vertically unresolved, and the total drag due to the horizontally resolved portion of the wave spectrum is computed through a superposition of the force from each mode. As LES can only resolve the horizontal wind–wave interactions to the filter scale Δ, the effects of the horizontally unresolved, subfilter waves are modeled by specifying a roughness length scale characterizing the unresolved wave energy spectrum. This subfilter roughness is set proportional to the subfilter root mean square of the wave height distribution, and the constant of proportionality is evaluated dynamically during the simulation based on the assumption that the total drag force at the wave surface is independent of the filter scale. The dynamic approach is used to simulate the airflow over a spectrum of moving waves, and the results are validated against high-fidelity phase-resolved simulations. The dynamic approach combined with the wave spectrum drag model is then used to study flow through a fixed-bottom offshore wind farm array, equivalent to an infinite farm, with each turbine represented using an actuator disk model. The dynamic model accurately adapts to the changing velocity field and accurately predicts the mean velocity profiles and power produced from the offshore wind farm. Furthermore, the effect of the wind–wave interactions on the mean velocity profiles, power production, and kinetic energy budget is quantified.

Ammonia (NH 3 ) is an attractive low-carbon fuel and hydrogen carrier. However, losses and inefficiencies across the value chain could result in reactive nitrogen emissions (NH 3 , NO x , and N 2 O), negatively impacting air quality, the environment, human health, and climate. A relatively robust ammonia economy (30 EJ/y) could perturb the global nitrogen cycle by up to 65 Mt/y with a 5% nitrogen loss rate, equivalent to 50% of the current global perturbation caused by fertilizers. Moreover, the emission rate of nitrous oxide (N 2 O), a potent greenhouse gas and ozone-depleting molecule, determines whether ammonia combustion has a greenhouse footprint comparable to renewable energy sources or higher than coal (100 to 1,400 gCO 2 e/kWh). The success of the ammonia economy hence hinges on adopting optimal practices and technologies that minimize reactive nitrogen emissions. We discuss how this constraint should be included in the ongoing broad engineering research to reduce environmental concerns and prevent the lock-in of high-leakage practices.

Due to the multitude of scales present in realistic oceanic conditions, resolving the surface stress is computationally intensive, motivating modeling approaches. In this work, a dynamic wave drag model is developed for Large Eddy Simulation to quantify the effects of multiscale dynamically rough surfaces on the atmospheric boundary layer. The waves are vertically unresolved, and the total drag due to the horizontally resolved portion of the wave spectrum is computed through a superposition of the force from each mode. As LES can only resolve the horizontal wind-wave interactions to the filter scale $Δ$, the effects of the horizontally unresolved, subfilter waves are modeled by specifying a roughness length scale characterizing the unresolved wave energy spectrum. This subfilter roughness is set proportional to the subfilter root-mean-square of the height distribution, and the constant of proportionality is evaluated dynamically during the simulation based on the assumption that the total drag force at the wave surface is independent of the filter scale. The dynamic approach is used to simulate the airflow over a spectrum of moving waves and the results are validated against high-fidelity phase-resolved simulations. The dynamic approach combined with the wave spectrum drag model is then used to study flow through a fixed-bottom offshore wind farm. The dynamic model accurately adapts to the changing velocity field and accurately predicts the mean velocity profiles and power produced from the offshore wind farm. Further, the effect of the wind-wave interactions on the mean velocity profiles, power production, and kinetic energy budget are quantified.

Physics-based uncertainty quantification is applied to a boundary layer over a flat plate with a statistically stationary separation bubble to assess sources and dynamics of model error (ME) in two-equation Reynolds-Averaged Navier-Stokes turbulence models in separated flows. Two distinct ME modes are found that correspond to the qualitative behavior of ME in a turbulent wall-bounded flow (upstream of the separation bubble) and turbulent free-shear flow (within the separation bubble), with a superposition of these ME modes in intermediate regions. A complex understanding of ME results as it changes throughout the flow, but is ultimately comprised of the elements of canonical flows.

View Video Presentation: https://doi.org/10.2514/6.2023-2529.vid An iterative algorithm to incorporate compressibility effects of high-speed flows into manifold-based turbulent-combustion models is developed. The algorithm allows for the equation of state---unclosed in compressible flow solvers---to be evaluated consistently with the manifold-based model, without further approximations. The manifold inputs (fuel and oxidizer temperatures and pressure) are determined iteratively to reflect the non-negligible variations in thermodynamic state (expressed in terms of transported density and energy in the flow solver) that are characteristic of supersonic combustion. The algorithm is demonstrated on data from simulations of high-speed reacting mixing layers and is significantly more accurate than established approaches that only partially couple the manifold to the compressible flow solver by only approximately evaluating the equation of state. Partial-coupling approximations can yield errors in temperature and water source term in excess of 10% and 20%, which are eliminated with the proposed iterative approach. Extensions and practical implementation are discussed.

Abstract Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that are routinely generated. In applications that are constrained by memory and computational intensity, excessively large datasets may hinder scientific discovery, making data reduction a critical component of data-driven methods. Datasets are growing in two directions: the number of data points and their dimensionality. Whereas dimension reduction typically aims at describing each data sample on lower-dimensional space, the focus here is on reducing the number of data points. A strategy is proposed to select data points such that they uniformly span the phase-space of the data. The algorithm proposed relies on estimating the probability map of the data and using it to construct an acceptance probability. An iterative method is used to accurately estimate the probability of the rare data points when only a small subset of the dataset is used to construct the probability map. Instead of binning the phase-space to estimate the probability map, its functional form is approximated with a normalizing flow. Therefore, the method naturally extends to high-dimensional datasets. The proposed framework is demonstrated as a viable pathway to enable data-efficient machine learning when abundant data are available.