Linear Eddy Model Research Articles

Physics of pressurized hydrogen spontaneous ignition in pipes containing bends of different angles

In the context of hydrogen-based energy storage systems, the safeguarding against spontaneous ignition during high-pressure hydrogen release is of paramount importance. This study delves into the thermal safety and management technologies pertinent to such systems by numerically investigating the effects of pipeline geometry on the risk of spontaneous ignition. Employing Large Eddy Simulation (LES) coupled with detailed chemical kinetics and a linear eddy model, the research assesses the impact of different pipe angles and burst pressures on ignition behavior. The simulations are validated against experimental data, ensuring the veracity of the findings. The results demonstrate a significant interplay between the ignition propensity and both the geometrical configuration of the pipeline and the pressure of hydrogen release. Notably, the emergence and interaction of transverse waves in pipe bends are revealed to amplify mixing processes, generating vortices that elevate the temperature and promote a conducive environment for chemical reactions leading to stable flame propagation. The ignition is shown to occur predominantly near the stoichiometric mixture ratio, suggesting a narrow ignition region. These insights are vital for enhancing the safety protocols and thermal management strategies of hydrogen-based energy storage systems, paving the way for safer and more efficient energy solutions.

Machine learning tabulation of thermochemistry for turbulent dimethyl ether (DME) flames

The present work applies a machine learning tabulation methodology for the thermochemistry of dimethyl ether (DME), a typical biodiesel fuel, to accelerate the real-time computation of a large-size DME mechanism in turbulent non-premixed combustion. This approach is known as the hybrid flamelet/random data and multiple multilayer perceptrons (HFRD-MMLP) method (Ding et al., 2021). The essence of the HFRD-MMLP method lies in the generation of training data using the HFRD approach, which enhances the capacity of generalisation for the reactive composition space encountered in practical turbulent combustion by using the random process to expand the training dataset from laminar flamelets. The MMLP artificial neural networks (ANNs) are then trained to predict different composition states, aiming to improve the accuracy of ANN predictions. To validate the effectiveness of the ANNs, they are initially tested on 1-D laminar flame simulations with varying strain rates. Subsequently, a test is conducted on Sandia non-premixed turbulent DME series flames D and F, with an increasing jet Reynolds Number. The results regarding species mole fractions and temperature show overall excellent agreement with the direct integration method. The HFRD-MMLP method achieves speed-up factors of over 16 and 10 for the reaction step, and total computational costs, respectively, in the LES-PDF simulation with the DME mechanism in this work, surpassing the speed-up factors of approximately 12–14, and below 5 for the reaction step, and total time costs, respectively, in previous works on GRI-1.2 mechanism for CH4 (Ding et al., 2021) and CH4/H2 (Ding et al., 2022) combustion. This indicates that the HRFD-MMLP method is highly effective for mechanisms of large size in reducing the computational cost by avoiding a significant number of highly stiff ordinary differential equations (ODEs) integration. This approach can be applied in real-time calculations of reaction source terms in methods including Direct Numerical Simulation (DNS), Probability Density Function (PDF) methods, unsteady flamelet, Conditional Moment Closure (CMC), Multiple Mapping Closure (MMC), Linear Eddy Model (LEM), Thickened Flame Model, the Partially Stirred Reactor (PaSR) method (as in OpenFOAM) and laminar flame computation.

A super-grid approach for LES combustion closure using the Linear Eddy Model

LES–LEM is a simulation approach for turbulent combustion in which the stochastic Linear Eddy Model (LEM) is used for sub-grid mixing and combustion closure in Large-Eddy Simulation (LES). LEM resolves, along a one-dimensional line, all spatial and temporal scales, provides on-the-fly local turbulent flame statistics, captures finite rate chemistry effects and directly incorporates turbulence-chemistry interaction. However, the approach is computationally expensive as it requires advancing an LEM-line in each LES cell. This paper introduces a novel turbulent combustion closure model for LES using LEM to address this issue. It involves coarse-graining the LES mesh to generate a coarse- level ‘super-grid’ comprised of cell-clusters. Each cell-cluster, instead of each LES cell, then contains a single LEM domain. This domain advances the combined advection–reaction–diffusion solution and also provides suitably conditioned statistics for thermochemical scalars such as species mass fractions. Local LES-filtered thermochemical states are then obtained by probability-density-function (PDF) weighted integration of binned conditionally averaged scalars, akin to standard presumed PDF approaches for reactive LES but with physics-based determination of the full thermochemical state for particular values of the conditioning variables. The proposed method is termed ‘super-grid LEM’ or ‘SG-LEM’. The paper describes LEM reaction–diffusion advancement, the LEM representation of turbulent advection, a novel splicing algorithm (a key feature of LES–LEM) formulated for the super-grid approach, a wall treatment, and a thermochemical LES closure procedure. To validate the proposed model, a pressure-based solver was developed using the OpenFOAM library and tested on a premixed ethylene flame stabilised over a backward facing step, a setup for which some DNS data is available. SG-LEM provides high resolution flame structures, temperature and mass fractions suitable for LES thermochemical closure. Additionally, it provides reaction-rate data at the coarse level, a unique feature compared to other mapping-type closure methods. Quantitative comparisons are made between the proposed model and time-averaged DNS data, focussing on velocity, temperature and species mass fraction. Results show good agreement downstream of the step. Furthermore, comparison with an equivalent Partially-Stirred Reactor (PaSR) simulation demonstrates the superior predictive capability of SG-LEM. Additionally, the paper briefly examines the sensitivity of the model to coarse-graining parameters and finally, explores computational efficiency highlighting the substantial speedup achieved when compared to the standard LES–LEM approach with potentially significant speedup relative to PaSR closure for the intensely turbulent regimes of principal interest.

Simulation of turbulent premixed flames with machine learning - tabulated thermochemistry

The numerical integration of the differential equations describing chemical kinetics consumes the majority of computational time in combustion simulations that involve direct coupling of chemistry and flow, such as transported probability density function (PDF) methods, direct numerical simulation (DNS), conditional moment closure (CMC), unsteady flamelet, multiple mapping closure (MMC), thickened flame model, linear eddy model (LEM), partially stirred reactor (PaSR) as in OpenFOAM and laminar flame computation. This step can be accelerated by tabulation, and artificial neural networks (ANNs) have recently emerged as a powerful technique in this domain. To be applicable to a wide family of problems, an ANN tabulation approach must be based on data generated by an abstract process, rather than from the turbulent flame to be simulated. In the present work, the hybrid flamelet/random data and multiple multilayer perceptrons (HFRD-MMLP) method (Ding et al., Combust. Flame 231, 111493, 2021) for non-premixed flames is taken as a basis to develop a thermochemistry tabulation method for premixed flames. In the spirit of maintaining an essentially random data set that still originates in meaningful composition states, a set of one-dimensional premixed flame simulations is employed to generate data that are used as starting points for a random data generation process and subsequently discarded. The approach is applied to large eddy simulations (LES) of the Cambridge/Sandia swirl burner in configurations five and six, with the transported PDF method employed to provide closure for the filtered reaction source terms and the stochastic fields method used for numerical solution. Very good agreement in both major and minor species is observed between the LES-PDF simulations using direct integration of the reaction source term and the ones with the ANNs. Furthermore, the average time taken for reaction source term computations is reduced by fourteen times, while memory requirements constitute only 1.4 MB.

A pressure-coupled Representative Interactive Linear Eddy Model (RILEM) for engine simulations

The Representative Linear Eddy Model (RILEM) was introduced by Lackmann et al. (2018) as an alternative modeling approach to simulate turbulent non-premixed combustion in engines. The model utilizes a RANS approach for turbulence and the Linear Eddy Model (LEM) with a presumed probability density function (PDF) approach for combustion closure. A distinct feature of RILEM is its potential to handle arbitrary combustion regimes and the consideration of complex physical phenomena such as differential diffusion effects. The original version of RILEM implemented a volume-based coupling between LEM and the flow solver. This work presents a new variant of RILEM, i.e., Multiple Representative Interactive Linear Eddy Model (MRILEM) based on a pressure-based coupling, to overcome some deficiencies of the original RILEM, namely statistical fidelity. Due to the introduced pressure coupling, the effects of heat losses (wall heat fluxes, latent heat of evaporation) on combustion are intrinsically included via the pressure trace. Furthermore, we introduce a new step function PDF for the progress variable defined by its mean value only. Issues with an incomplete solution space for mixture fraction and progress variable due to the stochastic nature of LEM are remedied with a PDF scaling technique, aided by a novel parameterization of the progress-variable PDF The new variant of RILEM is evaluated using part- and full-load cases of a heavy-duty metal engine. The impact of utilizing multiple LEM lines on the completeness of the solution space and its influence on the distribution of scalar values in the CFD domain was demonstrated. Results for pressure trace, flame structure, and CO emissions are analyzed and compared with simulations using the Multi-Zone Well-Mixed Model (MZWM) model and experiments. While pressure traces agree well among the different models and experiments, noteworthy differences are observed between the models regarding CO emissions and temperature. Effects of turbulence chemistry interaction were noticed when comparing MRILEM to the results of the MZWM simulation, namely flame brush and species mass fraction distribution.

Between Broadening and Narrowing: How Mixing Affects the Width of the Droplet Size Distribution

AbstractEntrainment and mixing play an essential role in shaping the droplet size distribution (DSD), with commensurate effects on cloud radiative properties or precipitation formation. In this paper, we use a model that considers all relevant scales related to entrainment and mixing by employing the linear eddy model (LEM) as a subgrid‐scale (SGS) mixing model, coupled with a large‐eddy simulation model and a Lagrangian cloud model (LCM) for a single cumulus congestus cloud. We confirm that the DSD is broadened toward small‐size droplets during homogeneous mixing. During inhomogeneous mixing, the DSD width remains almost unchanged. The DSD width can also be narrowed after mixing. We show that this happens when DSD is broadened toward small‐size droplets, which evaporate rapidly, while larger droplets are almost unaffected. In addition, when droplets ascend during mixing, DSD narrowing is caused when the adiabatic increase in supersaturation is slower than the average droplet evaporation, allowing only the largest droplets to benefit from the newly produced supersaturation. The narrowing mixing scenario prevents clouds from having too broad DSDs and causes the DSD relative dispersion to converge around 0.2 to 0.4. As this scenario is more frequent when the LEM SGS model is used, our results indicate that adequately modeling turbulent mixing is necessary to represent a realistic DSD shape.

A Pressure-Coupled Representative Interactive Linear Eddy Model (RILEM) for Engine Simulations

A Pressure-Coupled Representative Interactive Linear Eddy Model (RILEM) for Engine Simulations

Machine learning tabulation of thermochemistry of fuel blends

The objective of the present work is to develop a machine learning tabulation methodology for thermochemistry that accounts for fuel blends. The approach is based on the hybrid flamelet/random data and multiple multilayer perceptrons (HFRD-MMLP) methodology (Ding et al., 2021), the essence of which is to train a set of artificial neural networks (ANNs) using random data so as to anticipate the composition space encountered in turbulent flame simulations. As such, it is applicable to any combustion modelling approach that involves direct coupling of chemistry and flow, such as transported probability density function (PDF) methods, direct numerical simulation (DNS), conditional moment closure (CMC), unsteady flamelet, multiple mapping closure (MMC), thickened flame model, linear eddy model (LEM), partially stirred reactor (PaSR) as in OpenFOAM and laminar flame computation. In this paper, the HFRD approach is further developed to generate data of varying fuel ratios. Furthermore, radiative heat losses are included and it is shown that the ANN-based simulations are able to account for it. The ANNs generated are first tested on 1-D laminar flame simulations and then applied to two turbulent flames with different fuel compositions: a pure methane flame, Sandia flame D, and Sydney flame HM1, which is a methane/hydrogen flame. The results of species mass fraction and temperature are compared between ANN and direct integration, and excellent agreement are achieved. These results indicate that the methodology has great capacity for generalisation and is applicable to a range of blended fuels. Furthermore, a speed-up ratio of 14 to 17 is attained for the reaction step compared with direct integration, which greatly reduces the computational cost of turbulent combustion simulations.

Origins of instabilities in turbulent mixing layers behind detonation propagation into reactive–inert gas interfaces

Interactions of mildly irregular detonation waves with sharp interfaces separating combustible mixtures from an inert gas were modeled numerically using the compressible linear eddy model for a large eddy simulation (CLEM-LES) approach. In recent experiments of Lieberman and Shepherd [“Detonation interaction with an interface,” Phys. Fluids 19, 096101 (2007)], such interactions resulted in a transmitted shock-turbulent mixing zone (TMZ) complex as the reactive wave traveled through the interface separating fuel rich ethylene–oxygen mixtures and nitrogen. Kelvin–Helmholtz (K–H) instability was proposed as the main mechanism contributing to the formation of the turbulent mixing zone. This work aims to determine to what extent K–H plays a role and whether or not other sources of instability contribute to the observed evolution of the TMZ. The results show that full-scale simulations using CLEM-LES reproduce well (qualitatively and quantitatively) the experimental flow features. Upon recasting the simulations in the frame of reference of the node (i.e., the location where the detonation wave meets the interface) and by removing the cellular instability from the front, the growth rates of the TMZ only due to K–H instabilities originating from the velocity difference across the mixing layer were found to be insignificant. Conversely, the addition of controlled perturbations to the detonation front pressure resulted in significant growth of the TMZ. This outcome suggests that the TMZ formation and evolution are heavily influenced by instabilities originating at the front. In this regard, transverse waves associated with the detonation front cellular structure are likely to provide the bulk of TMZ growth through additional Richtmyer–Meshkov instabilities.

Turbulent jet ignition of ultra-lean methane/air mixture under engine-like condition

Turbulent jet ignition (TJI) is a promising technology that enables engines to operate stably at ultra-lean-burn conditions for improved thermal efficiency. In the present work, TJI of an ultra-lean methane/air mixture (excessive air ratio λ = 2.0) under an engine-like condition (temperature of 900 K and pressure of 5.8 MPa) was numerically studied, with particular interest on the ignition patterns and the critical/favorable conditions for successful ignition/rapid combustion. A high-fidelity large eddy simulation was performed, with the linear eddy model being incorporated to account for turbulence–chemistry interaction. To represent the different amount/state of energy released from a pre-chamber, a variety of turbulent jet temperatures, inlet velocities, and orifice diameters were covered. The results identified two successful ignition patterns, including a flame propagation pattern and a jet re-ignition pattern. An ignition regime was also established, with the boundary between ignition success/failure identified by a global Damköhler number (Da) of 0.1. In terms of the combustion rate, heat release in the propagative flame is governed by the growth of the flame surface, which is primarily controlled by stretch and enlarges with the jet Reynolds number (Re). The present results suggest that, for low-reactivity fuels such as methane, the pre-chamber combustion in a TJI system should pursue complete heat release and increase Re and Da simultaneously for the injected turbulent jet into the main combustion chamber.

Machine learning tabulation of thermochemistry in turbulent combustion: An approach based on hybrid flamelet/random data and multiple multilayer perceptrons

A new machine learning methodology is proposed for speeding up thermochemistry computations in simulations of turbulent combustion. The approach is suited to a range of methods including Direct Numerical Simulation (DNS), Probability Density Function (PDF) methods, unsteady flamelet, Conditional Moment Closure (CMC), Multiple Mapping Closure (MMC), Linear Eddy Model (LEM), Thickened Flame Model, the Partially Stirred Reactor (PaSR) method (as in OpenFOAM) and the computation of laminar flames. In these methods, the chemical source term must be evaluated at every time step, and is often the most expensive element of a simulation. The proposed methodology has two main objectives: to offer enhanced capacity for generalisation and to improve the accuracy of the ANN prediction. To accomplish the first objective, we propose a hybrid flamelet/random data (HFRD) method for generating the training set. The random element endows the resulting ANNs with increased capacity for generalisation. Regarding the second objective, a multiple multilayer perceptron (MMP) approach is developed where different multilayer perceptrons (MLPs) are trained to predict states that result in smaller or larger composition changes, as these states feature different dynamics. It is shown that the multiple MLP method can greatly reduce the prediction error, especially for states yielding small composition changes. The approach is used to simulate flamelets of varying strain rates, one-dimensional premixed flames with differential diffusion and varying equivalence ratio, and finally the Large Eddy Simulation (LES) of CH4/air piloted flames Sandia D, E and F, which feature different levels of local extinction. The simulation results show very good agreement with those obtained from direct integration, while the range of problems simulated indicates that the approach has great capacity for generalisation. Finally, a speed-up ratio of 12 is attained for the reaction step.

Dimensional Decomposition of Turbulent Reacting Flows

A dimensional-decomposition approach, decomposing 3D into 3×1D for turbulent (reacting) flows are motivated, discussed and investigated. In the three-dimensional Linear Eddy Model (LEM3D), three orthogonally intersecting arrays of 1D domains are coupled to capture the 3D characteristics of fluid flows. The currently used recouplings for LEM3D are enlightened and thoroughly discussed. A study of the flame front of a freely propagating laminar premixed flame shows that the flame stabilizes at the upstream face of the initial solution when both the advective and auxiliary recouplings are activated. Furthermore, results from LEM3D simulations of a vitiated co-flow burner are re-visited providing a more detailed discussion of the noted early mixing and reaction of the hydrogen fuel of the burner. The main conclusion of the present work is that the auxiliary coupling based on rotations of the 3D control volumes introduces very large gradients in the near-field geometry of jets, leading to a significant amount of artificial diffusion and locally increased burning rates. This implies that applications of LEM3D should be restricted to sub-regions where high-resolution treatment of scalar mixing and reaction is of particular interest.

Effects of Entrainment and Mixing on the Wegener–Bergeron–Findeisen Process

Abstract The growth of ice crystals at the expense of water droplets, the Wegener–Bergeron–Findeisen (WBF) process, is of major importance for the production of precipitation in mixed-phase clouds. The effects of entrainment and mixing on WBF, however, are not well understood, and small-scale inhomogeneities in the thermodynamic and hydrometeor fields are typically neglected in current models. By applying the linear eddy model, a millimeter-resolution representation of turbulent deformation and molecular diffusion, we investigate these small-scale effects on WBF. While we show that entrainment is accelerating WBF by contributing to the evaporation of liquid droplets, entrainment may also cause aforementioned inhomogeneities, particularly regions filled with exclusively ice or liquid hydrometeors, which tend to decelerate WBF if the ice crystal concentration exceeds 100 L−1. At lower ice crystal concentrations, even weak turbulence can homogenize hydrometeor and thermodynamic fields sufficiently fast so as to not affect WBF. Independent of the ice crystal concentration, it is shown that a fully resolved entrainment and mixing process may delay the nucleation of entrained aerosols to ice crystals, thereby delaying the uptake of water vapor by the ice phase, further slowing down WBF. All in all, this study indicates that, under specific conditions, small-scale inhomogeneities associated with entrainment and mixing counteract the accelerated WBF in entraining clouds. However, further research is required to assess the importance of the newly discovered processes more broadly in fully coupled, evolving mixed-phase cloud systems.

Multiscale modeling of turbulent atomization: Droplet-size sampling

With an interest on atomization in turbulent flows, and modeling alternatives to classic atomization models and Direct Numerical Simulations (DNS), the present work derives and tests two droplet-size distributions parametrized by local information about the flow. One distribution is heuristic and another one is based on the linear-eddy model. Predictions from these distributions are tested with numerical simulations in which the unresolved droplet-mass production is closed by assuming that turbulence is the rate controlling mechanism and by using a correction step. Moreover, the testing considers a round jet with a Reynolds number of 5000 from which DNS data is available. Overall, it is found that the present atomization model provides an enhancement of accuracy of the droplet-mass production and droplet-diameter distribution in comparison with using no model. Furthermore, the predicted droplet-diameter distribution is more accurate than that using a previous assumption of taking droplet diameters equal to local Taylor microscales. These results are obtained with simulations whose cost is orders of magnitude less than DNS.

Physically-derived reduced-order manifold-based modeling for multi-modal turbulent combustion

Turbulent combustion models can be divided into two broad classes: models that make no assumption about the underlying combustion processes and models that constrain the underlying combustion processes to some a priori presumed reduced-order manifold. The former class of models, including the Transported PDF (TPDF) approach and the Linear Eddy Model (LEM), is by nature more general but comes at increased computational cost. The latter class of models, including “flamelet”-like models and Conditional Moment Closure (CMC), is computationally more efficient albeit with the need to assume something about the underlying combustion processes a priori, traditionally limiting combustion processes to a single asymptotic mode. In this work, a new turbulent combustion model is developed that breaks this inherent trade-off and enables a computationally efficient description of multi-modal combustion. The model is constructed by first postulating that all (adiabatic, isobaric, two-stream) combustion processes can be described with a two-dimensional space whose coordinates are a mixture fraction and a generalized progress variable. The governing equations for the species mass fractions and temperature are then projected onto this two-dimensional manifold through a coordinate transformation to provide the evolution equations for the thermochemical state on the manifold; this approach results in an equilibrium manifold formulation. An explicit transport equation for the generalized progress variable is derived through the choice of a (set of weighted) arbitrary reference species and the functional dependence of the reference species on the generalized progress variable. The approach can accommodate both unity Lewis numbers and differential diffusion without issue. The mode of combustion is encoded into three scalar dissipation rates (the mixture fraction dissipation rate, the generalized progress variable dissipation rate, and the cross-dissipation rate), and the asymptotic modes of combustion are recovered under appropriate limits. However, the relative ease at which the nonpremixed limit is recovered depends on the reference species. Alternatively, the evolution of the thermochemical state on the manifold can be derived by conditionally filtering (or averaging) the governing equations with respect to the manifold coordinates, resulting in a non-equilibrium manifold formulation. Simplification of the non-equilibrium manifold formulation to the equilibrium manifold formulation reveals the implicit assumptions inherent to the equilibrium manifold formulation. A new solver PDRs is developed for solving the manifold equations, and example solutions demonstrate the ability of the model to describe general multi-modal combustion phenomena as the scalar dissipation rates are varied including not only the asymptotic modes of combustion but also partially premixed and stratified premixed combustion coupled or uncoupled with autoignition. The paper concludes with a discussion of open challenges for integrating the model with Large Eddy Simulation (LES) and Reynolds-Averaged Navier–Stokes (RANS) approaches.

Entrainment and Mixing in Stratocumulus: Effects of a New Explicit Subgrid-Scale Scheme for Large-Eddy Simulations with Particle-Based Microphysics

Abstract The entrainment and mixing of free-tropospheric air is an essential component of the observed microphysical structure of stratocumulus clouds. Since the relevant scales involved in this process are usually smaller than the grid spacing of typical large-eddy simulations (LESs), their correct representation is difficult. To adequately accommodate these small-scale processes, we apply a recently developed approach that explicitly simulates LES subgrid-scale (SGS) turbulence fluctuation of supersaturation using the one-dimensional linear eddy model. As a result of reduced numerical diffusion and the ability to explicitly represent the SGS distribution of liquid water and supersaturation, entrainment rates tend to be lower in the new approach compared to simulations without it. Furthermore, cloud holes comprising free-tropospheric air with negligible liquid water are shown to persist longer in the stratocumulus deck. Their mixing with the cloud is shown to be more sensitive to the microphysical composition of the cloud as a result of the explicitly resolved inhomogeneous mixing, which is also confirmed analytically. Moreover, inhomogeneous mixing is shown to decrease the droplet concentration and to increase droplet growth significantly, in contrast to previous studies. All in all, the simulations presented can be seen as a first step to bridge the gap between ultra-high-resolution direct numerical simulation and LES, allowing an appropriate representation of small-scale mixing processes, together with the large-scale dynamics of a stratocumulus system.

Subgrid Reaction-Diffusion Closure for Large Eddy Simulations Using the Linear-Eddy Model

Turbulent combustion models approximate the interaction between turbulence, molecular transport and chemical reactions. Among the many available turbulent combustion models, the present focus is the linear-eddy model (LEM) used as a subgrid combustion model for large eddy simulations. In particular this paper introduces a new LEM closure with the reaction-rate approach to close the filtered chemical source terms in the governing equations for species mass fractions and enthalpy. The new approach is tested using a non-premixed syngas flame and a bluff-body stabilized premixed flame problem. Simulation results are compared to data from a direct numerical simulation and experiments. This comparison shows that mean and rms quantities compare well with experiments and are in the range of previous simulation studies. These results are obtained with a pressure-based and unstructured computational-fluid-dynamics solver, an approach that is preferred in industry.

AUSM scheme: its application to a realistic combustor configuration, the Energy Efficient Engine

Highlights of work inspired by Liou and performed in the last few years with the ultimate goal of simulating combustor–turbine interactions are presented. First, we have updated the Open National Combustion Code (OpenNCC) by implementing the advection upstream splitting method (AUSM) and the extended version of the AUSM-family scheme (AUSM$$^+$$-up) and then performed a series of verification tests. The AUSM$$^+$$-up scheme and the standard Jameson–Schmidt–Turkel scheme are compared in terms of accuracy and convergence. Next, the second-order AUSM$$^+$$-up scheme is applied to model unsteady flow fields inside a combustor sector from the Energy Efficient Engine ($${\hbox {E}}^3$$) program, in conjunction with a sensitivity analysis of turbulent combustion models. Three different turbulent combustion models are considered: the eddy break-up model, the linear eddy model, and the probability density function model, as well as the laminar finite-rate chemistry model. A comprehensive comparison of the flow fields and the flame structures is provided. Our main interest here is not to select the best model out of four different models with lack of data under the exact same conditions, but to understand how different turbulent combustion models impact thermal variation along the surface of first-stage vanes (i.e., hot streaks). Considering that these models are often used in combustor/turbine communities, the intent of this study is to provide some guidelines on numerical modeling of combustor–turbine interactions and, thus, help improve future designs of the combustor and high-pressure turbine.

Inhomogeneous Mixing in Lagrangian Cloud Models: Effects on the Production of Precipitation Embryos

Abstract Although small-scale turbulent mixing at cloud edge has substantial effects on the microphysics of clouds, most models do not represent these processes explicitly, or parameterize them rather crudely. This study presents a first use of the linear eddy model (LEM) to represent unresolved turbulent mixing at the subgrid scale (SGS) of large-eddy simulations (LESs) with a coupled Lagrangian cloud model (LCM). The method utilizes Lagrangian particles to provide the trajectory of air masses within LES grid boxes, while the LEM is used to redistribute these air masses among the Lagrangian particles based on the local features of turbulence, allowing for the appropriate representation of inhomogeneous to homogeneous SGS mixing. The new approach has the salutary effect of mitigating spurious supersaturations. At low turbulence intensities, as found in the early stages of an idealized bubble cloud simulation, cloud-edge SGS mixing tends to be inhomogeneous and the new approach is shown to be essential for the production of raindrop embryos. At higher turbulence intensities, as found in a field of shallow cumulus, SGS mixing tends to be more homogeneous and the new approach does not significantly alter the results, indicating that a grid spacing of 20 m may be sufficient to resolve all relevant scales of inhomogeneous mixing. In both cases, droplet in-cloud residence times are important for the production of precipitation embryos in the absence of small-scale inhomogeneous mixing, either naturally due to strong turbulence or artificially as a result of coarse resolution or by not using the LEM as an SGS model.

Investigation of turbulence–chemistry interactions in a heavy-duty diesel engine with a representative interactive linear eddy model

Simulations of a heavy-duty diesel engine operated at high-load and low-load conditions were compared to each other, and experimental data in order to evaluate the influence of turbulence–chemistry interactions on heat release, pressure development, flame structure, and temperature development are quantified. A recently developed new combustion model for turbulent diffusion flames called representative interactive linear eddy model which features turbulence–chemistry interaction was compared to a well-stirred reactor model which neglects the influence of turbulent fluctuations on the mean reaction rate. All other aspects regarding the spray combustion simulation like spray break-up, chemical mechanism, and boundary conditions within the combustion chamber were kept the same in both simulations. In this article, representative interactive linear eddy model is extended with a progress variable, which enables the model to account for a flame lift-off and split injection, when it is used for diffusion combustion. In addition, the extended version of representative interactive linear eddy model offers the potential to treat partially premixed and premixed combustion as well. The well-stirred reactor model was tuned to match the experimental results, thus computed pressure and apparent heat release are in close agreement with the experimental data. Representative interactive linear eddy model was not tuned specifically for the case and thus the computed results for pressure and heat release are in reasonable agreement with experimental data. The computational results show that the interaction of the turbulent flow field and the chemistry reduce the peak temperatures and broaden up the turbulent flame structure. Since this is the first study of a real combustion engine (metal engine) with the newly developed model, representative interactive linear eddy model appears as a promising candidate for predictions of spray combustion in engines, especially in combustion regimes where turbulence–chemistry interaction plays an even more important role like, example given, in low-temperature combustion or combustion with local extinction and re-ignition.