We address a fundamental challenge in modern propulsion and energy systems: accurately modeling combustion under transcritical conditions, where operating pressures exceed the critical pressure of the fuel but still lower than cricondenbar values of the air-fuel mixture, leading to a complicated thermophysical mixture behavior. Transcritical regimes are characterized by strong non-idealities and the possible coexistence of vapor and liquid phases. The main objective of this work is to develop a high-fidelity, physically consistent, and computationally efficient simulation framework that captures these phenomena within a Large Eddy Simulation (LES) context, enabled by a Multiphase Thermodynamics (MT) approach.

Direct numerical simulations (DNS) are conducted for reactants-to-products counterflow configurations at turbulent conditions to understand how strain affects the structure and NOx emissions of lean premixed hydrogen flames. Two nominal equivalence ratio conditions, 0.5 and 0.7, are investigated. Under unstretched conditions, the Markstein length is negative for the former and slightly positive for the latter, indicating distinct responses of heat release rate and flame consumption speed to strain in each case. For each equivalence ratio condition, three levels of applied strain rate are considered, resulting in a total of six DNS. Results indicate that overall NOx emissions decrease with increasing strain at turbulent conditions, consistent with recent results for laminar conditions presented in Porcarelli et al. (2024). However, the relative decrease of NOx with strain is faster under turbulent conditions because turbulent mixing limits the occurrence of super-adiabatic temperatures. Moreover, the decrease of NOx is strongly correlated only to the mean applied tangential strain rate, while local fluctuations of strain due to vortices exhibit more stochastic behaviour. The detailed analysis presented in this article indicates that the applied strain can be used to substantially decrease NOx emissions in premixed hydrogen flames under practical conditions. Novelty and Significance statement: This work examines for the first time in detail the coupled effects of strain and turbulence in hydrogen flames, for various conditions spanning different signs of the Markstein length and increasing applied strain levels. In particular, it clarifies the different roles of applied strain, turbulence-driven strain, and curvature on both flame structure and NOx generation. Results further show for the first time that both in-flame and post-flame NOx can be suppressed at high strain levels under turbulent conditions. This result is of paramount importance as it implies that NOx can be suppressed at combustor-relevant conditions by straining the flame.

This study introduces a new numerical framework for the accurate simulation of transcritical reacting sprays using a multiphase, real-fluid, flamelet-based model. The transcritical flamelet library is combined with large-eddy simulations (LES) and rapid vapor–liquid equilibrium calculations in the context of a modern multiphase thermodynamic approach to explore vaporization dynamics, ignition characteristics, and soot formation. Current applications focus on the combustion of polyoxymethylene dimethyl ethers (OMEs), which are carbon-neutral e-fuels, in transcritical high-pressure configurations. Validation against experimental data shows a strong match in ignition delay and penetration lengths. The analysis of three OME₃– n-dodecane fuel blends reveals differences in evaporation, ignition, and soot production. Adding OME₃ to n-dodecane reduces soot production and shortens the liquid penetration length and ignition delay time. The findings highlight the importance of further investigation into the effects of transcritical states and fuel composition on combustion performance and emissions. Novelty and significance This work introduces a modeling technique for the use of transcritical counterflow flames in flamelet modeling, expanding the capabilities of large-eddy simulations with multiphase thermodynamics (LES-MT) to accurately modeling transcritical combustion. By incorporating real-fluid effects and two-phase interactions, the transcritical flamelet library provides a high-fidelity representation of the complex behaviors in high-pressure multiphase autoignition scenarios. This calibration-free approach can significantly improve our understanding of the transcritical combustion of emerging fuels such as OME₃ or their combination with traditional fuels such as n-dodecane.

Simulations of reacting multiphase flows tend to display an inhomogeneously distributed computational intensity over the spatial and temporal domains. The time-to-solution of chemical reaction rates can span multiple orders of magnitude due to the emergence of combustible kernels and thin turbulent reaction zones. Similarly, the time to solve the equation of state (EoS) for non-ideal fluid mixtures deviates substantially between the grid cells. These effects result in a performance profile that is unbalanced and rapidly changing for transient simulations, and therefore beyond the capabilities of traditional (quasi-)static mesh partitioning methods. We analyse this loss of parallel efficiency for large-eddy simulations of the ECN Spray-A benchmark with the multi-physics solver INCA and propose to mitigate the problem by introducing two independent repartitioning stages in addition to the classic domain decomposition for fluid transport: one for the EoS and one for chemical reactions. We explore various scalable repartitioning strategies in this context and observe that rebalancing computational load yields a significant speedup that is robust for various mesh resolutions and process numbers. The dynamic multistage load-balancing thus effectively removes obstacles towards good parallel scaling of INCA and similar solvers for reacting and/or multiphase flows.

A comprehensive set of accurate physical models and numerical simulation methods for transcritical dual fuel combustion systems is presented. The method combines multiphase real-fluid physical properties modeling, flamelet-based chemistry reduction, and large-eddy simulation (LES). It allows a fully integrated simulation of the multiphase region and the combustion zones in the turbulent flames. A central challenge in dual-fuel combustion applications is the successful ignition of low-reactivity ambient fuel by the high-reactivity pilot fuel jet. The interaction of the radical pools associated with both fuels is known to be an important characteristic. This study captures the evolution of this interaction across both the low-temperature combustion (LTC) and high-temperature combustion (HTC) regimes. Three cases are investigated, each involving the injection of an n-dodecane jet into a 6 MPa, 1000 K ambient. The cases differ only in ambient composition: (1) a single-fuel (SF) baseline case with a mixture of air and combustion products, and two dual-fuel (DF) cases with methane and a 90:10 (by volume) methane/ethane blend added to the ambient. Insights on ignition and flame structure are gained from homogeneous reactor simulations, transcritical counterflow diffusion flames, and LES. Combustion modes are defined by threshold levels of key species and temperature. The flame volume is subdivided according to the modes and for each mode the ignition delay and the temporal evolution of heat release rate (HRR) are obtained. The differences in the radical pools of SF and DF combustion are demonstrated. LTC ignition is shown to start in the multiphase region near the base of the jet. The high accuracy of the proposed methods provides a firm basis for modeling prospective dual-fuel systems using alternative fuels.

Transcritical fuel sprays form an indispensable part of high-pressure energy-conversion systems. Modeling the complex real-fluid effects in the high-pressure multiphase regime of such sprays accurately, especially the hybrid subcritical-to-supercritical mode of evaporation during mixing fuel and oxidizer, is essential and challenging. This paper represents a novel numerical framework for accurate and efficient simulations of transcritical sprays. The spray is modeled using a diffuse interface method with multiphase thermodynamics, which couples real-fluid state equations with vapor-liquid equilibrium (VLE) calculations to compute thermo-transport properties. A physically consistent turbulence model for large-eddy simulations (LES) is used, with combustion being modeled via real finite-rate chemistry based on the fugacity of the species. The current method is accurate and free from semi-empirical drop break-up/evaporation models. LES results for the Engine Combustion Network (ECN) Spray-A benchmark demonstrate the potential of the proposed method and its advantages over traditional approaches.

We present a novel framework for high-fidelity simulations of inert and reacting sprays at transcritical conditions with highly accurate and computationally efficient models for complex real-gas effects in high-pressure environments, especially for the hybrid subcritical/supercritical mode of evaporation during the mixing of fuel and oxidizer. The high-pressure jet disintegration is modeled using a diffuse interface method with multiphase thermodynamics, which combines multi-component real-fluid volumetric and caloric state equations with vapor-liquid equilibrium calculations for the computation of thermodynamic properties of mixtures at transcritical pressures. Combustion source terms are evaluated using a finite-rate chemistry model, including real-gas effects based on the fugacity of the species in the mixture. The adaptive local deconvolution method is used as a physically consistent turbulence model for large eddy simulation (LES). The proposed method represents multiphase turbulent fluid flows at transcritical pressures without relying on any semi-empirical breakup and evaporation models. All multiphase thermodynamic model equations are presented for general cubic state equations coupled with a rapid phase-equilibrium calculation method that is formulated in a reduced space based on the molar specific volume function. LES results show a very good agreement with available experimental data for the reacting and non-reacting engine combustion network benchmark spray A at transcritical operating conditions.

We present a new family of fast and robust methods for the calculation of the vapor–liquid equilibrium at isobaric-isothermal (PT-flash), isochoric-isothermal (VT-flash), isenthalpic-isobaric (HP-flash), and isoenergetic-isochoric (UV-flash) conditions. The framework is provided by formulating phase-equilibrium conditions for multi-component mixtures in an effectively reduced space based on the molar specific value of the recently introduced volume function derived from the Helmholtz free energy. The proposed algorithmic implementation can fully exploit the optimum quadratic convergence of a Newton method with the analytical Jacobian matrix. This article provides all required exact analytic expressions for the general cubic equation of state. Computational results demonstrate the effectivity and efficiency of the new methods. Compared to conventional methods, the proposed reduced-space iteration leads to a considerable speed-up as well as to improved robustness and better convergence behavior near the spinodal and coexistence curves of multi-component mixtures, where the preconditioning by the reduction method is most effective.