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.