[Paper Review] Multi-component vapor-liquid equilibrium model for LES and application to ECN Spray A

Jan Matheis, Stefan Hickel|arXiv (Cornell University)|Sep 27, 2016

Combustion and flame dynamics2 references18 citations

TL;DR

This paper presents a fully conservative, multi-component vapor-liquid equilibrium model for large-eddy simulations (LES) of high-pressure turbulent mixing in liquid-fuel sprays, specifically applied to the ECN Spray A benchmark. The model accurately captures coexisting supercritical and subcritical two-phase states, resolving numerical instabilities common in single-phase approaches and achieving excellent agreement with experimental data for vapor penetration and schlieren-like structures.

ABSTRACT

We present and evaluate a detailed multi-species two-phase thermodynamic equilibrium model for large-eddy simulations (LES) of liquid-fuel injection and mixing at high pressure. The model can represent the coexistence of supercritical states and multi-component subcritical two-phase states. LES results for the transcritical Spray A of the Engine Combustion Network (ECN) are found to agree very well to available experimental data. We also address well-known numerical challenges of trans- and supercritical fluid mixing and compare a fully conservative formulation to a quasi conservative formulation of the governing equations. Our results prove physical and numerical consistency of both methods on fine grids and demonstrate the effects of energy conservation errors associated with the quasi conservative formulation on typical LES grids.

Motivation & Objective

• Address the limitations of existing LES models for high-pressure liquid-fuel injection, particularly in transcritical and supercritical regimes.
• Overcome numerical instabilities caused by unphysical states in single-phase dense-gas models during vortex core development.
• Develop a physically consistent, multi-species two-phase thermodynamic equilibrium model capable of handling coexisting subcritical and supercritical states.
• Compare the performance of fully conservative (FC) and quasi-conservative (QC) formulations of the governing equations in LES for high-pressure flows.
• Achieve accurate prediction of vapor penetration, temperature, and pressure fields in the ECN Spray A benchmark case.

Proposed method

• Formulate the compressible multi-component Navier-Stokes equations in a fully conservative (FC) form, preserving mass, momentum, energy, and species conservation.
• Implement a quasi-conservative (QC) formulation using a pressure evolution equation (PEVO) to reduce computational cost while maintaining stability.
• Integrate a cubic equation of state (EoS) with vapor-liquid equilibrium (VLE) calculations to model phase coexistence in multi-component mixtures.
• Use Fick’s law with effective binary diffusion coefficients to compute species fluxes in the mixture, accounting for composition-dependent diffusion.
• Solve the isochoric-isoenergetic flash problem within computational cells to determine phase fractions and thermodynamic states under local conditions.
• Apply the model to the ECN Spray A case with n-dodecane injection at 6 MPa and 363 K into a 900 K nitrogen atmosphere, using high-fidelity LES on fine grids.

Experimental results

Research questions

• RQ1 Can a fully conservative, multi-component two-phase thermodynamic model improve numerical stability in LES of transcritical spray flows compared to single-phase dense-gas models?
• RQ2 How do the fully conservative (FC) and quasi-conservative (QC) formulations of the governing equations compare in terms of physical consistency and energy conservation on practical LES grids?
• RQ3 To what extent does the inclusion of multi-component VLE and phase coexistence improve the prediction of vapor penetration and flow structures in the ECN Spray A benchmark?
• RQ4 What are the effects of energy conservation errors in the QC formulation on temperature and pressure predictions in high-pressure turbulent mixing?
• RQ5 Can the model accurately reproduce experimental schlieren images and vapor penetration trajectories without relying on Lagrangian particle tracking or simplified single-phase assumptions?

Key findings

• The fully conservative (FC-EQ) LES model successfully simulates the ECN Spray A case without numerical instabilities, even in regions of low pressure within vortex cores.
• The model predicts vapor penetration depth with excellent agreement to experimental schlieren data, particularly up to 0.8 ms, with only slight over-prediction at later times.
• Numerical schlieren images based on axial density gradients show striking similarity to experimental schlieren images, validating the model's ability to capture flow structures.
• The 1% mixture fraction threshold under-predicts vapor penetration compared to schlieren-based measurements, especially in long-term evolution, and is therefore not recommended.
• The FC and QC formulations converge to the same solution on fine grids, confirming physical and numerical consistency, but the QC formulation introduces significant temperature over-prediction due to energy conservation errors on coarser LES grids.
• Local pressures in the jet tip drop to ~3 MPa due to vortex ring formation, demonstrating strong deviations from the nominal 6 MPa operating pressure, which stresses the need for robust two-phase thermodynamics.