# Numerical framework for transcritical real-fluid reacting flow simulations using the flamelet progress variable approach

## TL;DR

This paper introduces a numerical framework for simulating transcritical real-fluid reacting flows using an extended flamelet progress variable approach, addressing pressure oscillations and large density ratios in high-pressure combustion scenarios.

## Contribution

It develops a novel extension of the FPV model with a double-flux scheme and entropy-stable flux correction for robust transcritical flow simulations.

## Key findings

- Successfully simulates cryogenic LOX/GH2 mixing and reacting flows.
- Demonstrates robustness of the numerical schemes in multidimensional simulations.
- Applicable for LES of real transcritical combustion applications.

## Abstract

An extension to the classical FPV model is developed for transcritical real-fluid combustion simulations in the context of finite volume, fully compressible, explicit solvers. A double-flux model is developed for transcritical flows to eliminate the spurious pressure oscillations. A hybrid scheme with entropy-stable flux correction is formulated to robustly represent large density ratios. The thermodynamics for ideal-gas values is modeled by a linearized specific heat ratio model. Parameters needed for the cubic EoS are pre-tabulated for the evaluation of departure functions and a quadratic expression is used to recover the attraction parameter. The novelty of the proposed approach lies in the ability to account for pressure and temperature variations from the baseline table. Cryogenic LOX/GH2 mixing and reacting cases are performed to demonstrate the capability of the proposed approach in multidimensional simulations. The proposed combustion model and numerical schemes are directly applicable for LES simulations of real applications under transcritical conditions.