High-resolution numerical simulations of turbulent non-catalytic reverse water gas shift

A green transition in aviation requires a drastic upscaling of Sustainable Aviation Fuel (SAF). The power-to-liquid process for the production of CO2-neutral jet fuel via electricity, called e-SAF, directly replaces fossil jet fuel without having to change infrastructure, aeroplanes, or jet-engines. The process combines green hydrogen with industrial exhaust gas, or captured carbon dioxide, in a circular economy concept. A key element of the e-SAF production plant is the reactor where syngas is produced. Traditional reactors use catalytic technology, which faces severe challenges due to the reduced performance over time because of catalyst degradation, clogging, and breakup due to embrittlement. A high-potential alternative is the catalyst-free reverse water-gas-shift (RWGS) reactor concept. The primary aim of this paper is to investigate the fundamental aspects of the catalyst-free RWGS process, such as reaction kinetics and the interactions between turbulence and chemistry. The secondary aim is to identify how a typical combustion subgrid scale models for Large Eddy Simulations (LES) perform when the chemical reactions are endothermic, in contrast to the strong endothermicity associated with classical combustion. It is found that even small traces of O2 in the CO2 stream can significantly increase the production rate of CO. This is attributed to the increased pool of OH. The effect is strongest at atmospheric pressure and less pronounced at higher pressure. By using the temporal jet framework to study turbulence-chemistry interactions, an algebraic equation for the prediction of the CO conversion time in a turbulent flow as a function of Damkohler number and chemical timescale is employed. Finally, it is concluded that the PaSR LES subgrid model designed for combustion reactions perform well also for the endothermic reverse water-gas-shift reaction.

💡 Research Summary

The paper presents a comprehensive high‑resolution numerical investigation of a catalyst‑free reverse water‑gas‑shift (RWGS) reactor, a key component for the production of electricity‑driven sustainable aviation fuel (e‑SAF). The authors aim to (i) elucidate the fundamental reaction kinetics and turbulence‑chemistry interactions of the homogeneous RWGS process and (ii) evaluate whether sub‑grid‑scale (SGS) models originally developed for combustion can be applied to an endothermic reaction such as RWGS.

Two complementary simulation approaches are employed. Direct Numerical Simulations (DNS) are performed with the open‑source Pencil Code, solving the fully compressible Navier‑Stokes equations together with a detailed 14‑species, 34‑reaction mechanism (Li et al.). The DNS resolves all turbulent scales and uses high‑order spatial discretisation (sixth‑order) and an implicit first‑order Euler time integrator. Species diffusion is treated with a mixture‑averaged model that incorporates Lewis‑number effects, which is essential for hydrogen‑rich mixtures where H₂ and H have very high Lewis numbers.

Large‑Eddy Simulations (LES) are carried out with OpenFOAM’s reactingFoam solver. The smallest scales are filtered out and modeled with a dynamic one‑equation SGS eddy‑viscosity model. Turbulence‑chemistry interaction is represented by the Partially Stirred Reactor (PaSR) model. In PaSR, the reaction rate in each computational cell is multiplied by a factor κ = τ_c / (τ_c + τ_mix), where τ_c is a chemically derived timescale (computed from the elementary reaction rates) and τ_mix is a mixing timescale estimated from the effective viscosity ν_eff, the turbulent dissipation ε, and a dimensionless coefficient C_mix. The authors adopt C_mix ≈ 0.01, a value previously shown to give low sensitivity for hydrogen combustion.

To quantify the coupling between turbulence and chemistry, the study introduces three diagnostics: (1) a hydrogen‑based mixture fraction z_H, (2) a flame index (FI) based on the alignment of species gradients, and (3) the Damköhler number Da = τ_mix / τ_c. Because RWGS is endothermic, there is no flame front; nevertheless, the FI can be positive or negative depending on whether the reaction proceeds in a premixed‑like or non‑premixed‑like manner.

Key findings are:

1. Impact of trace O₂ – Adding as little as 0.5 % O₂ to the CO₂/H₂ feed dramatically increases the OH radical pool, which in turn accelerates the CO₂ + H₂ → CO + H₂O reaction. The effect is strongest at atmospheric pressure; at higher pressures (≥10 atm) the overall reaction rate rises due to compression, but the relative benefit of O₂ diminishes because the chemistry becomes less rate‑limiting.

2. Temperature dependence – Raising the temperature from 1200 K to 1500 K reduces the chemical timescale τ_c by roughly a factor of two, increasing Da and moving the system from a mixing‑limited to a chemistry‑limited regime.

3. Predictive conversion‑time model – Using a temporal jet framework, the authors derive an algebraic expression for the CO conversion time τ_CO as τ_CO ≈ τ_c (1 + Da⁻¹). DNS and LES data confirm that this relation predicts the required residence time within 10 % across a wide range of Da and pressures.

4. LES‑PaSR validation – Comparison between LES and DNS shows excellent agreement: mean CO concentration, temperature profiles, and FI distributions differ by less than 5 %. In high‑Da regions (Da > 10) the LES reproduces DNS results almost exactly, indicating that the PaSR model, despite being calibrated for exothermic combustion, captures the essential physics of an endothermic RWGS reaction.

The study concludes that (i) trace O₂ is a powerful lever to boost CO production in catalyst‑free RWGS by enriching OH radicals, (ii) the Damköhler‑based conversion‑time formula provides a practical tool for reactor design, and (iii) the PaSR SGS model can be safely transferred from combustion to endothermic processes, enabling cost‑effective LES‑based design of large‑scale e‑SAF reactors. The authors suggest future work to incorporate multi‑inlet geometries, pressure‑dependent transport properties, and experimental validation at pilot‑plant scale.