Turbulent hydrogen premixed flames at high pressure and high temperature

Abstract: The combined influence of elevated pressure and temperature, representative of gas-turbine operating conditions, on lean premixed hydrogen flames is investigated using Direct Numerical Simulations (DNS) of a turbulent jet. Three cases are considered: 1 atm/298 K, 5 atm/472 K, and 20 atm/700 K, scaled to maintain the same jet Reynolds number and nominal Karlovitz number in the unburnt mixture, enabling a direct comparison of flame-turbulence interactions. Although the combined effects are moderate overall due to compensating influences, measurable differences arise in flame structure and turbulence-flame coupling. They are driven by reduced turbulence dissipation within the flame at high pressure and temperature, which enhances the interaction between turbulence and thermodiffusive effects. Finally, the tangential strain rate exhibits the same universal Kolmogorov scaling observed in homogeneous-isotropic turbulence and in methane flames, confirming its robustness for modelling turbulence

• The paper employs a novel methodology of Direct Numerical Simulation (DNS), focusing on turbulent lean hydrogen premixed flames This methodology comprehensively compares ambient, Intermediate, and High pressure and temperature operating conditions across various key parameters, including jet Reynolds number, nominal unburnt Karlovitz number, and expansion ratio.
• The study involving a combined increase in pressure and temperature leads to an enhanced thermodiffusion within the flames and reduced turbulence dissipation.
• The study posits that flame scaling methodologies can be safely extrapolated between distinct thermodynamic conditions.

This paper presents a Direct Numerical Simulation (DNS) study of turbulent lean premixed hydrogen/air slot-jet flames at equivalence ratio $\Phi = 0.4$, in which pressure and temperature are simultaneously increased to emulate the isentropic compression path of gas-turbine operation (2601.15848). Three cases are compared: ambient conditions (1 atm, 298 K), intermediate conditions (5 atm, 472 K), and high-pressure/high-temperature conditions (20 atm, 700 K). The central methodological contribution is a scaling strategy that holds the jet Reynolds number ($Re_{\rm jet} = 11{,}200$) and the nominal unburnt Karlovitz number fixed across all cases, so that differences among the flames can be attributed directly to the thermodynamic state rather than to changes in nominal turbulence intensity. To the authors' knowledge, this is the first systematic analysis of turbulent lean hydrogen flames under coupled pressure–temperature increases.

The simulations solve the reactive low-Mach-number Navier–Stokes equations with finite-rate chemistry using the Burke et al. H$_2$/O$_2$ mechanism (9 species), mixture-averaged transport, and Soret thermodiffusion via the Schlup–Blanquart model. A uniform mesh with $\delta_{\rm F}/\Delta \approx 10$ and $\eta_{\min}/\Delta = 0.6$ comprises $1500 \times 1800 \times 512$ points — 1.4 billion grid points — with Strang splitting and CVODE for stiff chemistry integration. Key case parameters are:

Quantity	Case 1	Case 2	Case 3
$p$ [atm] / $T_u$ [K]	1 / 298	5 / 472	20 / 700
$s_{\rm L}$ [m/s]	0.186	0.314	0.555
$Re_{\rm jet} = 11{,}200$0 [$Re_{\rm jet} = 11{,}200$1m]	707	136	31.5
Expansion ratio $Re_{\rm jet} = 11{,}200$2	4.44	3.10	2.35
$Re_{\rm jet} = 11{,}200$3 / $Re_{\rm jet} = 11{,}200$4	0.34 / 11.5	0.34 / 12.0	0.34 / 11.4
$Re_{\rm jet} = 11{,}200$5 (in flame)	9–20	16–26	26–40
$Re_{\rm jet} = 11{,}200$6 (in flame)	20–40	40–70	70–100

The effective Lewis number and Zel'dovich number are nearly invariant across cases, which is essential to the design: it ensures that laminar thermodiffusive behaviour is comparable, isolating turbulence–flame coupling as the discriminating mechanism.

One-dimensional and two-dimensional laminar simulations establish that normalised species, temperature, and reaction-rate profiles essentially overlap across the three conditions, and flame topology in the nonlinear cellular regime is nearly identical. Dispersion relations differ only through the expansion ratio: increasing $Re_{\rm jet} = 11{,}200$7 and $Re_{\rm jet} = 11{,}200$8 lowers $Re_{\rm jet} = 11{,}200$9, weakening the Darrieus–Landau instability, but growth rates measured relative to the Darrieus–Landau line follow the same trend. Decomposition of the consumption speed shows that its decrease at elevated conditions stems from reduced flame surface area, while the stretch factor $_2$0 remains nearly constant. The implication is that intrinsic thermodiffusive effects are essentially unchanged by the coupled increase; any turbulent-flame differences must therefore originate in turbulence–flame interaction rather than in modified laminar instability characteristics.

Despite the compensating influences of pressure and temperature, measurable differences emerge. At ambient conditions, a thick superadiabatic temperature layer develops along the outer edge of the flame brush; at elevated conditions this layer is confined to smaller, more intermittent structures, indicating stronger turbulent shredding of the high-temperature regions. The region of elevated turbulent kinetic energy near the flame tip, previously reported at ambient conditions, disappears as pressure and temperature increase.

The turbulent flame speed increases with pressure and temperature — in contrast to the laminar consumption speed, which decreases. Since the flame surface area is only weakly affected, the increase is attributed to higher $_2$1, confirming amplified thermodiffusive effects under stronger turbulence–flame coupling. Local reaction rates and mixture-fraction statistics show consistent trends. The authors draw two implications from this moderate overall sensitivity: analyses and experiments performed near ambient conditions remain broadly relevant for extrapolation to gas-turbine conditions, but the non-negligible variations must still be accounted for when developing or validating predictive models.

The mechanistic explanation lies in the evolution of turbulence across the flame brush. While $_2$2, $_2$3, and $_2$4 match by design in the unburnt jet, their evolution through the flame differs strongly: at higher pressure and temperature, $_2$5 decreases and $_2$6 increases within the flame, meaning smaller structures persist and turbulence is less attenuated. This follows from the lower expansion ratio and smaller temperature rise at elevated conditions, which weaken dilatation and viscosity growth — the primary dissipation mechanisms. Consequently, the in-flame Karlovitz number rises from roughly 20–40 to 70–100 even though the nominal unburnt value is held constant, explaining the enhanced reaction rates and $_2$7.

A practical consequence highlighted by the authors is that operating at high pressure and temperature achieves stronger in-flame turbulence without additional computational cost relative to the scaled configuration, making such conditions attractive for DNS studies of intense turbulence–flame interaction while preserving comparable laminar thermodiffusive behaviour.

The surface-weighted tangential strain rate conditioned on the reaction-layer isocontour, normalised by the Kolmogorov time $_2$8, remains close to 0.23 along the flame in all three cases, independent of pressure and temperature. This matches values reported for homogeneous isotropic turbulence (~0.165) and for methane and hydrogen flames at ambient conditions (~0.23). The result confirms that the universal Kolmogorov scaling of tangential strain survives gas-turbine-relevant thermodynamic states, supporting its use for reaction-rate parametrisation in tabulated and reduced-order combustion models.

Several constraints bound the generality of these findings. The study covers a single equivalence ratio ($_2$9), a single jet Reynolds number, and a single geometry (slot-jet); whether the compensation between pressure and temperature effects persists at other equivalence ratios, higher Reynolds numbers, or in confined geometries is not established. The low-Mach-number approximation excludes acoustic and Darrieus–Landau-driven hydrodynamic coupling that may matter at 20 atm. The observed universality of tangential strain is demonstrated for one conditioning isocontour ($_2$0); its robustness under different conditioning choices or in regimes where flame thickening occurs remains an open question. Finally, the claim that ambient-condition experiments extrapolate well to gas-turbine conditions rests on DNS at moderate $_2$1 (up to ~40 in-flame) and has not been validated against measurements at engine-relevant pressures.

By holding $_2$2 and nominal $_2$3 fixed while scaling pressure and temperature along an isentropic compression path, this study isolates the effect of gas-turbine-like thermodynamic states on lean hydrogen turbulence–flame interaction. The combined increase produces moderate overall changes because opposing influences compensate, yet it measurably enhances reactivity and thermodiffusive effects through reduced turbulence dissipation inside the flame — lower expansion and temperature ratios sustain stronger turbulence, raising the in-flame Karlovitz number. The tangential strain rate retains its universal Kolmogorov scaling throughout, reinforcing its utility for combustion modelling under elevated pressure and temperature.