Sandia methane pool fire (Taha 2024 Case 2)

Important

Status: planned - not yet validated against reference data. This is the reacting end of the fire ladder: Case 2 of Taha et al. (2024), a real methane pool fire with combustion heat release and thermal radiation driving a buoyant plume. It is the most demanding case in this group: on top of the variable-density low-Mach closure it requires combustion, radiation and a Vreman SGS model, listed under the Prerequisites subsection. The setup, dimensionless matching and reference data are documented below; the comparison notebook is added once the prerequisites are met and a GPU validation run is committed. The case follows the helium plume, which validates the same closure without chemistry.

Why this case matters

The helium plume validates the variable-density low-Mach closure Taha et al.[1] in isolation: a large density ratio with no chemistry and no radiation. The Sandia 1 m methane pool fire is the next and final rung of the fire ladder from Taha et al. (2024): the same low-Mach core, now driving a reacting buoyant plume with combustion heat release and thermal radiation. It is the canonical compartment-free pool-fire benchmark and the case that demonstrates the solver on an actual fire rather than a buoyancy surrogate. It is Case 2 of Taha et al. (2024).

Physical description

A 1 m diameter methane inlet at the bottom centre of a 4 x 4 x 7 m domain injects fuel vertically at 0.097 m/s (the TEST-24 condition), surrounded by a 0.51 m wide steel plate modelled as an adiabatic no-slip wall (the ground plane). Air co-flows outside the plate at 0.14 m/s. The methane burns in a buoyant diffusion flame; the heat release warms the products, the equation of state drops their density, and the resulting buoyancy drives the plume and its puffing oscillation. A quarter of the local heat release is removed by thermal radiation. The fuel and ambient are at T = 285 K, p = 81.0 kPa.

Governing equations

The fluid uses the same variable-density low-Mach closure as the helium plume: the density is slaved to the equation of state

(1)\[\rho = \frac{P}{r\, T}\]

with the exact (rho - rho_inf) g buoyancy. On top of that closure the reacting case adds three terms:

• a single-step EDC combustion source. The irreversible reaction CH4 + 2 (O2 + 3.76 N2) -> CO2 + 2 H2O + 7.52 N2 is mixing-limited via the Eddy Dissipation Concept, with constant C_EDC = 4.0 and Kolmogorov mixing time tau_t = (nu/eps)^(1/2), producing the species consumption / production rates and the heat-release source for the energy equation;

• a radiant-fraction radiation sink that removes 25% of the local heat-release rate from the energy equation;

• the Vreman SGS model for the eddy viscosity, mu_t = rho C sqrt(B_beta / (alpha_ij alpha_ij)) with C = 2.5 Cs^2, used here instead of Smagorinsky.

Dimensionless numbers

Quantity	Sandia TEST-24 / Taha 2024	Notes
Inlet velocity U_inlet	0.097 m/s	methane fuel inlet
Co-flow velocity	0.14 m/s	air outside the plate
Molecular Prandtl Pr	0.7
Turbulent Pr_t = Sc_t	0.7
EDC constant C_EDC	4.0	mixing-limited reaction rate
Radiant fraction	25%	of local heat-release rate
Vreman constant C	2.5 Cs^2 (Cs = 0.1)	C = 0.025

Per-species molecular Schmidt numbers (CH4 0.7275, O2 0.8325, CO2 1.0425, H2O 0.6225) and a temperature-dependent molecular viscosity (power law) complete the transport model in the reference.

Simulation setup

The reference (Taha et al. 2024 Sec. 4) uses a non-uniform Cartesian mesh, dx_max = 4 cm, dx_min = 2 cm (~6M cells), a local time step at CFL ~ 0.7 (dt_min ~ 2e-4 s on the finest region), and ~27 s of physical time (first ~7 s discarded as the transient, remaining ~20 s for statistics).

Parameter	Value
Domain	4 x 4 x 7 m
Source	1 m diameter methane inlet; 0.51 m steel plate (adiabatic wall)
Inlet	methane at 0.097 m/s; air co-flow 0.14 m/s
Ambient	T = 285 K, p = 81.0 kPa
Velocity set / operator	D3Q27 / RRBGK
Closure	variable-density low-Mach (models.low_mach)
Turbulence model	Vreman SGS, Cs = 0.1 (C = 2.5 Cs^2, see Prerequisites)
Combustion	single-step EDC, C_EDC = 4.0 (see Prerequisites)
Radiation	prescribed radiant fraction, 25% (see Prerequisites)
Reference resolution	dx_max = 4 cm / dx_min = 2 cm (~6M cells)
Physical time	~27 s (~7 s transient + ~20 s statistics)

The 04_sandia_methane_pool_fire.nassu.yaml config carries the parts of this setup that the configuration surface supports: the domain, the models.low_mach closure, the energy / EOS block and the LES model. The combustion, radiation and Vreman SGS physics that drive the fire are listed under Prerequisites.

Reference and acceptance

Reference: Taha et al. (2024) Case 2 (Sec. 4, Figs. 13-19, Eqs. 21-25, 38); the Sandia methane pool-fire (TEST-24) measurements of Tieszen et al.; and the McCaffrey (1979) centreline correlations. See reference/REFERENCES.md for provenance and the digitization status.

A passing result reproduces:

• the puffing frequency in the same range as the paper (~1.3 Hz; the experimental 1.57 Hz is under-predicted, and the under-prediction is expected and must be noted), from the FFT of axial velocity at z = 0.5 m,

• the -5/3 inertial-range slope in the temporal energy spectrum at z = 0.5 m,

• the mean centreline axial velocity in reasonable agreement with experiment in the near field,

• the mean centreline temperature consistent with the McCaffrey correlation trend (slight over-prediction acceptable, as in the paper),

• the flame height ~4.8-5.2 m (reported experimental ~4.8 m), via the centreline mean-temperature threshold (550 K), within ~10%.

Prerequisites

The case depends on the following solver capabilities. The first is shared with the helium plume; the latter three are specific to the reacting fire:

• Composition-driven variable-density density. As for the helium plume, the density depends on a transported composition rather than a single specific gas constant. The reacting fire is a multi-species mixture whose composition varies strongly across the flame, so the dependence is stronger here.

• A single-step EDC combustion source term. A mixing-limited reaction-rate model (Eddy Dissipation Concept) producing the species production / consumption and the heat-release source for the energy equation.

• A radiant-fraction radiation model. A prescribed-fraction heat-release sink that removes a fixed fraction of the local heat-release rate from the energy equation.

• A Vreman SGS model. The Vreman eddy viscosity mu_t = rho C sqrt(B_beta / (alpha_ij alpha_ij)), C = 2.5 Cs^2, used here in place of Smagorinsky.

Results

Note

The quantitative comparison notebook (puffing FFT, energy spectrum, mean velocity / temperature profiles, TKE, and the flame-height estimate against Taha et al. (2024), the Sandia TEST-24 data and the McCaffrey correlations) and the digitized reference data are added once the Prerequisites are met and a GPU validation run is committed.

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[1]

Mostafa Taha, Song Zhao, Aymeric Lamorlette, Jean-Louis Consalvi, and Pierre Boivin. Large eddy simulation of fire-induced flows using lattice-boltzmann methods. International Journal of Thermal Sciences, 197:108801, 2024. doi:10.1016/j.ijthermalsci.2023.108801.