Sandia methane pool fire (Taha 2024 Case 2)

Important

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 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 covers the puffing FFT, the energy spectrum, the mean velocity / temperature profiles, TKE, and the flame-height estimate against Taha et al. (2024), the Sandia TEST-24 data and the McCaffrey correlations.

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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.