(vc_sandia_methane_pool_fire)= # 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 {ref}`helium plume `, which validates the same closure without chemistry. ``` ## Why this case matters The {ref}`helium plume ` validates the variable-density low-Mach closure {footcite:t}`taha2024fire` 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 ```{math} --- label: vc_methane_eos --- \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. ``` ```{footbibliography} ```