Sandia helium plume (Taha 2024 Case 1)

Important

Status: planned - not yet validated against reference data. This is the non-reactive benchmark Taha et al. (2024) used to validate the variable-density low-Mach closure, and it is the closure’s own validation target. The setup, dimensionless matching and reference data are documented below; the comparison notebook and digitized reference data are added once the prerequisites in the Prerequisites subsection are met. The primary validation quantity is the plume puffing frequency.

Why this case matters

The closed and Boussinesq buoyant cases (warm bubble and the Steckler room fire) prove the buoyancy coupling in the small-density-variation regime, where the density swing is a linear perturbation about a reference state. Real fire-induced flows are not in that regime: the density varies by a factor of several, so the buoyancy must come from the exact equation of state, not its Boussinesq linearization. Before stacking combustion and radiation on top (the methane pool fire), the variable-density low-Mach closure Taha et al.[1] must be validated on its own.

The Sandia FLAME helium plume is the clean check for exactly that. A light gas (helium mixture, mean molecular weight W ~ 5.45 g/mol) rises into air at a density ratio of order five, with no combustion and no radiation. It isolates the Tier 3 closure - the equation-of-state density slaving rho = P/(rT), the reduced-pressure split, and the exact (rho - rho_inf) g buoyancy term - from any chemistry. It is Case 1 of Taha et al. (2024), who validated it against the Sandia measurements of O’Hern et al. (2005) and Tieszen et al.; reproducing their result confirms our implementation of the same model.

The plume is also a dynamic check, not just a mean-profile one. The buoyant shear layer is unstable and the plume self-oscillates at a well-defined puffing frequency (~1.37 Hz in the experiment), which is the headline acceptance quantity.

Physical description

A 1 m diameter circular source at the bottom centre of an 8 x 8 x 4 m domain injects the helium mixture vertically at 0.325 m/s. The source is surrounded by a 0.51 m wide solid floor (the ground plane) and a 2.4 m diameter chimney above. Air co-flows outside the source annulus at 0.01 m/s. The injected gas is a mixture of 96.4% He, 1.9% O2 and 1.7% acetone by volume, with mean molecular weight W_He = 5.45 g/mol; the ambient is air at T_inf = 285 K, p_inf = 80900 Pa. The light core is buoyant, rises, and the surrounding shear layer rolls up into the periodic puffing structures that dominate the near field.

Because the gas is light rather than hot, the density contrast here is driven by composition (molecular weight), not temperature: the helium mass fraction is transported as a scalar and the local mixture molecular weight sets the density through the equation of state. This composition-driven density is the central modeling requirement for the case (see Prerequisites).

Governing equations

The density is slaved to the ideal-gas equation of state rather than read from the population sum,

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

and the buoyancy enters the fluid as the exact body force

(2)\[F_\alpha = (\rho - \rho_\infty)\, g_\alpha\]

with gravity along -z, of which the Boussinesq force is the linearized small-density-variation limit. For the helium plume the local density contrast comes from the mixture molecular weight: a helium-rich parcel has a lower mean W (equivalently a larger effective r = R_universal / W) and is therefore lighter than ambient air at the same P and T, so (2) lifts it. The composition is carried by a helium mass-fraction scalar transported by advection-diffusion and coupled back into the density.

Dimensionless numbers

Dimensionless group	Sandia / Taha 2024	This case (target)	Matched
Reynolds number Re = U D / nu	~3220	~3220	target
Richardson number Ri = g (rho_inf - rho_0) D / (rho_inf U^2)	~75.4	~75.4	target
Prandtl number Pr = nu / alpha	0.7	0.7	target
Helium Schmidt number Sc_He = nu / D_He	0.2	0.2	target
Density ratio rho_inf / rho_0	~5	~5	target
Mach number Ma = U / c_s	<< 0.1	<< 0.1	target

The driving group is the Richardson number Ri ~ 75.4 (strongly buoyancy dominated, as expected for a low-momentum light-gas plume), with Re ~ 3220 from the 1 m source diameter and 0.325 m/s inlet. The ~5 density ratio is what takes the case out of the Boussinesq regime and makes it a genuine variable-density test. Reaching the target density ratio requires the composition-driven density described under Prerequisites.

Simulation setup

The reference mesh study (Taha et al. 2024) used a coarse (dx = 2 cm, ~2M cells), medium (dx = 1 cm, ~4M cells) and fine (dx = 0.8 cm, ~7.8M cells) Cartesian mesh with refinement toward the source, converged at the medium level. LES uses Smagorinsky with Cs = 0.1. The reference runs ~26 s of physical time with the first ~13 s discarded as the initial transient and the remaining ~13 s used for statistics.

Parameter	Value
Domain	8 x 8 x 4 m
Source	1 m diameter inlet, floor centre; 0.51 m solid floor; 2.4 m chimney
Inlet	helium mixture W ~ 5.45 g/mol at 0.325 m/s; air co-flow 0.01 m/s
Ambient	T_inf = 285 K, p_inf = 80900 Pa
Velocity set / operator	D3Q27 / RRBGK
Closure	variable-density low-Mach (models.low_mach)
Turbulence model	LES Smagorinsky, Cs = 0.1
Transport	mu = 1.88768e-5 kg/m/s (constant); Pr = 0.7; Sc_He = 0.2
Reference resolution	coarse 2 cm / medium 1 cm / fine 0.8 cm; converged at medium
Physical time	~26 s (~13 s transient + ~13 s statistics)

The 02_sandia_helium_plume.nassu.yaml config carries the parts of this setup that the configuration surface supports: the domain, the models.low_mach closure and the energy / EOS block. The composition-driven density needed to reach the target helium-air density ratio is listed under Prerequisites.

Reference and acceptance

Reference: Taha et al. (2024) Case 1 (Sec. 3, Figs. 2-12); the underlying Sandia FLAME measurements of O’Hern et al. (2005) and Tieszen et al. See reference/REFERENCES.md for provenance and the digitization status.

A passing result reproduces:

• the puffing frequency within the experimental band (1.37 +/- 0.1 Hz), from the FFT of the centreline axial velocity at z = 0.5 m (primary quantity),

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

• the mean and rms axial velocity along the centreline up to z = 0.8 m,

• the mean and rms helium mass fraction along the centreline (rms at a looser tolerance),

• the radial profiles of mean / rms axial and cross-stream velocity at z = 0.2, 0.4, 0.6 m.

Prerequisites

The case depends on one solver capability beyond the variable-density low-Mach closure:

• Composition-driven density (helium-air mixture). The density must depend on a transported composition scalar, so that the local mixture molecular weight sets the density through the equation of state (a mixture r(Y_He) or W(Y_He)-driven EOS, coupled to the helium mass-fraction field). This is what carries the helium-air ~5 density ratio that defines the case.

Results

Note

The quantitative comparison notebook (puffing-frequency FFT, energy spectrum, and the centreline / radial velocity and helium-mass-fraction profiles against Taha et al. (2024) and the Sandia measurements) and the digitized reference data are added once the Prerequisites are met and a GPU validation run is committed.

---

[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.