A Parametric Study of LEM3D Based on Comparison with a Turbulent Lifted Hydrogen Jet Flame in a Vitiated Co-Flow

ABSTRACT

A novel model, the hybrid RANS-LEM3D model, is applied to a lifted turbulent N₂ diluted hydrogen jet flame in a vitiated co-flow of hot products from lean H₂/air combustion. In the present modeling approach, mean-flow information from RANS provides model input to LEM3D, which returns the scalar statistics needed for more accurate mixing and reaction calculations. The dependence of lift-off heights and flame structure on iteration schemes and model parameters are investigated in detail, along with other characteristics not available from RANS alone, such as the instantaneous and detailed species profiles and small-scale mixing. Two different iteration procedures, a breadth-first search (BFS) and a checkerboard algorithm, as well as parameters of the model framework are examined and tested for sensitivity toward the results. The impact of heat release and thermal expansion is demonstrated and evaluated in detail. It is shown for the current application that LEM3D provides additional details compared to the RANS simulation with a low computational cost in comparison with a conventional DNS simulation.

KEYWORDS:

• Turbulent mixing
• Linear Eddy Model
• vitiated co-flow burner
• Kolmogorov scale
• differential diffusion
• 3×1D solver

Nomenclature

Greek Symbols

η	=	Kolmogorov length scale= (vM/ε)1/4 [m]
νM	=	Molecular kinematic viscosity [m2/s]
νT	=	Turbulenlt kinematic viscosity [m2/s]
ωk	=	Chemical reaction rate [(kg)k/kg/s]
ρ	=	Density [kg/m3]
σT	=	Turbulent Schmidt number =vT/ DT
σh	=	Turbulent Prandtl number of the energy equation
σYi	=	Turbulent Schmidt numbers of the mass balance equations
ε	=	Dissipation term in the equation for turbulence energy [m2/s3]

Superscripts

−	=	Mean value
˜	=	Mass-weighted average value
	=	Fluctuating value

Latin Symbols

Δt	=	RANS time step [s]
Δx	=	RANS cell size [m]
Δxw	=	LEM cell size [m]
ξ	=	Mixture fraction
Cµ	=	Constant in the k-ɛ model
Dk	=	Molecular diffusivity [m2/s]
DT	=	urbulent dilfusivity [m2/s]
k	=	Turbulent kinetic energy [m2/s2]
Lint	=	Integral length scale [m]
p	=	Scaling exponent in the Linear Eddy Model
t	=	Time [s]
TM	=	Triplet Map
u	=	Fluid velocity [m/s]
W	=	Molecular weight [g/mol]
Xk	=	Mole fraction of species k [(mol)k/mol]
Yk	=	Mass fraction of species k [(kg)k/kg]
Z	=	Elemental mass fractions
fac	=	Under-resolving factor = Δxw/η
p	=	Static pressure [Pa=N/m2]

Aberrations

3DCV	=	Control volume in LEM3D
CFD	=	Computational Fluid dynamics
CFL	=	Advective Courant-Friedrichs-Lewy number
CV	=	Control volume
DNS	=	Direct Numerical Simulation
LEM	=	The standalone Linear Eddy Model
LEMres	=	# of LEM wafers in each direction of the 3DCVs
LEM3D	=	The three-dimensional Linear Eddy Model formulation
LES	=	Large Eddy Simulation
RANS	=	Reynolds Averaged Navier-Stokes equations

Acknowledgments

This work at the Norwegian University of Science and Technology and SINTEF Energy Research, Norway was supported by the Research Council of Norway through the project HYCAP (233722). The authors would also like to thank Alan R. Kerstein for numerous, invaluable discussions and support.

Compliance with Ethical Standards

Conflict of interests The authors declare that they have no conflict of interest.

Notes

¹ Let $x=(x_1,\dots ,x_n)$ and $y=(y_1,\dots ,y_n)\in {\mathbb{R}}^n$. Then the Manhattan metric is defined as $d(x,y)={\sum }_{i=1}^n\left|x_i-y_i\right|$.

Additional information

Funding

This work was supported by The Research Council of Norway [Grant no. 233722].