arXiv subjects

Wes Hellwig

Publications and source records attributed to Wes Hellwig.

3 recordsLinked to original sources

arXiv2024

Flamelet Connection to Turbulence Kinetic Energy Dissipation Rate

The turbulence kinetic energy dissipation rate $\epsilon$, from a turbulent combustion computation using either Reynolds-averaged Navier-Stokes (RANS) or large-eddy simulation (LES), is proposed for closure with a sub-grid non-premixed flamelet model. The intentions are to avoid the creation of artificial tracking or progress variables and to relate accurately the physics of turbulent non-premixed combustion at the resolved length scales to the small-scale physics where the mixing and chemical reactions occur. The analysis addresses the relations between $\epsilon$ and the strain rate, vorticity, viscous dissipation rate, scalar gradients, scalar dissipation rate, and burning rate at the smallest turbulence length scales where diffusion-controlled burning is faster than at larger length scales and thereby dominant. The imposed strain rate and vorticity on these smallest eddies are determined from the kinetic energy dissipation rate. Thus, an $\epsilon$ value at a specific time and location determines the two mechanical constraints (vorticity and strain rate) on the inflow to the counterflow flamelet. $\epsilon$ affects the sign of the Laplacian of pressure, which must be negative to allow the existence of the counterflow. Using different flamelet models, with and without vorticity, different results for maximum flamelet temperature, integrated flamelet burning rate, and maximum flamelet scalar dissipation rate are obtained. Flamelet models that consider the centrifugal effect of vorticity produce substantial enhancements in the accuracy and completeness of information for a turbulent combustion computation. $\epsilon$ may be used as a tracking variable that connects the sub-grid flamelet model to resolved-scale RANS or LES computations.

physics.flu-dyn↗

arXiv2024

Vortex Stretching of Non-premixed, Diluted Hydrogen/Oxygen Flamelets

A three-dimensional flamelet model considering vortex stretching with unitary Lewis number is used to simulate diluted hydrogen-oxygen diffusion flames. Non-reacting nitrogen is used as the diluent gas in the fuel stream. Unitary Lewis number provides a common thermal and mass diffusivity from which to create scalar dissipation rate. Both stable and unstable branches of flammability curves (S-curves) are calculated with three vorticity levels and plotted against multiple input and output parameters. The description of the three-dimensional flamelet structure, allowing vorticity and variable density to produce a centrifugal effect, is seen to be necessary for an accurate determination of the $\mathrm{H_2O}$ production rate when ambient inflow strain rate $(S^*)$ and vorticity $(\omega)$ are chosen as the key parameters. Maximum temperature and integrated $\mathrm{H_2O}$ production rate each nearly collapse to a single curve when plotted versus maximum scalar dissipation rate $(\chi_{max})$ but do not collapse when plotted versus the local maximum strain rate $(S^*_{local})$ or $S^*$. Additionally, $S^*_{local}$ and scalar dissipation rate $(\chi)$ depend strongly on vorticity and ambient inflow strain rate. It is argued that the controlling inputs for a flamelet embedded in a turbulent eddy are the ambient vorticity and strain rate which are thus the natural choice of parameterizing variables. These ambient quantities can be readily linked to the averaged or filtered turbulent flow by leveraging cascade theory, as opposed to local strain rate or scalar dissipation rate within the flame zone, which do not have a widely accepted, first-principles scaling connection to the turbulence cascade.

physics.flu-dyn↗

arXiv2023

Three-dimensional Vorticity Effects on Extinction Behavior of Laminar Flamelets

A recent rotational flamelet model is developed and tested with an improved framework of detailed chemistry and transport. The rotational flamelet model incorporates the effects of shear strain and vorticity on local flame behavior and is three-dimensional by nature. A similarity solution reduces the three-dimensional governing equations to ODEs involving a transformation to a non-Newtonian reference frame. A 9-species chemical kinetics model is used for H2-O2 combustion with non-reacting N2. Multiple flamelet cases including non-premixed, premixed, and partially-premixed flames are performed. Across all cases, vorticity extends flammability limits by up to 30% in terms of the ambient extinction strain rate and modifies both local flame structure and mixture composition. For non-premixed flames, where the location of minimum density coincides with the location of peak temperature, the centrifugal force induced by vorticity reduces the mass flow rate through the flame, effectively lowering the local strain rate. This increases residence time, thus extending flammability limits and reducing burning rates. This analysis is done also for premixed and partially-premixed flames. If minimum density lies between the flame zone and the fuel inlet boundary, centrifugal forces do not significantly modify flame behavior. Stable and unstable branches of S-curves for non-premixed and partially-premixed flames and stable branches for premixed flames show extended flammability limits due to vorticity. The capabilities of the rotational flamelet model reveal that vital physics are currently missing from two-dimensional, irrotational, constant-density, flamelet models. Improvements of detailed chemical kinetics, transport formulation, and thermo-physical properties bring the new flamelet model to par in these areas with existing models, while adding new features in terms of physical emulation.

physics.flu-dyn↗