(571b) A Cylindrical Formulation of the One Dimensional Turbulence (ODT) Model for Turbulent Jet Flames

The One Dimensional Turbulence (ODT) model has been successfully applied to a
wide range of turbulent flows including homogeneous turbulence, jets, wakes,
mixing layers, channel flows, Rayleigh-Taylor, buoyant wall flows, and others.
ODT solves a flow by temporally-evolving one-dimensional transport equations
for mass, momentum, and (optionally) reacting scalars. Advection is modeled
through stochastic eddy events that are implemented as triplet maps. The
size, location, and rate of these maps are drawn from an eddy rate
distribution in a manner that this consistent with turbulent inertial range
advection. The model is an extension to the Linear Eddy Model (LEM), and
differs from LEM in that, in ODT, momentum components are solved in addition
to scalar quantities, and these momentum components are used to define eddy
rate distribution function. Hence, ODT is a dynamic turbulence model and
can accurately capture velocity and mixing profiles in nonuniform
turbulence. Because the model is one dimensional, it is limited to
boundary-layer like flows, but such flows are important and widely studied,
with a wealth of experimental data available. ODT is unique in that it is
able to resolve a full spectrum of turbulent time and length scales (in one
dimension). Only direct numerical simulation is able to resolve all scales
of a turbulent flow, but this is done at a computational cost that is
prohibitive for engineering flows at realistic Reynolds numbers. Large Eddy
Simulation directly captures large eddies, but models small subgrid scale
motions. Conversely, ODT resolves fine scale structures, allowing diffusion
processes in the physical space coordinate, but models the large-scale
advection. Often the fine scales are more difficult to model since
nonlinear multi-component diffusion and reaction processes occur at
dissipation scales. Large-scale advection is often not too difficult to
model in boundary layer flows.

ODT has been recently validated quantitatively against several DNS in
compatible configurations, namely, temporal, planar jets. This has been done
for soot formation, and flame extinction and reignition using ethylene and
syngas fuels. Premixed flames have also been studied. As the model has been
extended to more and more complex flows, there has been a desire to use ODT
as a surrogate DNS, due to its low cost compared to DNS. Such validation
studies comparing ODT and DNS are promising in this area. However, DNS is
limited to relatively few simulations and relatively low Reynolds number.
Application of ODT to experimental flows is limited by the configuration.
Experimental jets are usually cylindrical and evolve spatially, whereas
existing ODT simulations are planar and (normally) evolve temporally.
(There is a spatial formulation of the model in which a one-dimensional
flow evolves spatially in a down-stream direction like a parabolic
boundary layer formulation.)

We extend the ODT model to a cylindrical formulation. The formulation is
presented, along with challenges and interpretations. We present comparisons of
the cylindrical ODT formulation to round pipe flow, round nonreacting jets at
high Reynolds number, and to reacting nonpremixed jet flames. The new
formulation is expected to improve previous predictions of jet flows,
including, for instance, particle flows. We discuss such expected improvements.