  A joint volume-surface formalism of the Multi-Moment Sectional Method (MMSM)
is developed to describe the evolution of soot size distribution in turbulent
reacting flows. The bivariate MMSM (or BMMSM) considers three statistical
moments per section, including the total soot number density, total soot
volume, and total soot surface area per section. A linear profile along the
volume coordinate is considered to reconstruct the size distribution within
each section, which weights a delta function along the surface coordinate. The
closure for the surface considers that the primary particle diameter is
constant so the surface/volume ratio constant within each section. The
inclusion of the new variable in BMMSM allows for the description of soot's
fractal aggregate morphology compared to the strictly spherical assumption of
its univariate predecessor. BMMSM is shown to reproduce bimodal soot size
distributions in simulations of one-dimensional laminar sooting flames as in
experimental measurements. To demonstrate its performance in turbulent reacting
flows, BMMSM is coupled to a Large Eddy Simulation framework to simulate a
laboratory-scale turbulent nonpremixed jet flame. Computational results are
validated against available experimental measurements of soot size
distribution, showing the ability of BMMSM to reproduce the evolution of the
size distribution from unimodal to bimodal moving downstream in the flame. In
general, varying the number of sections has limited influence on results, and
accurate results are obtained with as few as eight sections so 24 total degrees
of freedom. The impact of using a different statistical model for soot (HMOM)
is also investigated. The total computational cost of using BMMSM as low as
approximately 44% more than the cost of HMOM. The new formulation results in a
computationally efficient approach for the soot size distribution in turbulent
reacting flows.
