Turbulence Modeling of Strongly-Coupled Particle-Laden Flows

Abstract

Turbulent, disperse two-phase flows are pervasive in nature and industry. Some contemporary examples include the dispersion of respiratory droplets when coughing or sneezing, sedimentation transport in rivers and the upgrading of agricultural waste into usable biofuels. In many systems, the disperse phase (e.g., solid particles, liquid droplets, gas bubbles) modifies the turbulence in the carrier phase, giving rise to complicated flow features such as dense clusters (or bubble clouds) and regions nearly void of particles. This heterogeneity predicates a wide range of length- and time-scales, making fully-resolved computations at scales of interest intractable, even on modern super computers. Thus, the Reynolds-Averaged Navier-Stokes (RANS) equations, which depend heavily upon modeling, continue to be the primary tool for large-scale computations of both single and multiphase turbulence.

Despite the prevalence of these systems, developing accurate models, especially for the multiphase RANS equations, has remained an open challenge. Due to the large parameter space, brute-force modeling approaches are infeasible. Further, the presence of a disperse phase can generate energy at the small scales (i.e., wakes past particles) which induces turbulence at large scales. This is directly in conflict with energy cascade theory from single-phase turbulence, making extensions from traditional single-phase turbulence modeling inadequate.

Due to the lack of accurate, tractable models for the multiphase RANS equations, researchers and practitioners must rely on closures that make idealistic simplifications such as uniformity in the disperse phase or perfect mixing. These assumptions lead to large errors in predicting quantities of interest (like the thermal entrance length or rate of thermochemical conversion), because important multiphase physics have been neglected. To demonstrate this shortcoming, the conversion of biomass to biofuel is simulated using highly-resolved, Eulerian-Lagrangian simulations. In this example, highly-resolved data is compared with predictions of an idealized model typical of industry. It is found that assuming uniform particles and perfect mixing results in an under prediction of biofuel yield by 33%. This underscores a principal challenge for upscaling reactors to industrial scales.

Motivated by this disparity, the main objective of this work is to develop a modeling framework capable of accurately translating highly-resolved data into models that are rooted in knowledge of physics, interpretable and easy to share. While this framework will benefit specific multiphase applications, such as fluidized bed reactors, it also has broader implications as the framework itself presents a generalized means to model quantities of any dimension, from scalars to tensors, with guaranteed invariance, in compact, algebraic form.

In this work, two modeling methodologies are developed for the first time: (1) Sparse regression with embedded invariance and (2) Sparse regression blended with gene expression programming (GEP). These methodologies are validated and tested on single-phase turbulent flows and extended to gravity-driven gas-solid flows. Here, a minimal invariant tensor basis for this class of flows is derived for the first time and new models are proposed. Finally, new scaling and models are developed for systems with spatially evolving heat transfer.

The modeling advancements in this work enable the accurate prediction of large-scale, gas-solid flows. In the context of the conversion of biomass to biofuel, improved reduced order models are needed to scale up circulating fluidized bed reactors from lab-scale to industrial-scale. This scale up is essential for harnessing the carbon neutral, high efficiency benefits of this renewable energy source and meeting climate and emissions targets.