(273c) Filtered Drag Models for Euler-Lagrange Simulations of Gas-Solid Flow

It is well known that fluidized
gas-particle mixtures manifest meso-scale structures such as clusters and
bubbles. Resolving small meso-scale structures in device-scale simulations is too
expensive and this has led to the development of filtered Euler-Euler (EE)
two-fluid models and related constitutive models [1,2]. In this contribution, we ask how the
constitutive models for, say, fluid-particle interaction force, should be
filtered in Euler-Lagrange (EL) simulations (using the averaged equations for
the gas phase and Discrete Element Method for the particle phase ? sometimes
referred to as the CFD-DEM approach).

To address this question, we
performed CFD-DEM simulations of O(10⁶) particles that freely
sediment in a periodic box, and recorded statistics of the domain-averaged slip
velocity, as well as of numerous spatially-averaged (i.e., filtered)
quantities. Variations in the microscopic drag law, grid resolution, domain
size, and mapping schemes show that our results are robust with respect to
these settings.

We define two sets of filtered
slip velocities and corresponding drag laws: First, we filter only the fluid
velocity and define a filtered slip velocity as the difference between a
filtered fluid velocity and the instantaneous particle velocity. The
corresponding ?fluid-only? filtered drag model is relevant for simulations
where particles (or groups of particles) are tracked and coarse fluid grid
cells have to be used (e.g., MP-PIC [3], or other parcel-based approaches [4]). Second, we define the filtered slip
velocity based on the filtered fluid velocity and an average particle velocity
in the filter region. The corresponding ?particle-and-fluid? filtered drag
model is relevant for coarse-grid EE simulations. Finally, we discuss the
differences between the two classes of filtered drag laws, and provide closed
expressions for their inclusion in parcel- and EE-based coarse-grid simulations.
Variations in the particle size and density were used to extract the correct
reference length scale that makes our filtered model applicable to gas-particle
systems with sufficiently low particle Reynolds numbers.

Dimensionless
filtered drag coefficient for various filter sizes and volume fractions
(symbols: data from EL simulations; black lines: model prediction)

References