Characterization of two-way coupled thermovibrationally driven particle attractee

Abstract

Following the recent identification of a new category of thermovibrationally-driven particle attractors in dilute fluid-particle systems (Phys. Fluids, 26(9), 093301, 2014; Phys. Fluids, 31(7), 073303, 2019; Phys. Fluids, 32(5), 053314, 2020), some effort is provided to develop an integrated framework able to encompass earlier discoveries and account for new effects in a single treatment. In particular, we examine the alterations ('corrugation') that can be induced in the geometrically perfect particle structures pertaining to this class of phenomena as the percentage of dispersed solid mass is progressively increased. The related dynamics are explored within the framework of a two-way coupled model with respect to several parameters (solid mass load, density ratio, frequency and amplitude of the imposed vibrations). Ensuing results are interpreted by separating instantaneous and time-averaged contributions and using some ideas borrowed from the companion theory of bifurcations. We show that the back influence of particles on the carrier flow can lead to a variety of possible paths of evolution. While in some cases the original attractee can be overshadowed by particle-induced turbulence, in other circumstances new aggregates with heretofore unseen morphology show up.

On the Propagation of Hydrothermal Waves in a Fluid Layer with Two-Way Coupled Dispersed Solid Particles

“…Moreover, the following ranges are examined in terms of particle Stokes number and mass load: 10 −6 ≤ St ≤ 10 −5 , 0 ≤ χ ≤ 0.7. Particles are assumed to be made of tungsten (Table 3), which makes the corresponding volume fraction span the interval 0 ≤ ϕ ≤ 2.8 × 10 −2 (as in [40]).…”

“…As the solution technique we have implemented a projection method for incompressible fluid flow based on the use of primitive variables (namely, velocity, pressure and temperature; see, e.g., Lappa [40] for an exhaustive description). Here we limit ourselves to reporting that this method relies on an intermediate step where the momentum equation is integrated in time disregarding the pressure gradient.…”

“…Given these premises, we follow here the same strategy recently implemented by Lappa [40], i.e., a combined Eulerian-Lagrangian approach where the equations accounting for the liquid and solid mass are properly coupled through the presence of 'interphase exchange terms'. As further detailed in the next section, these coupling terms only relate to a subset of the involved transported quantities as in the present case the particles do not dissolve in the carrier fluid (i.e., they behave as an immiscible phase).…”

“…Closure of the two-way coupling strategy, whose foundations have been laid in the preceding two subsections, simply requires that an expression for the momentum and energy exchange terms appearing in Equations ( 2) and (3) is provided. Using the same formalism introduced by Lappa [40], by denoting the number of particles present at a given instant in any computational cell of the domain as n ij (i and j being the representative indexes of the x and y directions, respectively), the interphase terms can be expressed as…”

“…Finally, to make the overall theoretical architecture physically and numerically consistent (see again [40] and the references therein), the following two inequalities must be satisfied:…”