A level-set model for mass transfer in bubbly flows

Abstract

Navier-Stokes equations and mass transfer (or heat transfer) equation are discretized using a finite vol-31 ume method on a collocated unstructured mesh, whereas a multiple marker level-set approach is used 32 for interface capturing in bubble swarms. This method avoids the numerical coalescence of the fluid par-33 ticles, whereas the mass conservation issue inherent to standard level-set methods is circumvented. 34 Furthermore, unstructured flux-limiter schemes are used to discretize the convective term of momentum 35 transport equation, level-set equations, and chemical species concentration equation, to avoid numerical 36 oscillations around discontinuities, and to minimize the numerical diffusion. A convection-diffusion-37 reaction equation is used as a mathematical model for the chemical species mass transfer at the contin-38 uous phase. Because the mathematical analogy between dilute mass transfer and heat transfer, the same 39 numerical model is applicable to solve both phenomena. The capabilities of this model are proved for the 40 diffusion of chemical species from a sphere, external mass transfer in the buoyancy-driven motion of sin-41 gle bubbles and bubble swarms. Results are extensively validated by comparison with analytical solu-42 tions and empirical correlations from the literature.43

Tetrahedral adaptive mesh refinement for two‐phase flows using conservative level‐set method

“…The CLS method, 14,16 as introduced by Balcázar et al 16 in the framework of the finite‐volume approach and unstructured meshes is employed in this research. The CLS method uses a regularized indicator function, : where d ( x , t ) is a signed distance function, 8 ε = 0.5 h 0.9 sets the profile thickness, h is the local grid size defined in this work as the average distance between the local cell‐centroid and neighbor cell‐centroids with common face around the local cell 19 . The interface is defined by the isosurface : …”

“…As proposed by References 13,16,19, curvature is computed at the cell as , where f denotes the faces on the surface of , subindex P denotes the current cell, A f is the face‐area vector pointing outside , and V P is the volume of . Finite‐volume discretization of surface tension force (Equation (8)), as well as technical details on the regularization of the Dirac delta function, is reported in our previous works 13,16,19 . Finally, fluid properties are regularized using the level‐set function, as follows, …”

“…The reader is referred to References 13,16,19 for further details on the unstructured CLS method used in this work.…”

“…The governing equations have been discretized by a finite‐volume (FV) approach on collocated unstructured meshes as first introduced by References 13,16,17,19, which is coupled with the tetrahedral AMR framework. In what follows, the numerical approach is reviewed for the sake of completeness.…”

“…Even though each method has its advantages and disadvantages, one of the main issues that can arise is the mass conservation of fluid phases and accurate computation of curvatures. Lately, a finite‐volume CLS method for two‐phase flows on unstructured grids with surface tension has been proposed by Balcázar et al, 16 and further extended to interfacial flows with variable surface tension, 13 bubbly flows, 17‐20 and interfacial heat/mass transfer 19,20 . On the other hand the finite‐volume approach leads to the satisfaction of the integral forms of the conservation laws over the entire domain, the unstructured CLS method has further advantages such as numerical stability at high physical properties ratios (density and viscosity), mass conservation of fluid phases, accurate computation of surface tension, and efficient parallelization, as demonstrated in our previous works 13,16‐21 …”