Practical shape optimization of a levitation device for single droplets

Abstract

The rigorous optimization of the geometry of a glass cell with computational fluid dynamics (CFD) is performed. The cell will be used for non-invasive nuclear magnetic resonance (NMR) measurements on a single droplet levitated in a counter current of liquid in a conical tube. The objective function of the optimization describes the stability of the droplet position required for long-period NMR measurements.The direct problem and even more the optimization problem require an efficient method to handle the high numerical complexity implied. Here, the flow equations are solved two-dimensionally and in steady state with the finite-element code SEPRAN for a spherical droplet with ideally mobile interface. The optimization is performed by embedding the CFD solver SEPRAN in the optimization environment EFCOSS. The underlying derivatives are computed using the automatic differentiation software ADIFOR. An overall concept for the optimization process is developed, requiring a robust scheme for the discretization of the geometries as well as a model for horizontal stability in the axially symmetric case. The numerical results show that the previously employed measuring cell described by Schröter is less suitable to maintain a stable droplet position than the new cell.

Parallel re-initialization of level set functions on distributed unstructured tetrahedral grids

“…5. The domain X M is an optimized measurement cell used to investigate levitated droplets, see [50]. 6.…”

Modelling Mass Transfer Coefficients During Drop Formation

“…The different models are summarised in Table ( 1), they are of the same form with different constants for each mechanism.…”

“…Liquid-liquid extraction plays an important role as a separation technique because of its lower energy cost and more gentle treatment, in comparison with distillation its importance will increase in the future [1,2]. In most industrial extraction equipment one phase is dispersed as a swarm of drops in a second continuous phase.…”

Visualizing flow vortices inside a single levitated drop

“…One particular, perfectly symmetric cell was manufactured at Lehrstuhl fü r Thermische Verfahrenstechnik TVT, RWTH Aachen, that provided optimal conditions for generating and visualizing symmetric flow conditions for the case of toluene, and at the same time could fit in the NMR microimaging device. The geometry of this cell follows the experiences from a geometry optimization with the objective to maximize the stability of droplet position [23].…”