# Dr.-Ing. Johannes Kromer

work +49 6151 16-21466

fax +49 6151 16-21472

kromer@mma.tu-...

Work
Alarich-Weiss-Straße 10

64287
Darmstadt

Office: L2|06 407

## DNS & computer assisted stability analysis of fluid particles

### Research Motivation

Significant attention has been devoted to flow associated with both rigid and fluid particles that are either fixed or freely rising/falling through a continuous phase of a Newtonian fluid, due to the relevance of such flows to engineering systems, their common occurrence in geophysical flows, as well as their complex and fascinating nature.

A considerable body of literature addresses the subject of instabilities for fixed, rigid (i.e., non-deformable solid) bodies, freely rising or falling rigid bodies, and freely rising or falling fluid particles (gas or liquid). While these systems are related, they differ in the number of degrees of freedom they exhibit and this in turn impacts the types of instabilities that can occur. In the first case, an instability can only occur in the velocity field around the body.

### Scientific Project

The direct numerical simulation (DNS) of freely rising fluid particles employs the Finite Volume Code Free Surface 3D (FS3D). The modeling comprises incompressible two-phase flows with a sharp fluid interface, which is captured using an extended VOF method and is reconstructed piecewise linearly (PLIC).

The first part of the project covers the direct numerical simulation of high-viscosity oil droplets freely rising in water (viscosity ratio 45:1, [1] and 25:1). The initially spherical droplets rise freely due to buoyancy within a cuboidal domain. Exploiting a windowing technique, which ensures that the droplet center of mass stays close to its initial position, allows for spatially highly resolved computations over long periods of physical time. The shape deformation exhibits increasing complexity in its dynamics with increasing droplet diameter, reaching from quasi spherical regimes for the smallest droplets over stationary deformation with rocking center trajectories to low-frequent strong deformations of the interface, accompanied by trajectory oscillations, for the largest droplets. A decomposition into spherical harmonics allows for detailed insight to local quantities, such as curvature over time.

The second part of the project covers the global linear stability analysis of fluid particles. The system is represented in a state vector, which is governed by an evolution equation and, in the case of an incompressible two-phase flow involving Newtoninan fluids, contains the velocity field and interface position. After numerically computing a steady state of the system under consideration, a set of orthonormal perturbations are applied. The time evolution of the perturbations is computed using the flow solver FS3D and allows to assess the linear stability properities of the staedy state under consideration.

### Acknowledgements

This work is supported by the Excellence Initiative of the German Federal and State Governments, the Graduate School of Computational Engineering (GSC CE; GSC 233).

### Project References

[1] C. Albert, J. Kromer, A. M. Robertson and D. Bothe. Dynamic behavior of buoyant high viscosity droplets rising in a quiescent liquid. Journal of Fluid Mechanics, 778: 485 – 533, 2015