The study of single droplet combustion is an important step in understanding, designing and evaluating the performance of combustion systems as well as for understanding and modeling spray combustion, which plays a major role in many technical systems. The general research objective is to develop and implement a high-accurate numerical solver for the computation of the evaporation and combustion of a single fuel droplet in an ambient flow field with/without gravitational field. For this purpose, the Discontinuous Galerkin (DG) method is employed to accurately compute the two-phase liquid-gas flow with non-material deformable interface and the transport processes of the chemical species in the gas phase. Specifically, it is intended to extend the newly developed DG library BoSSS (Bounded Support Spectral Solver) for single phase flows to simulate the droplet combustion by an interface tracking method (level-set) combined with an extended DG method using non-smooth basis functions.

Contact person: Dipl.-Ing. Benedikt Klein

In this study, deformation of a water droplet on a solid surface within an exerted electric field will be numerically investigated. The fluid flow is governed by the

incompressible Navier-Stokes and continuity equations. The body force exerted from the electric field to the fluid flow is found from the Maxwell stress tensor (computed from electric field). Linear dielectric materials and the electrostatic case where electric field is stationary or changing slowly with time (low frequency) is considered. Another underlying assumption is that materials are assumed to be perfect dielectrics (insulators). Therefore the Electric field is computed from its potential, for which we need to solve a Laplace equation. The governing equations above are solved using NSE2 PCP solver developed based on BoSSS libraries, a general framework for solving conservation laws with discontinuous Galerkin Finite Element method (DG-FEM).

The motivation and application in mind is to study water droplets from rain or dew accumulated on hydrophobic surface of electric insulators. In presence of water droplets, in vicinity of the contact line of the droplet and the solid surface, electric field is intensified which leads to local electric discharges and damage the hydrophobic property of the surface.

Contact person: Nehzat Emamy, M.Sc.

We consider flows with a helical symmetry which is a twist of translational and rotational symmetry. The transport equations in helical coordinates are ”21/2D” which means they have three independent velocity components though only two independent spatial variables. We analyze the Euler and Navier-Stockes equations for new non-trivial conservation laws. It is to be expected that the new conservation laws may give some deeper insight into turbulence dynamics and hence bridging 2D and 3D turbulence.

Contact person: Dipl.-Math.-Ing. Olga Kelbin

The presence of surface-active molecules that adhere to phase interfaces and affect surface tension plays a critical role in many two-phase fluid systems and has a considerable significance in several industrial and biomedical applications. The transport process of these surfactants typically motivates the numerical treatment of interfacial partial differential equations in multiphase flow, or more generally, of PDEs residing on curved surfaces rather than flat Euclidean domains. These equations are defined through quantities intrinsic to surfaces, or interfaces respectively, characteristically involving tangential components of standard differential operators and hence, highly depend on the geometry of the surface.

Within this context, the numerical treatment of a possibly moving interface as well as interfacial convection-diffusion equations remains a challenging task, involving a simultaneous tracking of the interface position and the solution of both, the flow field and the interfacial equations with additional jump conditions.

In 2010, we have started to extend our numerical solver based on Discontinuous Galerkin methods aiming at the simulation of phase interfaces and interfacial transport equations, in particular with respect to surface active agents, and its integration into multiphase flow problems. This project is funded within the DFG priority programme 1506 (for more information, visit the website at http://www.dfg-spp1506.de/).

Contact Person: Dipl.-Math. Christina Kallendorf

The work focuses on a formulation of new modelling approaches to the ensemble averaged or spatially filtered equations describing two-phase flows with separated gas and liquid layers. The aim is to represent the influence of the unresolved part of the surface on the averaged/filtered variables describing the flow.

Contact person: Dr. Marta Waclawczyk

Application of the theory of Lie group analysis to the equations of turbulence and determining of scaling laws, e.g. log-law, decaying turbulence, rotating flows.

Contact Person: Dipl.-Math.-Phys.-Ing. Andreas Rosteck

by means of analytical methods from group theory and differential geometry, with the goal to apply them in the modeling process exactly there where traditional approaches fail due to lack of informations.

Contact person: Dr. rer. nat. Michael Frewer

In Premixed combustion, which occurs e.g. in Otto-engines, the chemical reaction occurs in a very narrow region, compared to any external length-scale. Therefore, the flow can be modelled mathematically as an incompressible two-phase flow consisting of an burned and unburned phase. In this setting, the flame itself is described as a 2-dimensional, non-material interface (there is mass flux across the interface !), and the whole chemistry and physics of the flame is replaced by a model that just describes the burning velocity of the flame in its normal direction.

Because of the jumps in velocity and pressure, its usually very difficult to capture the situation described above with a classical numerical scheme.The solution we come up with consists of the following ingredients:

A Level Set method to capture the movement of the front, which is actually quite standart;

The major novel development is an extended DG method, that is capeable of resolving the shocks desribed above with sub-cell accuracy. While the Level Set desribes the position of the front, the extended DG method is capeable of fullfilling the jump conditions for velocity and pressure at the interface.

Contact person: Dr.-Ing. Florian Kummer

by means of the Discontinuous Galerkin (DG) method and novel techniques for the treatment of phase interfaces.

Contact person: Björn Müller, M.Sc.

The term „disperse Fluid“ comprises solid particles dispersed in fluid. In general a differentiation can be made between Newtonian and non-Newtonian flows. As known from literature the rheological behaviour can change depending on the characteristics of the particles added to a flow.

The goal of this work is a better understanding of the rheology of particle flows in general and their effective viscosity in particular. There are two approaches possible – the analytical and the numerical point of view. The analytical results are planned to be substantiated by direct numerical simulation with spherical particles. One major challenge in that context is the numerical representation of the particles. For the numerical simulation a Discontinuous Galerkin based code has been developed at the FDY and is still further enhanced. During this research work this code is planned to be expanded by an implementation for particles.

Contact person: Laura Lukassen, M.Sc.

When a droplet spreads over a solid substrate, depending on the Capillary number and the wetting character of the system, the three-phase contact line can take a finger pattern as a result of instability. This finger pattern is undesirable for some industrial applications such as coating. Accordingly a reliable numerical tool could be beneficial in terms of prediction and design. Different numerical tools have been introduced for the numerical simulation of the contact line movement. Most of these tools suffer either a lack of consistent mathematical formulations, a lack of numerical preciseness, or an extreme simplification.

In the present research therein the numerical preciseness is emphasized, a Discontinuous Galerkin Finite Element Method is applied using the in-house code BoSSS as a general framework of solving transport equations. The following tasks are going to be done in this research:

- Implementation of the level set method, including the solutions of level set advection and reinitialization equations.

- Coupling of the level set code with the available Navier-Stokes code, following the diffuse interface approach.

- Performing a set of tests to verify the preciseness and performance of the multiphase Navier-Stokes code.

- Simulation of a set of flows including finger patterned moving contact lines.

Contact person: Roozbeh Mousavi, M.Sc.

The aim of this project is to study DNS of vibrating grid turbulence. Turbulence is generated at a grid in the plane which vibrates normally to itself. There is no mean velocity in the flow. Hence, in a statistical sense turbulence is generated in a plane and diffuses out while at the same time gets damped due to dissipation. Due to zero mean shear there is no production of turbulence apart from the region at grid. Numerical simulations for different Reynolds numbers (based on an amplitude and frequency of the grid) Re = 500, 1000, 3000 will be performed using a spectral code. The statistics of turbulence and the evolution of a turbulent/non-turbulent interface will be detected and compared to the theory.

Contact person: Dr.-Ing. George Khujadze

High-resolution data obtained by direct numerical simulation of turbulent boundary layers are analysed by means of orthogonal wavelets. This study is motivated by the importance of turbulent boundary layers in many fields of applied physics, for example, flows around technological devices such as airplanes, cars or golf balls, where determining the drag coefficient is directly related to this thin layer around the obstacle. Wavelet techniques have been developed for more than 20 years to analyse, model, and compute turbulent flows. The multiscale representation obtained by wavelet decompositions is useful in understanding the physics of turbulent flows as locality in both space and scale is preserved.

Contact person: Dr.-Ing George Khujadze

The object of the study is a 3D (spectrally stable) plane Couette flow. The main aim of the research is to separate the basic processes in the flow from each other and to study their interplay at different three stages (transition to turbulence, fully developed turbulence and spontaneous decay of turbulence) of the turbulent dynamics.

Contact person: Dr.-Ing. George Khujadze

fully developed turbulent Couette–Poiseuille flow with wall transpiration i.e. an extra transverse velocity with constant flux on the wall is carrying out. DNS of the flow for a wide range of transpiration velocities and Reynolds numbers is performed to test the theory and to obtain the data on the microstructure of turbulent motion that cannot be provided by the theory dealing with the Reynolds-averaged Navier–Stokes equations.

Contact person: Victor Avsarkisov, M.Sc.