FS3D – A DNS Code for Multiphase Flows

Institute of Aerospace Thermodynamics, University of Stuttgart (Germany)

Principal Investigator: Bernhard Weigand, HPC Platform: Hazel Hen of HLRS

The subject of multiphase flows encompasses many processes in nature and a broad range of engineering applications such as weather forecasting, fuel injection, sprays, and the spreading of substances in agriculture. To investigate these processes the Institute of Aerospace Thermodynamics (ITLR) uses the direct numerical simulation (DNS) in-house code Free Surface 3D (FS3D). The code is continually optimized and expanded with new features and has been in use for more than 20 years. Investigations were performed, for instance, for phase transitions like freezing and evaporation, basic drop and bubble dynamics processes, droplet impacts on a thin film (“splashing”), and primary jet breakup as well as spray simulations, studies involving multiple components, wave breaking processes, and many other applications. Complex phenomena demanding strong computational effort can be simulated because the code works on massive parallel architectures.

Project Description

Using the method of Direct Numerical Simulation (DNS), the smallest temporal and spatial scales are resolved, and no turbulence modeling is needed. In the last years, a vast number of investigations were performed with FS3D: for instance, phase transitions like freezing and evaporation, basic drop and bubble dynamics processes, droplet impacts on a thin film (“splashing”), and primary jet breakup as well as spray simulations, studies involving multiple components, wave breaking processes, and many more. FS3D is fully parallelized using MPI and OpenMP. This makes it possible to perform simulations with more than a billion cells on the Hazel Hen supercomputer (Cray-XC40) at the HLRS. Some applications of FS3D and results are presented in the following.

Fig. 1: Visualization of a hexagonally growing ice particle embedded in a supercooled water droplet. © ITLR, Universität Stuttgart

Supercooled water droplets exist in liquid form at temperatures below the freezing point. They are present in atmospheric clouds at high altitude and are important for phenomena like rain, snow, and hail. The understanding of the freezing process, its parametrization, and the link to a macro physical system such as a whole cloud, is essential for the development of meteorological models.

The diameter of a typical supercooled droplet, as it exists in clouds, is in the order of 100μm whereas the ice nucleus is in the nanometer range. This large difference in the scales requires a fine resolution of the computational grid. A visualization of a hexagonally growing ice particle embedded in a supercooled water droplet is shown in Fig. 1.

Evaporation of supercooled water droplets

Not only freezing processes but also the evaporation of supercooled water droplets need to be understood for the improvement of meteorological models. In the presented study the evaporation rate, depending on the relative humidity of the ambient air, is in the focus of numerical investigations with FS3D.

Several simulations of levitated supercooled water droplets are performed at different constant ambient temperatures and varying relative humidities Φ, with one example shown in Fig. 2. The evaporation rate β is determined and compared to experimental measurements [4].

Fig. 2: Simulation of an evaporating supercooled water droplet with FS3D. © ITLR, Universität Stuttgart
Fig. 3: Measured evaporation rates © ITLR, Universität Stuttgart

The resulting dependency of the evaporation rate on the relative humidity is depicted in Fig. 3, for an ambient temperature of T∞ = 268,15 K. The numerical results agree very well with experimental data. This shows that FS3D is capable of simulating the evaporation of supercooled water droplets and therefore can help to improve models for weather forecast. For example, future numerical simulations of the evaporation of several supercooled water droplets and their interaction could be investigated, a goal that is currently not feasible experimentally.

Non-Newtonian Jet Break Up

Liquid jet break up is a process in which a fluid stream is injected into a surrounding medium and disintegrates into many smaller droplets. It appears in many technical applications, for instance, fuel injection in combustion gas turbines, water jets for firefighting, spray painting, spray drying or ink jet printing. In some of these cases an additional level of complexity is introduced if the injected liquids are non-Newtonian; i.e., they have a shear dependent viscosity. Due to the complex physical processes, which happen on very small scales in space and time, it is hard to capture jet break up by experimental methods in great detail. For this reason it is a major subject for numerical investigations, and therefore, for investigations with FS3D.

In this project, the injection of aqueous solutions of the polymer Praestol into ambient air is simulated. The largest simulations are done using over 1.3 billion cells, where the cells in the main jet region have an edge length of 4∙10-5m . The simulated real time is in the order of 10 ms.

The influence of different destabilizing parameters on the jet (see Fig. 4), such as the Reynolds number, the velocity profile at the nozzle or the concentration of the injected solutions (and therefore the severity of the non-Newtonian properties) is investigated. The influence of these parameters on the jet break up behavior is analyzed, quantified by the liquid surface area, the surface waves disturbing the jet surface and the droplet size distribution [2]. The three dimensional simulation data, such as the velocity field or the internal viscosity distribution, is investigated in detail to explain the differences in jet behavior (see Fig. 5).

Fig. 4: Visualization of a jet break up simulated with FS3D. © ITLR, Universität Stuttgart

Fig. 5: Visualization of a transparent jet. In the background we show a slice through the centerline displaying the viscosity distribution on the lower half and the shear rate as well as the velocity vector on the upper half. © ITLR, Universität Stuttgart

Wave breaking

The interaction between an airflow and a water surface influences many environmental processes. This is particularly important for the formation and amplification of hurricanes. Water waves, wave breaking processes and entrained water droplets play a crucial role in the momentum, energy and mass transfer in the atmospheric boundary layer.

In order to simulate a wind wave from scratch a quiescent water layer with a flat surface and an air layer with a constant velocity field is initialized. Every simulation is performed on the Cray-XC40 at the HLRS with at least several thousand processors. Due to transition, the air interacts with the water surface and a wind wave develops, shown in Fig. 6. In the first step the occurring parasitic capillary waves on the front side of the wind wave are evaluated. Wave steepnesses and the different wave lengths of all parasitic capillary waves offer detailed insights into energy dissipation mechanisms, which could not be gained from experiments. In a second step the wind is enhanced by applying a wind stress boundary condition at the top of the computational domain. This leads to the growth of the wave amplitude and finally to wave breaking. Not only phenomenological comparison of this process with experiments, but also information about temporal evolution of the wave energy, structures in the water layer or dynamics of vortices are remarkable results of these simulations. For future investigations of wind waves and, for example, droplet entrainment from the water surface higher velocities, higher resolutions, and therefore, higher computational power will be needed. Such simulations requiring more than one billion cells makes the use of supercomputers indispensable.

Fig. 6: Simulation of a gravity-capillary wind wave with FS3D. The water surface is visualized in the front and the turbulent velocity field of the air layer on the left and rear boundaries of the computational domain. © ITLR, Universität Stuttgart

Droplet Splashing

If a liquid droplet impacts on a thin wall film, the resulting phenomena can be very complex. Impact velocity, droplet size and wall film thickness have a large influence on the shape and morphology of the observed crown. If the conditions are such that secondary droplets are ejected, this phenomenon is called splashing.

The splashing process is highly unsteady and its appearance is dominated by occurring in-stabilities that have a wide range of different scales. However, only a limited amount of properties are accessible through experiments. For example thickness of the crown wall and velocity profiles are difficult to obtain experimentally.

Currently, the researchers are able to perform simulations with up to one billion cells. A rendering of an exemplary simulation is shown in Fig. 7. In order to capture splashing processes on the smallest scale, a very high resolution is required. Therefore, often only a quarter of the physical domain is simulated by applying symmetry boundary conditions.

When the droplet and the wall film consist of two different liquids, additional phenomena occur that cannot be explained anymore with single-component splashing theories. One reason for this is that not only the properties of the liquids themselves but also their ratio matters.

Due to this, a multi-component module is implemented in FS3D, which captures the concentration distribution of each component within the liquid phase. This makes it possible to evaluate, for example, composition of the secondary droplets. One technical application for which this is important is the interaction of fuel droplets with the lubricating oil film on the cylinder in a diesel engine. This interaction occurs during the regeneration of the particle filter and leads to both a dilution of the engine oil wall film and to higher pollutant emissions. Here, a better understanding of two-component splashing dynamics can be a great advantage in order to minimize both engine emissions and lubrication losses.

Fig. 7: Visualization of a splashing droplet. © ITLR, Universität Stuttgart


[1] Eisenschmidt, K., Ertl, M., Gomaa, H., Kieffer-Roth, C., Meister, C., Rauschenberger, P., Reitzle, M., Schlottke, K., Weigand, B.: Direct numerical simulations for multiphase flows: An overview of the multiphase code FS3D, Applied Mathematics and Computation, 272, pp. 508-517, 2016.

[2] Ertl, M., Weigand, B.: Analysis methods for direct numerical simulations of primary breakup of shear-thinning liquid jets. Atomi-zation and Sprays 27(4), 303–317, 2017.

[3] Reitzle, M., Kieffer-Roth, C., Garcke, H., Weigand, B.: A volume-of-fluid method for three-dimensional hexagonal solidification processes, J. Comput. Phys. 339: 356-369, 2017.

[4] Ruberto, S., Reutzsch, J., Roth, N., Weigand, B.: A systematic experimental study on the evaporation rate of supercooled water droplets at subzero tem-peratures and varying relative humidity, Exp Fluids, 58:55, 2017.

Scientific Contact

Prof. Dr.-Ing. Bernhard Weigand
Institute of Aerospace Thermodynamics (ITLR)
University of Stuttgart, Germany
Pfaffenwaldring 31, D-70569 Stuttgart, Germany
E-Mail: bernhard.weigand@itlr.uni-stuttgart.de

http://www.uni-stuttgart.de/itlr/forschung/tropfen/fs3d October 2017

October 2017