Primary research topics in the research group "Thermo-Fluid Dynamics" are around modeling of unsteady processes in fluid and thermo-dynamics resulting from transient microscale phenomena in plasma and gas dynamics. The correlation between momentum transfer and thermo-fluxes is analyzed by disturbance calculation methods and stability evaluations. To achieve this, the dynamics of microscale particles and molecules has to be modeled. Based on statistical physics the molecular motion is described, among other formulations, by the Brownian motion. Physical quantities of molecular flows are described through spectral methods as transport equations for the probability density function over the phase space. The research topic focuses on the combination of flow modeling and the thermodynamic aspects of molecular and turbulent flows.

Rarefied Gas Dynamics and Trans-sonic Microflows

In the main field of research the frontiers of classical flow descriptions are investigated. High Knudsen numbers lead to a molecular, non-continuous fluid behavior. As a consequence, high Knudsen numbers deny the description of a flow by a continuous approach and additional statistical models have to be defined. In this case, a quasi-continuous transport model for dispersed systems based on transport equations for statistical moments is used.

A further example is the relation between flow behavior and Reynolds number. High Reynolds numbers result in the flow leaning away from a laminar and towards a turbulent behavior. When critical velocities with very low specific shear forces are reached, the stability of laminar flows disappears and a transient turbulent flow is developed. Finally, for high Mach numbers we no longer speak about incompressible, but compressible flows. The scale-independent investigation of the interaction of these three dimensionless values is one of the main scientific fields of research in the domain of thermofluid dynamics.

Computational Particle-in-Cell modelling for Plasma Flow

Plasma is the most abundant state of matter in the universe, it consist of ionized atoms or molecules and free electrons. Compared to ordinary matter it has some special properties, among other there exist long-ranging attraction and repulsion of charges through electrostatic forces, from which a verity of other fascinating effects emerge. Next to the experimental observation and measuring of plasma in laboratory settings exist the computational simulation of plasma using a variety of methods, one of which is the modeling as fluid using magneto-hydrodynamics.

Another method is the so called Particle-in-Cell method, which uses discrete particles moving on trajectories which are influenced by electro-magnetic fields computed on an numerical grid and collisions that may occur with other particles. Thus this method is of statistical nature, which requires the averaging of a multitude particles over several simulation time steps to acquire macroscopic properties like the conductivity of the plasma. Thereby compared to other methods, using particles to simulate plasma is computational expansive, however, it allows for a more precise view on the plasma behavior and its properties. In continuum approaches like magneto-hydrodynamics properties like the conductivity are prescribed to the simulation using theoretical model, while in the Particle-in-Cell method the property emerges from the distribution and state of the particles.
Using in-house developed open-source software, the Particle-in-Cell method is used for the simulation of electric discharge in plasma devices like thermal electric arc-jet thrusters. Which allow for a study on the behavior of the arc and consequential development of more accurate models for the simulation with different computational methods. Additionally, the study of the motion of charged species in magnetic fields bears the potential to gain new insights into the to this day not completely understood behavior of electrons in hall thrusters. Here, electrons move in higher numbers across magnetic field lines, than can be explained by classical theories.

Electric Propusion Systems for Space Transport

The present situation of space exploration calls for missions beyond the moon and for such missions, chemical propulsion is not a viable option, except for the case of launch vehicles where high thrust is required. Functionally, the inability of chemical propulsion systems to achieve higher exhaust velocities is due to limitation in the maximum tolerable temperature in the combustion chamber and to avoid excessive heat transfer to the walls.

Both these limitations can be overcome by use of electric propulsion, which can be defined as the acceleration of gases for propulsion by electrical heating and/or by electric and magnetic volume forces. The magnetoplasmadynamic (MPD) thrusters have the unique capability, among all other developed electric propulsion systems, of processing megawatt power levels in a simple, small and robust device, producing thrust densities as high as 10µ N / m2.
These features render it an attractive option for high energy deep space missions requiring higher thrust levels than other electric thrusters. The specific impulse of a self-field MPD thruster is related to the parameter beta (the square of the discharge current divived by the mass flow rate), which is often used to characterize MPD thruster performance. High value of beta correspond to predominantly electromagnetic acceleration, and provide higher values of specific impulse. Low values of beta correspond to predominantly electrothermal acceleration, and lower values of specific impulse. MPD efficiency typically increases with increasing beta, but this also leads to strong numerical instabilities. This project deal with the modeling of the MPD thruster through a new approach, which consist to solve the compressible MHD equations in the density-based compressible flow solver platform available in the open source CFD package OpenFOAM. The main objectives of this project is to understand the complex nature of the coupled electromagnetic and gasdynamic acceleration processes and the effects of relevant flow-field parameters which are otherwise quite hard to analyse with experiments.

Turbulence Modeling: Boundary Layers and Scale Transitioning

Thanks to numerous technical studies the physical law of periodic flow instability in fluid flows with high Reynolds numbers is well-known. The laminar character (stream lines positioned in laminar layers) is destroyed by perturbations, which diffuse from the wall through the complete flow domain. The change from a steady laminar stream to an unsteady turbulent flow is defined as transient.

The transient behavior in turbulent flows is investigated by modeling the velocity correlations in the fluid. Statistical models are used to describe the turbulent momentum and energy diffusion inside the fluid flow. Turbulence models based on this method are called eddy-diffusivity models. The velocity correlations are modeled by an increased viscosity diffusion term. Alternative models are based on transport equations for the Reynold-averaged velocity-correlation tensor (RANS), an approach called Reynolds-averaged Navier-Stokes simulation. The models mentioned above describe the unsteady behavior through averaged steady state transport equations. Current methods use unsteady transport equations describing the diffusion and convection of large vortices (eddies). This approach, which resolves small time and length scales, is used for the description of fluid/wall interactions, for averaging physical properties and in order to resolve shear stresses at the wall.
Both the convection and the diffusion processes of mass, momentum and energy inside the computational domain must be described by discrete fluxes between the cell volumes. As a result, the influence of not directly calculated fluxes has to be described by so-called sub-grid scale-models (SGS), whose development represents the main research topic in computational modeling.