# Events

# Magin Seminar

**Cooled Pitot probe in air plasma jet. What do we measure?**

**Prof. Dr. Thierry Magin****Aeronautics and Aerospace Department **Von Karman Institute for Fluid Dynamics Belgium

**Abstract**

The aerothermodynamic environment of spacecraft entering into a planetary atmosphere can be reproduced in high enthalpy facilities such as the Plasmatron facility of the von Karman Institute for Fluid Dynamics, a 1.2MW inductively coupled plasma windtunnel. The total pressure in a plasma jet at temperatures of the order of 10,000 K can be measured by means of a water-cooled Pitot probe. We propose to study this measurement technique by means of numerical simulations. A magneto-hydrodynamic computational model for inductively coupled plasma flows allow us to examine three sources of departure of the stagnation point pressure measured by the probe from the total pressure computed theoretically: the viscous effect, the heat transfer to the probe, and the reference static pressure.

name: Vanessa Schiffers

kontakt-e-mail: schiffers@aices.rwth-aachen.de

# Steering Committee

# I³MS - Lukacova Seminar

## Prof. Dr. Maria Lukacova - Asymptotic Preserving IMEX Schemes for Singulary Perturbed Flows

Department of Mathematics, Johannes Gutenberg University Mainz

In this contribution we present our recent results on the second order asymptotic preserving well-balanced schemes for the Euler equations with the gravity force. In the case of low Mach number flows, which typically arise in geophysical applications, the flow has multiscale behaviour. Our aim is to present and analyse new well-balanced asymptotic preserving scheme that efficiently works for different Mach numbers, in particular also for weakly compressible regime. In order to efficiently resolve slow dynamics we split the whole nonlinear system in a stiff linear part governing the acoustic and gravity waves and a non-stiff nonlinear part that models nonlinear advection effects. For time discretization we use a special class of the so-called globally stiffly accurate IMEX schemes and approximate the stiff linear operator implicitly and the non-stiff nonlinear operator explicitly. Finite volume approximation with the central fluxes and the Rusanov or Lax-Friedrichs numerical fluxes is used for the spatial approximation of the linear and nonlinear subsystem, respectively. We prove theoretically that the methods are asymptotically consistent and asymptotic stable uniformly with respect to small Mach numbers and analyse their convergence rates in the singular limit when the model parameters tend to zero. This work has been obtained in the cooperation with G. Bispen, L. Yelash and S. Noelle, it has been supported by the German Grant Foundation (DFG) under LU 1470/2-3.

# EU Regional School - Saxena Seminar

## Prof. Dr. Saxena - Systematic Synthesis of Large Displacement Compliant Mechanisms: A Structural Optimization Approach

Compliant and Robotic Systems Laboratory

Indian Institute of Technology Kanpur, India

### Abstract

Topology optimization entails determining optimal material layout of a continuum within a specified design domain for a desired set of objectives. Irrespective of the parameterization used, material state of a point/sub-region/cell/finite-element should ideally toggle between ‘solid’ and ‘void’ states eventually leading to a well-defined optimized solution. In other words, material assignment must, ideally, be discrete.

Two parameterization schemes will be described – line element and honeycomb tessellation, both in context of synthesizing large displacement compliant continua. The latter could be monolithic (single-piece), partially compliant, or some of their members could physically interact via ‘contact.’ With line element parameterization, topology-size decoupling will be emphasized as in how it helps pose topology, shape and size optimization independent of each other. Furthermore, such a framework also helps in introducing, say, rigid members and pin joints within a network of flexible frames leading to the possibility of synthesizing partially compliant continua. As discrete material assignment is strictly adhered to, notwithstanding efficiency, the solitary choice of using a stochastic optimization approach also helps in rejecting ‘non-convergent’ (from the perspective of large displacement analysis) intermediate continua, which, otherwise, tends to impede the functioning of a gradient-based optimization algorithm. Co-rotational beam theory to model frames undergoing geometrically large displacements will be briefed followed by a Fourier Shape Descriptors based objective and a random mutation hill climber algorithm to synthesize ‘path-generating’ continua exemplifying large displacement compliant mechanisms.

In continuum parameterization, traditionally, each sub-region is represented by a single (or a set of) Lagrangian (e.g., triangular/rectangular) type finite element(s). With such parameterization however, numerous connectivity singularities such as checkerboards, point flexures, layering/islanding, right-angled notches and ‘blurred’ boundaries are observed, unless ‘additional’ filtering-type methods are used. Use of honeycomb tessellation will be described. As hexagonal cells provide edge-connectivity between any two contiguous cells, most geometric singularities get eliminated naturally. However, numerous ‘V’ notches persist at continuum boundaries which are subdued via a winged-edge data structure based boundary resolution scheme. Consequently, many hexagonal cells get morphed into concave cells. Finite element modeling of each cell is therefore accomplished using the Mean-Value Coordinate based shape functions that can cater to any generic polygonal shape. Overlaying negative circular masks are used to assign material states to sub-regions. Their radii and center coordinates are varied in a manner that material is removed from sub-regions lying beneath the masks so that remnant, unexposed sub-regions constitute a realizable continuum.

Honeycomb tessellation, boundary smoothing and Mean Value Coordinates based analysis, all pave way to synthesize Contact-aided Compliant Mechanisms (CCMs) with suitable modifications in the topology optimization formulation which will be highlighted. Augmented Lagrangian method along with active set constraints has been used for contact analysis. Synthesis of large displacement CCMs is exemplified via path generation. Self-contact between continuum subregions undergoing large deformation can also occur, a feature that could be used by such continua to assist them in performing special tasks, such as, attaining negative stiffness and static balancing. Contact analysis is extended to cater to deforming bodies. Numerous examples will be presented to showcase a variety of design features and highlight the ability of Contact-aided Compliant Mechanisms to achieve/accomplish complex kinematic tasks.

Lecture Material I

Lecture Material II

# I³MS - Spatschek Seminar

## Prof. Dr. Robert Spatschek - Stability and Failure of Frictional Interfaces: Generating Earthquakes on the Computer

Institute for Energy and Climate Research IEK-2, Research Center Jülich

Frictional processes are a natural feature of our daily life, yet their dynamics are not well understood. Recent experimental data have revealed that velocity strengthening friction, where frictional resistance increases with sliding velocity over some range, is a generic feature of such interfaces. Moreover, transitions between velocity weakening and strengthening regimes have recently been linked to slow fronts ("slow earthquakes"). Here we elucidate the importance of velocity strengthening friction by theoretically studying variants of a realistic friction model, all featuring identical logarithmic velocity weakening at small sliding velocities, but different high velocity behaviour. We find a dramatic influence on front velocity, event magnitude, dissipation and radiation rates. Additionally, we show that velocity strengthening can give rise to a new kind of frictional instability for sliding on a rigid substrate, which is related to interval vibrational high frequency excitations in the sliding object.