Theoretische, numerische und experimentelle Untersuchungen tropfenförmiger Fluidschichten auf elektrisch hochbelasteten Isolierstoffoberflächen

• Applicants: Professor Dr.-Ing. Martin Oberlack; Professor Dr.-Ing. Thomas Weiland
• Subject Area: Fluid Mechanics
• Term: from 2009 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 138260376

• Final Report Year: 2015

Final Report Abstract

The goal of this project was to develop an efficient simulation approach for the numerical modeling of multiphase fluid flow under the influence of strong electric fields. This research was originally motivated by a practical problem arising in high-voltage engineering. Therein, rain droplets gathering on the surface of high-voltage insulators give rise to partial electrical discharges. This leads to damage of the device associated with the loss of its surface hydrophobicity and insulation quality. The frequency and strength of electrical discharges depends on droplet’s shape while the latter is dynamically changing under the influence of the time harmonic electric field. Thus, in order to understand the effect of water droplets on high-voltage insulators, it is necessary to investigate first the fluid dynamical motion of water droplets driven by strong, time dependent electric fields. From the numerical point of view, this task represents a coupled multiphysical problem involving the solution of Navier-Stokes equation for the droplet dynamics as well as the numerical simulation of transient low frequency electric fields in the vicinity of the droplet. The coupled simulation procedure poses several issues which make the modeling task extremely difficult. These issues may be summarized as follows: (i) The spatial resolution of phase boundaries in multiphase flow simulations is very critical for the numerical accuracy of the fluid dynamical solver. Hereby, an extremely fine mesh is needed when conventional discretization methods are used. A much more accurate, alternative discretization approach based on a high-order Discontinuous Galerkin method for Navier-Stokes equation is developed in the framework of a DFG proposal of the Fachgebiet für Strömungsdynamik. (ii) A physics based model for the dynamics of the contact line between droplet and insulating layer is needed. It must take into account the effect of electric fields as well as the hydrophobicity of the insulator surface. The fluid dynamical part of the joint research (issues (i) and (ii), respectively) was performed at the Fachgebiet für Strömungsdynamik. (iii) Similarly to the fluid dynamical solver, also for the electric field solution an extremely high spatial resolution of the phase boundary (droplet surface) is required. This is because electric forces are basically surface forces acting primarily at the air-water interface. Thus, the overall numerical field accuracy is closely related to the quality of the local approximation of the droplet surface by the computational mesh in the electric field simulation. (iv) To improve numerical accuracy it is, furthermore, desirable to apply specialized numerical models for the field singularity arising at the contact line between water droplet, air and insulating layer. The presence of this singularity affects the contact line dynamics and thus the overall fluid dynamical motion of the water droplet.

Publications

• Modeling and simulation of electric field problems with moving boundaries, 2nd International Conference on Computational Engineering (ICCE 2011), Oktober 2011, Darmstadt
  A. Fröhlcke, H. Songoro, E. Gjonaj, T. Weiland
  
• Modeling of field singularities at dielectric edges using grid based methods, Adv. Radio Sci. 9 (2011), 39-44
  C. Classen, E. Gjonaj, U. Römer, R. Schuhmann, T. Weiland
  
• Some extensions to the DGM for electromagnetic field problems, Workshop on Discontinuous Galerkin Methods in Computational Electromagnetics, Amsterdam, Netherlands, May 2011
  E. Gjonaj
  
• A boundary conformal Discontinous Galerkin approach for electro-quasistatic problems, Bastiaan Michielsen (Eds.) and Jean-René Poirier (Eds.), Scientific Computing in Electrical Engineering (SCEE 2010): The European Consortium for Mathematics in Industry, 16 (2012), 153-161, Springer-Verlag, Berlin/Heidelberg
  A. Fröhlcke, E. Gjonaj, T. Weiland
  
• A boundary conformal Discontinuous Galerkin approach for transient electro-quasistatic problems with moving boundaries, International Conference on Electromag-netics in Advanced Applications (ICEAA 2012), Cape Town, South Africa (2012), 606-609
  A. Fröhlke, E. Gjonaj, T. Weiland
  
• Electromagnetic field singularities at straight re-entrant edges, U.R.S.I. Kleinheubacher Tagung, Miltenberg, September 2012
  O. Ivanyshyn, E. Gjonaj, T. Weiland
  
• A boundary conformal Discontinuous Galerkin method for electromagnetic field problems on Cartesian grids, PhD Thesis, (2013), TU Darmstadt
  A. Fröhlcke
  
• Computation of singular electromagnetic fields using a hybrid DG-FEM method, Symposium on Electromagnetic Theory (EMTS 2013), Hiroshima, Japan (2013), pp. 745-748
  O. Ivanyshyn, E. Gjonaj, T. Weiland
  
• A boundary conformal discontinuous Galerkin approach for electroquasistatic field problems on Cartesian grids, Int. J. Comp. Sci. Eng., Vol. 9, Issue 5/6 (2014), pp. 478-483
  A. Fröhlke, E. Gjonaj, T. Weiland