Plenary Lecture

Numerical Simulations of Incompressible Flows Using the Finite-Element-Method

Associate Professor Karel Frana
Technicka univerzita v Liberci
Katedra energetickych zarizeni (KEZ)
Studentska 2
461 17, Liberec 1
Czech Republic
E-mail: Karel.Frana@seznam.cz

Abstract: A numerical simulation of fluid flows is an essential part of flow investigations currently emerged in the wide range of technical applications. Various combinations of the mathetical approaches have been design, investigated and successfully applied in the computational codes in order to achieve the effectiveness and robustness of computational methods. For instance, powerful stabilization techniques based on the pressure-stabilized Petrov-Galerkin and streamline Petrov-Galerkin approaches are widely used in the finite-element codes in order to effectively suppress any numerical instabilities and oscillations that can appear during calculation processes. To solve the mathematical equation system of the incompressible fluid flow, for instance, a splitting scheme is commonly used that yields an implicit Poisson-type equation for the pressure and an explicit predictor-corrector step for the velocity calculation, respectively.
In the frame of this invited paper, a finite-element code partially based on the previous mentioned methods will be introduced. This code was successfully validated on several test cases including a transient channel flow or a flow driven by a rotating magnetic field in the laminar Stokes flow regime. The convergence study proved the second order accuracy in time and space. In the transient flow regime, this code was validated by means of the linear stability analysis carried out in the flow driven by the rotating and traveling magnetic fields. Results obtained were in good agreement to results observed experimentally as well as numerically. Numerical results of the magnetically induced flow were also compared with experiments and good agreement in the mean velocity field and turbulent properties was found.
The mathematical model was implemented on top of the multi-grid library that provides data structures and procedures for grid handling and adaptation. The parallelization is based on the grid partitioning where the grid generated by an external grid generator is decomposed into a specific number of partitions using the MeTiS package. This parallel implementation was tested on the simple flow problem and the excellence effectiveness of the parallelization process (depended on the local computational station) was demonstrated.
The computational finite-element-code have been used for numerical studies of the unsteady flows driven by a rotating and traveling magnetic fields in a axisymmetrical and non-axisymmetrical containers. By means of RMF flow studies in the cylindrical container, important roles of the Taylor-Gotler type vortices on the formation of mixing processes inside of the container was revealed and studied in detail. For result verifications, mean velocity profiles at different moderate Taylor numbers (proportional to Reynolds numbers) were confronted by experimental results and good agreement within a tolerance of 3 % was found even for energy spectra. In the flow study of the non-axisymetrical container, similar flow features were observed in axisymmetrical and non-axisymmetrical containers, however, we did also find differences e.g. in the velocity field distribution.
In last several months, the finite-element code was also significantly extended about new turbulent models based on a hybrid URANS/LES approach. This promising method provides nowadays the best approach to the turbulence modeling in numerical simulations. The preliminary simulations of unsteady turbulent flows past a cylinder calculated using the Detached Eddy Simulation approach were carried out and results obtained were in good agreement to experimental results.

Brief Biography of the Speaker:
Assoc. Prof. Karel Frana Ph.D. is working at the Technical University of Liberec, Department of Power Engineering Equipment Czech Republic. He provides lectures for numerical methods in the Thermodynamics and Fluid Mechanics and he is supervisor of Ph.D. students at the same university. Simultaneously, he is active as a guest in several German research projects at the Technical University in Dresden in Germany.
In 1999, he received the Master Degree by the Technical University of Liberec, from 2001 to 2005; he worked as a research assistant at the Technical University in Dresden, Institute of Aerospace Engineering, Germany. In 2004, he received Ph.D. by Technical University of Liberec. Since 2005, he has been working at TU Liberec, at the Department of Power Engineering Equipment.
In 2006, he carried out several lectures at the Jiaotong University in China. In 2007 he visited as a guest the Technical University in Vienna, Austria and had several lectures connected to the topic of numerical methods in CFD. Meanwhile, he has been regularly a guest at the Technical University in Dresden in the frame of Collaborative research SFB 609.
Mr. Frana works in 2 domestic and 1 international (EU) projects. He is interested for numerical methods in the Fluid Mechanics and Thermodynamics, visualization techniques, Finite-Element Methods (FEM), parallelization and grid adaptations. He has developed a finite-element code that is used by Ph.D. students for numerical simulations of the incompressible turbulent flow.
In the last five years, he has 3 papers in cited journals e.g. Physics of Fluids, European Journal of Mechanics Fluids B, Journal of Visualization, more than 8 papers in the other journals e.g. Journal of Magnetohydrodynamics, Astronomical Notes etc., about 20 paper contributions on the international conferences.
He is a member of the editorial board of the Journal of Applied Science in Thermodynamics and Fluid Mechanics regularly published by the Technical University in Liberec Czech Republic (http://astfm.tul.cz).
To find more about personal facts or interest, please, visit http://orion.kez.tul.cz/frana