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Magnetohydrodynamic flows

My main field of research has been the numerical modeling of magnetohydrodynamic (MHD) flows. In particular, the development of one-point turbulence models (K-epsilon, K-omega, Reynolds-stress closures, etc.) which can account for magnetic dissipation in a physically sensible way. I started these activities in February of 1996, with the beginning of my thesis at the Faxén Laboratory (KTH, Stockholm) under the direction of Professors Fritz Bark and Said Zahrai. The practical application we had in mind was continuous casting of steel and the project was sponsored by ABB Automation Systems in Västeras, Sweden, a leading world-wide supplier of electromagnetic devices and process-control equipment for the steel industry.

Magnetic fields are used in many important materials processing applications. In casting of steel, for example, static or traveling magnetic fields are used for stirring the liquid metal, or for breaking and damping the flow in the casting mold. In crystal growth applications magnetic fields are used to control thermal convection. Physical experiments in liquid metals are very complicated, and it is impossible to "see" or even measure in detail what is going on in a liquid metal flow. Numerical modeling is therefor a very important tool both for scientists and process engineers.

The numerical modeling of magnetohydrodynamic flows involves a few special challenges. Three of these will be discussed in more detail. First of all, the fluid flow itself is counter-acted by magnetic Lorentz forces. Before we can compute the Lorentz forces, we need to compute the electrical currents in the fluid. Secondly, many industrial MHD flows are turbulent. Since the magnetic field will damp and modify also the turbulence, we need to develop new statistical turbulence models which capture these effects. Finally, the electrical currents in an MHD flow tend to close in very thin boundary layers, the properties of which tend to control also the bulk flow. The numerical resolution of these boundary layers is very costly, even for relatively modest magnetic fields.

Follow the links below for more specific information:


Peer-reviewed journals

  1. O. Widlund, S. Zahrai and F. H. Bark (1998), "Development of a Reynolds stress closure for modeling of homogeneous MHD turbulence", Physics of Fluids 10, pp. 1987-1996. (Abstract)

  2. O. Widlund, S. Zahrai and F. H. Bark (2000), "Structure information in rapid distortion analysis and one-point modeling of axisymmetric magnetohydrodynamic turbulence", Physics of Fluids 12, pp. 2609-2620. (Abstract)

  3. O. Widlund (2001), "Modeling anisotropic MHD turbulence in simulations of liquid metal flows", Magnetohydrodynamics 37, pp. 3-12. (Abstract)

  4. O. Widlund (2003), "Wall functions for numerical modeling of laminar MHD flows", European J Mechanics B/Fluids 22, pp. 221-237. (Abstract)

Conference proceedings   

  1. O. Widlund, S. Zahrai and F. H. Bark (1999), "On MHD turbulence models for simulation of magnetic brakes in continuous steel casting processes", in Transfer Phenomena in Magnetohydrodynamic and Electroconducting Flows, eds. A. Alemany, Ph. Marty, J. P. Thibault. Selection of full-length articles, 3rd Int. PAMIR Conference, Aussois, France, Sept. 1997. Kluwer Academic Publishers, Dordrecht.

  2. O. Widlund and G. Tallbäck, "Modeling of anisotropic turbulent transport in simulations of liquid metal flows in magnetic fields". 3rd Int. Symposium on Electromagnetic Processing of Materials, EPM2000, April 2000, Nagoya, Japan. ISIJ. (PDF download, 70 KB)

  3. O. Widlund, "Modeling anisotropic MHD turbulence in simulations of liquid metal flows". 4th Int. PAMIR Conference, Sept. 2000, Presqu'île de Giens, France. PAMIR.

  4. O. Widlund, "Using structure information in modeling of magnetohydro-dynamic turbulence". TSFP-2, 2nd Int. Symp. on Turbulence and Shear Flow Phenomena, June 2001, Stockholm, Sweden. KTH. (PDF download, 925 KB)

  5. O. Widlund, "Wall functions for numerical modeling of laminar MHD flows". 5th Int. PAMIR Conference, Sept. 2002, Ramatuelle, France. PAMIR.

Theses and reports   

  1. A Reynolds stress closure for magnetic dissipation of turbulence in liquid metals. "Licentiate of Technology" thesis (Swedish diploma: half-way Ph.D.). TRITA-MEK 99:1, KTH, Stockholm, 1999.

  2. Implementation of MHD model equations in CFX 4.3. Technical Report TRITA-MEK 2000:10, KTH, Stockholm, 2000. (PDF download, 750 KB)

  3. Modeling of magnetohydrodynamic turbulence. Ph.D. thesis, TRITA-MEK 2000:11, KTH, Stockholm, 2000. (Abstract and PDF download)