Karl-Hermann Tacke

Characteristics of round vertical gas bubble jets

Radial and axial profiles of gas concentration and bubble frequency have been measured for vertical gas bubble jets in the systems air/water, helium/water, and nitrogen/mercury using an electroresistivity probe. Gas velocities have been determined in the air/water system. All radial profiles were close to Gaussian. An integral model was applied to calculate axial distributions theoretically. Entrainment coefficients were determined for the experimental conditions. Axial profiles were correlated also in nondimensional representations. The bubble frequencies were used to compute local and average values of bubble size. Jet expansion and bubble size were found to depend considerably on the physical properties of the system.

Flow fields in electromagnetic stirring of rectangular strands with linear inductors: Part I. theory and experiments with cold models

A model is presented to compute the electromagnetic force fields and fluid flow fields in electromagnetic stirring of continuously cast strands with rectangular cross-section. The model involves the solution of the Maxwell equations, the Navier-Stokes equations, and the transport equations for the turbulence characteristicsk and e. The procedure of depth-averaging is applied in the treatment of several three-dimensional flows. Experiments were performed to check the computations using mercury as fluid. The spatial distribution of the magnetic induction and of the force density was determined for the laboratory inductor used in the stirring experiments. The flow velocity was measured photographically or with a drag probe, respectively. The agreement between experimental and theoretical data was found to be within 25 pct. It is concluded that the theory is sufficiently reliable to predict the flow fields in electromagnetic stirring of steel strands. In Part II of this paper the model is applied to analyze stirring situations in continuous casting of steel.

Flow fields in electromagnetic stirring of rectangular strands with linear inductors: Part II. computation of flow fields in billets, blooms, and slabs of steel

The model presented in Part I of this series of papers is used to compute flow velocities in the longitudinal stirring of steel blooms and billets, and in the horizontal stirring of steel slabs. In longitudinal stirring of blooms and billets the reverse flow is on the side of the strand opposite to the inductor. The effects of penetration depth of the electromagnetic force, of the force itself, of the length of the stirrer, and of the width of the liquid core were determined. In horizontal stirring of slabs the reverse flow takes place outside of the stirrer region, forming the so-called butterfly stirring pattern. The characteristics of this flow field depend to a considerable extent on the width of the stirrer. The effects of stirrer width, of thickness of the liquid core, of force and of width of the slab were elucidated. The maximum velocities in both types of stirring are represented as simple formulae.

Generalized enthalpy method for multicomponent phase change

Phase change problems with coupled transport of heat and species occur in solidification and other fields of materials processing. This article describes a new formulation for numerical modeling of coupled phase transformation. The technique is an extension of the conventional heat diffusion enthalpy method and uses the control volume approach. Numerical time-steps are separated into a transport section which updates extensive molar quantities from flux expressions and balance equations, and a thermodynamic section which computes intensive quantities from state functions through local entropy maximization. Heat and species transport are handled in a symmetrical manner with flux expressions from irreversible thermodynamics. The scheme is general enough to cover an unrestricted number of species and phases in various systems and is appropriate for three-dimensional modeling. Applications of the algorithm are illustrated by computations on isomorphous, eutectic, and peritectic binary systems; a simplified dendritic growth problem with coupled heat and species transport is also presented.