Rüdiger Schwarze

Mathematical Models and Numerical Schemes for the Simulation of Human Phonation

Acoustic data has long been harvested in fundamental voice investigations since it is easily obtained using a microphone. However, acoustic signals alone do not reveal much about the complex interplay between sound waves, structural surface waves, mechanical vibrations, and fluid flow involved in phonation. Available high speed imaging techniques have over the past ten years provided a wealth of information about the mechanical deformation of the superior surface of the larynx during phonation. Time-resolved images of the inner structure of the deformable soft tissues are not yet feasible because of low temporal resolution (MRI and ultrasound) and x-ray dose-related hazards (CT and standard x- ray). One possible approach to circumvent these challenges is to use mathematical models that reproduce observable behavior such as phonation frequency, closed quotient, onset pressure, jitter, shimmer, radiated sound pressure, and airflow. Mathematical models of phonation range in complexity from systems with relatively small degrees of freedom (multi-mass models) to models based on partial differential equations (PDEs) mostly solved by finite element (FE) methods resulting in millions of degrees-of-freedom. We will provide an overview about the current state of mathematical models for the human phonation process, since they have served as valuable tools for providing insight into the basic mechanisms of phonation and may eventually be of sufficient detail and accuracy to allow surgical planning, diagnostics, and rehabilitation evaluations on an individual basis. Furthermore, we will also critically discuss these models w.r.t. the used geometry, boundary conditions, material properties, their verification, and reproducibility.

Modelling of unsteady electromagnetically driven recirculating melt flows

A numerical model for the recirculating flow of an electromagnetically stirred iron melt in a cylindrical induction furnace crucible is presented. Due to the parameters of the problem, the full set of magnetohydrodynamic flow equations decouples into magnetic and hydrodynamic parts. The diffusion approach of the magnetic vector potential describes the magnetic part of the model. The hydrodynamic part of the model is based on the unsteady ensemble-averaged Navier–Stokes equations in conjunction with a Reynolds stress turbulence model. Such an approach is commonly termed the unsteady Reynolds averaged approach. Here the influence of the electromagnetic field is included by means of a Lorentz force density.The diffusion equation is solved by a finite-element method. The Lorentz force density in the melt can be deduced from the results. Then the unsteady Reynolds averaged equations are solved by the finite-volume method.The results of the unsteady Reynolds averaged approach are analysed and compared to the results of the steady Reynolds averaged equations of the flow under consideration and to experimental results obtained from other studies. It is found that the toroidal vortex pair, which is the dominating structure within the flow, interacts by intermittent streamline connections.

Numerical simulation of fluid flow and disperse phase behaviour in continuous casting tundishes

A new Euler-Lagrange model of steel melt flows including dispersed secondary phases in continuous-casting tundishes is presented. The system of fundamental equations for the flow field is closed by different turbulence models. The calculation of tundish flows and a comparison with experimental results show that the flow fields of the steel melt and the behaviour of the dispersed secondary phases in the melt are described adequately by the model. However, the quality of the results for the dispersed phase depends essentially on the choice of turbulence model. Criteria for deciding which turbulence model is best suited for a specific flow situation are suggested. These criteria are deduced from investigations of different tundish flows.

Model Investigations on the Stability of the Steel-Slag Interface in Continuous-Casting Process

In the continuous-casting mold, the mold powder in contact with the liquid steel surface forms a liquid slag layer. The flow along the steel-slag interface generates shear stress at the interface, waves, and leads to fingerlike protrusions of liquid slag into steel. Reaching a critical flow velocity and thereby shear stress, the protrusions can disintegrate into slag droplets following the flow in the liquid steel pool. These entrained droplets can form finally nonmetallic inclusions in steel material, cause defects in the final product, and therefore, should be avoided. In the current work, the stability of a liquid-liquid interface without mass transfer between phases was investigated in cold model study using a single-roller driven flow in oil-water systems with various oil properties. Applying the similarity theory, two dimensionless numbers were identified, viz. capillary number Ca and the ratio of kinematic viscosities ν1/ν2, which are suitable to describe the force balance for the problem treated. The critical values of the dimensionless capillary number Ca* marking the start of lighter phase entrainment into the heavier fluid, are determined over a wide range of fluid properties. The dimensionless number ν1/ν2 was defined as the ratio of kinematic viscosities of the lighter phase ν1 and heavier phase ν2. The ratios of kinematic viscosities of different steel-slag systems were calculated using measured thermophysical properties. With the knowledge of thermophysical properties of steel-slag systems, Ca* for slag entrainment as a function of v1/v2 is derived. Assuming no reaction between the phases and no interfacial flow, slag entrainment should not occur under the usual casting conditions.

Numerical study of effects of pour box design on tundish flow characteristics

Abstract In the paper, the effects of special pour box design on tundish flow characteristics are investigated with the help of computational fluid dynamics. The numerical model is based on an Eulerian–Lagrangian approach for melt flow and non-metallic inclusion behaviour, respectively. For a prototypical twin strand tundish configuration, basic features of the mean tundish flow, residence time distributions and parameters of the melt history are discussed. It is shown that the pour box design is not only of importance for the tundish flow field but also of significance for processes of secondary metallurgy.

Experimental and numerical investigation of a gearless one-motor contra-rotating fan

A gearless one-motor concept for contra-rotating fans is presented in this article. The rotors are mounted to an electric motor using only one shaft. The coupling between both rotors is realised by utilising the conservation of angular momentum. The contra-rotating fans has a diameter of 200 mm at a design speed of 2100 min−1 for the first stage and 1200 min−1 for the second stage. It has been designed and investigated through a series of experiments by the Institute of Air Handling and Refrigeration in Dresden. The performance map and 2D particle image velocimetry measurements have been conducted. Numerical models for 3D quasi-steady state and transient simulations have been implemented and carried out by the Institute of Mechanics and Fluid Dynamics. The results show a good agreement between the quasi-steady, the transient simulations and the experiment. However, when close to stall, the time-resolved simulations show a superior performance compared with steady-state computations.

Influence of drag closures and inlet conditions on bubble dynamics and flow behavior inside a bubble column

ABSTRACT In this paper, the hydrodynamics of a bubble column is investigated numerically using the discrete bubble model, which tracks the dispersed bubbles individually in a liquid column. The discrete bubble model is combined with the volume of fluid approach to account for a proper free surface boundary condition at the liquid–gas interface. This improves describing the backflow region, which takes place close to the wall region. The numerical simulation is conducted by means of the open source computational fluid dynamics library OpenFOAM®. In order to validate the numerical model, experimental results of a bubble column are used. The numerical prediction shows an overall good agreement compared to the experimental data. The effect of injection conditions and the influence of the drag closures on bubble dynamics are investigated in the current paper. Here, the significant effect of injection boundary conditions on bubble dynamics and flow velocity in the studied cavity is revealed. Moreover, the impact of the choice of the drag closure on the liquid velocity field and on bubble behavior is indicated by comparing three drag closures derived from former studies.

Investigation of the Gas‐Liquid Flow in a Stopper‐Rod Controlled SEN

The behaviour of two-phase gas-liquid flows in a stopper-rod controlled submerged entry nozzle (SEN) is investigated in water model experiments. The observed two-phase flow patterns can be classified into either bubble coring or bubbly slug. The scaling of the two-phase flows by means of similarity parameters is discussed. In the experiments, it is found that the liquid flow rates depend strongly on the two-phase flow patterns. Additionally, the influence of swirl on the flow patterns is investigated in detail. It is shown that swirl has a marked impact on the transition from bubble coring to bubbly slug. Finally, an estimation of the two-phase argon-steel flow patterns in industrialscale SEN flows is given.

Numerical and Experimental Modeling of the Recirculating Melt Flow Inside an Induction Crucible Furnace

In the paper, a new water model of the turbulent recirculating flow in an induction furnace is introduced. The water model was based on the principle of the stirred vessel used in process engineering. The flow field in the water model was measured by means of particle image velocimetry in order to verify the model’s performance. Here, it is indicated that the flow consists of two toroidal vortices similar to the flow in the induction crucible furnace. Furthermore, the turbulent flow in the water model is investigated numerically by adopting eddy-resolving turbulence modeling. The two toroidal vortices occur in the simulations as well. The numerical approaches provide identical time-averaged flow patterns. Moreover, a good qualitative agreement is observed on comparing the experimental and numerical results. In addition, a numerical simulation of the melt flow in a real induction crucible furnace was performed. The turbulent kinetic energy spectrum of the flow in the water model was compared to that of the melt flow in the induction crucible furnace to show the similarity in the nature of turbulence.

Mathematical Modeling of Molten Salt Electrolytic Cells for Sodium and Lithium Production

Sodium (Na) and Lithium (Li) are produced using molten salt electrolysis. The electrochemistry of the electrolyte is well-researched; however, there are benefits to understanding the melt flow and implications on it for cell design modifications. The basic configuration of alkali metal cells is the Downs cell. This consists of a central anode surrounded by a cathode, and this geometry was the basis for this mathematical modeling study. The behavior of gas bubbles in molten electrolyte was studied in both Na and Li cells through the use of computational fluid dynamics (CFD) techniques. The distance between the anode and the cathode was varied in the CFD model to ascertain whether strong circulatory flows would change significantly in the cell. The standard k-e turbulence model was used to mimic turbulent flow, and a two-way coupled Discrete Phase Model (DPM) was adopted to simulate flotation behavior of chlorine bubbles and liquid metal droplets. The liquid metal distribution on the free surface was predicted using the Volume of Fluid (VOF) multi-phase model.