Guido Thömmes

NUMERICAL METHODS AND OPTIMAL CONTROL FOR GLASS COOLING PROCESSES

ABSTRACT In this paper, we discuss numerical and analytical approximations of radiative heat transfer equations used to model cooling processes of molten glass. Simplified diffusion type approximations are discussed and investigated numerically. These approximations are also used to develop acceleration methods for the iterative solution of the full radiative heat transfer problem. Moreover, applications of the above diffusion type approximations to optimal control problems for glass cooling processes are discussed.

A lattice Boltzmann method for immiscible multiphase flow simulations using the level set method

We consider the lattice Boltzmann method for immiscible multiphase flow simulations. Classical lattice Boltzmann methods for this problem, e.g. the colour gradient method or the free energy approach, can only be applied when density and viscosity ratios are small. Moreover, they use additional fields defined on the whole domain to describe the different phases and model phase separation by special interactions at each node. In contrast, our approach simulates the flow using a single field and separates the fluid phases by a free moving interface. The scheme is based on the lattice Boltzmann method and uses the level set method to compute the evolution of the interface. To couple the fluid phases, we develop new boundary conditions which realise the macroscopic jump conditions at the interface and incorporate surface tension in the lattice Boltzmann framework. Various simulations are presented to validate the numerical scheme, e.g. two-phase channel flows, the Young-Laplace law for a bubble and viscous fingering in a Hele-Shaw cell. The results show that the method is feasible over a wide range of density and viscosity differences.

A comparison of approximate models for radiation in gas turbines

Approximate equations for radiative heat transfer equations coupled to an equation for the temperature are stated and a comparative numerical study of the different approximations is given. The approximation methods considered here range from moment methods to simplified PN-approximations. Numerical experiments and comparisons in different space dimensions and for various physical situations are presented.

New Frequency-Averaged Approximations to the Equations of Radiative Heat Transfer

We develop new direction- and frequency-averaged approximations to the equations of radiative heat transfer in glass for optically thick, diffusive regimes. These approximations, which are based on the

Numerical investigation of a combined lattice Boltzmann-level set method for three-dimensional multiphase flow

\rm SP_N

Lattice Boltzmann simulation of depth-averaged models in flow hydraulics

approach given in [E. Larsen, G. Thommes, A. Klar, M. Seaid, and T. Gotz, J. Comput. Phys. 83 (2002), pp. 652--675], represent asymptotic corrections to the familiar Rosseland, or equilibrium diffusion, approximation. Numerical results for realistic problems in the simulation of radiative heat transfer in glass cooling confirm the accuracy and efficiency of the new approximations.

A combined lattice BGK/level set method for immiscible two-phase flows

We simulate rising bubbles using a hybrid lattice Boltzmann scheme based on the lattice BGK model coupled with the level set method (Thömmes et al., 2009. A lattice Boltzmann method for immiscible multiphase flow simulations using the level set method. Journal of Computational Physics). This method uses special boundary conditions at the interface between the two phases which realise the macroscopic jump conditions on the kinetic level and incorporate surface tension into the model. Previous experience with the approach has already demonstrated that it is feasible over a wide range of density and viscosity differences. We utilise this method to simulate the classical immiscible multiphase problem of rising bubbles driven by buoyancy forces. In particular, simulations with large density ratios are performed. The numerical results are compared with available reference solutions.

Numerical Methods for Radiative Heat Transfer in Diffusive Regimes and Applications to Glass Manufacturing

We apply a lattice Boltzmann method (LBM) for the simulation of depth-averaged models in flow hydraulics and dispersion of pollutants. The mathematical equations for these models can be obtained from the incompressible Navier–Stokes equations under the assumptions that the vertical scale is much smaller than any typical horizontal scale and the pressure is hydrostatic. The effects of bed slope, bed friction, Coriolis forces and wind stresses are also accounted for in our simulations. Our aim is to develop a simple and accurate representation of the source terms in order to simulate practical shallow water flows without relying on upwind algorithms or Riemann problem solvers. For the transport of pollutants, a depth-averaged convection–diffusion equation is used. We validate the algorithm in problems where analytical solutions are available. Furthermore, we test the algorithm in the case of a practical application by simulating the tidal flow and pollutant transport in the Strait of Gibraltar. The focus is to examine the performance of the LBM for irregular geometry with complex bathymetry. The method demonstrates its capability to capture the main flow features. Obviously, some of the conclusions in the current work are specific to the employed implementation of the LBM. For instance, the LBM in its implementation as described in the current study failed to approximate numerical solutions for hydraulic problems involving a Froude number larger than the unity.

Simplified P N approximations to the equations of radiative heat transfer and applications

We present a lattice Boltzmann method (LBM) for simulating immiscible multi-phase flows which is based on a coupling of LBM with the level set method. The computation of immiscible flows using the LBM with BGK collision operator is done separately in each of the fluid domains and coupled at the interface by an appropriate boundary condition. In this way we preserve sharp interfaces between different fluid phases. We apply a new interface condition that represents the fluid mechanical jump conditions at the interface in the kinetic LBM framework. The level set method is applied to compute the evolution of the interface between fluids. Numerical results demonstrate the applicability of the method even in the presence of large viscosity and density ratios.

Optimal boundary control of glass cooling processes

In this paper, different approaches for the numerical solution of radiative heat transfer problems in diffusive regimes are considered. We discuss asymptotic preserving schemes, domain decomposition methods and the development of improved diffusion approximations. Problems related to glass manufacturing processes are numerically investigated.