The Lattice-Boltzmann-model is analyzed with regard to application to numerical solution of flow acoustic problems. In the first part of this study the description of sound wave propagation by common variants of the Lattice-Boltzmann-model is examined by calculation of phase velocity and effective viscosity for sound waves. Schemes with nine velocities in two dimensions and nineteen velocities in three dimensions are considered. For each of these a single relaxation time model (LBGK-model) and a multiple relaxation time model (MRT) is investigated. All schemes exhibit an almost isotropic error in phase speed of sound waves. With a spatial resolution of 10 or 30 grid spacings per wavelength the deviation of phase speed is less than 1 % or 0.1 %, respectively. The dissipation of sound waves is not simulated correctly by LBGK-models since there the bulk viscosity is fixed to the shear viscosity. Apart from that there is only very little numerical dissipation. The dissipation error therefor is negligible in the audible frequency range in air as long as the simulation volumes do not become very large, i.e. much more than some hundred wavelengths. The MRT-models allow to adjust the bulk viscosity by a suitable choice of relaxation parameters. However, if the bulk viscosity is set to a realistic value, stability of the scheme requires free relaxation parameter values which are close to the relaxation parameters that determine the viscosities. Then the gain in stability of MRT-models compared to LBGK-models is lost to some extent. All schemes considered here are able to reproduce the effect of sound wave convection in homogeneous background flows. Although additional numerical errors arise in transport coefficients, the overall errors are of the same order of magnitude as in the case with zero background flow and are not critical in practical applications. In the second part of the work numerical experiments are described which demonstrate the coupling of the flow- and sound field. Three test cases are considered: Sound generation by a single vortex interaction with the leading edge of a semi-infinite flat plate, sound generation by a grazing flow over a partially covered cavity and instationary flow around a half-cylinder with an attached wedge tail. The first test case is simulated in two dimensions with a self-written program. The sound calculated directly is compared to prediction based on an acoustic analogy. The observed amplitudes of the radiated sound agree quantitatively well for all flow and eddy velocities considered here. This implies, that the coupling of the sound and flow field is correct. In the case of the cavity the flow is computed in two dimensions with a self-written program as well as in three dimensions with the commercially available program PowerFLOW. The simulated pressure fluctuations in the cavity are compared to results of a wind tunnel experiment. Good agreement between simulation and wind tunnel experiment is found. The instationary flow around a half cylinder with an attached wedge tail is simulated in three dimensions using PowerFLOW. The radiated sound cannot be captured with PowerFLOW because of insufficient quantization of fluid density. However, pressure fluctuations on the surface of the body exhibit good agreement with the result of a wind tunnel test. Summarizing the results of this work it can concluded, that the Lattice-Boltzmann-model is well suited to numerical solutions of flow acoustic problems.

The Lattice-Boltzmann-model is analyzed with regard to application to numerical solution of flow acoustic problems. In the first part of this study the description of sound wave propagation by common variants of the Lattice-Boltzmann-model is examined by calculation of phase velocity and effective viscosity for sound waves. Schemes with nine velocities in two dimensions and nineteen velocities in three dimensions are considered. For each of these a single relaxation time model (LBGK-model) and a multiple relaxation time model (MRT) is investigated. All schemes exhibit an almost isotropic error in phase speed of sound waves. With a spatial resolution of 10 or 30 grid spacings per wavelength the deviation of phase speed is less than 1 % or 0.1 %, respectively. The dissipation of sound waves is not simulated correctly by LBGK-models since there the bulk viscosity is fixed to the shear viscosity. Apart from that there is only very little numerical dissipation. The dissipation error therefor is negligible in the audible frequency range in air as long as the simulation volumes do not become very large, i.e. much more than some hundred wavelengths. The MRT-models allow to adjust the bulk viscosity by a suitable choice of relaxation parameters. However, if the bulk viscosity is set to a realistic value, stability of the scheme requires free relaxation parameter values which are close to the relaxation parameters that determine the viscosities. Then the gain in stability of MRT-models compared to LBGK-models is lost to some extent. All schemes considered here are able to reproduce the effect of sound wave convection in homogeneous background flows. Although additional numerical errors arise in transport coefficients, the overall errors are of the same order of magnitude as in the case with zero background flow and are not critical in practical applications. In the second part of the work numerical experiments are described which demonstrate the coupling of the flow- and sound field. Three test cases are considered: Sound generation by a single vortex interaction with the leading edge of a semi-infinite flat plate, sound generation by a grazing flow over a partially covered cavity and instationary flow around a half-cylinder with an attached wedge tail. The first test case is simulated in two dimensions with a self-written program. The sound calculated directly is compared to prediction based on an acoustic analogy. The observed amplitudes of the radiated sound agree quantitatively well for all flow and eddy velocities considered here. This implies, that the coupling of the sound and flow field is correct. In the case of the cavity the flow is computed in two dimensions with a self-written program as well as in three dimensions with the commercially available program PowerFLOW. The simulated pressure fluctuations in the cavity are compared to results of a wind tunnel experiment. Good agreement between simulation and wind tunnel experiment is found. The instationary flow around a half cylinder with an attached wedge tail is simulated in three dimensions using PowerFLOW. The radiated sound cannot be captured with PowerFLOW because of insufficient quantization of fluid density. However, pressure fluctuations on the surface of the body exhibit good agreement with the result of a wind tunnel test. Summarizing the results of this work it can concluded, that the Lattice-Boltzmann-model is well suited to numerical solutions of flow acoustic problems.

Liquid film flow is an important flow type in many applications of process engineering. For supporting experiments, theoretical and numerical investigations are required. The present state of the art is to model the liquid film flow with Navier--Stokes-based methods, whereas the lattice Boltzmann method is employed here. The final model has been developed within this treatise by means of a two-phase flow and a heat transfer model, and boundary and initial conditions. All these sub-models have been applied to simple test cases. It could be found that the two-phase model is capable of solving flow phenomena with a large density ratio which has been shown impressively in conjunction with wall boundary conditions. The heat transfer model was tested against spectral method results with a transient non-uniform flow field. It was possible to find optimal parameters for computation. The final model has been applied to steady-state film flow, and showed very good agreement to OpenFOAM simulations. Tests with transient film flow demonstrated that the model is also able to predict these flow phenomena. / Flüssigkeitsfilmströmungen kommen in vielen verfahrenstechnischen Prozessen zum Einsatz. Zur Unterstützung von Experimenten sind theoretische und numerische Untersuchungen nötig. Stand der Technik ist es, Navier--Stokes-basierte Modelle zu verwenden, wohingegen hier die Lattice-Boltzmann-Methode verwendet wird. Das finale Modell wurde unter Verwendung eines Zweiphasen- und eines Wärmeübertragungsmodell entwickelt und geeignete Rand- und Anfangsbedingungen formuliert. Alle Untermodelle wurden anhand einfacher Testfälle überprüft. Es konnte herausgefunden werden, dass das Zweiphasenmodell Strömungen großer Dichteunterschiede rechnen kann, was eindrucksvoll im Zusammenhang mit Wandrandbedingungen gezeigt wurde. Das Wärmeübertragungsmodell wurde gegen eine Spektrallösung anhand eines transienten und nichtuniformen Strömungsproblemes getestet. Stationäre Filmströmungen zeigten sehr gute Übereinstimmungen mit OpenFOAM-Lösungen und instationäre Berechungen bewiesen, dass das Model auch solche Strömungen abbilden kann.

Liquid film flow is an important flow type in many applications of process engineering. For supporting experiments, theoretical and numerical investigations are required. The present state of the art is to model the liquid film flow with Navier--Stokes-based methods, whereas the lattice Boltzmann method is employed here. The final model has been developed within this treatise by means of a two-phase flow and a heat transfer model, and boundary and initial conditions. All these sub-models have been applied to simple test cases. It could be found that the two-phase model is capable of solving flow phenomena with a large density ratio which has been shown impressively in conjunction with wall boundary conditions. The heat transfer model was tested against spectral method results with a transient non-uniform flow field. It was possible to find optimal parameters for computation. The final model has been applied to steady-state film flow, and showed very good agreement to OpenFOAM simulations. Tests with transient film flow demonstrated that the model is also able to predict these flow phenomena. / Flüssigkeitsfilmströmungen kommen in vielen verfahrenstechnischen Prozessen zum Einsatz. Zur Unterstützung von Experimenten sind theoretische und numerische Untersuchungen nötig. Stand der Technik ist es, Navier--Stokes-basierte Modelle zu verwenden, wohingegen hier die Lattice-Boltzmann-Methode verwendet wird. Das finale Modell wurde unter Verwendung eines Zweiphasen- und eines Wärmeübertragungsmodell entwickelt und geeignete Rand- und Anfangsbedingungen formuliert. Alle Untermodelle wurden anhand einfacher Testfälle überprüft. Es konnte herausgefunden werden, dass das Zweiphasenmodell Strömungen großer Dichteunterschiede rechnen kann, was eindrucksvoll im Zusammenhang mit Wandrandbedingungen gezeigt wurde. Das Wärmeübertragungsmodell wurde gegen eine Spektrallösung anhand eines transienten und nichtuniformen Strömungsproblemes getestet. Stationäre Filmströmungen zeigten sehr gute Übereinstimmungen mit OpenFOAM-Lösungen und instationäre Berechungen bewiesen, dass das Model auch solche Strömungen abbilden kann.