The prediction of bubble defects in castings
Objective of this research was to develop models that capture the entrainment, breakup and transport of gas bubbles in solidifying TiAl castings. The candidate has reviewed the literature, programmed in FORTRAN code, and validated a number of competing techniques for two phase flow relevant to the filling of moulds. He has developed a hybrid (Donor-acceptor/ Level Set) method, which captures the characteristics of gas bubbles based on the surface tension —fluid inertia balance on the free surface. He has demonstrated the ability of this method to reproduce observed phenomena. The candidate also conducted an experimental campaign in Birmingham University under the supervision of Dr R.A. Harding to provide real casting data for his simulations. KAP Edited extract from RD3 MPhil/PhD form: "This research was carried out at the University of Greenwich in conjunction with the University of Birmingham as part of a larger EPSRC- funded project concerned with the development of a casting process route for the production of gamma-TiAl components. Focus of the research was the development of a model of entrained bubbles in the metal casting process. This model comprises the combination of several physical phenomena coupled within the PHYSICA multi-physics framework. The key areas the research has touched on are, surface tension modelling and free-surface modelling using the finite volume technique. A model has been developed that simulates bubble formation during the filling of castings due to surface entrainment and subsequent motion. Once entrained these bubbles tend to solidify in the casting where the rate of solidification is too fast for escape by buoyancy. This problem is particularly acute in thin blade sections of TiAl, where sufficient superheat cannot be maintained during the casting process. Mould filling techniques have to be modified accordingly to improve the mechanical integrity of components. Two phase systems with a sharp, well-defined interface governed by surface tension are required to be modelled. The Level Set Method (LSM) is such a method, used to maintain the position of the interface as it moves through a fixed computational grid. The interface is moved or distorted by the advection equation. In this case two numerical methods are used in differencing: Van-Leer and Donor Acceptor. The Donor Acceptor method is of use when modelling highly dynamic surfaces, such as those encountered during the metal pouring phase in castings, or when fuel sloshes in a fuel tank. This method is best for capturing the entrapment of large bubbles of gas by surface folding. A process directly related to the moving surface. However, the LSM, which allows many surface properties to be calculated, cannot be used in conjunction with the Donor Acceptor method which uses heuristics to sharpen the interface in each compu6tational cell. Once bubbles are formed, their existence and motion are governed by the action of surface tension, therefore the mathematically more rigorous Van-Leer differencing scheme is used in conjunction with the LSM. Bubbles are then tracked using the freesurface method. The tracking limit is determined by the fineness of the mesh used. Sub grid bubbles or bubbles that only occupy a small number of cells can no longer be tracked in a continuum Eulerian simulation. Lagrangian particle tracking is then necessary. The original work in this research can be described as the coupling of the formation of bubbles using the Donor Acceptor method, with the LSM / Van-Leer technique for their subsequent motion and behaviour. This involves: • Modelling the initial free-surface dynamics with the Donor Acceptor technique. • Modelling bubble formation using the Donor Acceptor technique. • Using Results from bubble formation database to "re-start" the simulation with the inclusion of surface tension. • Tracking bubbles as a free-surface, computing their subsequent break up or coalescence • Once the bubbles reach a minimum size for a given mesh, continue tracking using the Lagrangian particle tracking technique. The model was applied to: • Simple validation experiments to test the correctness of the coding • Sloshing/collapsing column experiments to evaluate bubble formation • Simple geometry situations where the combined model is used with Bubble Formation/Tracking Surface Tension • Model the filling of the flat plate experimental setup Future work (not completed ...) • Develop criteria for switching between the Eulerian (free surface) and Lagrangian (particle tracking) scheme • Compare with Experimental Data obtained at the University of Birmingham • Run 3D Cases representing real geometries with HT and solidification • Model the counter-gravity filling process"