On surface tension modelling using the level set method

The paper describes and compares the performance of two options for numerically representing the surface tension force in combination with the level set interface-tracking method. In both models, the surface tension is represented as a body force, concentrated near the interface, but the technical implementation is different: the first model is based on a traditional level set approach in which the force is distributed in a band around the interface using a regularized delta function, whereas in the second, the force is partly distributed in a band around the interface and partly localized to the actual computational cells containing the interface. A comparative Study, involving analysis of several two-phase flows with moving interfaces, shows that in general the two surface tension models produce results of similar accuracy. However, in the particular case of merging and pinching-off of interfaces, the traditional level set model of surface tension produces an error that results in non-converging solutions for film-like interfaces (i.e. ones involving large contact areas). In contrast, the second model, based on the localized representation of the surface tension force, displays consistent first-order convergence

A Higher-Order VOF Interface Reconstruction Scheme for Non-Orthogonal Structured Grids - with Application to Surface Tension Modelling

The volume-of-fluid (VOF) method [24] is widely used to track the interface for the purpose of simulating liquid-gas interfacial flows numerically. The key strength of VOF is its mass conserving property. However, interface reconstruction is required when geometric properties such as curvature need to be accurately computed. For surface tension modelling in particular, computing the interface curvature accurately is crucial to avoiding so-called spurious or parasitic currents. Of the existing VOF-based schemes, the height-function (HF) method [10, 16, 18, 42, 46, 53] allows accurate interface representation on Cartesian grids. No work has hitherto been done to extend the HF philosophy to non-orthogonal structured grids. To this end, this work proposes a higher-order accurate VOF interface reconstruction method for non-orthogonal structured grids. Higher-order in the context of this work denotes up to 4 th-order. The scheme generalises the interface reconstruction component of the HF method. Columns of control volumes that straddle the interface are identified, and piecewise-linear interface constructions (PLIC) are computed in a volume-conservative manner in each column. To ensure efficiency, this procedure is executed by a novel sweep-plane algorithm based on the convex decomposition of the control volumes in each column. The PLIC representation of the interface is then smoothed by iteratively refining the PLIC facet normals. Rapid convergence of the latter is achieved via a novel spring-based acceleration procedure. The interface is then reconstructed by fitting higher-order polynomial curves/surfaces to local stencils of PLIC facets in a least squares manner [29]. Volume conservation is optimised for at the central column. The accuracy of the interface reconstruction procedure is evaluated via grid convergence studies in terms of volume conservation and curvature errors. The scheme is shown to achieve arbitrary-order accuracy on Cartesian grids and up to fourth-order accuracy on non-orthogonal structured grids. The curvature computation scheme is finally applied in a balanced-force continuum-surface-force (CSF) [4] surface tension scheme for variable-density flows on nonorthogonal structured grids in 2D. Up to fourth-order accuracy is demonstrated for the Laplace pressure jump in the simulation of a 2D stationary bubble with a high liquid-gas density ratio. A significant reduction in parasitic currents is demonstrated. Lastly, second-order accuracy is achieved when computing the frequency of a 2D inviscid oscillating droplet in zero gravity. The above tools were implemented and evaluated using the Elemental®multi-physics code and using a vertex-centred finite volume framework. For the purpose of VOF advection the algebraic CICSAM scheme (available in Elemental®) was employed

Simulating changes in shape of thermionic cathodes during operation of high-pressure arc discharges

A numerical model of current transfer to thermionic cathodes of high-pressure arc discharges is developed with account of deviations from local thermodynamic equilibrium occurring near the cathode surface, in particular, of the near-cathode space-charge sheath, melting of the cathode, and motion of the molten metal under the effect of the plasma pressure, the Lorentz force, gravity, and surface tension. Modelling results are reported for a tungsten cathode of an atmospheric-pressure argon arc and the computed changes in the shape of the cathode closely resemble those observed in the experiment. The modelling has shown that the time scale of change of the cathode shape during arc operation is very sensitive to the temperature attained by the cathode. The fact that the computed time scales conform to those observed in the experiment indicate that the model of non-equilibrium near-cathode layers in high pressure arc discharges, employed in this work, predicts the cathode temperature for a given arc current with adequate accuracy. In contrast, modelling based on the assumption of local thermodynamic equilibrium in the whole arc plasma computation domain up to the cathode surface could hardly produce a similar agreement.info:eu-repo/semantics/publishedVersio

A Volume of Fluid (VoF) based all-mach HLLC Solver for Multi-Phase Compressible Flow with Surface-Tension

This work presents an all-Mach method for two-phase inviscid flow in the presence of surface tension. A modified version of the Hartens, Lax, Leer and Contact (HLLC) approximate Riemann solver based on Garrick et al. [1] is developed and combined with the popular Volume of Fluid (VoF) method: Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM). This novel combination yields a scheme with both HLLC shock capturing as well as accurate liquid-gas interface tracking characteristics. To ensure compatibility with VoF, the Monotone Upstream-centred Scheme for Conservation Laws (MUSCL) [2] is applied to non-conservative (primitive) variables, which yields both robustness and accuracy. Liquid-gas interface curvature is computed via both height functions [3, 4] and the convolution method [5]. This is in the interest of applicability to both cartesian and arbitrary meshes. The author emphasizes the use of VoF in the interest of surface tension modelling accuracy. The method is validated using a range of test-cases available in literature. The results show flow features that are in agreement with experimental and benchmark data. In particular, the use of the HLLC-VoF combination leads to a sharp volume fraction and energy field with improved accuracy (up to secondorder)

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

Flow dynamics in the closure region of an internal ship air cavity

This work is dedicated to providing a detailed account of the flow dynamics in the closure region of an internal ship air cavity. A geometrically simple multiwave test cavity is considered, and a simulation of the flow is conducted using large-eddy simulation coupled with an algebraic Volume of Fluid interface capturing method. Results reveal that the flow in the closure region is highly unsteady and turbulent. The main cause of this is established to be the pressure gradient occurring due to the stagnation of the flow on the beach wall of the cavity. The pressure gradient leads to a steep incline in the mean location of the air-water interface, which, in turn, leads to the flow separating from it and forming a recirculation zone, in which air and water are mixed. The separated flow becomes turbulent, which further facilitates the mixing and entrainment of air. Swarms of air bubbles leak periodically. Upstream of the closure region, the phase and length of the wave are found to be well-predicted using existing approximations based on linear flow theory. However, for the corresponding prediction of the amplitude of the wave the agreement is worse, with the estimates under-predicting the simulation results