TVD differencing on three-dimensional unstructured meshes with monotonicity-preserving correction of mesh skewness

This data set contains the data accompanying the article F. Denner and B. van Wachem, TVD differencing on three-dimensional unstructured meshes with monotonicity-preserving correction of mesh skewness, Journal of Computational Physics (2015), http://dx.doi.org/10.1016/j.jcp.2015.06.008.This data set contains the data accompanying the article F. Denner and B. van Wachem, TVD differencing on three-dimensional unstructured meshes with monotonicity-preserving correction of mesh skewness, Journal of Computational Physics (2015), http://dx.doi.org/10.1016/j.jcp.2015.06.008

Artificial viscosity model to mitigate numerical artefacts at fluid interfaces with surface tension

The numerical onset of parasitic and spurious artefacts in the vicinity of uid interfaces with surface tension is an important and well-recognised problem with respect to the accuracy and numerical stability of interfacial ow simulations. Issues of particular interest are spurious capillary waves, which are spatially underresolved by the computational mesh yet impose very restrictive time-step requirements, as well as parasitic currents, typically the result of a numerically unbalanced curvature evaluation. We present an arti cial viscosity model to mitigate numerical artefacts at surface-tension-dominated interfaces without adversely a ecting the accuracy of the physical solution. The proposed methodology computes an additional interfacial shear stress term, including an interface viscosity, based on the local ow data and uid properties that reduces the impact of numerical artefacts and dissipates underresolved small scale interface movements. Furthermore, the presented methodology can be readily applied to model surface shear viscosity, for instance to simulate the dissipative e ect of surface-active substances adsorbed at the interface. The presented analysis of numerical test cases demonstrates the e cacy of the proposed methodology in diminishing the adverse impact of parasitic and spurious interfacial artefacts on the convergence and stability of the numerical solution algorithm as well as on the overall accuracy of the simulation results

Self-similarity of solitary waves on inertia-dominated falling liquid films

We propose consistent scaling of solitary waves on inertia-dominated falling liquid films, which accurately accounts for the driving physical mechanisms and leads to a self-similar characterization of solitary waves. Direct numerical simulations of the entire two-phase system are conducted using a state-of-the-art finite volume framework for interfacial flows in an open domain that was previously validated against experimental film-flow data with excellent agreement. We present a detailed analysis of the wave shape and the dispersion of solitary waves on 34 different water films with Reynolds numbers Re=20–120 and surface tension coefficients σ=0.0512–0.072Nm−1 on substrates with inclination angles β=19◦ − 90◦. Following a detailed analysis of these cases we formulate a consistent characterization of the shape and dispersion of solitary waves, based on a newly proposed scaling derived from the Nusselt flat film solution, that unveils a self-similarity as well as the driving mechanism of solitary waves on gravity-driven liquid films. Our results demonstrate that the shape of solitary waves, i.e., height and asymmetry of the wave, is predominantly influenced by the balance of inertia and surface tension. Furthermore, we find that the dispersion of solitary waves on the inertia-dominated falling liquid films considered in this study is governed by nonlinear effects and only driven by inertia, with surface tension and gravity having a negligible influence

Estimation of curvature from volume fractions using parabolic reconstruction on two-dimensional unstructured meshes

This paper proposes a method to estimate the curvature of an interface represented implicitly by discrete volume fractions on an unstructured two-dimensional mesh. The method relies on the computation of local parabolic reconstructions of the interface. The parabolic reconstruction of the interface in a given computational cell is obtained by solving a local non-linear minimisation problem, and only requires additional information from two neighbouring cells. This compactness ensures a robust behaviour on poorly-resolved interfaces. The proposed method is proven to be analogous to the height-function method for Cartesian configurations with consistent heights, and can be interpreted as a generalisation of the height-function method to meshes of any type. Tests are conducted on a range of interfaces with known curvature. The method is shown to converge with mesh refinement with the same order of accuracy as the height-function method for all three types of meshes tested, i.e. Cartesian, triangular, and polygonal

Fully-coupled pressure-based finite-volume framework for the simulation of fluid flows at all speeds in complex geometries

A generalized finite-volume framework for the solution of fluid flows at all speeds in complex geometries and on unstructured meshes is presented. Starting from an existing pressure-based and fully-coupled formulation for the solution of incompressible flow equations, the additional implementation of pressure–density–energy coupling as well as shock-capturing leads to a novel solver framework which is capable of handling flows at all speeds, including quasi-incompressible, subsonic, transonic and supersonic flows. The proposed numerical framework features an implicit coupling of pressure and velocity, which improves the numerical stability in the presence of complex sources and/or equations of state, as well as an energy equation discretized in conservative form that ensures an accurate prediction of temperature and Mach number across strong shocks. The framework is verified and validated by a large number of test cases, demonstrating the accurate and robust prediction of steady-state and transient flows in the quasi-incompressible as well as subsonic, transonic and supersonic speed regimes on structured and unstructured meshes as well as in complex domains

Thermographic laser Doppler velocimetry using the phase-shifted luminescence of BAM:Eu2+ phosphor particles for thermometry

Simultaneous point measurements of gas velocity and temperature were recently demonstrated using thermographic phosphors as tracer particles. There, continuous wave (CW) excitation was used and the spectral shift of the luminescence was detected with a two-colour intensity ratio method to determine the gas temperature. The conventional laser Doppler velocimetry (LDV) technique was employed for velocimetry. In this paper, an alternative approach to the gas temperature measurements is presented, which is instead based on the temperature-dependence of the luminescence lifetime. The phase-shift between the luminescence signal and time-modulated excitation light is evaluated for single BaMgAl10O17:Eu2+ phosphor particles as they cross the probe volume. Luminescence lifetimes evaluated in the time domain and frequency domain indicate that in these experiments, interferences from in-phase signals such as stray excitation laser light are negligible. The dependence of the phase-shift on flow temperature is characterised. In the temperature sensitive range above 700 K, precise gas temperature measurements can be obtained (8.6 K at 840 K) with this approach

Capillary waves with surface viscosity

Experiments over the last 50 years have suggested a tentative correlation between the surface (shear) viscosity and the stability of a foam or emulsion. We examine this link theoretically using small-amplitude capillary waves in the presence of a surfactant solution of dilute concentrations where the associated Marangoni and surface viscosity effects are modelled via the Boussinesq-Scriven formulation. The resulting integro-differential initial value problem is solved analytically and surface viscosity is found to contribute an overall damping effect on the amplitude of the capillary wave with varying degrees depending on the lengthscale of the system. Numerically, we find the critical damping wavelength to increase for increasing surface concentration but the rate of increase remains different for both the surface viscosity and the Marangoni effect