Physical experimentation and numerical simulation of liquid film: comparison of Eulerian Methods

Abstract

The present work is based on current models and results published in the literature to implement and evaluate different methodologies in order to simulate the behaviour of a liquid film. The main objective of this work was to compare the methodologies for numerical solution of liquid film formation, presenting the main advantages of each one of them. Two different approaches were used, the Volume of Fluid (VOF) method and the Eulerian Wall Film (EWF) method. To fulfil the objective of the thesis, the commercial software Convergent Science Inc.'s CONVERGE $^{TM}$ CFD was used to run the simulations with the VOF method. This software adopts adaptive mesh refinement (AMR) techniques, which were used to perform the simulations. Another technique used was the adaptive time step. The variations were dependent on the Courant–Friedrichs–Lewy (CFL) number and had a big difference for High-Resolution Interface Capturing (HRIC) and Piece-wise Linear Interface Calculation (PLIC) simulations. For the HRIC scheme, the simulations were run with a time step of approximately $5.10^{-6}$, while the simulations using the PLIC scheme were run with a predefined minimum time step of $1.10^{-7 }$, which means it would require even smaller time steps. These observations were contrary to the results observed for flows aligned with the mesh presented in previous works. The gas flow was considered incompressible. The maximum number of PISO iterations per time step was set to 20 with a tolerance of $10^{-5}$. To model the turbulence closure model, the $RNG~k-\epsilon$ model was used. The models used in this work for EWF modelling were implemented in the code Unsteady Cyclone Flow - 3D (Unscyfl3D), code that is under constant development in the fluid mechanics laboratory of the Federal University of Uberlândia. This code is characterised by simulating laminar and turbulent multi-phase flows. For this, the Navier-Stokes equations are solved in incompressible form by means of the finite volume method in unstructured meshes and co-localised array. For pressure-velocity coupling the SIMPLE algorithm was implemented. This code has already been widely validated with relevant results in the literature for particle flows. In the first stage of the work, physical experiments were carried out in the laboratory of Otto-von-Guericke-Universität Magdeburg. For physical experimentation, an injector was used to generate a chain of water droplets that collide with the opposite wall, forming a liquid film. Droplet images were obtained using two high-speed recording cameras. The results for different droplet sizes and impact angles are presented and a relation between the momentum parameter and the dimensionless pool size was established. These results are also used for comparison with numerical results. In the second part of the work the results of the physical experiments were compared with the results of the numerical simulations with the VOF method. It was concluded that the HRIC scheme can better deal with the non-alignment of the fluid flow with the mesh, as the PLIC scheme distorted the shape of the round drops. However, the PLIC scheme maintained a sharper interface than the HRIC scheme. On the other hand, the HRIC scheme was more computationally efficient than the PLIC scheme. In the third part of the work, two test cases were analysed. The first case refers to the spreading of a drop on a flat surface. This case was solved analytically and is found on the literature and compared to physical experimentation tests. This case is simpler and therefore can be used to validate the numerical scheme and the effects of capillary pressure. The second experiment consists of a jet that interacts with a cross flow, which is very similar to fuel injection in air jet atomisers, whose experiments were performed another author and was published as a paper. In this case, the Eulerian Wall Film (EWF) model was validated for different turbulence models. Assessments of the stability of the model against the main variables that consists the same were carried out. The results of the formation of liquid film were satisfactory when compared with tests of physical experiments. The main observation was that the SST model can better predict the liquid film behaviour, since the optimised k-$\epsilon$ and k-$\epsilon$ underestimate the liquid film formation. An extensive study of different methodologies was presented. Each of the evaluated techniques has its importance in engineering problems. As VOF methodologies are more time consuming than EWF approaches, they are used to solve problems involving smaller computational domains, as well as to deepen the knowledge on phenomena involving multi-phase flows. The numerical results of this type of simulation can be used to develop less time consuming numerical tools, such as the EWF method. As the EWF method is less time consuming than the VOF method, it can be used to optimise more realistic engineering process. As an example, the flow within a turbine combustion chamber can be predicted by these models, aiding in faster design optimisation. Although further evaluation is still needed to cover a wider range of cases and a greater variety of numerical approaches, an important step has been taken in the present work towards a better understanding of liquid film dynamics and improvement of numerical techniques.