This research project aims at providing the aeronautical industry with a modelling
capability to simulate the fuel injection in gas turbine combustion chambers.
The path to this objective started with the review of state-of-the-art numerical
techniques to model the primary breakup of liquid fuel into droplets. Based on this
and keeping in mind the requirements of the industry, our modelling strategy led to
the generation of a mass-conservative method for efficient atomisation modelling on
unstructured meshes. This goal has been reached with the creation of high-order
numerical schemes for unstructured grids, the development of an efficient numerical
method that transports the liquid-vapour interface accurately while conserving
mass and the implementation of an algorithm that outputs the droplet boundary
conditions to separate combustion codes.
Both high-order linear and WENO schemes have been created for general polyhedral
meshes. The notorious complexity of high-order schemes on 3D mixed-element
meshes has been handled by the creation of a series of algorithms. These include
the tetrahedralisation of the mesh, which allows generality of the approach while
remaining efficient and affordable, together with a novel approach to stencil generation and a faster interpolation of the solution. The performance of the scheme has been demonstrated on typical two-dimensional and three-dimensional test cases for both linear and non-linear hyperbolic partial differential equations.
The conservative level set method has been extended to unstructured meshes and
its performance has been improved in terms of robustness and accuracy. This was achieved by solving the equations for the transport of the liquid volume fraction
with our novel WENO scheme for polyhedral meshes and by adding a flux-limiter
algorithm. The resulting method, named robust conservative level set, conserves
mass to machine accuracy and its ability to capture the physics of the atomisation
is demonstrated in this thesis.
To be readily applicable to the simulation of atomisation, the novel interfacecapturing technique has been embedded in a framework — within the open source CFD code OpenFOAM — that solves the velocity and pressure fields, outputs
droplet characteristics and runs in parallel. In particular, the production of droplet boundary conditions involves a set of routines handling the selection of drops in the level set field, the calculation of relevant droplet characteristics and their storage into data files. An n-halo parallelisation method has been implemented in OpenFOAM to perform the computations at the expected order of accuracy.
Finally, the modelling capability has been demonstrated on the simulation of
primary liquid-sheet breakup with relevance to fuel injection in aero-engine combustors.
The computation has demonstrated the ability of the code to capture the
physics accurately and further illustrates the potential of the numerical approach