3.2 Numerical Methods and Grids
3.2.1 Numerical schemes and boundary conditions
(O. Colin, F. Nicoud)
A set of several new boundary conditions has been implemented into AVBP
[Nicoud, 2000a],
in order to satisfy the various aspects related to unsteady flow simulations
in internal geometries: pulsating inlet conditions, relaxation of all three
velocity components and the temperature towards target values (while
preserving a non-reflecting behavior), swirled flows conditions, etc.
A novel integral formulation allows to impose integral values for the
mass flux at inlet and outlet boundaries. The main area of application for
this new boundary condition are combustion instabilities, where often only
integral values of the experimental data are available at inlet sections.
Another development was tested to increase the computation speed for low
velocity flows by rescaling the sound velocity: it enabled significant CPU
reduction for these cases
[Cuenot, 2000].
3.2.2 Computational grids (J.-D. Müller,
T. Schönfeld)
One of the main characteristics of AVBP is the capability to handle cells of
different types within the frame of the same mesh. With the use of these
hybrid grids, one aims to combine advantages of structured and unstructured
grid methodologies. One of the clear benefits ofusing hybrid meshes is the
ability to minimize the number of grid points and to optimize their position
in the global grid.
Most grid related aspects (like grid adaptation or the extrusion of 2-D grid
towards 3-D grids) are handled by the grid manipulation tool 'hip', developed
by J.-D. Müller (now at Belfast University). New features are implemented
frequently into hip, such as new file formats but also routines that allow
for generic 1-D cuts in an unstructured grid or the interpolation between two
arbitrary grids.
In a feasibility study, conducted in 2000, the existing adaptive local grid
refinement tool for steady state external flows has been extended to time
dependent cases
[Müller, 2001].
The method has been applied to unsteady flows through the usage of a C-shell
script that couples the grid refinement module of hip with the CFD flow
solver AVBP. Fig. 3.1 shows the locally refined domains of the
computational grid for the reactive flow in a combustion chamber. This grid
is adapted on the gradient of the temperature and nicely captures the steep
gradients across the flame front. The work has evidenced certain limitations
of the local grid refinement method when applied to unsteady flows. Most
importantly, the very small cells can result in unrealistically small time
steps. Further, in the context of rapidly moving flow features (like a flame
front) de-refinement capabilities and frequent adaptation steps are crucial,
but slow down the overall computing times. The entire procedure must be
developed in a parallel framework. This work will be intensified in
collaboration with IFP: an ALE formulation is now available in AVBP to
compute flow in moving meshes and the strategy to handle variable meshes now
becomes critical; it will be the topic of a PhD thesis at CERFACS starting in
2002 with the support of IFP.
Figure 3.1: Global view of temperature field and final adapted grid (zoom of
inlet section).
|
|
