184 11 A Way towards Virtual Engine Development
cells by solving the conservation equations for each cell central node (Eulerian formulation)
[53,54,56]. Since the Eulerian formulation assumes a homogeneous distribution of all variables
within each cell, it is evident that the dimension of the cells, especially in the near nozzle region,
drastically influences the shape of the simulated jet and its axial and radial penetration.
Here, a high refinement and adaptation of the mesh with cells much smaller than the injector
orifice certainly ensures a better resolution of the flow field, but on the other hand, the exorbitant
CPU-time in combination with an increased “numerical instability” of the small cells make this
way unjustifiable. Exemplarily in the case of a local cell discretization of 0.1 mm and a fluid
velocity equal to the injection velocity
Inj
V
, in order to satisfy the condition imposed by the
Courant number (see Eq. 7.1) an exorbitant small computation time
t'
=0.0002 ms (ca. M'
=0.002 deg at 2,000 rpm) is required. In particular, in case of either a multi-hole injector or an
injector that generates a hollow jet cone, it is very difficult to find an affordable compromise
between the appropriate mesh discretization that permits a good simulation of the jet
development and the required efforts.
11.4.2 Gas Injection Modeling in QuickSim
A new approach towards an improved gaseous fuel injection has been tested and implemented in
QuickSim. Here the modeling of the injected fuel in the near nozzle region introduces the
concept of gaseous bubbles that numerically are treated as “fictive” gas droplets (see Figure
11.6). This numerical approach is well known in case of liquid injection (spray injection) and in
this 3D-CFD-tool it has been adapted to the gaseous fuel injection. In 3D-CFD-codes the charge
assumed as a continuous fluid is modeled by a standard Eulerian formulation and the methane
bubbles are added to the gas phase using the Lagrange formulation [53,54,56]. Since modeling
the millions of individual methane bubbles would lead to a prohibitive computational time, the
Lagrange formulation introduces the concept of the parcel which represents a sample of many
“fictive” gas droplets (Discrete Droplet Method). The parcels are introduced in the mesh with
initial values of position, size
, velocity, temperature and number of “fictive” gas droplets per
parcel (Injector Model).
The numerical two-way-coupling of the Eulerian and the Lagrange equations allows the
modeling of the exchange processes (mass, momentum and energy) between the charge and the
injected methane. Thanks to this approach the number of the information saved in the total
amount of the parcels is very high and independent on the discretization degree of the cells in the
near nozzle region. The increased CPU-time required for the “fictive” gas droplets remains in an
acceptable range. The droplets are introduced in the 3D-CFD-mesh randomly in a space outside