Yearbook 2013/2014 - ehedg

56 Spray cleaning systems in food processing machines and the simulation of CIP-coverage tests
type as required, into the scene. The computer program is
directly connected with a public nozzle database in which
the specific characteristics of different nozzles are stored
together with the related single spray pattern. Consequently,
the same nozzle doesn’t have to be measured twice at the
same operating parameters. The determination of a single
spray pattern can be managed with an adequate cleaning
test like that described below, or with impact measurements
for example. After insertion, the nozzles can be positioned
and aligned in the scene. The activated nozzle is marked
with a pyramid. This pyramid shows the maximum nozzle
distance in which the nozzle was measured. If the nozzle
is moved outside this range, no cleaning effect is shown on
the surface. The expected cleaning results are calculated
and shown in real-time, so the cleaning system can be
optimised (e.g., insert more nozzles or change their
alignment) in an iterative way without large response time.
After all, the nozzles positions can be exported for using in
CAD software.
Functional principles
Depending on the application area, one could model the
effect of a nozzle as a stream or as a spray of single particles
– omitting particle-particle interaction. In our experiments the
latter approach proved the most feasible. The behaviour of
such an isolated particle could be approximated using the
following formula:
0
Figure 3. Projection principle, from 3D space onto 2D plane with
depth information (as Z). A brighter colour is equivalent to a shorter
distance to the projection plane. Note the intersection of the ray
with the 2D plane.
After identifying where the particles collide with the surface,
the exerted influences
0
on the surface have to be computed.
For this, every nozzle gets a spate of spray masks that are
determined by cleanability tests or impact measurements
(Figure 4).
z
z
where the forces are defined as
•
•
•
•
Numerical algorithms for solving the time integration can be
found in Press et al. (2007) and are efficiently computable
on the GPU (graphics processing unit) as described by
Nguyen (2007). 1,2 But, solving the equation of motion for
millions of particles is just one step. For the interesting
effect of a particle-surface interaction, the intersection of a
particle with a surface has to be found. Despite several
well-known acceleration techniques, a lot of work had to be
done in every time step of the simulation. 3 But experiments
showed that the process could be approximated as linear
with respect to the input parameter domain in focus. These
experiences effectively broke down the simulation to a onetime
step at which the intersection occurs. In the field of
computer graphics this is known as ray-tracing, but instead
of tracing light, the ray’s linear particle paths are traced. 4 A
first implementation produced reasonable results for further
investigations, but it was too slow to be used in interactive
applications. Therefore, the process was modelled as a
projection of surface points in 3D space to 2D points on the
escape plane of the nozzle which is exactly what graphics
processing units (GPUs) are good at doing (Figure 3).
Figure 4. (Left) 2D impact map. Red means high impact. (Right) 2D
spray pattern. A black colour means a point got cleaned during the
spray process.
Thus, deciding whether a point is cleaned through the spray
process becomes essentially the inversion of the projection
mentioned before. This is equivalent to the functional
principle of a slide or movie projector. Here the nozzle is the
projector, the film or slide to be projected is the impact or
spray pattern and the to-be-cleaned surface is the functional
equivalent of the projection screen (Figure 5). In computer
graphics this technique is known as projective texture
mapping or perspective shadow mapping. 5-9
(a)
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