PuK - Process Technology & Components 2024

Vacuum technology
Screw spindle vacuum pumps
Fig. 6: Simulation domain for a pressure-driven flow through a channel with structured
surfaces
a) L/h=1 b) L/h=10
Fig. 7: Mass flow rate through a channel with structured surfaces related to the respective
mass flow rate through a channel with smooth surfaces as a function of the inlet pressure p 1
for different profile parameters α = β [Saz20].
Fig. 7a shows this for a length to
height ratio of one, which corresponds
approximately to an orifice
flow. It can be seen that all four
curves cause an increased throttling
effect with decreasing pressure,
which can be explained analogously
to Fig. 3 by the fact that the proportion
of gas-surface interactions increases.
Furthermore, the throttling
effect depends on the shape of the
surface structure. A very wide profile
angle causes only a slight reduction
in the mass flow rate, while a profile
angle α = β = 45° already causes
a reduction in the mass flow rate of
about 10 % in the orifice flow. If the
profile angle is reduced further, the
flow stagnates. This can also be seen
in Fig. 7b, where the same situation
is shown for a length to height ratio
of ten and the molecules therefore
have to pass through a significantly
longer channel. Here, a reduction of
about 25 % can already be achieved
for smaller profile angles. It is also
noticeable that the effect becomes
smaller for increasing inlet pressures,
so that a transfer to the vacuum
pump is particularly interesting
for the low-pressure side of the machine.
This results in promising synergy
possibilities with the previously
described approach by Kösters
and Eickhoff, as larger machine gaps
could be realised on the low-pressure
side in order to prevent overcompression
during start-up. As soon
as the pressure on the low-pressure
side is low enough, the increased gap
size would be compensated for with
the help of the surface structures by
reducing the mass flow rate even further
than is already the case due to
the rarefied gas flow with technically
smooth walls.
Since there is always a superposition
of a pressure-driven Poiseuille
flow and a shear-driven Couette flow
in the gaps of vacuum pumps, the
DSMC method is used to analyse the
effect of such a surface structure on
a pure Couette flow. The corresponding
simulation domain is shown in
Fig. 8. With a gap height of h = 0.3
mm, a profile depth Λ = 0.03 mm is
used. Since the gap length and the
gap width in vacuum pumps are
much greater than the gap height,
an infinitely wide and long channel is
simulated for simplification, so that
symmetrical boundary conditions are
used in the depth direction (z) and
cyclic boundary conditions in the flow
direction (x) to reduce the computational
effort. The latter have the property
that the left and right cells are
linked to each other as if the channel
were continuing. Accordingly, a particle
that crosses the cyclic boundary
condition on the right-hand side
is initialised again on the left-hand
side and vice versa. The lower wall
has a wall velocity of U = 10 m/s in
the positive x-direction. In the reference
plane shown in green, the mass
flow rate is determined by calculating
the sum of the particle masses in the
positive x-direction minus the sum
of the particle masses that cross the
plane in the negative direction within
a time step and then dividing by the
time step:
Eq. 1
Regardless of the pressure range,
the mass flow rate
for a pure
Couette flow with technically smooth
surfaces can be calculated via
Eq. 2
incorporating the density ρ and the
smallest cross-section area A = h b
[Ple22a, Ple22b].
Fig. 8: DSMC simulation domain of a pure
Couette flow through a channel with onesided
surface structure.
Fig. 9 shows the simulated mass
flow rate of a Couette flow for different
profile angles α = β in relation to
the mass flow rate through a channel
with smooth walls with the same
gap height as a function of the pres-
50 PROCESS TECHNOLOGY & COMPONENTS 2024