Vacuum Technology Know How - Triumf

Formula 2-9
Turbopump K 0
Formula 2-10
Turbopump
pumping speed
Formula 2-11
Turbopump S eff
Formula 2-12
Specific pumping speed
www.pfeiffer-vacuum.net
K 0 = exp
The geometric ratios are taken from Figure 2.17. The factor g is between 1 and 3 [10]. From
the equation, it is evident that K increases exponentially with blade velocity v as well as
0
with M because
8
(Formula 1-7).
Consequently, the compression ratio for nitrogen, for example, is significantly higher than
for hydrogen.
. R . T
c – =
p . M
Pumping speed
Pumping speed S is proportional to the inlet area A and the mean circumferential velocity of
0
the blades v, i.e. rotational speed [9]. Taking the blade angle a into account produces:
1
S 0 = . A . v . sin a . cos a
2
c
Taking the entry conductivity of the flange into account, (Formula 1-19)
as well as the optimal blade angle of 45°, produces the approximate effective pumping
speed S of a turbopump for heavy gases (molecular weight > 20) in accordance with
eff
the following formula:
–
L = . A
Bm
4
S 0 + L Bm A . v
S eff = =
S 0 . LBm
v
c – . g . t . sin a
4 .
v
c –
Dividing the effective pumping speed by the bladed entry surface of the uppermost disk
and taking the area blocked by the blade thickness into consideration with factor d ~= 0.9
f
provides the specific pumping speed of a turbopump for nitrogen, for example (curve
in Figure 2.18):
S d eff f . v
S = =
A
A v
4 .
c –
+ 1
In Figure 2.18, the specific pumping speed d f = 1 in l / (s . cm²) is plotted on the ordinate and
the mean blade speed on the abscissa v = p .f .(R a + R i ). Moving up vertically from this point,
the point of intersection with the curve shows the pump’s maximum specific pumping speed
2 2 S . Multiplying this value by the bladed surface area of the inlet disk: A = (R - Ri ) . p, yields
A a
the pumping speed of the pumps and enables it to be compared with the catalog information.
The points plotted in Figure 2.18 are determined by Pfeiffer Vacuum on the basis of the
measured values of the indicated pumps. Points that are far above the curve are not realistic.
+ 1
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