520
14 Radial Compressors
the slip factor s , with
s
− = s 2
1
v u . According to Wiesner (Chap. 3, Sect. 3.3.3),
it applies that
with b
b
2 the outlet blade angle. For radial end blades b =
b
2
0. With Z = 20, it follows
that σ ≈ 0.9.
Rotor work is D
s
=
=
2
2 2u
2
W u v
u .
The pressure ratio follows from
g
g−
=
1
03
03s
00
00
p
T
(
)
p
T
.
Total-to-total efficiency is h
−
=
−
03s
00
tt
03
00
T
T
T
T
.
Thus:
For radial end blades:
Example: T 00 = 300 K, c 00 = 347 m/s, u 2 = 450 m/s, γ = 1.4, η tt = 0.8, σ = 0.9.
This combination gives r
p
p
= =
03
00
4.
The peripheral rotor speed is commonly expressed by a Mach number, called the
rotor Mach number, as M
u
c
u0
2
00
=
.
To the given example corresponds M u0 = 1.3. The outlet Mach number may, with
radial end blades, be determined with the approximation v 2 ≈u 2 (Fig. 14.3).
So
or
or
,
b
s
− =
b
2
0.7
cos
1
Z
D
D
h
h
h
=
+
−
=
+
=
+
03s
00
tt
03
00
00
tt
00
tt
p
p 00
W
W
T
T
( T
T ) T
T ( 1
).
C
C T
Further :
g
g
g
=
=
−
−
2
p 00
00
00
1
C T
RT
c .
1
1
( )
2
1
03
2
tt
2
00
00
p
u
r
1
1
.
p
c
g
g
s
h g
−


=
= +
−






02
00
h
h
W ,
D
=
+
thus
2
2
2
1
1
2
2
00
2
2
00
2
2
2
h
v
h
u ,
h h
(
)u ,
s
s
+
=
+
≈
+ −
2
2
2
1
2
00
2
2
1
1
c
c
(
)u .
1
1
s
g
g
≈
+ −
−
−