Page 431 - Compression Machinery for Oil and Gas

410 SECTION III Applications

where.
b 2 ¼impeller exit width
μ 0 ¼viscosity at the inlet conditions
U 2 ¼impeller tip speed
ρ 00 ¼gas density at inlet conditions

Impeller Work Coefficient

The impeller imparts energy to the working fluid to raise the total enthalpy and
the impeller work coefficient is defined as
Δh C p T 02 T 01 Þ
ð
τ ¼ 2 ¼ 2 (10.4)
u u
2
where
T 01 and T 02 ¼total inlet and outlet temperature
C p ¼specific heat
U 2 ¼impeller tip speed
Polytropic efficiency. The polytropic efficiency is given by

p 2
log
k 1 p 1
η ¼ (10.5)
p
k T 2
log
T 1
where
k¼C p /C v
P 2 and P 1 ¼outlet and inlet pressure
T 2 and T 1 ¼outlet and inlet temperature
The head coefficient μ is defined as
μ ¼ τη p (10.6)

Two-dimensional (2D) and 3D Impellers

Impeller flow coefficient and geometry are related. Lower flow coefficients
correspond to shrouded, two-dimensional (2D) impeller geometry. Higher flow
coefficients correspond to shrouded, 3D impeller geometry. For very high flow
coefficients, an axial flow blade design is utilized. The LNG centrifugal com-
pressors typically use a combination of 2D and 3D impellers.
A 2D impeller basically has a constant blade angle from disk to shroud along
the leading edge of the blade. It can therefore only match the incidence angle at
one point on the leading edge, and has an increasingly mismatched leading edge
flow field in moving toward the disk or shroud from that point. However, as 2D