Environmental Engineering Reference
In-Depth Information
The theoretical energy consumption of a compressor (as well as any machine
transforming mechanical energy) in reversible adiabatic conditions can be calcu-
lated by the following equation:
L
i
mecc
¼
h
2
h
1
¼
Z
p
2
vdp
ð
4
:
1
Þ
p
1
id
is the reversible ideal mechanical work necessary to actuate the
compressor, h
1
and h
2
are the enthalpy of the fluid before and after the com-
pression stage, v is the specific volume of the fluid, and p is the working pressure,
that changes from the entering value p
1
to the exit value p
2
.
The operative conditions suitable for air feeding section in H
2
FCS suggest that
the air stream can be considered as ideal gas mixture. The relationship of poly-
tropic compression for an ideal gas is:
where L
mecc
k
p
2
p
1
T
2
¼
T
1
ð
4
:
2
Þ
and in adiabatic conditions:
k
¼ð
c
1
Þ =
cc
¼
c
p
=
c
v
where T
1
is the entering temperature value, T
2
represents the exit value after
compression stage, c
p
and c
v
are the specific heat at constant pressure and volume,
respectively. The parameter k assumes the value of 0.285 for air.
The ideal power consumption (P
id
) related to isoentropic (adiabatic) com-
pression can be calculated according to:
"
#
k
1
p
2
p
1
P
id
¼
m
a
c
p
T
1
ð
4
:
3
Þ
where m
a
is the air mass flow rate. The equation (
4.3
) evidences that the theoretical
energy losses necessary to run a compressor depend almost exclusively on mass
flow rate and on compression ratio (p
2
/p
1
).
Furthermore, a real machine designed for adiabatic compression does not reach
the ideal point of reversible iso-entropic process, because of unavoidable irre-
versible transformations. The reversible work associated to the pressure increase
inside a fluid can be always calculated as
R
p
2
p
1
vdp, while the net enthalpy variation is
directly
related
to
mechanical
energy
consumption,
which
increases
with
irreversibilities.
Then the efficiency (g
c
) of a compressor is defined as:
g
c
¼
R
p
2
p
1
vdp
L
mecc
ð
4
:
4
Þ
