Concept of isentropic efficiency
Gap-fill exercise
Complete the following text. Click "Correction" when you are done.
Representation in the (h, ln (P)) chart
In reality, a compressor or a turbine is not perfect, and the compression and expansion follow
blue
less than or equal to 1
non-reversible adiabatics
real process
real work
red
reverse
reversible compression
reversible expansion
we divide
. It is customary to characterize the
blue
less than or equal to 1
non-reversible adiabatics
real process
real work
red
reverse
reversible compression
reversible expansion
we divide
by an
isentropic efficiency
η, defined in the case of a compressor as the ratio of the work of the
blue
less than or equal to 1
non-reversible adiabatics
real process
real work
red
reverse
reversible compression
reversible expansion
we divide
to the
blue
less than or equal to 1
non-reversible adiabatics
real process
real work
red
reverse
reversible compression
reversible expansion
we divide
.
Perfect compression follows the reversible adiabatic (1-2), thick curve in
blue
less than or equal to 1
non-reversible adiabatics
real process
real work
red
reverse
reversible compression
reversible expansion
we divide
in the figure, and involves the work τs= h2 - h = 360 kJ / kg
To find the real point 2',
blue
less than or equal to 1
non-reversible adiabatics
real process
real work
red
reverse
reversible compression
reversible expansion
we divide
work τs by η, which gives the value of the real work τ.
Since τ= h2 ’- h1, the enthalpy of point 2' is equal to that of point 1 plus τ.
In the present case, taking η = 0.8, we have:
τ = τs/ η = 360 / 0.8 = 450
h2’ = 450 kJ / kg
The non-reversible compression corresponds to curve (1-2 ’), thick curve in
blue
less than or equal to 1
non-reversible adiabatics
real process
real work
red
reverse
reversible compression
reversible expansion
we divide
in the figure.
In the case of a turbine, isentropic efficiency η is defined as the ratio of the actual work to the work of the
blue
less than or equal to 1
non-reversible adiabatics
real process
real work
red
reverse
reversible compression
reversible expansion
we divide
, ie the
blue
less than or equal to 1
non-reversible adiabatics
real process
real work
red
reverse
reversible compression
reversible expansion
we divide
of its definition for a compressor.
It will be noted that thus it is
blue
less than or equal to 1
non-reversible adiabatics
real process
real work
red
reverse
reversible compression
reversible expansion
we divide
for compression as for expansion.
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