lecture 33: isentropic efficiencies
TRANSCRIPT
1.1
ME 200 –Thermodynamics I Spring 2016
Lecture 33: Isentropic Efficiencies
Yong Li
Shanghai Jiao Tong University
Institute of Refrigeration and Cryogenics
800 Dong Chuan Road Shanghai, 200240, P. R. China
Email : [email protected]
Phone: 86-21-34206056; Fax: 86-21-34206056
1.2
Lecture Contents
Previous Lectures
» Closed system entropy balance
» Other forms of the entropy balance
» Increase of entropy principle
– the entropy of an isolated system during a process always increases or, in
the limiting case of a reversible process, remains constant. In other words, it
never decreases.
» Control volume entropy rate balance
Steady state
1.3
Lecture Contents
Last Lecture
» Isentropic process for air modeled as
IG
» Isentropic Processes of air (IG) with
constant specific heat
This Lecture
» Isentropic Efficiencies:
» Internally reversible, steady-state flow
processes
)(]/)(exp[ TpRTs r
o relative pressure.
)(/)( TpRTTv rr relative volume
Variable specific heat
Comparison at the same inlet state and the same exit pressure
shh
hh
21
21
0
2 1
2 1
sh h
h h
1.4
Turbines
Turbine ::: a steady-flow engineering device used to produce work
output by expansion process
Features
» v from inlet to exit as the working fluid expands
» Work interaction device – desired output mechanical shaft work due to v
» Negligible heat transfer
» PE changes usually negligible;
» May need to consider KE changes if given
2 2
1 21 1 2 2
2 2cv
V Vm h gz W m h gz
0 0 0 0
Review
1.5
Isentropic Efficiencies
Isentropic Efficiencies ::: Comparison between the
actual performance of a device and the performance that
would be achieved under idealized circumstances for
the same inlet state and the same exit pressure.
Turbine
isentropic turbine efficiency
h2 > h2s
ηt<1
work turbineIsentropic
work turbineActual
shh
hh
21
21
Concepts
1.6
Isentropic Turbine Efficiency (ηt)
ηt ::: determined by measuring the actual work output of the turbine
and by calculating the isentropic work output for the measured inlet
conditions and the exit pressure.
The value of ηt greatly depends on the design of
the individual components that make up the turbine.
Well-designed, large turbines have ηt > 90%.
Small turbines may drop to 70 %.
Used conveniently in the design of power plants.
2
(measured)
calculated based on measured state 1 and p
Actual turbine work
Isentropic turbine )work (t
Concepts
1.7
Example : Isentropic Efficiency of a Steam Turbine
Known: Steam enters an adiabatic turbine steadily
Find: (a) ηt (b) mass flow rate
Assumptions: 1) Steady state. 2) ΔKE=ΔPE=0.
Analysis:
1.8
Nozzle & Diffuser
Nozzle ::: a flow passage of varying cross-sectional area in which
the velocity of a gas or liquid increases in the direction of flow.
Diffuser ::: a flow passage of varying cross-sectional area in which
the velocity of a gas or liquid decreases in the direction of flow.
Review
1.9
Isentropic Efficiencies of Nozzles
Nozzle efficiencies of 95% or more are
common, indicating that well-designed
nozzles are nearly free of internal
irreversibilities.
0 0 0
isentropic nozzle efficiency
exit at nozzle KEIsentropic
exit at nozzle KEActual
Concepts
1.10
Example : Effect of Efficiency on Nozzle Exit Velocity
Known: acceleration of air in a nozzle, ηN = 92 %
Find: (a) vexit max (b) Texit (c) vexit actual .
Assumptions: 1) Steady state. 2) ideal gas.
3) inlet KE=0.
Analysis:
1.11
Compressor and Pumps Compressor::: device in which work is done on a gas passing
through them in order to raise the pressure.
Pumps ::: the work input is used to raise the pressure of a liquid
In a compressor, v from inlet to exit as the working fluid is compressed
In a pump, change in v negligible
Work interaction device – desired output increase in pressure due to
compression
Negligible heat transfer
PE changes usually negligible; may need to consider KE changes if given
0 0 0 0 0 0
Review
1.12
Isentropic Efficiencies of Compressors and Pumps
ηc is typically 75 to 85% for compressors.
Isentropic compressor work
Actual compressor workc
2 1
2 1
sh h
c h h
2 2sh h
Concepts
1.13
Example : Effect of Efficiency on Compressor Power Input
Known: Air is compressed from 100
kPa and 12 oC to 800 kPa at a steady
rate of 0.2 kg/s. If the ηc =80 %
Find: (a) Texit (b) W .
Assumptions: 1) Steady state. 2)
ideal gas. 3) ΔKE=ΔPE=0.
Analysis: