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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 : liyo@sjtu.edu.cn

Phone: 86-21-34206056; Fax: 86-21-34206056

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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

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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

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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

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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

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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

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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:

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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

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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

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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:

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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

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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

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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: