NOTES CHAPTER 6 (6.5)k (1).ppt

CHAPTER 6

ENTROPY

Sub-chapter covered

6.5 Isentropic Efficiencies of Steady Flow Devices

Isentropic efficiencies

- Parameter that expresses quantitatively how efficiently an actual device approximate an idealized one.

- Isentropic or adiabatic efficiency which is measure of the deviation of actual process from the corresponding idealized one.

- Isentropic efficiency are defined differently for different devices since each device is set up for different tasks.

Isentropic

Sin = Sout

Isentropic Efficiencies of Turbines

o the ratio of the actual work output of the turbine to the work output that would be achieved if the process between the inlet state and the exit state were isentropic

s

aT w

w

workturbineIsentropic

workturbineActual

process

isentropicandactualfor

stateexittheatenthalpythe

arehandhwhere

hh

hh

sa

s

aT

22

21

21

• So what is x2 & h2s at isentropic condition? Ws?

Isentropic Efficiencies of Compressor and Pump

o the ratio of the work input required to raise the pressure of a gas to a specified value in an isentropic manner to the actualwork input

a

sC w

w

workcompressorActual

workcompressorIsentropic

12

12

22

12

12

)(

hh

PPv

w

w

processncompressio

isentropicandactualfor

stateexittheatenthalpythe

arehandhwhere

hh

hh

aa

sP

sa

a

sC

• If isentropic efficiency 80%, find the T2 and W?

Find h1 and Pr1 from air tableUse isentropic relation for IG to find Pr2 then get h2s from air table.Use the isentropic efficiency eqn to find h2aUse h2a to find T2

Isentropic Efficiencies of Nozzle

o adiabatic devices

o the ratio of the actual kinetic energy of the fluid at the nozzleexit to the kinetic energy value at the exit of an isentropic nozzle for the same inlet state and exit pressure

s

a

N V

V

exitnozzletheatKEIsentropic

exitnozzletheatKEActual

22

22

process

isentropicandactualfor

stateexittheatenthalpythe

arehandhwhere

hh

hh

velocityexittorelative

smallisfluidthe

ofvelocityinletthewhere

Vhh

sa

s

aN

a

a

22

21

21

22

21 2

• Find the v2s and T2 of isentropic nozzle.

Step 1

Step 2

Step 3

T2s = 748 K, V2s = 666 m/s,T2a = 764 K, V2a = 639 m/s

Summary: Isentropic device

• Isentropic turbine• Ws > Wa

• Isentropic compressor• Ws < Wa

• Isentropic nozzle

• V2s > V2a

A turbine operating at steady state receives air at a pressure of p1 3.0 bar and a temperature of T1 390 K. Air exits the turbine at a pressure of p2 1.0 bar. The work developed is measured as 74 kJ per kg of air flowing through the turbine. The turbine operates adiabatically, and changes in kinetic and potential energy between inlet and exit can be neglected. Using the ideal gas model for air, determine the turbine efficiency.

A steam turbine operates at steady state with inlet conditions of p1 5 bar, T1 320C. Steam leaves the turbine at a pressure of 1 bar. There is no significant heat transfer between the turbine and its surroundings, and kinetic and potential energy changes between inlet and exit are negligible. If the isentropic turbine efficiency is 75%, determine the work developed per unit mass of steam flowing through the turbine, in kJ/kg.

Air enters an adiabatic compressor at 100 kPa and 17°C at a rate of 2.4 m3/s, and it exits at 257°C. The compressor has an isentropic efficiency of 84%. Neglecting the changes in kinetic and potential energies, determine(a) the exit pressure of air(b) the power required to drive the compressor.

• Exercise• Steam enters a nozzle operating at steady state

at p1 1.0 MPa and T1 320C with a velocity of 30 m/s. The pressure and temperature at the exit are p2 0.3 MPa and T2 180C. There is no significant heat transfer between the nozzle and its surroundings, and changes in potential energy between inlet and exit can be neglected. Determine the nozzle efficiency.