More Thermodynamic Cycles

P M V SubbaraoProfessor

Mechanical Engineering Department

The Engineering Systems for High end Extra-somatic Needs…

Brayton Cycle for Power Generation

1-2 Adiabatic compression (in a compressor)

2-3 Constant pressure heat addition

3-4 IAdiabaticexpansion (in a turbine)

4-1 Constant pressure heat rejection

Thermodynamic Analysis of Adiabatic Compression

CompWhmhm 2211

2

1

2211 vdpmhmhm

For an infinitesimal compression:

vdpmdhhmhm

vdpmdhm

vdpdTcp

Model for infinitesimal Adiabatic Process by a perfect Gas

p

dp

T

dT

1

CpT lnln1

ln

CpT lnlnln

1

C

p

Tlnln 1

C

p

T

1

CTp 1

Finite Compression of Perfect gas

CTp 1

Cpv

2

1

11

21 1

p

p

pCmhmhm

2

1

21 vdpmhmhm

2

1121p

dpCmhmhm

2

1

11

21 1

p

pcomp pCmhhmW

Constant Pressure Heat Addition (combustion)

Adiabatic Expansion

4

3

11

43 1

p

pturb pCmhhmW

)( 1212 TTchhw pcomp 1 –2 : Specific work input :

2 – 3 : Specific heat input :

3 – 4 : Specific work output :

4 – 1 : Specific heat rejection :

)( 2323 TTchhq pin

)( 4343 TTchhw ptur

)( 1414 TTchhq pout Adiabatic Processes:

1

1

2

1

2

p

p

T

T 1

4

3

4

3

p

p

T

T

Cycle Analysis

1243 hhhhwww compturnet

)1(1

)()(

13

113

3

TTc

TTT

Tcw

p

pnet

)( 13

13

T

TTTcw pnet

)()( 1243 TTTTcw pnet

)( 1323 TTchhq pin

)(

13

13

13

TTc

TT

TTc

q

w

p

p

in

netth

in

netth q

w

113

13

TTc

TT

c

p

p

11

1

1 1

pr

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 10 20 30

th

pr

Pressure Ratio Vs Efficiency

Reciprocating IC Engine : A Heat Engine

QinQout

Wout

Greatness of Heat Engines

• Balance Sheet for A Heat Engine:– All heat inputs consume resources : Total Input Heat :

Qin (Cost incurred).– All heat outputs are just mere a loss.– Net work Out put is positive and this is the final

benefit : Wnet (Benefit Achieved)– Performance : Benefit to cost ratio (in energy units).

11 iiii WQ

out

iiin

iiout

iiin

ii WWQQ 1111

Otto’s Engine for Propulsion

Modification of Brayton Cycle for Air Craft Propulsion : Invented by Frank Whittle

Large Aircrafts : Boeing 747

Physical Properties of Standard Atmosphere

Altitude(meters)

Temperature(K)

Pressure(kPa)

0 288.15 101.31,000 281.65 89.872,000 275.15 79.493,000 268.65 70.104,000 262.15 61.645,000 255.65 54.026,000 249.15 47.187,000 242.65 41.068,000 236.15 35.599,000 229.65 30.7410,000 223.15 26.4312,000 216.65 19.3315,000 216.65 12.04

Air Craft Engine Bleed for Refrigeration System

Air Standard Refrigeration Cycle for Aircraft Cooling

Air Craft Engine Refrigeration System

Air to Cabin

•The gas power cycle can be used as refrigeration cycles by simply reversing them. •Of these, the reversed Brayton cycle, which is also known as the gas refrigeration cycle, is used to cool aircraft. • Further Modification this cycle is used to obtain very low (cryogenic) temperatures. •The work output of the turbine can be used to reduce the work input requirements to the compressor. •Thus, the performance index of a gas refrigeration cycle is defined as

COPq

w

q

w wRL

net in

L

comp in turb out

, , ,

Gas Refrigeration Systems

More Cycles for Exotic Needs of Urban World …….

An Urban world that was present till the end of first decade of the 20th century.

• Only fresh foods that could be grown locally were available, and they had to be purchased and used on a daily basis.

• Meat was bought during the daily trip to the butcher's; the milkman made his rounds every morning.

• If you could afford weekly deliveries of ice blocks—harvested in the winter from frozen northern lakes—you could keep some perishable foods around for 2 or 3 days in an icebox.

• New York was a virtual ghost town in the summer months.

• Homes were built with natural cooling in mind.

• Ceilings were high, porches were deep and shaded, and windows were placed to take every possible advantage of cross-ventilation

Urban Life after the end of first decade of the 21st century.

• Frozen foods of all kinds were available just about anywhere in the world all year round.

• The milkman was all but gone and forgotten, and the butcher now did his work behind a counter at the supermarket.

• Indeed, many families concentrated the entire week's food shopping into one trip to the market, stocking the refrigerator with perishables that would last a week or more.

• New York is a busy town even in the summer months.

• Buildings are totally isolated from fresh air.

Creation of Artificial Temperature/Quality

Why not use the reversed Rankine cycle for Refrigeration ?• Very costly to expand the liquid using a turbine with very low

or negligible power output!?!

• May become negative under friction.

• Cheaper to have irreversible expansion through an expansion valve.

Thermodynamics of Ideal VCR Cycle

• Ideal Vapor-Compression Refrigeration Cycle

• Process Description

• 1-2 Adiabatic compression

• 2-3 Constant pressure heat rejection in the condenser

• 3-4 Throttling in an expansion valve

• 4-1 Constant pressure heat addition in the evaporator

Performance Index

The performance of refrigerators and heat pumps is expressed in terms of coefficient of performance (COP), defined as

COPQ

W

COPQ

W

RL

net in

HPH

net in

Desired output

Required input

Cooling effect

Work input

Desired output

Required input

Heating effect

Work input

,

,Under the same operating conditions, the COPs are related by

COP COPHP R 1

Samsung Split A/c Model No : AQ24UUA

Cooling Capacity : 7.03kW

Power Consumption (Cooling) : 2,600Watts

Refrigerant Type R22

The refrigerant leaves the evaporator at 7.2oC Condenser pressure : 2.71 MPa.

Heat Pump Systems