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Engineering and Computer ScienceConcordia University

Montral, Qubec H3G 1M 1

Tutorial 8

!utorial "eader# $ndre% &a'oe

(e)t *ee+# Qui -

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-

-

Review: The Otto Cycle

!.e /tto cycle is a standard t.ermodynamic cycle t.at represents an

idealied internal combustion engine0

!.e cycle is a series o' closed system processes

10 !.e cycle begins %it. a polytropic compression o' an ideal gas n2104 'rom

t.e bottom dead center to t.e top dead center0-0 !.is compressed gas is t.en .eated isoc.orically represents 'uel ignition40

30 !.e .ot gas e)pands polytropically n2104 bac+ to t.e bottom dead center0

0 !.e e)panded .ot gas is cooled isoc.orically bac+ to t.e original

temperature and pressure0

!erminology. !op &ead Center !&C4# !.e volume o' t.e system %.en t.e piston

is at t.e top

. 5ottom &ead Center 5&C4# !.e volume o' t.e system %.en t.e

piston is at t.e bottom

. Compression ratio#

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3

3

The Otto Cycle

16-# 7olytropic Compression n2104

-63# 8soc.oric Heat $ddition

36# 7olytropic E)pansion n2104

61# 8soc.oric Heat 9e:ection

P

V

1

2

3

4

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The Brayton Cycle

!.e 5rayton cycle is a standard air cycle t.at operates as a steady 'lo%system0

Heat addition;re:ection are done at constant pressure

Compressor and !urbine %or+ isentropically polytropic %it. n210 'or

air, and adiabatically4

Ho% does t.is di''er 'rom t.e /tto cycle

>

Brayton Cycle Example

State 1: State 2:Polytropic (n=1.4)

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??

Brayton Cycle Example

State 1: State 2:Polytropic (n=1.4)

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Brayton Cycle Example

State 2: State 3:Isobaric

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@@

Brayton Cycle Example

State 3: State 4:Polytropic (n=1.4)

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1A1A

Brayton Cycle Example

State 3: State 4:Polytropic (n=1.4)

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1111

Brayton Cycle Example

State 4: State 1:Isobaric (n=1.4)

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1-1-

Sanity Check

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1313

Sanity Check

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11

Brayton efficiency

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1=1=

Unsteay !rocesses

8' t.e mass o' t.e system c.anges %it. time, t.e process is unsteady

is t.e mass 'lo% rate 4

Bor unsteady 'lo% control volumes, t.e energy o' t.e system changes

%it. time#

*e no% need to account 'or t.is c.ange in energy o' t.e control volume

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1>1>

Unsteay Example

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1?1?

Unsteay Example

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11

The !rocess

5! vol. vap

5! vol. li"#i$

1! vol. vap

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1@1@

The !rocess

5! vol. vap

5! vol. li"#i$

1! vol. vap

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-A-A

The !rocess

5! vol. vap

5! vol. li"#i$

1! vol. vap

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-1-1

The !rocess

5! vol. vap

5! vol. li"#i$

1! vol. vap

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----

The !rocess

5! vol. vap

5! vol. li"#i$

1! vol. vap

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-3-3

The !rocess

5! vol. vap

5! vol. li"#i$

1! vol. vap

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--

The !rocess

5! vol. vap

5! vol. li"#i$

1! vol. vap