diesel cycle and the brayton cycle chapter 9b. rudolph diesel german inventor who is famous for the...

Diesel Cycle and the Brayton Cycle

Chapter 9b

Rudolph Diesel

German inventor who is famous for the development of the diesel engine

The diesel engine is based on a compression ignition system http://www.autonews.com/

files/euroauto/inductees/diesel.htm

Diesel Engines

No spark plugFuel is sprayed into hot compressed

air

State Diagrams for the Diesel Cycle

Diesel Cycle Otto Cycle

The only difference is in process 2-3

Consider Process 2-3

This is the step where heat is transferred into the system

We model it as constant pressure instead of constant volume

23,23, uuuwq outbin

2323, TTChvPuq pin

Consider Process 4-1

This is where heat is rejectedWe model this as a constant v process

That means there is no boundary work

uwq 4141

4141 TTCuqq vout 14 TTCq vout

As for any heat engine…

in

out

in

netth q

q

q

w 1 substitute

2314 and TTCqTTCq pinvout

23

14,

)(1

TTC

TTCn

p

vdieselth

23

141TTk

TT

Rearrange

1

11

232

141,

TTkT

TTTn dieselth

PV

T

PV

TP P

T

T

V

Vrc

3 3

3

2 2

23 2

3

2

3

2

where

rc is called the cutoff ratio – it’s the ratio of the cylinder volume before and after the combustion process

1

11

232

141,

TTkT

TTTn dieselth

rc

PV

T

PV

TV V

T

T

P

P

4 4

4

1 1

14 1

4

1

4

1

where

This doesn’t do us much good

4 4 3 3

1 1 2 2

andk k

k k

PV PV

PV PV

1

11

232

141,

TTkT

TTTn dieselth

rc

14 PP

Since Process 1-2 and Process 3-4

are both isentropic

k

k

k

k

V

V

P

P

V

V

P

P

2

3

2

3

1

4

1

4

1 1

kc

k

rV

V

2

3

1

,

2

11

1

kc

th diesel

c

T rn

kT r

Finally, Since process 1-2 is isentropic

1

1

2

2

1

k

V

V

T

TThe volume ratio from 1 to 2 is the compression ratio, r

1

2

1 1

k

rT

T

Which finally gives…

1

111

1,c

kc

kdieselth rk

r

r

k=1.4

The efficiency of the Otto cycle is always higher than the Diesel cycle

Why use the Diesel cycle?Because you can use higher

compression ratios

Typical range for gasoline engines

P-v Diagram for an ideal dual cycle

Brayton Cycle

Ideal Cycle for Gas Turbine EnginesUsually operate on an open cycle

Closed cycle model for a gas turbine engine

1-2 Isentropic Compression

2-3 Constant Pressure heat addition

3-4 Isentropic Expansion

4-1 Constant Pressure heat rejection

Closed cycle model for a gas turbine engine

1-2 Isentropic Compression

2-3 Constant Pressure heat addition

3-4 Isentropic Expansion

4-1 Constant Pressure heat rejection

23

14, 11

q

q

q

qn

in

outBraytonth

1414 TTChhq pout

2323 TTChhq pin

kkp

Braytonth r 1,

11

1

2

P

Prp

Remainder of the Chapter

I’m not skipping the other sections in this chapter because they are unimportant, or uninteresting

We just don’t have time!!