Department of Mechanical EngineeringME 322 – Mechanical Engineering

Thermodynamics

Lecture 28

Internal Combustion Engine ModelsThe Otto CycleThe Diesel Cycle

IC Engine TerminologyFinally … here is one of the reasons we spent so much time analyzing piston-cylinder assemblies in the early part of the course!

disp BDC TDC

BDC

TDC

V V V

VCR

V

BDCV

TDCV

2

IC Engine Terminology• Fuel-Air ignition

– Spark• Gasoline engines

– Compression• Diesel engines

• 4-Stroke Engine– Four strokes (intake, compression, power stroke, exhaust)

are executed for every two revolutions of the crankshaft, and one thermodynamic cycle

• 2-Stroke Engine– Two strokes (intake, compression, power stroke, and

exhaust) are executed for every one revolution of the crankshaft, and one thermodynamic cycle

3

IC Engine PerformanceThermal Efficiency

netth

in

WQ

Mean Effective Pressure

net work for one cyclemepdisplacement volume

The mep provides a way to compare two engines that have the same displacement volume

4

Modeling the IC Engine• Air Standard Analysis (ASC or hot ASC)

– The working fluid is a fixed mass of air treated as an ideal gas

• No intake or exhaust– The combustion process is replaced with a heat transfer

from a high-temperature source– The exhaust process is replaced with a heat transfer to a

low-temperature sink– All processes are internally reversible

• Cold Air Standard Analysis (cold ASC)– All of the above– Heat capacity of the air is assumed to be constant at the

ambient temperature

5

SI Engine - Otto Cycle

6

• 1-2 Isentropic compression from BDC to TDC

• 2-3 Isochoric heat input (combustion)

1 2 3 4

BDC

TDC

P

1

2

3

4

BDCTDC

T

s1

2

3

4v = co

nst

v = co

nst

v

12 2 1W m u u

23 3 2Q m u u

SI Engine - Otto Cycle

7

• 3-4 Isentropic expansion (power stroke)

• 4-1 Isochoric heat rejection (exhaust)

1 2 3 4

BDC

TDC

P

1

2

3

4

BDCTDC

T

s1

2

3

4v = co

nst

v = co

nst

v

34 3 4W m u u

41 4 1Q m u u

Otto Cycle Performance

34 12 4 1,ASC

23 3 2

1netth

in

W W W u uQ Q u u

Thermal Efficiency

P

1

2

3

4

BDCTDCv

Compression Ratio

1 4

2 3

v vCRv v

11,cold ASC

2

1 1 kth

T CRT

T

s1

2

3

4v = co

nst

v = co

nst

8

Otto Cycle PerformanceMean Effective Pressure

3 4 2 134 12

1 2

mep net

disp disp

u u u uW W WV V v v

P

1

2

3

4

BDCTDCv

T

s1

2

3

4v = co

nst

v = co

nst

3 4 2 1cold ASC

1 2

mep vc T T T Tv v

Btu Btu0.24 0.172lbm-R lbm-R

1.4

p v

p

v

c c

ck

c

Cold ASC values (Table C.13a) ...

9

CI Engine - Diesel Cycle

10

• 1-2 Isentropic compression from BDC to TDC

• 2-3 Isobaric heat input (combustion)

1 2 3 4

BDC

TDC

P

1

2 3

4

BDCTDC

T

s1

2

3

4

P = const

v = co

nst

v

12 2 1W m u u

23 23 3 2Q W m u u

CI Engine - Diesel Cycle

11

• 3-4 Isentropic expansion (power stroke)

• 4-1 Isochoric heat rejection (exhaust)

1 2 3 4

BDC

TDC

34 3 4W m u u

41 4 1Q m u u

P

1

2 3

4

BDCTDC

T

s1

2

3

4

P = const

v = co

nst

v

Diesel Cycle Performance

23 34 12 4 1,ASC

23 3 2

1netth

in

W W W W u uQ Q h h

Thermal Efficiency

Compression Ratio

1

2

vCRv

1

,cold ASC

11

1

k k

th

CR CO

k CO

Cutoff Ratio3

2

vCO

v

P

1

2 3

4

BDCTDC

T

s1

2

3

4

P = const

v = co

nst

v

12

Diesel Cycle PerformanceMean Effective Pressure

3 2 4 123 34 12

1 2

mep net

disp disp

h h u uW W W WV V v v

3 2 4 1cold ASC

1 2

mep p vc T T c T Tv v

P

1

2 3

4

BDCTDC

T

s1

2

3

4

P = const

v = co

nst

v

Btu Btu0.24 0.172lbm-R lbm-R

1.4

p v

p

v

c c

ck

c

Cold ASC values (Table C.13a) ...

13

Cycle Evaluation• Strategy

– Build the property table first, then do the thermodynamic analysis

• Real fluid model– EES (fluid name = ‘air_ha’)

• Air standard model– Ideal gas with variable heat capacities

• Table C.16 (Air Tables)• EES (fluid name = ‘air’)

• Cold air standard model– Ideal gas with constant heat capacities evaluated at the

beginning of compression• Atmospheric conditions

14

IC Engine Performance• Known Parameters

– Number of cylinders in the engine– Enough information to determine

the mass of the air trapped in thecylinder

– Engine ratios (compression and cutoff)– Rotational speed of the engine (rpm)– Engine type

• All cylinders complete a thermodynamic cycle in either two or four strokes

– P and T at the beginning of compression– P or T at the end of combustion

15

IC Engine Performance

16

The power developed by the engine can be determined by

net cyl netr

W N WN

rev

Btu hp-minmincylcyl-cycle Bturev

cycle

netW

From the Otto or Diesel Cycle analysis conversion factor

Crankshaft revolutions per cycle

Crankshaft rotational speedNumber of cylinders