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Engine Cycles

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(1)

Engine Cycles

Internal Combustion Engines

(2)

Air-standard Cycles

Real air-fuel cycles approximated with air-standard cycles due to difficulties in analysis

Differences from the actual cycles

Gas mixtures treated as air

Closed cycles assumed instead of actual open cycles Combustion replaced with heat addition

Exhaust replaced with heat rejection Ideal processes assumed (reversible)

Intake and exhaust: Constant pressure processes Compression and expansion: Isentropic process

Combustion: Constant volume (for SI) and constant pressure (for CI) processes

Exhaust blowdown: Constant volume process

(3)

Ideal Gas Relationships

Thermodynamics Air properties

k T T

w R

k v P v

w P TP Tv

Pv

dT c du

dT c dh

RT P

mRT PV

RT Pv

k k k

k v p

1

) (

1

constant constant constant

1 2 2

1

1 1 2

2 2

1

/ ) 1 (

1

K - kJ/kg 287

. 0 1.35 /

K - kJ/kg 821

. 0

K - kJ/kg 108

. 1

v p

v p v

p

c c

R

c c k c c

K - kJ/kg 287

. 0 1.40 /

K - kJ/kg 718

. 0

K - kJ/kg 005

. 1

v p

v p v

p

c c

R

c c k c c

Inside engines in operation and exhaust flows

Inlet flows in turbochargers etc and air flow in radiators

Isentropic process

(4)

Variables for Cycle Analysis

air-fuel ratio mass flow rate

heat transfer per unit mass for one cycle heat transfer rate per unit mass

heat transfer for one cycle heat transfer rate

heating value of fuel compression ratio

work for one cycle power

combustion efficiency

Subscripts

m f a

ex

air fuel

exhaust

mixture of all gases

c c HV

W W r Q

Q Q q q m

AF

(5)

Otto Cycle

Four-stroke, naturally apsirated SI engines at WOT approximated with an Otto cycle

6 5

1 4 3

2

P0

Pressure, P

Volume, V

TDC BDC

Volume, V

Pressure, P

(6)

Otto Cycle: Intake Stroke

Process 6-1: Constant pressure

Intake valve open and exhaust valve closed

1 6

0 1

6

0 6

1

v v

P w

P P

P

6 5

1 4 3

2

P0

Pressure, P

Specific volume, v

TDC BDC

Actual pressure > P0 Temperature rise bet’n 25-35°C

Real cycles

(7)

Otto Cycle: Compression Stroke

Process 1-2: Isentropic All valves closed

   

   

 

1 2

2 1

1 2

1 1 2

2 2

1 2 1

1 2

1 1 2

1 1

1 2 1 1 2

1 1

0

/ /

T T

c u

u

k T T

R k

v P v

w P q

r P v

v P P

r T v

v T T

v

k c k

k c k

6 5 1

4 3

2

P0

Pressure, P

Specific volume, v

TDC BDC

Beginning: Slight opening of intake vale aBDC End: Firing of spark plug bTDC

Real cycles

(8)

Otto Cycle: Combustion

Process 2-3: Constant-volume heat input All valves closed

 

   

   

 

max 3

max 3

2 3

2 3

in 3

2

2 3

2 3

2 3

in 3

2 3 2

TDC 2

3

1 AF 0

P P

T T

u u

T T

c q

q

T T

c Q

T T

c m m

T T

c m

Q m Q

Q w

v v

v

v v c

HV

v f a

v m

c HV f

6 5

1 4 3

2

P0

Pressure, P

Specific volume, v

TDC BDC

(9)

Otto Cycle: Power Stroke

Process 3-4: Isentropic All valves closed

   

   

 

3 4

4 3

3 4

3 3 4

4 4

3

3 4

3 3 4

1 3

1 4 3 3 4

4 3

1 1

/ 1 /

/ 1 /

0

T T

c u

u

k T T

R k

v P v

w P

r P

v v P P

r T

v v T T

q

v

k c k

k c k

6 5 1

4 3

2

P0

Pressure, P

Specific volume, v

TDC BDC

Beginning: Combustion

End: Exhaust valve opening bBDC

Real cycles

(10)

Otto Cycle: Exhaust Blowdown

Process 4-5: Constant-volume heat rejection Exhaust valve open and intake valve closed

Enthalpy carried away, limiting thermal efficiency

 

 

 

1 4

4 5

4 5

out 5

4

4 1

4 5

out 5

4 5 4

BDC 1

4 5

0

T T c u

u

T T

c q

q

T T c m

T T

c m Q Q

w

v v

v v

v v v m

v m

6 5 1

4 3

2

P

0

Pressure, P

Specific volume, v

TDC BDC

(11)

Otto Cycle: Exhaust Stroke

Process 5-6: Constant pressure

Exhaust valve open and intake valve closed

Processes 6-1, 5-6

sometimes left off since these cancel each other

 

6 1

0

5 6

0 6

5

0 5

6

v v

P

v v

P w

P P

P

6 5 1

4 3

2

P0

Pressure, P

Specific volume, v

TDC BDC

Actual pressure < P0

Real cycles

(12)

Otto Cycle: Thermal Efficiency

Thermal efficiency: Depending only on temperature

Using relations for processes 1-2, 3-4

Therefore,

 

 

34 21

34 21

OTTO

1 1

/ 1

/

T T

T T

T T

c

T T

c

q q

q w

v v

in out

in net

t

   

2 3 1

4

4 3 1

3 4 1

2 1 1

2

/ /

/ /

/ /

T T T

T

T T v

v v

v T

T k k

 

 

 

 

1

1 2 1

2 OTTO 1

/ 1 1

/ / 1 1

/ 1

k c

k t

r v v T

T

Compression ratio, rc Thermal efficiency, t (%)

Prob. 3-1

1

4 3

2

Entropy, s

Temperature, T

(13)

Real Air-fuel Cycles

Open cycle with changing compositions

Gas compositions change during combustion Molar quantities change

Fuels added sometimes during the cycles (CI, some SI) Liquid fuel droplets introduced sometimes

Crevice flows and blowby past the pistons

Non-ideal and no air

Inlet flow: Air with up to 7% fuel

Exhaust flow: CO2, H2O, N2, CO, HC, part, etc.

Non-ideal gas behavior during combustion (high pressure)

Non-constant specific heats: As high as 30% change in the engine temperature range

(14)

Real Air-fuel Cycles

Heat loss during the cycle

Power stroke starts at a lower pressure and work output is decreased Lowered temperature and pressure at the power stroke end

Lower indicated thermal efficiency

Short but finite combustion time

Finite time desirable; e.g. supersonic detonation would result in a rough cycle and shorten engine life

Starts bTDC: Negative work in the compression stroke Completes aTDC: Some power lost in the power stroke

Combustion efficiency of >100%: incomplete mixing, local variations in temperature, turbulence, quenching, etc. (SI: ~95%, CI: ~98%)

(15)

Real Air-fuel Cycles

Finite blowdown time

Exhaust valves open 40-60° bBDC → Some work lost

Intake valves open bTDC

Due to flow restriction (lowered volumetric efficiency otherwise) Compression delayed → lowered temperature and pressure rise before combustion

Finite valve times: Smooth cam profiles

Valve overlap

Errors with QLHV since different property values Approximation

 

t actual 0.85

 

t OTTO

(16)

SI Engine Cycle at Part Throttle

Flow restriction with a partially closed throttle

Pressure drop in the incoming air (Temperature similar)

The lower loop: negative work

The lower pressure →

lower pressures throughout the rest of the cycle (exception: atmospheric press at exhaust stroke)

Less air, fuel → Less thermal energy, work out (similar temperature rise)

 

 

 

 

pump

net d i ex d

ex net i

pump

d ex ex

d i i

P P

V W

V P P

W

V P V

V P W

V P V

V P W

/ pmep

5 6

6 5

6 1

1 6

Specific volume, v

Pressure, P

P0

TDC BDC

1 5 4 3

2

6

6a

(17)

Part Throttle SI w/Super-, Turbochargers

Intake pressure > Atmospheric pressure → Higher pressure throughout the cycle

Positive net pumping work Increased air and fuel

Increased temperature (compressive heating)

Sometimes, self-ignition or knocking

Aftercooler or

Lower compression ratio

(18)

Exhaust Process

Consists of blowdown and exhaust stroke Blowdown: A large % of gases leaving

Approximated with ideal gas isentropic relationship Temperature decrease due to expansion cooling

Modeling an actual open system as a closed system

(7: Hypothetical state)

   

ex

k k

 

k k

k k k

k

P P T P

P T

P P T P

P T T

/ ) 1 ( 4 4 0

/ ) 1 ( 4 4

/ ) 1 ( 3 3 7

/ ) 1 ( 4 4 7

7

/ /

/ /

Specific volume, v

TDC BDC

7 7c 7b 7a 5

1 4

(19)

Exhaust Residual

Mass bet’n blowdown and exhaust stroke Mass after the exhaust stroke

Mass in the cylinder during the entire cycle Exhaust residual

7 1 7

5 5

7 V /v V /v V /v

m ex

7 2 7

6 /v V /v

V

mex

7 7 4

4 3

3 2

2 1

1 /v V /v V /v V /v V /v

V

mm

7 2 7

7 7

2 / )/( / ) /

(V v V v V V

xr

 

) / )(

/ )(

/ 1 (

) / /(

) / (

) / 1 (

) / )(

/ 1 ( ) / )(

/ ( ) / /(

) / (

4 4

7 7 4

4

7 4 7

4 4 6 4

4 7

6

P P

T T r

P RT

P RT

r

v v r v

v V V v

V v

V x

ex ex

c c

c r

OR

m ex

r m m

x /

(20)

Gases leaving during blowdown have high kinetic energy due to high velocity

Enthalpy (temperature) rise in exhaust manifold This rise is progressively reduced

It is desirable to mount the turbine of a turbocharger close to the exhaust manifold

Exhaust Kinetic Energy

Specific volume, v

TDC BDC

7 7c 7b 7a 5 1

4

(21)

Energy Balance during Intake

Total enthalpy conserved for incoming and exhaust air

Temperature of the gas mixture at the compression stroke start

Volumetric efficiency is reduced due to hot exhaust residual, which reduces incoming air density

exex p mex

exa

p aa mm

pa m m

m m a

a ex

ex

T T

m m

T m m

T c m T

c m T

c m

h m h

m h

m

/ /

 

Tm 1 xrTex

1 xr

T a

Prob. 3-2,3

(22)

Diesel Cycle: Combustion

Combustion lasts into the expansion stroke due to ignition delay and finite injection time

→ Constant-pressure process for combustion Combustion: Process 2-3 (heat input)

Cutoff ratio: V3 /V2 v3 /v2 T3 /T2

 

 

   

 

max 3

2 3 2 2

3 3

2 3

2

2 3 2

3 in

3 2

2 3

2 3 2 3 in

3 2

) (

) (

1 AF

T T

v v P u

u q

w

h h T

T c q

q

T T c Q

T T c m m

T T c m

Q m Q

Q

p p c

HV

p f a

p m

c HV f

0

Specific volume, v

TDC BDC

Pressure, P

Entropy, s

Pressure, P

(23)

Diesel Cycle: Thermal Efficiency

Thermal efficiency

With rearrangements

The number in the bracket > 1

Thermal efficiency: Otto > Diesel for a given compression ratio Compression ratio: CI > SI

 

 

34 12

 

43 12

DIESEL

1 1

/ 1

/

T T

k

T T

T T

c

T T

c

q q

q w

p v

in out

in net

t

 

 

1 1 1 1

1

DIESEL

k r

k k

c t

Prob. 3-4

(24)

Dual Cycle

Modern CI engine: Injection of fuel ~20° bTDC

Const. P heat combustion + const. V heat combustion

Modern CI: Dual cycle

Historic CI: Diesel cycle

Volume, V Volume, V

Pressure, P

(25)

Dual Cycle: Combustion

Process 2-x: Constant-volume heat input

Pressure ratio

 

 

 

2

2 max

2 2

2

2 2

2 2

2

/ 0

T T P P

P

u u

T T

c q

T T

c m m

T T

c m Q

w

V V

V

x x

x x

v x

x v f a

x v m x

x

TDC x

   3 1

2 2

3

2 / / 1/ /

/P P P T T r P P

Px x c k

TDC BDC

Specific volume, V

Pressure, P 2

x 3

Temperature, T

Entropy, s 2

x

3

(26)

Dual Cycle: Combustion

Process x-3: Constant-pressure heat input

Cutoff ratio Heat in

 

   

 

max 3

3 3 3

3 3

3

3 3

3

3 3

3

max 3

) (

) (

) (

T T

v v

P v

v P

u u

q w

h h

T T

c q

T T

c m m

T T

c m Q

P P

P

x x

x

x x

x

x x

p x

x p

f a

x p

m x

x

TDC BDC

Specific volume, V

Pressure, P 2

x 3

Temperature, T

Entropy, s 2

x

3 x

x v v V V T T

v

v3 / 3 / 2 3 / 2 3 /

x   x

x x

in

c HV f x

x in

h h u

u q

q q

Q m Q

Q Q

3 2

3 2

3

2

(27)

Dual Cycle: Thermal Efficiency

Thermal efficiency:

With rearrangements

For real diesel engines

 

x p x x   x

v

v

in out in

net t

T T k T T

T T T

T c T T c

T T c

q q

q w

3 2

1 4 3

2

1 4 DUAL

1 1

/ 1

/

 





1 1

1 1 1

1

DUAL



k r

k k

c t

   

 

actualactual 0.85

 

DUALDIESEL

85 . 0

t t

t t

: History engines

: Modern engines

(28)

Comparison of Different Engines

For a given compression ratio:

Heat transfer:

Area under the process line

 

t OTTO

 

t DUAL

 

t DIESEL

in out

q

q : Identical : Different

(29)

Comparison of Different Engines

For a given peak pressure:

Heat transfer:

Area under the process line

For the most efficient engine

Combustion as close to constant volume

Higher compression ratio

 

t DIESEL

 

t DUAL

 

t OTTO

in out

q

q : Identical : Different

Prob. 3-5

(30)

Two-stroke Cycles

Very small and large engines in two-stroke cycles

Small engines: No valves etc. → Lightweight and inexpensive

Large engines: One power stroke per cycle → Smooth operation at low RPM

No exhaust stroke and imperfect scavenging

Large amount of exhaust residual

Air-fuel mixture diluted and combustion temperature lowered Reduces NOx emissions but creates other problems in catalytic systems

(31)

Two-stroke SI Engine Cycles

Process 1-2: Isentropic power or expansion All ports closed

Process 2-3: Exhaust blowdown Exhaust port open, intake closed

Process 3-4-5:

Intake and exhaust scavenging Exhaust and intake ports open

 

 

 

k T T R k

v P v

w P q

v v P P

v v T T

k k

1 1

0 / /

1 2 1

1 2 2 2

1 2 1

2 1 1 2

1 2 1 1 2

Volume, V

(32)

Two-stroke SI Engine Cycles

Process 5-6: Exhaust scavenging Exhaust open, intake closed

Process 6-7: Isentropic compression all ports closed

Process 7-1: Constant-volume heat input (combustion)

All ports closed

Volume, V

 

 

 

k 1

T T R k

1

v P v

w P

0 q

/v v P P

/v v T T

6 7 6

6 7 7 7

6 7 6

k 7 6 6 7

1 k 7 6 6 7

1 7

7 max 1

max 1

7 1 v m c

HV f in 1

7 1 7

TDC 1

7

/T T P P

P T T

T T c η m

Q m Q

Q

0 W

V V V

(33)

Two-stroke CI Engine Cycles

Combustion approximated by a two-step process Process 7-x:

Constant-volume heat input

Process x-1:

Constant-pressure heat input

7

7 max

7 7

7 7

/ 0

T T P P

P

T T c m Q

W

V V V

x x

x v m x

x

TDC x

max 1

1 1

1 1 1

max 1

T T

T T c m Q

V V P W

P P P

x v

m x

x x

x

Prob. 3-7

(34)

Miller Cycle

Modern modification of the Atkinson cycle Expansion ratio > compression ratio

Utilizing a unique valve timing

Intake valve closed bBDC or aBDC

Read 3.9, 3.10 Prob. 3-6

Atkinson cycle Miller cycle Super- or turbocharged

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