ENGINES, REFRIGERATORS, AND HEAT PUMPS

This lecture highlights aspects in Chapters 9,10,11 of Cengel and Boles. Every thermodynamic device has moving parts. To understand these movements, it is important that you watch some videos on the Internet. I will go through these slides in two 90-minutes lectures. Zhigang Suo, Harvard University

How humans tell each other something?

• • • •

The thing itself Pictures Words Equations • • • • Language Books Movies The Internet 2

Thermodynamics =

heat + motion

Too many devices to classify neatly • • • • •

Fuel (input):

electricity.

biomass, fossil, solar thermal, geothermal, nuclear,

Application (output):

mobile power plant (transpiration in air, land, sea), stationary power plant (electricity generation), refrigerator, heat pump. Power cycle, refrigeration cycle.

Working fluid:

Gas cycle (air), vapor cycle (steam, phase change).

Fluid-solid coupling:

piston engine (reciprocating, crankshaft), turbine engine (jet, compressor).

Site of burning:

external combustion, internal combustion.

3

Plan •

•

• • • •

Internal combustion engines Gas turbines Stirling and Ericsson engines Vapor power cycle Refrigeration cycle Thermodynamics in a nutshell 4

Combustion engine

burns to move BOILER STEAM WATER

Combustion Engiine I

PISTON PISTON External combustion engine Internal combustion engine (ICE) • • • Steam engine Stirling engine Ericsson engine • • • • Otto (gasoline) engine Diesel engine Gas turbine Jet propulsion US Navy Training Manual, Basic Machines 5

Reciprocating engine

also known as piston engine, converts linear motion to rotation CYLINDER PISTON CONNECTING ROD CRANKSHAFT US Navy Training Manual, Basic Machines 6

1 cycle 4 strokes 2 revolutions Animated engines http://www.animatedengines.com/ exhaust valve closed fuel-air mixture entering cylinder air entering fuel-air mixture being compressed piston moving down Fuel discharging intake from nozzle valve open valve tappet lifting valve cam lobe lifting valve tappet both valves closed piston moving up INTAKE STROKE spark igniting mixture both valves closed COMPRESSION STROKE exhaust valve open intake valve closed piston moving up piston moving down valve tappet lifting valve cam lobe lifting valve tappet EXHAUST STROKE 7 US Navy Training Manual, Basic Machines POWER STROKE

Spark-ignition engine (gasoline engine, petrol engine, Otto engine ) 8

Air-standard assumptions

1.

2.

3.

4.

Model the engine as a

closed system,

and the working fluid as

air

(an ideal gas).

The cycle is

internally reversible

.

Model combustion by

adding heat

from an external source Model exhaust by

rejecting heat

to an external sink 9

Cold

air-standard assumption

Model air as an ideal gas of

constant specific heat

at room temperature (25 ° C).

2 independent variables to name all states of thermodynamic equilibrium 6 functions of state: PTvush 4 equations of state

Pv u

2

h

2

s

2 = -

u

1 -

h

1 -

s

1

RT

=

c v

=

c P

=

c v

( (

T

2

T

2 log è -

T

1 -

T

1

T

2

T

1 ) ) ö

R

log ø

v

2

v

1 Gibbs equation

ds

= 1

T du

+

P T dv c P

/

c v

=

k

,

c P

-

c v

=

R

,

R

= 0.2870kJ/kg isentropic process

Pv k

= constant,

Tv k

× K, 1

k

= 1.4

= constant,

TP

-

k

-

k

1 = constant 10

Thermal efficiency of

Otto cycle

Compression ratio: Conservation of energy: Isentropic processes:

r

=

V BDC V TDC q in w in

=

u

3 -

u

2 =

u

2 -

u

1 =

c v

=

c v

( (

T

3 -

T

2

T

2 -

T

1 , ) ) ,

T

2

T

1 = è

v

1

v

2 ö

k

1 ø =

r k

1 ,

T

3

T

4 =

q out w out

=

u

4 -

u

1 =

u

3 -

u

4 =

c v

=

c v

(

T

4 -

T

1 (

T

3 -

T

4 ) )

v

4

v

3 ö

k

1 =

r k

1 Thermal efficiency: h th, Otto =

w out

-

w in q in

= 1 -

T

4 -

T

1

T

3 -

T

2 = 1 1

r k

1 w out w in 11

Otto cycle

represented in planes of different variables

s 3 q in 2 1 4 q out v

Pv u

2

s

2 = -

u

1 -

s

1

RT

=

c v

=

c v

(

T

2 log è -

T

1

T

2

T

1 ) ö

R

log ø

v

2

v

1 12

Reciprocating engines of two types

Spark-ignition engine (Otto, 1876) Compression-ignition engine (Diesel, 1892) https://ccrc.kaust.edu.sa/pages/HCCI.aspx

13

Compression-ignition engine ( Diesel engine ) compression ratio: cut-off ratio: Conservation of energy: Isentropic processes Thermal efficiency:

r

=

v

1 /

v

2

r c

=

v

3 /

v

2

q in

=

h

3 -

h

2

w net

,

out

=

q in

=

c P

(

T

3 -

T

2 , ) -

q out T

2

T

1 = è

v

1

v

2 ö

k

1 ø =

r k

1 ,

T

3

T

4 =

q out

=

u

4 -

u

1 =

c v

(

T

4 -

T

1 )

v

4

v

3 ö

k

1 =

r

è

r c

ö

k

1 ø h th, Diesel = 1 -

q out q in

= 1 (

T

4

k T

3 -

T

1 -

T

2 ) = 1 1

r k

1 é ê ë

r c k k r c

1 ( ) ù ú û 14

Plan • •

•

• • •

Internal combustion engines Gas turbines Stirling and Ericsson engines Vapor power cycle Refrigeration Thermodynamics in a nutshell 15

Gas turbine ( Brayton cycle ) 4 steady-flow components: isobaric and isentropic P 2 q in 3 1 q out s 4 16

Thermal efficiency of

Brayton cycle

Definition of pressure ratio: Conservation of energy: Isentropic processes: Thermal efficiency:

r p

=

P

2 /

P

1

q in w in

=

h

3 -

h

2 =

h

2 -

h

1 =

c P

=

c P

(

T

3 -

T

2 (

T

2 -

T

1 , ) ) ,

q out w out

=

h

4 -

h

1 =

h

3 -

h

4 =

c P

=

c P

(

T

4 -

T

1 (

T

3 -

T

4 ) )

T

2

T

1 = è

P

2

P

1 ø

k

1

k

=

r P k

1

k

,

T

3

T

4 =

P

3

P

4

k

1

k

=

r P k

1

k

h th, Brayton =

w out

-

w in q in

= 1 -

T

4 -

T

1

T

3 -

T

2 = 1 -

r P k

1 ( ) /

k

17

Brayton cycle has large

back work ratio

w in w out

=

T

2

T

3 -

T

1 -

T

4 =

T

1

T

4 w in w out 18

Intercooling, reheating, regeneration

19

Gas turbine for jet propulsion

Thousands of years of history Who invented this? Hero of Alexandria Frank Whittle (UK), Hans von Ohain (Germany) (first century AD) (during World War II) 20 http://www.techknow.org.uk/wiki/index.php?title=File:Hero_4.jpg

Gas turbine for jet propulsion 6 steady-flow components Propulsive force: Propulsive power: Propulsive efficiency:

F

= ( exit -

V

inlet )

W P

=

FV

h =

W P Q

in 21

http://www.ae.utexas.edu/~plv955/class/propulsion/Cp_air.GIF

22

Air as an ideal gas of

variable specific heat

Pv

=

RT

,

R

= 0.2870kJ/kg × K

u

= ( )

h

= ( )

ds

= 1

T du

+

P T dv s

2 -

s

1 =

s

0 ( ) -

s

0 ( ) -

R

log

P

2

P

1 isentropic process

P

1

P

2 =

P r P r T T

1 ( ) ,

v

1

v

2 =

v r v r

( ) ( ) See section 7.9 for the use of this table 23

Plan • • • •

•

•

Internal combustion engines Gas turbines Stirling and Ericsson engines Vapor power cycle Refrigeration cycle Thermodynamics in a nutshell 24

Displacer-type Stirling engine

https://www.stirlingengine.com/faq/ 25

Stirling engine and regenerator (1816)

reversible cycle between two fixed temperatures, having the Carnot efficiency https://people.ok.ubc.ca/jbobowsk/Stirling/how.html

26

Stirling vs. Carnot

for given limits of volume, pressure, and temperature • On PV plane, the black area represents the Carnot cycle, and shaded areas represent addition work done by the Stirling cycle.

• On TS plane, the black area represents the Carnot cycle, and the shaded areas represent additional heat taken in by the Stirling cycle.

• The Stirling cycle and the Carnot cycle have the same thermal efficiency.

• The Stirling cycle take in more heat and give more work than the Carnot cycle. 27 Walker, Stirling Engine, 1980.

Work out by Stirling cycle

Specific work

w out

= ò

Pdv

=

v

2

v

1 ò

RT H v dv

-

v

2

v

1 ò

RT L v dv

= (

H

-

T L

) log è

v

2

v

1 ø Specific gas constant

Gas

R

=

k B m

molecule

Formula R (kJ/kgK)

Air Steam Ammonia Hydrogen Helium H 2 O NH 3 H 2 He 0.2870

0.4615

0.4882

4.124

2.077

28

Ericsson engine with regenerator (1853)

reversible cycle between two fixed temperatures, having the Carnot efficiency 29

Plan • • • • •

• Internal combustion engines Gas turbines Stirling and Ericsson engines Vapor power cycle Refrigeration cycle Thermodynamics in a nutshell 30

Coal power station

coverts coal to electricity 31

Brayton Point Power Station Sommerset, Massachusetts

Mount Hope Bay http://www.clf.org/blog/clean-energy-climate-change/brayton-point-retirement-means-game-coal-new-england/ 32

Nuclear power station

converts uranium to electricity Animation https://www.awesomestories.com/images/user/be4285df4b.gif

http://www.nuclear-power.net/nuclear-power-plant/ 33

Nine Mile Point Nuclear Power Plant, New York Lake Ontario Cooling tower 34

• • • •

Why water? Why steam?

Water is cheap.

Water flows!

Water is a liquid at the temperature of heat sink (rivers, lakes,...). Vaporization changes specific volume greatly: a lot of work at relatively low pressure.

https://www.ohio.edu/mechanical/thermo 35

Rankine cycle

4 steady-flow components: isobaric and isentropic w pump,in = h 2 - h 1 q boiler,in = h 3 - h 2 w turbine,out = h 3 – h 4 q condenser,out = h 4 – h 1 h thermal =

w

turbine,out -

w

pump,in

q

boiler,in back-work ratio =

w

pump,in

w

turbine,out P q boiler,in 2 3 w pumo,in 1 q condenser, out 4 w turbine,out s 36

Rankin cycle has small back work ratio

back-work ratio =

w

pump,in

w

turbine,out

dh

=

Tds

+

vdP w

pump,in =

h

2

w

turbine,out -

h

1 = =

h

3 -

h

4

P

2

P

1 ò

v dP

=

P

3

P

4 ò

v dP

37

Rankin cycle Vapor cycle Steam turbine Small back-work ratio Brayton cycle Gas cycle Gas turbine Large back-work ratio 38

Carnot cycle is unsuitable as vapor power cycle

Issues with the in-dome Carnot cycle Process 1-2

limits the maximum temperature below the critical point (374 ° C for water)

Process 2-3.

The turbine cannot handle steam with a high moisture content because of the impingement of liquid droplets on the turbine blades causing erosion and wear.

Process 4-1.

It is not practical to design a compressor that handles two phases.

Issues with supercritical Carnot cycle Process 1-2

requires isothermal heat transfer at variable pressures.

Process 4-1

requires isentropic compression to extremely high pressures.

39

Cogeneration

40

Plan • • •

•

• •

Internal combustion engines Gas turbines Stirling and Ericsson engines Vapor power cycle Refrigeration cycle Thermodynamics in a nutshell 41

Refrigerator and heat pump

4 steady-flow components animation

COP R

=

Q L W net

,

in

=

h

1 -

h

4

h

2 -

h

1

COP HP

=

Q H W net

,

in

=

h

2 -

h

3

h

2 -

h

1 42

Selecting Refrigerant

1.

2.

3.

4.

5.

6.

Large enthalpy of vaporization Sufficiently low freezing temperature Sufficiently high critical temperature Low condensing pressure Do no harm: non-toxic, non-corrosive, non-flammable, environmentally-friendly Low cost • • • R-717 (Ammonia, NH 3 ) used in industrial and heavy commercial sectors. Toxic.

R-12 (Freon 12, CCl 2 F 2 ). Damage ozone layer. Banned.

R-134a (HFC 134a, CH 2 FCF 3 ) used in domestic refrigerators, as well as automotive air conditioners.

43

44

45

Plan

•

• • • • •

Internal combustion engines Gas turbines Stirling and Ericsson engines Vapor power cycle Refrigeration cycle Thermodynamics in a nutshell 46

Brayton cycle Jet propulsion, power station Internal combustion Gas cycle Gas turbine Compressor Large back-work ratio Rankin cycle Power station External Combustion Vapor cycle Steam turbine Pump Small back-work ratio Refrigeration cycle Refrigerator, heat pump Electricity Vapor cycle No turbine Vapor compressor No back work w in w out 47

https://flowcharts.llnl.gov/ 48

Pure substance

weights

T

liquid gas vapor liquid P = 0.1 MPa fire

s

2

independent variables to name all states of thermodynamic equilibrium

6

functions of state: PTvush

4

equations of state Incompressible liquid liquid-gas mixture ideal gas

v u

2

s

2 = constant

h

= -

u

1 -

s

1 =

c v

=

c v u

+

Pv

(

T

2 -

T

1 log è

T

2

T

1 ø )

P

=

v u h

= =

s

= =

P sat

1 -

x

( ) ( )

v f

( )

u f

( )

s f

( )

h f

( ) +

xv g

( ) +

xu g

( ) +

xs g

( ) +

xh g Pv

=

RT u

2 -

u

1

s

2 -

s

1 =

c v

=

c v

(

T

2 -

T

1 log è

T

2

T

1 ) ö

R

log

v

2 ø

v

1

h

=

u

+

Pv

49

Concepts and definitions

Isolated system Quantum states of an isolated system Fundamental postulate States of thermodynamic equilibrium Functions of state Phases Number of quantum states of an isolated system: Entropy of an isolated system: Isolated system generates entropy. Irreversibility Isolated system conserves energy and volume: Model a closed system as a family of isolated systems: Definition of temperature (Gibbs equation 1): Definition of pressure (Gibbs equation 2): W

S

=

k B

log W 1

U

,

V

( )

T

= ¶ ( ) ¶

U P T

= ¶ ( ) ¶

V

Definition of enthalpy: Definition of Helmholtz function (free energy): Definition of Gibbs function: Definition of heat capacities:

H

=

U

+

PV F

=

U G

=

U

-

TS

-

TS

+

PV C V

= ¶ ( ) ¶

T

,

C P

= ¶ ( ) ¶

T

50

Theory of everything

the world according to entropy • • • • • • • • • • Entropy Equilibrium Irreversibility Temperature, energy Pressure, volume Phases Ideal gas Osmosis Turbines, compressors, throttling valves, heat exchangers, diffusers, nozzles Engines, refrigerators, heat pumps 51

Summary

• • • • • • • • Engine converts fuel to motion.

Refrigerator and heat pump use work to pump heat from a place of low temperature to a place of high temperature. Many ideal cycles are internally reversible, but externally irreversible.

Stirling and Ericsson cycles are internally and externally reversible, so they have the same thermal efficiency as the Carnot cycle.

Use ideal-gas model to analyze gas as working fluid.

Use property table to analyze vapor as working fluid.

Model piston engine as a closed system (Otto, Diesel, Stirling, Ericsson).

Model turbine (or compressor) device as steady-flow components in series (Brayton cycle, Rankine cycle, refrigeration cycle).

52