Mechanical Engineers Data Handbook Episode 6 ppsx

116 MECHANICAL ENGINEER’S DATA HANDBOOK 3.7.3 Reheat factor and overall efficiency Referring to the ‘condition curve’ on the h-s diagram: AhA =available stage enthalpy drop Ah, = isen

THERMODYNAMICS A N D HEAT TRANSFER 115

Velocity compounded impulse turbine

One row of nozzles is followed by two or more rows of

moving blades with intervening rows of fixed blades of

the same type which alter the direction of flow

Two-row wheel Assume PI = P2, k = 1 and that all

blades are symmetrical

c,

(exit velocitv)

Maximum efficiency vmax =cosz a (at p = y)

in which case the steam leaves the last row axially

3.7.2 Impulse-reaction turbine

In this case there is ‘full admission’, i.e e= 360” Both

nozzles and moving blades are similar in shape and

have approximately the same enthalpy drop Referring

to the figure:

Enthalpy drop = (h, - h , ) (for the fixed blades)

= (h, - h 2 ) (for the moving blades)

50% reaction (Parson’s) turbine

In this case the velocity diagram is symmetrical

2nR,hC sin a

Mass flow rate m =

V

where: a= blade outlet angle

Enthalpy drop per stage Ahs = C’p(2 cos a - p)

2 cos2 a

(1 + cos2 .) Maximum efficiency qmX = (when p =cos a )

116 MECHANICAL ENGINEER’S DATA HANDBOOK

3.7.3 Reheat factor and overall efficiency

Referring to the ‘condition curve’ on the h-s diagram:

AhA =available stage enthalpy drop

Ah, = isentropic stage enthalpy drop

AhoA = available overall enthalpy drop

Aho, = isentropic overall enthalpy drop

Stage efficiency qs=- Ah,

The gas turbine unit operates basically on the con-

stant-pressure cycle, particularly in the case of the

‘closed cycle’ In the ‘open cycle’ air is drawn in from

the atmosphere, compressed and supplied to a com-

bustion chamber where fuel is burnt with a large

amount of ‘excess air’ The hot gases drive a turbine

which drives the compressor and also provides useful

work The efficiency increases with compression ratio

The output power increases with both compression ratio and turbine inlet temperature

The effect of losses and variation in fluid properties

is shown on the basic cycle The efficiency of the basic cycle can be greatly increased by incorporating a heat exchanger between the compressor outlet and the combustion chamber inlet It uses the exhaust gases from the turbine to preheat the incoming air

(cP = specific heat for turbine

cccp = specific heat for combustion chamber

yc = ratio of specific heats for compressor

yl =ratio of specific heats for turbine

qc = isentropic compressor efficiency

ql = isentropic turbine efficiency

J

1

3.8.1 Simple cycle

Pz P3 Comnrensinn rg tin r = - = -

s

Heat supplied Q = c , T , ( t - c ) per kg of air

Work done =Turbine work out -Compressor work in

CC = wmbustion chamber tubine

Simple cycle with isentropic eficiencies and variable specijc heats

Work done = Turbine work out - Compressor work in

Heat supplied Q = ==cP T3 - TI - ~ (Tz-T1)] per kg of air

v c

W lcp( T3 - T,)ql

118 MECHANICAL ENGINEER’S DATA HANDBOOK

3.8.2 Simple cycle with heat exchanger T

The ideal gas cycle is the Carnot cycle and, in practice,

only about half of the Carnot cycle efficiency is realized

between the same temperature limits

4

T2 Efficiency q = 1

THERMODYNAMICS A N D HEAT TRANSFER 119

Work done (per kg) W = ( T , - T 2 ) ( s 1 -s4)

Heat supplied (per kg) Q = T , (s, - s4)

3.9.2 Constant pressure cycle

In this cycle, heat is supplied and rejected at constant

pressure; expansion and compression are assumed to

take place at constant entropy The cycle was once

known as the Joule or Brayton cycle and used for

hot-air engines It is now the ideal cycle for the closed

gas turbine unit

Work ratio = 1 - - r

3.9.3 O t t o cycle (constant-volume cycle)

This is the basic cycle for the petrol engine, the gas engine and the high-speed oil engine Heat is supplied and rejected at constant volume, and expansion and compression take place isentropically The thermal efficiency depends only on the compression ratio

1 Efficiency q= 1 r Y - l

P

I

V

120 MECHANICAL ENGINEER’S DATA HANDBOOK

3.9.5 Dual combustion cycle

Modern diesel engines follow a similar cycle to this

ideal one In this case combustion takes place partly at

constant volume and partly at constant pressure

(kPY - 1 )

C(k-l)+(B-l)yk]rY-l

Efficiency q = 1 -

V

3.9.6 Practical engine cycles

In actual engines the working substance is air only in the induction and compression strokes During expan- sion and exhaust the working substance consists of the products of combustion with different properties to air In addition, the wide variations in temperature and pressure result in variation in the thermal proper- ties Another factor is ‘dissociation’ which results in a lower maximum temperature than is assumed in elementary treatment of the combustion process

3.10 Reciprocating spark ignition internal combustion engines

3 IO I Four-stroke engine

The charge of air and fuel is induced into the engine

cylinder as the piston moves from top dead centre

(TDC) to bottom dead centre (BDC) The charge is

then compressed and ignited by the sparking plug

before TDC producing high pressure and temperature

at about TDC The gas expands and work is produced

as the piston moves to BDC A little before BDC the

exhaust valve opens and the gases exhaust The

process is completed during the next stroke A typical

‘timing diagram’ (section 3.10.3) and the p-v diagram

are shown Formulae are given for power, mean effec-

tive pressure, efficiency and specific fuel consumption

Pressure-volume (p-v) diagram:

A=area of power loop

B=area of pumping loop

THERMODYNAMICS AND HEAT TRANSFER 121

Coding water jacket-

Crank angle, e

Typical timing diagram

where: N =number of revolutions per second,

n =number of cylinders, A , =piston area (m'),

jackel

zmiw-I -

Combustion chamber Push md

where: m=mass flow rate of fuel (kgs-I), LCV=

lower calorific value of fuel (J kg-')

Specific fuel consumption SFC =- m (kg s- ' W - ')

P b

Volume of induced air at NTP Swept volume of cylinder Volumetric efficiency )I,, =

where: NTP = normal temperature and pressure

Pressure-volume ( p u ) diagram:

A =area of power loop

B = area of pumping loop

K

Indicated mean effective pressure (IMEP): pi = ( A - B ) -

L*

V

122 MECHANICAL ENGINEER'S DATA HANDBOOK

Crankcase diagram

where: K =indicator constant

Indicated power P,=p,A,LNn

Both four-stroke and two-stroke engines may have

compression ignition instead of spark ignition The air

is compressed to a high pressure and temperature and

the fuel injected The high air temperature causes

combustion

3.10.3 Timing diagrams

Four-stroke engine

IO =inlet valve opens

IC =inlet valve closes

EO=exhaust valve opens

EC = exhaust valve closes

S =spark occurs

I =inlet angle (approx 80')

E =exhaust angle (approx 120")

T = transfer angle (approx 100")

THERMODYNAMICS AND HEAT TRANSFER 123

Mechanical efliclency ' s brake power

Power, MEP, mechanical efficiency vs speed

Max '\i power

Max economy

124 MECHANICAL ENGINEER'S DATA HANDBOOK

3 I I Air compressors

The following deals with positive-displacement-type

compressors as opposed to rotodynamic types The

reciprocating compressor is the most suitable for high

pressures and the Roots blower and vane compressor are most suitable for low pressures

3 I I I Reciprocating compressor

This consists of one or more cylinders with cranks,

connecting rods and pistons The inlet and outlet

valves are of the automatic spring-loaded type Large

cylinders may be water cooled, but small ones are

usually finned

Air is drawn into the cylinder at slightly below

atmospheric pressure, compressed to the required

discharge pressure during part of the stroke, and

finally discharged at outlet pressure A small clearance

volume is necessary The cylinders may be single or

T = free air temperature

T , =inlet air temperature

T2 =discharge temperature

V, = swept volume

Vc =clearance volume

Va - Vd =induced volume

R = gas constant for air

n =index of expansion and compression

y = ratio of specific heats for air

rit = air mass flow rate

Q = free air volume flow rate

N = number of revolutions per second

Z = number of effective strokes per revolution

(= 1 for single acting; 2 for double acting)

THERMODYNAMICS A N D HEAT TRANSFER 125

The efficiency is increased by using more than one

stage if intercooling is used between the stages to

reduce ideally the temperature of the air to that at the

first stage inlet The cylinders become progressively

smaller as the pressure increases and volume de-

~ 3 0 for two stages

This has two rotors with 2,3 or 4 lobes which rotate in

opposite directions so that the lobes mesh Compres-

sion takes place at approximately constant volume

Work input per revolution W = p , VS(r- 1 )

of non-metallic material, between which the air is trapped Reduction in the volume between vanes as the

126 MECHANICAL ENGINEER'S DATA HANDBOOK

3.12.1 Power and flow rate

Referring to the p V diagram:

Power P = N pI(Vl- V 6 ) + (P1 v1- Pz VZ)

-p3(v3 - v4)- (J'5v5 P4v'J]

n- 1 where n = index of expansion and compression

rotor rotates produces compression Higher pressures

may be attained by using more than one stage The

work is done partly isentropically and partly at

constant volume Assuming ideal conditions:

Isentropic work done Wi=-p, V s ( r ( T ) - 1)

Pi

where: r = -

P1

Y Y - 1 (Y-1)

p 6

4

(P, -Pi) V, Constant-volume work done W, =

r1$

PZ where r1 =-

Pi

Total work done per revolution W, = Wi + W ,

Pressure ratio: G8.5 normally

Two-stage vane compressor

3.12 Reciprocating air motor

Reciprocating air motors are used extensively for tools

such as breakers, picks, riveters, vibrators and drillers

They are useful where there is fire danger such as in

coal mines The operating cycle is the reverse of that for the reciprocating compressor

Mass flow rate of air m = N

where: "=(?r P4 and z=(?Y

THERMODYNAMICS AND HEAT TRANSFER 127

3 I 3 Refrigerators

Two basic types are considered, the ‘vapour compres-

sion refrigerator’ and the ‘gas refrigerator’ The former

consists of a compressor followed by a condenser

where the refrigerant is liquified at high pressure It is

then expanded in a ‘throttle valve’ to a lower pressure

and temperature and finally evaporated in an ‘evapor- ator’ before re-entry into the compressor The cycle is similar to the Rankine cycle in reverse

The gas cycle is the reverse of a closed gas-turbine cycle, Le the constant pressure or Joule cycle

3.13 I Vapour compression cycle

The process can be shown on the temperature entropy

(T-s) chart for the appropriate refrigerant, e.g ammo-

Degree of undercooling AT= T3 - T4

(4) Throttling from 4 to 5 Therefore h , = h 4 and

W

Heat removed Q = mRE where: m = mass flow rate of refrigerant

3.13.2 Pressure-enthalpy chart

The pressure-enthalpy chart is a more convenient way

of showing refrigeration cycles Work in and refriger- ation effect can be measured directly as the length of a line

If p , , pz and the under cooling temperature T4 are

known, the diagram can be easily drawn and RE and

W scaled off as shown

3.13.3 Gas refrigeration cycle

Referring to the T-s diagram:

128 MECHANICAL ENGINEER'S DATA HANDBOOK

Refrigeration effect RE = cp( TI - T 3 ) + cpq,( T3 - T,)

Work in W=cp cpqt( T3 - T,)

RE Coefficient of performance COP = -

Heat transfer by conduction is the transfer of heat from

one part of a substance to another without appreciable

displacement of the molecules of the substance, e.g

heat flow along a bar heated at one end This section

deals with conduction of heat through a flat wall, a

composite wall, a cylindrical wall and a composite

cylindrical wall A table of thermal-conductivity coeffi-

q = heat flow rate, W

h=heat transfer coefficient, WrnW2K-'

U =overall heat transfer coefficient, Wm-2K-1

Conduction from JIuid to Jluid through wall

In this case the surface coefficients are taken into account

k A

q=Aha(ta-tl)=-(tl - t 2 ) = A h b ( t 2 - t b )

X

THERMODYNAMICS AND HEAT TRANSFER 129

3.14.4 Heat transfer from fins

The heat flow depends on the rate of conduction along the fin and on the surface heat-transfer coefficient The theory involves the use of hyperbolic functions

Fin of constant cross-section with insulated t i p

130 MECHANICAL ENGINEER’S DATA HANDBOOK

Heat flow from fin Heat flow if fin all at t ,

Temperature profile along fin:

Temperature at distance x from root

where: A,=surface area=n(r:-r?)+2ar2t

Efficiency is plotted against the function

figure where L=fin length=(r,-r,) and A=cross- sectional area = tL

Hyperbolic section circular fins: curves are given for hyperbolic fins using the appropriate values of A, and

THERMODYNAMICS AND HEAT TRANSFER 131

I I I I

3.14.2 Thermal conductivity coefficient

The fo1low;i;g table gives values of conductivity for

solids, liquids and gases

Thermal conductivity coeffieients (W tn-l K-') at W C and 1 bar

Ether Glycerine Kerosene Mercury Methanol Oil: machine Water

(ethyl alcohol)

(methyl alcohol) transformer

Gases

Air Ammonia Argon Carbon dioxide Carbon monoxide Helium

Hydrogen Methane Nitrogen Oxygen Water vapour

0.16 0.11 0.18 0.14 0.29 0.15 8.80 0.21 0.15 0.13 0.58

0.024 0.022 0.016 0.015 0.023 0.142 0.168 0.030 0.024 0.024 0.016

Plastics

Acrylic (Perspex) Epoxy

Epoxy glass fibre Nylon 6

Polyethylene : low density high density PTFE PVC

Refrigerants at critical temperature

Ammonia (132.4"C) Ethyl chloride (187.2"C)

Freon 12 (112°C) Freon 22 (97°C) Sulphur dioxide (157.2")

Insulating materials

Asbestos cloth Balsa wood (average) Calcium silicate Compressed straw slab Corkboard

Cotton wool

Diatomaceous earth Diatomite

Expanded polystyrene

0.20 0.17 0.23 0.25 0.33

0.50

0.25 0.19

0.049 0.095 0.076 0.10 0.0087

0.13 0.048

0.05

0.09 0.04 0.029 0.06 0.12

0.03/0.04

132 MECHANICAL ENGINEER’S DATA HANDBOOK

Thermal conductivity coefficients (W m - K - ’) at 20°C and 1 bar (continued)

0.6-1 .o

1.6 1.7 0.1-0.3 0.4-0.7

Felt Glass fibre quilt Glass wool quilt Hardboard Kapok Magnesia Mineral wool quilt Plywood

Polyurethane foam Rock wool Rubber, natural Sawdust Slag wool Urea formaldehyde Wood

Wood wool slab

0.04 0.043 0.040 0.13 0.034 0.07 0.04 0.13 0.03 0.045 0.130 0.06 0.042 0.040 0.134.17 0.10.15

3.14.6 Convection

Convection is the transfer of heat in a fluid by the

mixing of one part of the fluid with another Motion of

the fluid may be caused by differences in density due to

temperature differences as in ‘natural convection’ (or

‘free convection’), or by mechanical means, such as

pumping, as in ‘forced convection’

3.14.7 Dimensionless groups

In the study of heat transfer by convection it is

convenient to plot curves using dimensionless groups

Those commonly used are:

pcC RePr

B9P2L30 P2

Grashof number Gr = ~

where : p=fluid density

p = fluid viscosity

k =fluid conductivity

c = fluid specific heat

B = fluid coefficient of cubical expansion C=fluid velocity

9 =acceleration due to gravity

L = characteristic dimension

h = heat transfer coefficient

0 =fluid temperature difference 3.14.8 Natural convection

Natural convection from horizontal pipe