approximate method of fuel-air cycle 1calculation(lec 1).pptx

8/13/2019 Approximate Method of Fuel-Air Cycle 1calculation(lec 1).pptx

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Approximate Method ofFuel –Air Cycle

Calculation



Residual gases fraction (by

weight), and temperature ofthe mixture at the beginning

of compression T1



A) Constant volume combustion

cycle

The following average values are

assumed



i) Inlet pressure p1 and exhaust pressure

pex

ii) Atmospheric temperature Tat

iii)Gas pressure at the beginning of exhaust

p4

iv) Gas temperature at the beginning ofexhaust T4



If fuel –air ratio F

then for 1 kg of air(1+F) kg of products will be formed

prod kg F air kg el .).1()..(1)



(1+F) kg products of combustion at p4,T4

4

2 1 .

blow down process 4 to p exhaust at const vol v1 &T4 then a part

is exhausted until the vol = v2 while temp & pressure =const



This (1+F) kg of products of

combustion at pressure p4 and

temperature T4 undergo blow

down process from p4 to pex at

constant volume v1 (T4=constant)and then a part of this gas is

exhausted until the volume is v2 (temperature and pressure

remains constant).



The weight of this volume v2

of

products of combustion at

pressure pex and temperature T4

from (1+F) kg of products ofcombustion is called residual gas

fraction



Residual fraction of gas [for (1+F)

kg of products of combustion]



1

2

4

ex

144

14

44

4

24

4

2

p

pF)(1

)1(

)1(

v

v f

F R

v p

T

vv

F R

v p

T

f R

v pT

T R

v p f

ex

ex



This residual gas mixes with fresh

fuel -air charge

the composition of the mixture

becomes

kg of residual gas(1- ) kg of air

(1- )F kg of fuel



Equating the sum of the enthalpies

of these components with

enthalpy of the mixture, the

temperature of the mixture can beobtained (F is a small quantity

and can be neglected)

hmh mixmixi

i

m



Example

a constant volume fuel air cycle has

the following values of pressure and

temperature for a fuel air ratio of

0.0785 ,& 117.75 % of theoretical fuelp1=1.1 atm

pex=1.1kg/cm2

Tat=325 Kp4=4.5 atm

T4=1600 K



For a compression ratio of 7

calculate: the value of and T1 (

latent heat of evaporation at 25 C

is 83 Kcal/kg

Solution

1

2

4

ex

p pF)(1

vv f



0368.07

1

4.5

1.10.0785)(1

f

f



Composition of fresh mixture at

point 1 Residual gas= 0.037 kgAir= (1-0.037)=0.963 kg

Fuel=0.963*0.0785 kg

Total weight of mixture

=0.037+0.963+0.0755

=1.0755 kg .



Assuming the specific heat at constant pressure cp of

residual gas and air =0.24, of liquid fuel =0.5 and of

vapor=0.4

Enthalpy of 1 kg of petrol vapor at 323 K

kg kcal h

h

T chT chh

nevaporatioof heat latent h

dT chh

dhhh

vapor p fg liquid p

fg

p

/5.10510835.12

2983234.01832732985.01

...

323298)(298273)(273323

323

273

273323

323

273

273323



Assume that that fuel needs this

amount of energy to be at 323 K

needed enthalpymT c f T cm fuel pat pair

07.0)2731600(24.0037.027332324.0963.0)273

..273273 4



B) Limited pressure fuel –air cycle

The same procedure may be

followed for calculating and T1 for

fuel – air cycle. Calculation of T1 willnot require the enthalpy of fuel

because fuel will not be presentduring the compression process



Examples

1) In a constant volume combustion

fuel air cycle with compression ratiorv=9, the mixture has a fuel air ratio of

0.0785. The fuel is C8H17 and lower

heating value of 10500 kcal/kg (44000

kJ/kg). Assume mixture pressure and

temperature at the beginning of 1 atmand 328 K. Calculate the indicated

thermal efficiency, specific fuel

consumption & m.e.p. of the cycle.



It can be assumed that =0.03

cp can be calculated at an averagetemperature of 2800 K

assume also that the drop in

temperature due to dissociation maybe assumed equal to 10% of the

temperature rise without considering

dissociation. Z correction factor = 0.9

’ b d h f



Let’s start by determining the cp for

the different species

K kmole KJ K kmolekcal T

T

K kmole KJ K kmolekcal T T

vapor O

kmo KJ K kmolekcal T T

O


O


oo p

oo

p

o

p

o

p

o

p

/18.4)/15100004.176.5(

/18.4)/4150442

86.19(

)(

/18.4)/10333.01083.1

63.9(

/18.4)/

10435.01062.3

2.16(

/18.4)/10358.01093.1

47.9(

2

2

2

2

63

2

63

2

2

632


http://slidepdf.com/reader/full/approximate-method-of-fuel-air-cycle-1calculationlec-1pptx 23/40oxmoles

moles

m

m

m

m

O

f

o

f

o

air

..

..

2

22



2

2

2

22 /

/

..

..

o

ai

air

f

O

f o

f

f

O

f

Oo

f f

m

m

m

m

M M m

m

M M

m

M m

M m

oxygen s

fuel les



Combustion calculation of C8H17 having

a fuel air ratio of 0.0785

45.10

.....

.....

3.4320785.0113

..........

)76.32832(.....

.....

)(

1

.....

.....

2

2

2

2

2

2

fuel of Moles

Oof Moles

fuel of MolesOof Moles

F

M

fuel of Moles

Oof Moles

M

M ratioOair ratioair fuel

fuel of Moles

Oof Moles

f

f

O



The combustion equation

by O2 balance

10.45=8(1-Φ)+4 Φ +4.25-2 Φ

Φ =0.3

2222178 488176.345.1045.10 H COCO N O H C



The combustion equation

mol of mixture

Molesmix = 50.75

Molesprod = 55.80

222178 4.26.576.345.1045.10 C CO N O H



Composition by volume

705.08.55

3.39

131.08.55

3.7

021.08.55

2.1

043.08.55

4.2

10.08.556.5

2

2

2

2

N

O H

H

CO

CO



Rmix and Mmix

75.275.30

848

5.3075.27

848

705.018131.02021.028043.0441.0

848

mix

mix

mix



Composition by weight

710.0705.075.27

28

085.0131.0

75.27

18

001.0021.075.27

2

044.0043.075.27

28

160.0100.075.27

44

2

2

2

2

N

O H

H

CO

CO



Assume T=2800 K

K kmolekcal C N K kmolekcal C O H

K kmolekcal C H

K kmolekcal C CO

K kmolekcal C CO

o

P

o

P

o

P

o

P

o

P

/83.8:/0.13:

/94.8:

/86.8:

/97.14:

2

2

2

2



Get Cp for burnt products



Get Cv



Temperature rise during combustion

ΔT

vprod f T c F f 11



ΔT=2450 K

temperature rise considering

dissociation

ΔT’=0.9*2450=2205 K



Work done during expansion for 1.076 kg

of products or 1kg of air

air of kg kcal W

W

..../351

427)13.1(147028395.30076.1

exp

exp



R for fuel, air

and residual

gases



1. Get masses

kg weight total

kg air kg gasesresidual

kg fuel

076.1...

97.003.0103.0..

076.003.010785.0



2.Composition by weight

approximate method of fuel-air cycle 1calculation(lec 1).pptx

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