Performance Factors_Volumetric Efficiency

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Performance Factors

Volumetric Efficiency



1a. Indicated Power.

Indicated Power (IP) : Power obtained at the cylinder.Obtained from the indicator diagram. Given by:

IP = PiLANn/60x in Watts

where Pi is the indicated mean effective pressure,

in N/m2,L is the stroke length, in m

A is the area of cross section of the piston,m2,

N is the engine speed in rev/min,n is the number of cylinders and

x =1 for 2 stroke and 2 for 4 stroke engine.



1b. Brake Power

Brake Power (BP) : Power obtained at the shaft.Obtained from the engine dynamometer.

Given by:BP = 2NT/60 in Wattswhere T is the brake torque, in Nm, given byT = W.Lwhere W is the load applied on the shaft by the

dynamometer, in N andL is the length of the arm where the load is

applied, in mN is the engine speed, in rev/min



1c. Friction Power

Friction Power (FP) : Power dissipated asfriction. Obtained by various methods likeMorse test for multi-cylinder engine,

Willan’s line method for a diesel engine,

and Retardation test and Motoring testfor all types of engines. Given in terms of

IP and BP by:FP = IP – BP in Watts



2. Mean Effective Pressure.

Indicated Mean Effective Pressure (IMEP). This is alsodenoted by Pi and is given by

Pi = (Net work of cycle)/Swept Volume in N/m2

The net work of cycle is the area under the P-V diagram.

Brake Mean Effective Pressure (BMEP). This is alsodenoted by Pb and is given byPb = 60.BPx/(LANn) N/m2 This is also the brake power per unit swept volume of the

engine.

Friction Mean Effective Pressure (FMEP). This is alsodenoted by Pf and is given by

Pf = Pi - Pb N/m2



3. Efficiencies.Indicated Thermal Efficiency (i) given by

i = IP/(mf . Qcv)mf is the mass of fuel taken into the engine in kg/sQcv is the calorific value of the fuel in J/kg

Brake Thermal Efficiency (b) given by

b = BP/(mf . Qcv)Indicated Relative Efficiency (i,r) given by

i,r = i /ASEASE is the efficiency of the corresponding air standard

cycleBrake Relative Efficiency (b,r) given by

b,r = b /ASEMechanical Efficiency (m) given bym = BP/IP = Pb /Pi = b / i = b,r / I,r



Specific Fuel Consumption (sfc orSFC)

This is the fuel consumed per unit power.

Brake Specific Fuel Consumption (bsfc). This is given by

bsfc = mf /BP kg/J

if BP is in W and mf

is in kg/s

bsfc is usually quoted in kg/kWh. This is possible if BP is inkW and mf is in kg/h.

Indicated Specific Fuel Consumption (isfc). This is given by

isfc = mf /IP kg/J

if IP is in W and mf is in kg/s

isfc is also usually quoted in kg/kWh. This is possible if IPis in kW and mf is in kg/h.

Mechanical Efficiency in terms of the sfc values is given by

m = isfc/bsfc



Specific Energy Consumption (secor SEC).

This is the energy consumed per unit power.

Brake Specific Energy Consumption (bsec).This is given by

bsec = bsfc.Qcv

We can similarly define indicated specific

energy consumption (isec) and based onthe two quantities also we can definemechanical efficiency.



Air Capacity of Four-stroke cycle

Engines

• The power, P, developed by an engine isgiven by

• Power will depend on air capacity if the

quantity in the bracket is maximized.• Plot of power versus air flow rate is

normally a straight line.

ca QF M P




Indicates air capacity of a 4 stroke engine. Given by

Mi is the mass flow rate of fresh mixture.N is the engine speed in rev/unit time.Vs is the piston displacement (swept volume).ρi is the inlet density.

is

iv

V

2

N

M

NV

M2

si

i




Can be measured:

At the inlet port

Intake of the engineAny suitable location in the intake manifold

If measured at the intake of the engine, it is

also called the overall volumetricefficiency.



Volumetric Efficiency Based on

Dry Air

Since there is a linear relationship betweenindicated output (power) and air capacity(airflow rate), it is more appropriate to

express volumetric efficiency in terms ofairflow rate (which is the mass of dry airper unit time).

Since fuel, air and water vapor occupy thesame volume

Va = Vf = Vw = Vi

Thus we have:

aM



i

i

i

a

aaaa V

M M v M V

Here ρa is the density of dry air or the mass of dry air per unitvolume of fresh mixture.Thus, since

id

iv

V2

NM

ad

av

V2

NM



Also Vd = ApLs = 2LN

L2

s

N

L is the piston stroke and s is the pistonspeed.

sA

M4

LAL2

s

M2

pa

a

ap

av



Measurement of Volumetric

Efficiency in EnginesThe volumetric efficiency of an engine can be

evaluated at any given set of operatingconditions provided and ρa can beaccurately measured.

Measurement of Air Flow

Airflow into the engine can be measured withthe help of a suitable airflow meter. Thefluctuations in the airflow can be reducedwith the help of surge tanks placedbetween the engine and the airflow meter.

.

a M



Measurement of Inlet Air Density

By Dalton’s Law of partial pressures:

pi = pa + pf + pw

In this case pi is the total pressure of the fresh mixture,

pa is the partial pressure of air in the mixture,

pf is the partial pressure of fuel in the mixture,

pw is the partial pressure of water vapor in theair.

Since each constituent is assumed to behave as a perfect

gas, we can write

wf a

a

i

a

ppp

p

p

p



a

aa

oa

V

M T

R pSince

29

f

f f

f

of

V

MT

m

Rp

w

ww

ow

V

MT

18

Rp

iw f a T T T T Now

w f a V V V



1829

29

w

f

f a

a

i

a

M

m

M M

M

p

p Hence

M indicates mass of the substance,29 is the molecular weight of air,

mf is the molecular weight of the fuel, and18 is the molecular weight of water vapor.

18

29291

1

a

w

f a

f i

a

M

M

m M

M p

p

h6.1m

29

F1

1

f i



Fi is the ratio of mass of fuel vapor to that of dry air and h is

the ratio of mass of water vapor to that of dry air at thepoint where pi and Ti are measured.

io

a

ao

aa

T R

p

T R

p Now

29

29

hmF

T R

p

f

i

io

ia

6.129

1

129

This indicates that the density of air in the mixture is equalto the density of air at pi and Ti multiplied by a correction

factor, that is, the quantity in the parentheses.



The value of h depends on the humidity ratio of the air and isobtained from psychrometric charts.

For conventional hydrocarbon fuels, the correction factor isusually around 0.98, which is within experimental error.For diesel engines and GDI engines, Fi is zero.

In practice, with spark ignition engines using gasoline andwith diesel engines the volumetric efficiency, neglectingthe terms in the parentheses, is given by

4

sA

TR

p29

M

p

io

i

av



If we do not neglect the terms in the parentheses we getthe following relation for volumetric efficiency:

hm

F

s AT R p

M

f

i

p

io

i

av

6.129

1

14

29

If the humidity is high or a low molecular weight fuel is usedin a carbureted engine, the correction factor cannot beignored.For example, with methanol at stoichiometric conditions

and h = 0.02, the correction factor is 0.85.



Volumetric Efficiency, Power and

Mean Effective Pressure

Since

and

ca QFMP

sAM4

pa

av

cavp QFsA4

1P



For an engine, the mean effective pressure, mep, is given by

221

N V

P

V V

Pmep

s

sAP4p

cav QF

Performance Factors_Volumetric Efficiency

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