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Performance Factors
Volumetric Efficiency
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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.
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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
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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
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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
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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
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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
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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.
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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
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Volumetric Efficiency
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
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Volumetric Efficiency
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.
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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
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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
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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
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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
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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
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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
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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
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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.
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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
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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.
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Volumetric Efficiency, Power and
Mean Effective Pressure
Since
and
ca QFMP
sAM4
pa
av
cavp QFsA4
1P
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For an engine, the mean effective pressure, mep, is given by
221
N V
P
V V
Pmep
s
sAP4p
cav QF
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