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What you will learn:
• First law of thermodynamics• Isothermal process, adiabatic process,
combustion process for petrol/diesel engines• Volumetric Efficiency; spark ignition/
compression; ignition process and tests
First Law of Thermodynamics
Conservation of Energy for Thermal Systems
Joule Equivalent of Heat
• James Joule showed that mechanical energy could be converted to heat and arrived at the conclusion that heat was another form of energy.
• He showed that 1 calorie of heat was equivalent to 4.184 J of work.
1 cal = 4.184 J
Energy
• Mechanical Energy: KE, PE, E • Work is done by energy transfer.• Heat is another form of energy.
Need to expand the conservation of energy principle to accommodate thermal systems.
1st Law of Thermodynamics
• Consider an example system of a piston and cylinder with an enclosed dilute gas characterized by P,V,T & n.
1st Law of Thermodynamics
• What happens to the gas if the piston is moved inwards?
1st Law of Thermodynamics
• If the container is insulated the temperature will rise, the atoms move faster and the pressure rises.
• Is there more internal energy in the gas?
1st Law of Thermodynamics
• External agent did work in pushing the piston inward.
• W = Fd• =(PA)Dx
• W =PDV
Dx
1st Law of Thermodynamics
• Work done on the gas equals the change in the gases internal energy,
W = DU
Dx
1st Law of TD
• Let’s change the situation:
• Keep the piston fixed at its original location.
• Place the cylinder on a hot plate.
• What happens to gas?
Heat flows into the gas.
Atoms move faster, internal energy increases.
Q = heat in Joules
DU = change in internal energy in Joules.
Q = DU
1st Law of TD
• What if we added heat and pushed the piston in at the same time?
F
1st Law of TD• Work is done on the
gas, heat is added to the gas and the internal energy of the gas increases!
Q = W + DU
F
1st Law of TD
Some conventions:For the gases perspective: • heat added is positive, heat removed is
negative.• Work done on the gas is positive, work done
by the gas is negative.• Temperature increase means internal energy
change is positive.
1st Law of TD
• Example: 25 L of gas is enclosed in a cylinder/piston apparatus at 2 atm of pressure and 300 K. If 100 kg of mass is placed on the piston causing the gas to compress to 20 L at constant pressure. This is done by allowing heat to flow out of the gas. What is the work done on the gas? What is the change in internal energy of the gas? How much heat flowed out of the gas?
• Po = 202,600 Pa, Vo = 0.025 m3, To = 300 K, Pf = 202,600 Pa, Vf=0.020 m3, Tf=
n = PV/RT.W = -PDVDU = 3/2 nRDTQ = W + DU
W =-PDV = -202,600 Pa (0.020 – 0.025)m3
=1013 J energy added to the gas.DU =3/2 nRDT=1.5(2.03)(8.31)(-60)=-1518 JQ = W + DU = 1013 – 1518 = -505 J heat out
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 by T = W.Lwhere W is the load applied on the shaft by the
dynamometer, in N and L is the length of the arm where the load is
applied, in m N is the engine speed, in rev/min
1c. Friction Power
Friction Power (FP) : Power dissipated as friction. Obtained by various methods like Morse test for multi-cylinder engine, Willan’s line method for a diesel engine, and Retardation test and Motoring test for 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 also denoted by
Pi and is given byPi = (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 also denoted 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 also denoted by
Pf and is given byPf = 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/s Qcv is the calorific value of the fuel in J/kg
Brake Thermal Efficiency (b) given byb = BP/(mf . Qcv)
Indicated Relative Efficiency (i,r) given byi,r = i/ASE
ASE is the efficiency of the corresponding air standard cycleBrake Relative Efficiency (b,r) given by
b,r = b/ASEMechanical Efficiency (m) given by m = BP/IP = Pb/Pi = b/i = b,r/I,r
Specific Fuel Consumption (sfc or SFC)
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/sbsfc is usually quoted in kg/kWh. This is possible if BP is in kW
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/sisfc is also usually quoted in kg/kWh. This is possible if IP is 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 (sec or SEC).
This is the energy consumed per unit power.Brake Specific Energy Consumption (bsec). This
is given bybsec = bsfc.Qcv
We can similarly define indicated specific energy consumption (isec) and based on the two quantities also we can define mechanical efficiency.
Air Capacity of Four-stroke cycle Engines
• The power, P, developed by an engine is given 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 QFMP
Volumetric EfficiencyIndicates 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
V2
NM
NV
M2
si
i
Volumetric Efficiency
Can be measured: At the inlet portIntake of the engineAny suitable location in the intake manifold
If measured at the intake of the engine, it is also called the overall volumetric efficiency.
Volumetric Efficiency Based on Dry Air
Since there is a linear relationship between indicated output (power) and air capacity (airflow rate), it is more appropriate to express volumetric efficiency in terms of airflow rate (which is the mass of dry air per unit time).
Since fuel, air and water vapor occupy the same volume
Va = Vf = Vw = Vi
Thus we have:
aM
ii
i
a
aaaa V
MMvMV
Here ρa is the density of dry air or the mass of dry air per unit volume of fresh mixture.Thus, since
id
iv
V2
NM
ad
av
V2
NM
Also Vd = ApL
s = 2LN
L2
sN
L is the piston stroke and s is the piston speed.
sA
M4
LAL2
sM2
pa
a
ap
av
Measurement of Volumetric Efficiency in Engines
The volumetric efficiency of an engine can be evaluated at any given set of operating conditions provided and ρa can be accurately measured.
Measurement of Air FlowAirflow into the engine can be measured with the
help of a suitable airflow meter. The fluctuations in the airflow can be reduced with the help of surge tanks placed between the engine and the airflow meter.
.
aM
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 the air.Since each constituent is assumed to behave as a perfect gas, we
can write
wfa
a
i
a
ppp
p
p
p
a
aa
oa V
MT
RpSince
29
f
ff
f
of V
MT
m
Rp
w
ww
ow V
MT
18
Rp
iwfa TTTTNow
wfa VVV
1829
29
w
f
fa
a
i
a
M
m
MM
M
p
pHence
M indicates mass of the substance, 29 is the molecular weight of air,
mf is the molecular weight of the fuel, and 18 is the molecular weight of water vapor.
182929
1
1
a
w
fa
fi
a
MM
mM
Mp
p
h6.1m
29F1
1
fi
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 the point where
pi and Ti are measured.
io
a
ao
aa TR
p
TRp
Now29
29
hm
FTR
p
fi
io
ia
6.129
1
129
This indicates that the density of air in the mixture is equal to 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 is obtained from psychrometric charts.
For conventional hydrocarbon fuels, the correction factor is usually 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 and with diesel engines the volumetric efficiency, neglecting the 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 get the following relation for volumetric efficiency:
hm
F
sA
TRp
M
fi
p
io
i
av
6.129
1
14
29
If the humidity is high or a low molecular weight fuel is used in a carbureted engine, the correction factor cannot be ignored. 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
sA
M4
pa
av
cavp QFsA4
1P
For an engine, the mean effective pressure, mep, is given by
221
NV
P
VV
Pmep
s
sA
P4
p
cav QF
Ways to increase power and mep
• The mean effective pressure may be indicated or brake, depending on whether η is indicated or brake thermal efficiency. Thus, the mean effective pressure is proportional to the product of the inlet density and volumetric efficiency when the product of the thermal efficiency, the fuel-air ratio, and the heat of combustion of the fuel is constant.
• From the preceding two expressions we can figure out ways to increase the power and mep of an engine.
OTTO CYCLE-THE IDEAL CYCLE FOR SPARK-IGNITION ENGINES
• The Otto cycle is the ideal cycle for spark-ignition reciprocating engines. It is namedafter Nikolaus A. Otto, who built a successful four-stroke engine in 1876 in Germany using the cycle proposed by Frenchman Beau de Rochas in 1862. In most spark-ignition engines, the piston executes four complete strokes (two mechanical cycles) within the cylinder, and the crankshaft completes 2 revolutions for each thermodynamic cycle. These engines are called FOUR-STROKE internal combustion engines.
THANK YOU
