I.C. ENGINES
LECTURE NO: 13
(28 Apr 2014)
ENGINE PERFORMANCE
PARAMETERS
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Indicated Thermal Efficiency
Brake Thermal Efficiency
Mechanical Efficiency
Volumetric Efficiency
Relative Efficiency
Mean Effective Pressure
Mean Piston Speed
Specific Power Output
Specific Fuel Consumption
ENGINE PERFORMANCE
PARAMETERS
• Inlet Value Mach Index
• Fuel Air Ratio
• Calorific Value of the Fuel
Atmospheric Pressure
Work
• Work is the movement of a body against an
opposing force.
Torque
Conversion of Work into Torque
Power
• Rate of doing Work is called power
• Through testing, it was found that the average
horse could lift a 200-lb. weight to a height of
165 ft in 1 minute. The equivalent of one
horsepower can be reached by multiplying
165 ft by 200 lb. (work formula) for a total of
33,000 ft lb. per minute
Power
Dynamometer
• Pony Brake
Dynamometer
Classic Dynamometer
Indicated Thermal Efficiency
• Indicated thermal efficiency is the ratio of
energy in the indicated power ip, to the input
fuel energy in appropriate units
ηith =
ip [kJ/s]
energy in fuel per second [kJ/s]
ηith =
ip [kJ/s]
mass of fuel/s x calorfic value of fuel
Brake Thermal Efficiency
• Brake thermal efficiency is the ratio of energy
in the brake power bp, to the input fuel
energy in appropriate units
ηbth =
bp [kJ/s]
energy in fuel per second [kJ/s]
ηith =
ip [kJ/s]
mass of fuel/s x calorific value of fuel
Mechanical Efficiency
• Mechanical efficiency is the ratio of bp
(delivered power) to indicated power ( power
provided to the piston)
ηm = bp [kJ/s] =
bp
ip [kJ/s]
bp+fp
fp = ip - bp
Volumetric Efficiency
• Volumetric efficiency is the ratio actual
volume flow rate of air into the intake system
to the rate at which the volume is displaced by
the system
.
ηv = ma / ρa
V disp N/2
ρa = Inlet density
SI = 80 to 85 %
CI = 85 to 90 %
Volumetric Efficiency
• Alternative equivalent definition of Volumetric
• 𝜂𝑣 =
𝑚𝑎
ρ𝑎 𝑉𝑎
• ρ𝑎 = is atmospheric air density
• 𝜂𝑣 = the pumping performance of the entire
inlet system
• And if it is taken as the air density in the
manifold then 𝜂𝑣 is the pumping performance
of the inlet port and valve only
Relative Efficiency or Efficiency Ratio
• Relative efficiency is the ratio thermal
efficiency of actual cycle to ideal cycle
.
ηrel = Actual Thermal Efficiency
Air Standard Efficiency
Mean Effective Pressure
• 𝑖𝑝 =
ip
pim
L
A
N
n
K
𝑝𝑖𝑚 𝐿𝐴 𝑛𝐾
60 ×1000
= Indicated power [kW]
= Indicated mean effective pressure [N/m2 ]
= Length of the stock [m]
= Area of the piston [m2]
= Speed in revolutions per minute [rpm]
= Number of stock N/2 & N
= Number of cylinder
• 𝑝𝑖𝑚 =
𝑖𝑝 6000
𝐿𝐴𝑛𝐾
Mean Effective Pressure
• indicated mean effective pressure is
𝑖𝑝 6000
• 𝑝𝑖𝑚 =
𝐿𝐴𝑛𝐾
• Break mean effective pressure is
𝑏𝑝 6000
• 𝑝𝑏𝑚 =
𝐿𝐴𝑛𝐾
ip
= Indicated power [kW]
pim = Indicated mean effective pressure [N/m2 ]
L
= Length of the stock [m]
A
= Area of the piston [m2]
N
= Speed in revolutions per minute [rpm]
n
= Number of stock N/2 & N
K
= Number of cylinder
Mean Piston Speed
•
Sp = 2LN
L
N
= Length of the stock [m]
= Crank Speed in revolutions per minute
[rpm]
Specific Power Output
•
Ps = bp/A
= constant x pbm x Sp
Specific Fuel Consumption
•
• sfc = Fuel Consumption per unit Time
Power
Inlet – Valve Mach Index (Z)
• 𝑢=
•
•
•
•
𝐴𝑝
𝐶𝑖 𝐴𝑖
𝑉𝑝
u = Gas velocity through the inlet valve
Ap = piston area
Ai = nominal intake valve operating area
Ci = inlet valve flow coefficient
Inlet – Valve Mach Index (Z)
𝐴𝑝 𝑉𝑝
𝑏 2 𝑉𝑝
( )
𝐷𝑖
𝐶𝑖
•
𝑢
𝛼
•
•
•
•
•
•
•
Where
b = cylinder diameter
Di = inlet valve diameter
V = mean piston speed
𝛼 = inlet sonic velocity
C = inlet valve average flow coefficient
Z = inlet valve Mach index
=
𝐴𝑖 𝐶𝑖
=
=𝑍
Fuel – Air ( F/A) or Air –Fuel Ratio (A/F)
• ϕ=
𝐴𝑐𝑡𝑢𝑎𝑙 𝑓𝑢𝑒𝑙−𝑎𝑖𝑟 𝑟𝑎𝑡𝑖𝑜
𝑆𝑡𝑜𝑖𝑐ℎ𝑖𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝑓𝑢𝑒𝑙−𝑎𝑖𝑟 𝑟𝑎𝑡𝑖𝑜
• Where
• ϕ = 1 means stoichiometric ( chemically correct)
mixture
• ϕ ˂ 1 means lean mixture
• ϕ ˃ 1 means rich mixture
Calorific Value ( CV)
• Calorific value of a is the thermal energy released
per unit quantity of the fuel when the fuel is
burning completely and the products of
combustion are cooled back to the initial
temperature of the combustible mixture.
PROBLEMS
PROBLEM NO 1
• The Mechanical effencicy of a single cylinder
four stroke engine is 80 %. The frictional
power is esitmated to be 25 kW. Calculate:Ip
bp
SOLUTION
• ηm =
bp/ip
• fp =
ip - bp
PROBLEM NO 2
• A 42.5 kW has a mechanical efficiency of 85%.
Find the ip and fp. If the frictional power is
assumed to be constant with load, What will
be mechanical efficiency at 60 % of the load?
SOLUTION
• ηm =
bp / ip
• fp =
ip – bp
• ηm =
bp / (bp + fp)