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Internal Combustion EngineInduction Tuning
ME 468 Engine DesignProfessor Richard Hathaway
Department of Mechanical and Aeronautical Engineering
Port Sizing Considerations
Swept and Displaced Volumes
• Swept Volume/cylinder:
sA sd 4
= V p2Bs
Vs = swept volume dB = bore diameters = stroke
s
s x Ap
Inlet Port
Note: In valve design the Volume which flows into the cylinder must equal the volume which flows through the inlet port. The velocity past the valve must then be considerably greater than the velocity in the cylinder.
Port Sizing and Mach Index (Z)
• Mach Index is the ratio of the velocity of the gases flow area to the speed of sound
Soundof Speed speedPiston
d x nd = Z
2p
2b
Db = cylinder bore dia.Dp = port dia.n = number of ports
For mean values:strokeRPM speedPiston MEAN 2
Soundof SpeedstrokeRPM
d x nd = Z
2p
2b 2
• For instantaneous relationships:
c1
Soundof Speed
)(24Ls+
2s
602 RPM
d x n
d = Zd
2p
2b
i
SinSin
s = length of stroke L = length of connecting rodθ = crank position Cd = flow coefficient
Port Sizing and Mach Index (Z)
• Speed of Sound:– Temperature and F/A ratio dependant– At Standard Temperature and Pressure
c = 1100 ft/sec
c = 340 m/sec
R T 49.02 = c oft/ sec
K T 20.05 = c om/ sec
Port Sizing and Mach Index (Z)
• Modern performance engines will use multiple inlet and exhaust valves per cylinder.
• Many are using multiple intake runners per cylinder to improve cylinder filling over a broader range of RPM.– A single runner is used at lower RPM while a second runner will
be opened at higher RPM.– The second and the combined each have their own tuning peak.
Port Sizing and Mach Index (Z)
Inlet Air Density and Performance
Inlet air density
• Law of Partial Pressures:
• If each is considered as a perfect gas
t
i air fuel vap water vap
P = Partial PressuresP = P + P + P
P = Mass
Molecular wt. =
Mm
Inlet air density
• Inlet Pressures and Densities:
m/M + m/M + m/Mm/M =
P + P + PP =
PP
wwffaa
aa
waterfuelair
air
inlet
air
ma = 29 mw = 18 mgas = 113
Fc = chemically correct mix
Fi = % vaporized (Fc)
Inlet air density• Inlet Pressures and Densities:
• From Ideal Gas Law
a
i
a
a f f w w
a
i i f
PP
= M / 29
M / 29 + M / m + M / m
PP
= 1
1 + F (29 / m ) + h(1.6)
T x RP x 29 =
T x Rp x m =
i
aa
R = 1545 ft-lb/(lbm-mole-oR)
Inlet air density
• Inlet Densities:
ai
i i f =
29 x PR x T
1
1 + F (29 / m ) + h(1.6)
T x RP x 29 =
i
aa
for P in psia and T in oR
ai
i i f =
2.7 x PT
1
1 + F (29 / m ) + h(1.6)
Inlet air density
• Example Problem: – Find the change in indicated power when changing
from Gasoline to Natural Gas fuels Assume: Pi = 14.0 psia Ti = 100oF
= 1.2 => 20 % Richh = 0.02 lbm/lbm air
GASOLINE:F/A = 1.2 x 1/14.8 = 0.081 lbfuel/lbair
Assume fuel is 40% vaporized
(Use fuel distilation curves)
Inlet air density
Gasoline:
Natural gas:F/A = 1.2 x 1/17.2 = 0.0697 lbfuel/lbair
Fuel is a gaseous fuel and is 100% vaporized
mix
mix m3
= 2.7 x 14.0460 +100
1
1+(.4)(.081)(29 / 113)+0.02(1.6)
= 0.06488 lb / ft
Inlet air density
• NATURAL GAS:
mix
mix m3
= 2.7 x 14.0460 +100
1
1 + (1)(.06977)(29 / 18.3) + 0.02(1.6)
= 0.0591 lb / ft
ai
i i f =
2.7 x PT
1
1 + F (29 / m ) + h(1.6)
Inlet air density
• NATURAL GAS:
• INDICATED POWER RATIO:
mix
mix m3
= 2.7 x 14.0460 +100
1
1 + (1)(.06977)(29 / 18.3) + 0.02(1.6)
= 0.0591 lb / ft
nat gas
gasoline
mix c
c c
IhpIhp =
x F / A x e x F / A x e
nat gas natgas
gasoline gasoline
Inlet air density
Indicated power ratio:
nat gas
gasoline
mix c
c c
IhpIhp =
x F / A x e x F / A x e
nat gas natgas
gasoline gasoline
nat gas
gasoline
IhpIhp =
0.0591 x 0.0697 x 21,8000.06488 x 0.081 x 19,000
= .8993 90%
The above indicates an approximate 10% loss in power output by changing to the gaseous fuel.
nat gas
gasoline
IhpIhp =
0.0591 x 0.0697 x 21,8000.06488 x 0.081 x 19,000
= .8993 90%
Note: Gasoline performance decreases more rapidly with increasing temperature.
Inlet air density
ACOUSTIC MODELING
Induction System Comparisons
Courtesy: Dan Butts, Derek Harris, Chris Brockman, Tiffany Dickinson
• Closed Ended Organ Pipe:
Acoustic Modeling
Acoustic Modeling
• Closed Ended Organ Pipe:
length effective = .3d + l = L
(Hz) 4Lc = f p
V x LA
2c = f H
Helmholtz Resonator:
V x LA
2c = f H
Acoustic Modeling
Build Considerations• Variable Length Runners for RPM
matching• Materials Selection Criteria:
– Weight, Fabrication, Surface Finish, Heat Isolation
• Intake placement– Isolate from heat sources (Engine,
Exhaust, Radiator, Pavement)• Fuel Injector Placement
Courtesy: Dan Butts, Derek Harris, Chris Brockman, Tiffany Dickinson
Acoustic ModelingInduction System Model
Multiple Stack with pressure box
Courtesy: Dan Butts, Derek Harris, Chris Brockman, Tiffany Dickinson
• For a single degree of freedom system
Acoustic Modeling
1 + CR1 - CR
V LA x C x K = N
d1
11p
A1 = Average Area of Runner and Port L1 = LPort + Lrunner
K1 = 77 (English) K1 = 642 (Metric)
C = Speed of Sound
Individual Throttle Body with Plenum
Courtesy: Dan Butts, Derek Harris, Chris Brockman, Tiffany Dickinson
Helmholtz Tuning• Writing Clearance Volume in Terms of Compression
Ratio:
• The Primary Volume is considered to be the Cylinder Volume with the Piston at mid-stroke (effective volume).
VV + V = CR
CC
CCS
1) - (CRV = V S
CC
1) - (CRV +
2V = V DD
P1) - 2(CR
V 2 + 1) - (CR V = V DDeff
1) - (CR1) + (CR
2V = V D
eff
• The tuning peak will occur when the natural Helmholtz resonance of the cylinder and runner is about twice the piston frequency.
Volume (V1) = Cylinder Volume
Volume (V2) = Volume in the path from V1 to the Plenum
Using Engelman's electrical analogy we can define the system as a system defined by capacitances and inductances.
AL = )I( Inductance
ii
Helmholtz Tuning
• The EFFECTIVE INDUCTANCE for a pipe with different cross-sections may be defined as the sum of inductances of each section.
AL + .... +
AL +
AL = )I(
n1+iie
The INDUCTANCE RATIO (a) is defined as the ratio of the secondary inductance to the primary inductance.
Helmholtz Tuning
• INDUCTANCE RATIO (a)
• The CAPACITANCE RATIO (b) is defined as the ratio of the Secondary Volume to the Primary Volume.
ALAL
= a
1
2
Helmholtz Tuning
1 + CR1 - CR 2 x
VV =
VV = b
D
2
eff
2
V2 = Secondary Volume
= Volume of Intake Runners that are ineffective (n-1)
• Calculate the Separate Inductances:
• Determine the Inductance Ratio (a)
Helmholtz Tuning
AL = I
port
portport
AL = I
runner
runnerrunner
AL = I
plenum
plenumplenum
AL = I
bodyT
bodyTbodyT
.
..
I + I I + I
ALAL
= arunnerport
plenumbodyT
1
2 .
• Determine the Capacitance Ratio (b)
• Determine the Induction system Resonances
V x 1)-(nV = b
runner
eff
V x )(IND b a x 2B - A
21 = f
eff11 V x )(IND b a x 2
B + A 21 = f
eff12
b a 4 - )1 + a + b (a = B1) + a + b (a = A 2
Helmholtz Tuning
(IND)1 = Inductance of the primary length
(IND)1 = Iport + Irunner
• Determine the Primary Resonance:
• Determine the Frequency Ratios:
• Determine the Tuning Peak:
Helmholtz Tuning
V x I + I
1 21 = f eff
runnerportp
ff = X
ff = X
p
22
p
11
1 + CR1 - CR
V LA x C x K = N
d1
11p
A1 = Average Area of Runner and Port L1 = LPort + Lrunner
K1 = 77 (English) K1 = 642 (Metric)
C = Speed of Sound
• Intake Tuning Peaks become:
N x X = N p11 N x X = N p22
V x )(IND b a x 2B - A
21 = f
eff11 V x )(IND b a x 2
B + A 21 = f
eff12 V x I + I
1 21 = f eff
runnerportp
ff = X
ff = X
p
22
p
11
1 + CR1 - CR
V LA x C x K = N
d1
11p
Helmholtz Tuning
• A combined equation is possible indicating it’s 2nd order
PV4
1+CR1-CR
VV2
effP4-1+
effP+
1+CR1-CR
VV2
effP+1+
effP+
1+CR1-CR
VV2
effP
)C77(=N2
D
2
d
2
2
d
2
21
S1,2
AL = P
2
AL = EFF
eff
1)-(NC* A* )L+ L( = V mportman2
* s b* 4
= V 2d
Helmholtz Tuning
David Visard’s “Rule of thumb” Equations
Using Visard's Equation for Runner Length1. Starting point of 7 inches for 10,000 RPM2. Add length of 1.7 inches for each 1000 RPM less
Using Visard's Equation for Runner Diameter
The End
Thank You!