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!