16 Frequencies, wavelengths and lengths of pipes

502



The Motor Vehicle



where c is the velocity of sound in air and λ is the wavelength. The

frequencies of the first three modes of vibration in each case therefore are as

follows—

Pipes with closed ends

One end open

Both ends open



f1 = c/2L

f1 = c/4L

f1 = c/2L



f2 = C/L

f2 = 3c/4 L

f2 = c/L



f3 = 3c/L

f3 = 5c/4L

f3 = 3c/2L



For waves of small amplitude the velocity of sound in dry air is √γp/ρ,

where p is the gas pressure, ρ is the density, and γ is the ratio of the specific

heats of the gas. At the standard temperature and pressure in free air, this

velocity becomes 331.4 m/s. Standard temperature and pressure is 298.15 K

and 105Pa (1 bar). Potential for some slight confusion arises, however, when

referring back to data predating the universal introduction of SI units because,

at the latter point, it became 273.15 K (0°C) and 101.325 Pa. At velocities of

more than Mach 0.25, viscous friction losses impair performance.

Whichever version of the speed of sound in free air is taken, it is independent

of frequency and, because pressure divided by density is constant, it can be

considered also to be independent of variations of pressure, certainly of the

magnitudes experienced in inlet manifolds. The velocity of sound varies

with temperature according to the following relationship—

cθ = c0 √(1 + αθ)

where cθ and c0 are the velocities of sound at θ and 0°C respectively, and α

is the coefficient of expansion of the gas. While the local velocity of sound

is dependent only on the temperature and composition of the gas, in induction

pipes it is influenced also by diameter, Fig. 13.24. This is because of the

effect of viscous friction between the gas and the walls of the pipe. Frequency

is also affected, but relatively slightly, by the length: diameter ratio and

internal smoothness of the pipe, both of which influence the degree of damping

of the flow.

Since γ is dependent on the nature of the gas, the presence of fuel vapour,

as in carburetted or throttle body injected spark ignition engines, will also

affect the speed of sound in the manifold. Even so, because extreme accuracy

of calculation is generally unattainable, except possibly where the system

comprises a set of straight tubes, this is not of much practical significance.

Indeed, induction systems have to be optimised experimentally, for example

by the use of telescopic elements, during development.

The amplitudes of the resonant pressure pulsations too are modified by

damping. This can be due to roughness of the inner faces of the walls of the

induction tract, the presence of bends, and obstructions such as throttle

valves and inlet valve stems and guide ends. From damped and undamped

resonance curves in Fig. 13.25, it can be seen that the effect of damping is

not only a reduction in maximum amplitude but also it rounds off the peak,

and spreads the resonance over a significantly wider range of frequencies.

In general, any bends in the pipes should be as close as practicable to the

inlet valve ports, blended smoothly into the straight sections, and their radii

should not be less than four times that of the bore of the pipe. This arrangement

leads to a minimum of both viscous losses and interference with the tendency

for the air in the pipe to resonate freely.



Induction manifold design

20°C



40°C



60°C



0.75

(19.05)

1.0

(25.40)

0°C



Pipe bore, in (mm)



1.5

(32.00)

2.0

(50.80)



3.0

(76.20)



5.0

(12.70)



20

1000

(304.8)



40



60



80



20 40 60 80

1100

1200

(335.28)

(365.76)

Velocity of sound in pipe, ft/s (m/s)



Fig. 13.24 Variation of the velocity of sound with diameter of pipe



Undamped



Amplitude



Damped



Resonant frequency



Lightly damped



Frequency



Fig. 13.25 Curves showing the effect of two different degrees of damping on the

amplitudes of vibration around the resonant frequency. Without any damping the

curve rises to a sharp peak at the point of resonance



503



504



13.17



The Motor Vehicle



Tuning the pipe to optimise standing-wave effects



The time δt, expressed in terms of degrees rotation, required for a single

standing wave to be reflected back to its point of origin (the inlet valve) is

twice the length of the pipe divided by the velocity of sound (2L/c). From the

lower diagram in Fig. 13.21, it can be seen that the wavelength of the

fundamental frequency is 4L, so δt is in fact half the periodic time.

During the time δt, the crankshaft rotates through an angle θt = 360Nδt/

60. If we substitute for δt, this becomes θt = NL/c, where the suffix t refers

to the time of the reflection, to distinguish it from θd, which is the time the

valve is open, again expressed in degrees. It follows that if it were practicable

for the single wave to be an exact fit in the induction period, it would occur

when θt = θd = 720/2n, where n is the number of the harmonic or overtone.

If, in our calculations, we substitute the actual velocity of sound in the

pipe for that of sound in free air, we have what might be termed an induction

wavefront velocity. Then perhaps the simplest way to exemplify the time for

the wavefront to travel one pipe length is to assume a wavefront velocity of

330 m/s and a pipe length of 330 mm which, of course, will give a time of

1 ms.



13.18



Harmonics of standing waves



In addition to the standing wave at the fundamental frequency, harmonics are

generated too by the initial impulse, Fig. 13.26, so a number of modes of

vibration, superimposed on each other, occur simultaneously. Consequently,

the initial reflection at the fundamental frequency is accompanied by a ripple

of reflections at the smaller wavelengths of the overtone frequencies. The

successive reflected pulses are of progressively smaller amplitudes owing to

attenuation by viscous friction and out-of-phase reflections from bends and

other obstructions in their paths. Consequently, no more than one, or possibly

two, of the overtones are of significance, depending on whether the valve

timing is late or early. Long pipes and high speeds of flow increase both the

flow losses and the degree of attenuation of pulses.

The actual timing, relative to the depression wave, of the appearance of

the succession of waves at the inlet port can be adjusted by advancing or

retarding the opening of the valve. Neither the timing of valve opening nor

the duration of overlap, however, have any significant effect on inertia ram,

as distinct from resonance (or standing wave) ram, but they do affect exhaust

assisted scavenge. Clearly, considerable advantage could be gained by

combining induction system tuning with variable valve timing, Section 3.36.

To fit the waves due to resonance into the valve-open period, the following

condition must be met—

n = θt = θd = 720/2n

where n is the periodic time of the fundamental standing wave. If θt is less

than 720/2n, ripples will be superimposed on the depression pulse; if it is

more, they may or may not affect it at all.

Clearly, the inertia effect will be predominant at high speeds. This is

because not only do the magnitudes of these pulses increase with speed, but

also, as the speed falls, the time available to fit more harmonics into the

valve open period increases and, as previously mentioned, each successive



Induction manifold design



505



Overtones

2



Bmep



3

5



4



(a)



Engine speed



Bmep



3

5



2



4



(b)



Engine speed

3



Bmep



4



(c)



5



2



Engine speed

Inertia wave



Resonance wave



Fig. 13.26 The combined effects of the inertia and resonant standing waves. At (a) the

system is tuned for maximum power, at (b) to obtain a flat torque curve; and at (c) for

good torque back-up



wave reflection is weaker than its predecessor. Maximum amplitude of the

standing wave occurs when the pipe length is such as to contain a single

wave, which occurs when L = θt = θd = 120°, and maximum overall amplitude

is obtained when both the inertia and the standing-wave effects coincide.

Only the basic information has been given here. In practice, the situation

is further complicated by end-effects due to the presence of throttle valves,

bends and the progressive motion of the closure of valves and by other

factors. For more comprehensive and detailed information, the reader is

advised to refer to articles by D. Broome, of Ricardo Consulting Engineers

Ltd, and papers by K. G. Hall of Bruntel Ltd. The former is a series in

Automobile Engineer, Vol. 59, pp. 130, 180 and 262, while the latter were

papers presented to the IMechE and AutoTech 89, Ref. C399/20. The last

mentioned contains a design chart presenting the graphical parameters in a

manner such as to facilitate conceptualisation to an optimum inductionsystem geometry.



13.19



Some practical applications of pipe tuning



The obvious way to vary the length of the induction pipes to vary their

resonant frequencies and the timing of the arrival of the reflection of the

inertia wave back at the inlet valve is to have telescopic pipes, the lengths of



506



The Motor Vehicle



which are controlled by the engine electronic management system. This was

in fact done by Mazda on their le Mans winning, Wankel powered racing car.

However, whether infinitely variable or a two-position pipe control is used,

as in the le Mans car, the mechanism is complex and the whole system bulky

and awkward to accommodate in a car. A more practicable alternative is the

Tickford rotary manifold, Fig. 13.27, in which the central portion rotates to

vary the effective length of the inlet pipe.

A commendably simple system was introduced in 1990 for some of the

GM Vauxhall Carlton/Opel Senator models, and a similar principle has been

applied to the Toyota 7M-GE engine. The GM system will be described here.

As previously stated, the larger the number of cylinders that have to fire

during the two revolutions of the Otto cycle, the more difficult it is to avoid

overlap of valve open periods, and therefore inter-cylinder robbery. This

problem has been avoided in the GM system, called Dual Ram, by controlling

the flow through the induction manifold so that at low speeds it has long

pipes functioning like those in an in-line six and, at high speeds, it becomes

in effect two integrated three-cylinder engines with short induction pipes.

How this is accomplished can be seen from Fig. 13.28.

Two tuned pipes take the air from throttle body and inlet plenum to a

second, or intermediate, plenum chamber. This chamber is divided by a flap

valve so that, when the valve is open it is in effect one, and when closed, two

chambers. From the intermediate chamber, the incoming air passes through

three short pipes to the six inlet ports in the cylinder head. When the flap

valve is closed, which is at the lower end of the speed range, each of the two

sets of one long and three short pipes, together with the half plenum between

them, form a single tuned duct. At higher speeds, however, the flap valve is

open, so that the intermediate plenum, now double the volume, isolates the

six short inlet pipes, which of course resonate at a higher frequency. The

flap valve is opened at the speed corresponding to the cross-over point of

the two torque curves in Fig. 13.29. This valve is actuated by manifold

depression and controlled by the ECU. The six 60-mm diameter short pipes

are 400 mm long and the length from the inlet valves to the plenum chamber

next to the throttle barrel is 700 mm. A smooth transition between the resonant

speeds of 4400 and 3300 rev/min respectively is the outcome of this

arrangement.



Fig. 13.27 In the Tickford manifold, a central casting, distinguished by closer

hatching, can be rotated to vary the effective length of the induction pipes. This

portion, extending the whole length of the cylinder block, serves also as a

plenum chamber



Induction manifold design



507



2-position

valve



Plenum



Cylinder

head

casting



chamber



Throttle

body



Induction manifold

branch pipes



Fig. 13.28 The Dual Ram system, with the two-position valve closed for operation in

the 2 × three-cylinder mode. When it is open, the plenum chamber, then unobstructed

from end to end, breaks the continuity of the tracts so that only the six short pipes

resonate



170

150 kW @

6000 rev/min



160



140



340



130



320

170 Nm @

3600 rev/min



Torque, Nm



300



120



280



110



260



Power, kW



150



100



240

220

200



6-cylinder

mode



180

0



2000



2 × 3-cylinder

mode



4000

Rev/min



6000



Fig. 13.29 Power and torque curves for the Carlton GSi 300 24V engine equipped

with the Dual Ram system



508



The Motor Vehicle



Another tuned induction pipe system of interest is that of the Volvo 2 litre

850 GLT engine, Fig. 13.30. Each induction pipe comprises a pair of siamesed

ducts, a section through the top of the pair resembling a figure-of-eight. The

diameter of the upper loop of the eight is slightly smaller and its length about

twice that of the lower one over which, at its end nearest the head, is a steel

flap valve. Under the control of the ECU, this valve is initially held fully

open by its return spring, but moves towards the fully closed position as the

manifold depression increases. Each valve is fitted with a rubber seal to

obviate the need for machined seats and, when open, is parked in a recess in

the pipe so that it does not interfere with the air flow.

At speeds below 1800 rev/min, both ducts are open, providing capacity

for acceleration, though whether this adversely affects transient response is

open to question. Between 1800 and 4200 rev/min, but only so long as the

throttle is 80° or more open, the shorter duct is closed. Above 4200 rev/min,

both ducts are open again to afford maximum flow potential. In this condition,

because one pipe is half the length of the other, the air is both resonate

simultaneously but in different modes. Calculated volumetric efficiencies

are shown in Fig. 13.31 and the actual power and torque curves in Fig. 13.32.



13.20



The Helmholtz resonator



Another device that is being applied increasingly to induction systems is the

2



1



4



3

5



evolve



Fig. 13.30 A sectioned V-VIS induction pipe of the Volvo 850 GLT engine. The pipe

(1) is about twice the length of pipe (2), and (3) is a plenum chamber. Flap valves (4),

one in each pair of pipes, are all moved simultaneously by a single manifold

depression actuator (5). (Right) The complete system with, inset, a diagram showing

how, by thickening one edge of the throttle valve, two-stage opening is obtained to

provide a smooth take up of drive from the closed throttle condition. See also

Fig. 11.10



Induction manifold design

Closed control valve



100



Volumetric efficiency, %



509



90



80

Open control valve

70



1000



2000



3000

4000

5000

Engine speed, rev/min



6000



Fig. 13.31 Estimated volumetric efficiencies obtained with the Volvo V-VIS system



hp

180

170



kW

Nm kpm



130



280



160 120



260

240

220



26

24

22



120



90



110



80



200 20



70



180 18



60



160 16



100

90

80

70



140 14



50



60

50



Torque



Power



150 110

140

100

130



28



120 12



40

20

1000



40

2000



60

3000



4000



80

5000



rev/sec

100



100 10



6000 rev/min



Fig. 13.32 Power and torque curves of the Volvo 850 GLT engine



Helmholtz resonator, Fig. 13.33, which, because a larger mass of air may be

displaced by it, can be more powerful in its effect than pipe tuning. Because

it is effective over only a very narrow band of frequencies, its use has been

confined in the past to generating what has now become known as antisound, to eliminate induction pipe roar and exhaust boom. Anti-sound is of

course a sound of the same frequency but opposite in phase to that which has

to be eliminated. More recently, the principle of its application to boost the



510



The Motor Vehicle



S = cross sectional

area of neck



L = length of

neck



L



V = volume

of cavity



Fig. 13.33 Diagrammatic representation of

the Helmholtz resonator



low speed performance of turbocharged engines has been described in two

papers presented before the IMechE in May 1990, at the Fourth International

Conference on Turbocharging and Turbochargers. One is Paper C405/013,

by G. Cser, of Autokut, Budapest, and the other is Paper C405/034, by K.

Bsanisoleiman and L. Smith, of Lloyd’s Register, and B. A. French, of the

Ford Motor Company. An earlier and equally interesting paper on this subject

by Cser was C64/78, presented at the 1978 conference.

In general, Helmholtz resonators have been used also to detect extremely

faint noise signals. Another application is the damping of resonant vibrations,

the damping effect being increased by, for example, placing porous material

in the neck of the resonator. Also, it can be used to increase the sound

pressure in an acoustic field at a particular frequency. This is of interest

because of its potential for enhancing the effectiveness of a tuned manifold.

By the late 1980s, Helmholtz resonator principle began to be widely applied

also as a primary engine-tuning device. Although it is effective at only one

frequency, it is particularly useful for improving volumetric efficiency at

relatively low engine speeds.

For influencing induction-pipe resonances, either of two locations for the

open end of the neck of the resonator are effective. If it is positioned at a

displacement anti-node in the induction tract, it is in phase and therefore

increases the amplitude of displacement of air in the tract. On the other hand,

if placed at a displacement node, it tends to counteract the resonant vibration

of the air in the tract, because it is π/2 out of phase.

The Helmholtz resonator generally comprises a short tube connected to

an otherwise totally enclosed cavity. This cavity can be of any shape, though

a bulbous form may be preferred because it is less likely than almost any

other to have natural modes of vibration that could influence the system as

a whole. The air in the neck is assumed to act like a piston, alternately



Induction manifold design



511



compressing and expanding that in the cavity. In other words, the air in the

neck constitutes the mass, while the compressibility of that in the cavity

forms the spring of a spring–mass system.

The wavelength of the vibrations it generates is large relative to the

dimensions of the cavity. Its natural frequency f corresponds to the value of

the angular frequency at which the reactance term disappears, and is therefore

given by—

2πf = c√ (S/LV)

i.e



f = (c/2π)√(S/LV)



where c is the speed of sound, L the length of the neck, S the area of the neck

and V the volume of the cavity. From the last term in the equation, it can be

seen that the natural, or resonant, frequency increases as the square root of

the area of the neck, and decreases as both the square root of the length of the

neck and of the volume of the cavity, or resonant chamber, are increased.

Incidentally, provided the length of the tube is small relative to the wavelength

of the sound at the resonant frquency, the effective length of the neck

numerically is approximately the actual length plus 0.8 times S. As the crosssectional area of the neck is increased, the mass of air in it increases, but the

relative viscous damping effect falls rapidly. Clearly, however, both the mass

of the air and the viscous friction in the neck increase linearly, with its

length, so the main consideration is the area : length ratio. As regards the

volume of the resonator cavity, the smaller it is the higher is its spring rate

and therefore also both the amplitude and frequency of oscillation.

An important consideration is the energy content, or what might be termed

the ‘power’ of the resonator, which is a function of the mass of the air in the

neck. Therefore, the larger the volume of the neck, the greater is the effectiveness

of the system. In acoustical applications, the Helmholtz resonator is most

effective at the lower end of the audible frequency range, down to about 20

Hz which, expressed in terms of incidence of inlet valve closure, is from

about 600 rev/min upwards.



13.21



Helmholtz resonators in automotive practice



In automotive applications, however, things are not at all simple. For instance,

it has been suggested that the Helmholtz system may comprise the induction

pipes with their cylinders acting as resonant cavities, but the volumes of the

cylinders are of course varying continuously. The suggestion is that the

resonator volume can be taken to be that when the piston is at mid-stroke,

which is half the piston displacement plus the clearance volume. At this

point, when the downward velocity of the piston is at its maximum, a rarefaction

wave transmitted from the inlet valve to the open end of the pipe is reflected

back as a pressure wave into the cylinder. Optimum tuning is obtained when

this wave arrives in the cylinder just before the inlet valve closes. Since the

resonance does not continue after valve closure, this type of resonator acts

independently of engine speed and therefore can be effective over the whole

speed range but, as previously indicated, decreasing in effectiveness as

frequency increases. Peak effectiveness occurs when the resonator frequency

is approximately double that of the piston reciprocation. Application of the

Helmholtz resonator has been investigated in detail and reported by Thompson



512



The Motor Vehicle



and Engleman, in ASME publication 69-GDP-11, and a good summary of

the situation is presented by Tabaczinski, in SAE Paper 821577.



13.22



Alternative Helmholtz arrangements



In some instances, though mainly in the past, plenum chambers have been

designed into the system simply to smooth out pulsations in the flow, or as

a means of terminating, or isolating, the ends of tuned inlet pipes. However,

as a Helmholtz cavity, it may be a separate component introduced into almost

any part of the induction system. For instance, a plenum chamber or the filter

housing with its inlet, or zip, tube may be utilised for this purpose.

In most instances, the pressures and densities (and therefore the masses)

of air in the pipes will be lower than that of the air in the plenum, and this

will affect the resonant frequency. Moreover, the effective volume of the

plenum and therefore the resonant frequency and effectiveness of the system

may vary according to whether the throttle valve is open or closed. In the

latter condition, the incoming air will be passing the edges of the throttle at

or near sonic velocity. Other factors come into play too, such as the damping

effect of various features of the induction system, including the throttle

valve. Damping can be actually helpful, in that it reduces the peakiness of

the resonance curve and spreads the response of the resonator over a broader

speed, or frequency, range.

With the advent of computer modelling, the introduction of Helmholtz

resonators into induction systems no longer involves tedious and repetitive

calculations. One such model is the Merlin Model for the Diesel Engine

Cycle, information on which is available from Dr Les Smith, Performance

Technology Department, Lloyd’s Register, Croydon CR0 2AJ.



13.23



Examples of the application of the

Helmholtz principle



Perhaps the most common practical application of the Helmholtz principle

in the 1960s and 1970s was the suppression of unwanted frequencies in the

noise spectrum issuing from the air intake. For this purpose, the air passes

through a tuned length of pipe into the filter housing, which serves as the

resonator. Any damping provided by the presence of the filter element broadens

the band of frequencies over which the noise suppression system is effective.

More recently, it has been used on, for example, turbocharged diesel

engines. As the engine speed falls, so also does the torque but at a

disproportionately high rate, owing to the square-law performance characteristic

of the turbocharger. There is also a tendency for black smoke to be generated.

In these circumstances, the low frequency effectiveness of the Helmholtz

resonator can be put to good use. A paper on this subject, No. 790069, by

M.C. Brands, was presented at the February 1979 SAE Congress.

Similar conditions can arise in naturally aspirated engines with tuned

induction pipes. The energy content, or power, of the inertia wave of a tuned

induction pipe falls with engine speed. More significantly, however, not only

is the tuning of the pipes invariably optimised for the upper speed range, but

also, at some speeds, the pulse can actually be in a negative phase when the

inlet valve is open, thus reducing the mass of air entering the cylinders below

that which would occur even without a tuned system. Consequently, a Helmholtz